review of south african live load models for traffic loading on bridge and culvert structures

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REVIEW OF SOUTH AFRICAN LIVE LOAD MODELS FOR TRAFFIC

LOADING ON BRIDGE AND CULVERT STRUCTURES USING

WEIGH-IN-MOTION (WIM) DATA

WRITTEN BY

JOHN ROBERT BEVERIDGE ANDERSON

BEng (Hons) PrEng MSAICE

A thesis submitted in partial fulfilment of the requirements for the degree of

MASTER OF SCIENCE (STRUCTURES)

In the

FACULTY OF ENGINEERING AND THE BUILT ENVIRONMENT

UNIVERSITY OF CAPE TOWN

February 2006

REVIEW OF SOUTH AFRICAN LIVE LOAD MODELS FOR TRAFFIC

LOADING ON BRIDGE AND CULVERT STRUCTURES USING

WEIGH-IN-MOTION (WIM) DATA

WRITTEN BY

JOHN ROBERT BEVERIDGE ANDERSON

BEng (Hons) PrEng MSAICE

A thesis submitted in partial fulfilment of the requirements for the degree of

MASTER OF SCIENCE (STRUCTURES)

In the

FACULTY OF ENGINEERING AND THE BUILT ENVIRONMENT

UNIVERSITY OF CAPE TOWN

February 2006

The copyright of this thesis vests in the author No quotation from it or information derived from it is to be published without full acknowledgement of the source The thesis is to be used for private study or non-commercial research purposes only

Published by the University of Cape Town (UCT) in terms of the non-exclusive license granted to UCT by the author

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ABSTRACT

This thesis uses the axle weights and axle spacings of vehicles recorded by

(WIM) sensors to calculate the load effects on single lane supported structures up to

30m The main was to compare the load effects caused by the recorded vehicles with those

calculated using TMH7 Part 2 and the alternative live load models proposed in subsequent research

Through the of the truck survey the thesis predicts the magnitude of extreme

events that may occur within a bridge structures life The results reinforce the deficiencies of

TMH7 Part 2s NA curve to cater for normal traffic conditions on spans of 10m and less

also highlight the conservative assumptions made in the of vehicle convoys used to

simulate loads in 20m to 30m spans The of the thesis support the need for the

rational calibration of the factors used in limit state

The WIM data was analysed to highlight the extent of overloading The results provide evidence that

the of individual axles and axle sets is and that overloading has a

on Sm and 10m spans than 30m spans

Research was carried out into the basis of the live load models in TMH7 Part 2 and those

in the United States and Canada The thesis documents the advancement of

rationally based live load models derived from actual vehicle data

Alternative live load models were calibrated the extreme events the WIM data

The results independently validate the alternative live load model proposed by the latest research

commissioned by the Department of This live load model takes a similar form to the one

nrrnPIl in the Eurocode - ENV 1991-3

(ii)

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DECLARATION

I know the meaning of plagiarism and declare that all work in the document save for that which is

properly acknowledged is my own

Sgnoo~ February 2006

John R B Anderson

(iii)

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ACKNOWLEDGMENT

I wish to thank the late Professor Rolf Kratz for his mentorship during my professional career and Vela

VKE Consulting Engineers for their support in completing this thesis The guidance and direction

provided by my supervisor Dr Pilate Moyo is gratefully acknowledged Finally I thank my wifes for

her support and motivation

(iv)

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TABLE CONTENTS

No

1 INTRODUCTION

11 BACKGROUND 1-1

12 OF THE STUDy 1-2

1-3 13 SCOPE OF THE

14 METHODOLOGy 1-4

141 Review of Bridge Live Load Models 1-4 142 Analysis of Traffic WIM Data 1-4 143 Critical Assessment of TMH7 Part 2 1-5

15 ALTERNATIVE LIVE LOAD MODEL TO TMH7 PART 2 1-6

16 CONCLUSIONS AND RECOMMENDATIONS 1-6

17 REPORT STRUCTURE 1-7

2 DEVELOPMENT OF BRIDGE LIVE LOAD MOiDElS

21 INTRODUCTION 2-1

22 DETERMINISTIC AND PROBABILISTIC DERIVATIONS 2-2

23 DETERMINISTIC APPROACH 2-2

24 PROBABILISTIC APPROACH 2-4

241 BD 3788 2-4 242 AASHTO LRFD 2-7 243 CANADIAN CODE 2-9 244 EUROPEAN CODE 2-12

25 CONCLUSIONS 2-15

3 ANALYSIS OF WEIGH-IN-MOTION DATA 3-1

31 INTRODUCTION 3-1

32 ANALYSIS OF WEIGH-IN MOTION DATA 3-1

321 Actual Vehicles 3-2 322 Legal Vehicles 3-3 323 National Road Traffic 3-4

33 STATISTICAL APPROACH 3-6

331 Accuracy of Data 3-6 332 General Statistical Properties of WIM Data 3-7

34 STATISTICAL DISTRIBUTIONS 3-10

341 Normal Distribution 3-11 342 Extreme Distributions 3-13 343 Confidence limits 3-22

35 RESULTS 3-23

36 OVERLOADING 3-27

37 CONCLUSiONS 3-31

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4 CRITICAL REVIEW OF TMH7 PART 2 amp SUBSEQUENT RESEARCH 4-1

41 TMH7 PART 2 4-1

411 Background and Development 4-1 412 NA Loading Curves 4-3 413 Review of Truck Combinations 4-5 414 Comparison of Dynamic to Static Loads 4-7 415 Lateral Bunching 4-8 41 6 NB Loading 4-8

42 RR 9100401 - PERMISSIBLE HEAVY VEHICLE LOAD RESEARCH 4-9

421 Problem Statement 4-9 422 Development of Live Load Model 4-9 423 Critical Review 4-11

43 RR 9100402 - DEVELOPMENT OF ALTERNATIVE DESIGN LOAD TO TMH7 4-13

431 Traffic loading 4-13 432 Impact Factor 4-14 433 Test Loading 4-15 434 Assessment amp Design Loads 4-15 435 Report Conclusions 4-17 436 Critical Review 4-17

44 COMPARISON OF DESIGN LOADS VERSUS ACTUAL LOADS 4-19

441 TMH7 versus Actual Traffic Measurements 4-20 442 RR 9100402 versus Actual Traffic Measurements 4-21

45 CONCLUSIONS 4-23


51 CALCULATION OF LOAD FACTOR 5-1

52 RESULTS 5-3

6 FINAL CONCLUSIONS AND RECOMMENDATIONS 6-1

Appendix A Vehicle Configurations and Classifications

Appendix B Statistical Distributions

Appendix C Liebenberg Combinations

Appendix D Impact Formula

Appendix E Alternative Load Model

Appendix F Visual Basic Programs

(vi)


41 TMH7 PART 2 4-1








45 CONCLUSiONS 4-23



52 RESULTS 5-3








(vi)

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List of

11 - of National Route 3 (Source Wikipedia Encyclopedia) 1-3

Figure 21 Ministry of Transport Standard Loading Train (1922) (b) BS 153 Unit Loading Train (1923) OConnor C 2001) 2-3

Figure 22 Hendersons Vehicle Combination 1 2-3

Figure 23 Revised HA loading curve 2003) 2-5

Figure 24- of H20 Design Truck LRFD 1994) 2-7

Figure 25- IJVIClU Moments from Distribution Functions (Source Nowak 1991) 2-9

Figure 26 - CL-W Truck CANCSA-S6-00) 2-10

Figure 27 - CL-W Load (Source CANCSA-S6-00) 2-10

Figure 28 - Histogram in WBM Space Ontario 1967 Census Data (Source OConnor 1981)2-11

Figure 29 - ENV 1 -3 Load Model 1 (Source 2-13

Figure 31 - Histogram of S~lmnl GVMs 3-8

Figure 32- Function of GVMs - 6 Axle Vehicles 3-9

33 - Probability Function of Bending Moments 30m span 3-9

Figure 34 - Probability Function of Bending Moments 5m span 3-9

Figure 35 - Distribution of Bending Moments - 30m span 3-14

Figure 36 - Distribution of Forces - 30m span 3-15

37 - Fit of Theoretical to Plotted Points - 6 Axle Vehicles on 15m spans 3-18


Figure 39 - Fit of Theoretical Distributions to Plotted Points - 8 Axle Vehicles on 15m spans 3-20

Figure 310 - Confidence limits for Gumbel Distribution for 7 Axle Vehicle on 30m Span 3-23

311 - Cumulative Distribution of Axle Weights 3-27

41 - Uniformly Distributed Lane Loads Derived From Moments 4-4

42 - Uniformly Distributed Lane Derived From Shear Forces 4-5

43 - Plot of Bending Moments Due to Travelling and Stationary 4-7

44 Configuration of Class 14 Vehicle (Source RR 9100402 1 4-14

45 -live Load Model Proposed in RR 9100402 (Source RR91100402) 4-16

46 - Comparison of Bending Moments 4-19

47 - Comparison of Shear Forces 4-20

51 - Equivalent Load Models 5-2

52 - Moment Load Factors Models 1 amp 2 5-3

(vii)

List of

of National Route 3 1-3

22 Hendersons Vehicle Combination 2-3

23 Revised HA curve 2-5

24 - of H20 LRFD 1 2-7

25 - Moments from Distribution Functions 19912-9

26 CL-W Truck 2-10

2-10 27 - CL-W

28 - nn in v~ Ontario 1967 Census Data 1981 2-11

31 -

32 -

33 -

34 -

-3 Load Model 1 2-13

of GVMs 3-8

Function of GVMs - 6 Axle Vehicles 3-9

Function of

Function of

Moments 30m span

Moments 5m span

3-9

3-9

35 Distribution of Moments 30m span 3-14

36 - Distribution of

37 - Fit of Theoretical


Forces - 30m span 3-15

to Plotted Points - 6 Axle Vehicles on 15m spans 3-18


39 Fit of Theoretical Distributions to Plotted Points - 8 Axle Vehicles on 15m spans 3-20

310 - Confidence limits for Distribution 7 Axle Vehicle on 30m 3-23

311 - Cumulative Distribution of Axle 1I~~l~ 3-27

41 -

42 -

44

Distributed Lane Loads Derived From Moments 4-4

Distributed Lane

Moments Due to

of Class 14 Vehicle

Derived From Shear Forces 4-5

and 4-7

4-14

45 Live Load Model rooc)sea in RR 9100402 RR91 4-16

46 -

47 -

51 -

52 -

of Moments 4-19

gtr of Forces

lIltgtltgtnI Load Models ~ ~ ~ ~ a bullbullbullbullbullbullbullbull ~ bullbullbullbullbullbullbullbull ~ bullbullbullbullbullbull ~ bullbullbullbullbullbullbull ~ bullbullbull ~ bullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbull ~ bullbullbull

4-20

5-2

Moment Load Factors Models 1 amp 2 5-3

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Figure 53 - Bending Moment Load Factors using WIM data- Models 3 6 7 amp 8 5-4

Figure 54 - Shear Force Load Factors using WIM data - Models 3 6 7 amp 8 5-4

Figure 55 - Bending Moment Load Factors using RR 9100402 - Models 3 6 7 amp 8 5-5

Figure 56 - Shear Force Load Factors using RR 9100402 - Models 3 6 7 amp 8 5-5

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List of Tables

Table 21 - Basic Values of ENV 1991-3 Load Model 1 (Source ENV 1991-3 2-13

Table 31 - Number of Recorded Heavy Vehicles 3-2

Table 32 - Actual Vehicle Bending Moments - Statistical Properties 3-3

Table 33 - Actual Vehicle Shear Forces - Statistical Properties 3-3

Table 34 - Legal Vehicle Bending Moments - Statistical Properties 3-4

Table 35 - Legal Vehicle Shear Forces - Statistical Properties 3-4

Table 36 - Counts of Axle Mass Distributions 3-7

Table 37 - Bending Moments Extrapolated using the Normal Distribution 3-12

Table 38 - Shear Forces Extrapolated using the Normal Distribution 3-12

Table 39 - Statistical Properties of Recorded Vehicle Classes 3-12

Table 310 - Sensitivity of Predicted Bending Moments for 6 Axle Vehicles 3-16

Table 311 - Sensitivity of Predicted Bending Moments for 6 Axle Vehicles to Sample Size 3-17

Table 312 - Extrapolated Bending Moments 3-23

Table 313 - Extrapolated Shear Forces 3-23

Table 314 - Statistical Properties of Axle Weights and GVM 3-24

Table 315 - Predicted Bending Moment Confidence Limits 3-24

Table 316 - Predicted Shear Force Confidence Limits 3-25

Table 317 - NowakGumbel Comparison - Bending Moments 3-25

Table 318 - NowakGumbel Comparison - Shear Forces 3-25

Table 319 - Bending Moments for 6 Axle Vehicles with Varying Return Periods 3-26

Table 320 - Number of Observed Illegal Vehicles 3-27

Table 321 - Percentage of Overloaded Axles 3-28

3-29 Table 322 - Variance of Load effects derived from Complete Set of Events and Extreme Set of Events

Table 323 - Overloading Results using Normal Distribution - Bending Moments 3-29

Table 324 - Overloading Results using Normal Distribution - Shear Forces 3-30

Table 41 - Following Probability 4-6

Table 42 - Impact Allowance in TMH7 4-7

Table 43 - Impacts Allowances 4-14

Table 44 - Design Load Values 4-16

Table 45 - Comparison of Bending Moments RR 9100402 versus TMH7 4-17

(ix)

List of Tables

Table 21 - Basic Values of ENV 1991-3 Load Model 1 ENV1991 2-13

Table 31 - Number of Recorded Vehicles 3-2

Table 32 - Actual Vehicle Moments - Statistical I-Jrron 3-3

Table 33 - Actual Vehicle Shear Forces - Statistical 3-3

Table 34- Vehicle Moments Statistical 3-4

Table 35 Vehicle Shear Forces Statistical I-Jnort 3-4


Table 37 - Moments the Normal Distribution 3-12

Table 38 - Shear Forces the Normal Distribution 3-12

Table 39 - Statistical of Recorded Vehicle Classes 3-12

Table 310 - Sensitivity of Predicted Moments for 6 Axle Vehicles 3-16

Table 311 - of Moments for 6 Axle Vehicles to Size 3-17

Table 312- Moments 3-23

Table 313- Shear Forces 3-23

Table 314 - Statisticall-Jrnnortac of Axle f1~~ t~ and GVM 3-24

Table 315 - Predicted Moment Confidence Limits 3-24


Table 317 - NowakGumbel - Bending Moments 3-25

Table 318 NowakGumbel - Shear Forces 3-25

Table 319 Moments for 6 Axle Vehicles with Return Periods 3-26

Table 320 - Number of Observed Vehicles 3-27

Table 321 - Prtlnttl of Overloaded Axles 3-28

Table 322 Variance of Load effects derived from Set of Events and Extreme Set of Events 3-29

Table 323- Results Normal Distribution - Moments 3-29

Table 324- Results Normal Distribution - Shear Forces 3-30

Table 41 - 4-6

Table 42- Allowance in TMH7 4-7

Table 43- Allowances 4-14

Table 44- Load Values 4-16

Table 45- of RR 9100402 versus TMH7 4-17

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Table 46- of Shear Forces RR 9100402 versus TMH7 4-17

Table 47- Moments Results 4-19

Table 48 - Shear Force Results 4-20

Table 49 Bending Moment Comparison WIM data v TMH7 4-20

Table 410 - Shear Force Comparison WIM data v TMH7 4-21

Table 411 - Bending Moment Comparison WIM data v RR 4-22

Table 412 Shear WIM data v RR 91 4-22

Table 51 - Calibration of Model Bending Moments to WIM Data 5-7

Table 52 - Calibration Model Shear Forces to WIM data 5-8

Table 53 - Model Bending Moments to RR 9100402 5-9

Table 54 - Calibration Model Shear Forces to RR 9100402 5-10

(x)

Table 46

Table 47-

of Shear I-nrlPlt RR 9100402 versus TMH7 4-17

Moments Results 4-19


Table 49 Moment WIM data v TMH7 4-20

Table 410 - Shear Force

Table 411 -

Table 412 Shear

Table 51 -

Table 52 - Calibration

Table 53-

Table 54-

rlcnn WIM data v TMH7 ~ ~ ~ 4-21

WIM data v RR 4-22

cnn WIM data v RR 91 4-22

Model Moments to WIM Data 5-7

Model Shear I-nrloc to WIM data 5-8

Model Moments to RR 9100402 5-9

Shear Forces to RR 9100402 5-10

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1 INTRODUCTION

11 BACKGROUND

The live load model used to simulate traffic loading on structures in South Africa is specified in

the Code of Practice for the of Bridges and Culverts in South Africa TMH7 Part 2

The code bridge with an exact for live loads

Rigorous for applying the live load model are set (Liebenberg 1974) with the aim of

simulating the most onerous global and local load effects

TMH7 was first published in 1981 and the live load model was taken from research work

carried out by (1974) revisions and errata for TMH7 Part I and 2 were issued in

1988 associated with the live load model for normal traffic conditions on narrow and

short span were identified 1988) Under normal traffic loading the live load model

was found to underestimate the bending moments for spans between 4m and 9m Shear forces were

found to be underestimated on spans less than 23m TMH7 Part 2 caters for this by

specifYing that the live load model for abnormal loads be applied to all bridges

Since 1988 the of Transport has received requests from various bodies

the Road to increase the axle mass limits for trucks In response the DOT

commissioned the following reports to consider the possible amendments to the National Road Traffic

Regulations

(i) Report RR 9100401 The effect of an Increase in the Permissible Vehicle Loads on

June 1994

(Ii) Report RR 91004102 The effect of an Increase in the Permissible Vehicle Loads on

Bridges Assessment Code December 1995

The main objective of the reports was to compare the load effects caused by vehicles complying with

the specified limits to those calculated TMH7 Part 2 The effect of the increased

permissible axle and vehicle loads on road was also considered within the reports

As a result of the abovementioned research in 1996 the DOT increased the axle loads

and amended the formula (National Road Traffic Regulations 1996) However the main

conclusion of the reports was that the live load model in TMH7 Part 2 underestimated the load effects

in short span structures The results of the research also demonstrated the variance in the

load effects caused by different overloading Overloading allowances were derived from

vehicle statistics collected in Switzerland (Bez 1989) and from the limited data available in South

Africa at the time In conclusion RR 9100402 called for the verification of TUf1 ratios based

on the analysis of traffic survey data collected on South African roads

(1-1 )

1

11

The live load model used to simulate traffic on structures in South Africa is in

the Code of Practice for the of and Culverts in South Africa TMH7 Part 2

The code nrc pn(1nf~lrlt with an exact for live loads

with the aim of

the most onerous

the live load model are set

and local load effects

TMH7 was first p He in 1981 and the model was taken from research work

carried out revisions and errata for TMH7 Part I and 2 were issued in

Sh()rtcoIlllnjS associated with the live load model for nonnal traffic conditions on narrow and

short span were identified Under nonnal traffic loading the live load model

was found to underestimate the moments for spans between 4m and 9m Shear forces were

found to be underestimated on spans less than 23m TMH7 Part caters for this lthnrt(frn1

that the live load model for abnonnalloads be

Since the of has received from various

the Road

commissioned the

to increase the

to consider the

axle mass limits for trucks In response the DOT

amendments to the National Road Traffic

(i)

The main

the

RR 9100401 The effect an Increase in the Pennissible

June 994

The effect of an Increase in the Pennissible

Assessment Code December 1995

Vehicle Loads on

Vehicle Loads on

of the reports was to compare the load effects caused vehicles with

limits to those calculated TMH7 Part 2 The effect of the increased

axle and vehicle loads on road was also considered within the reports

As a result of the abovementioned the DOT increased the axle loads

and amended the fonnula Road Traffic the main

conclusion of the was that the live load model in TMH7 Part 2 underestimated the load effects


load effects caused different allowances were derived from

statistics collected in Switzerland and from the limited data available in South

Africa at the time In RR 9100402 called for the verification of ratios based

on the of traffic survey data collected on South African roads

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In drafting TMH7 Part 2 (1978) judged that a of extreme truck events

was not viable due to a lack of statistical infonnation Possible future trends in vehicle

and weights were judged to add a level of uncertainty that would invalidate the original assumptions

made in the fonnulation of the loads The loading fonnulas were therefore developed using a

vVIVUY approach where pHiHpri judgement was used to detennine probable combinations and

Tln(Tmfnt of heavy vehicles

In contrast the reports RR 9100401 amp 02 employed a probabilistic lnrr()middotn in developing a live load

modeL The approach entailed the use of a Monte Carlo simulation to generate random vehicle streams

as by researchers Bez (1991) and Moses and Venna (1987)

FitzGerald (1998) highlighted the level of dissatisfaction among South African bridge engineers with

the relating to the of traffic loading within TMH7 Part 2 Specifically Ullman

(I stated that the application of the live load model was cumbersome and that there was

room for its simplification Given the deficiencies of TMH7 Part 2 and the findings of FitzGerald

(1 and Ullman (1988) there is an need to update the live load model contained within the

code The availability of adequate traffic survey data removes the constraints listed Liebenberg

(1978) and adds impetus to the required

12 OBJECTIVES OF THE STUDY

The advent of toll roads in South Africa has facilitated the collection of traffic survey information

the use of weigh-in-motion (WIM) sensors Concessionaires are to continuously

collect vehicle data including the axle and axle of individual trucks

The WIM data provides infonnation on heavy vehicles travelling on South African roads that was not

available when reports RR 91100401 amp 02 were drafted In those reports virtual simulations were used

to model heavy vehicle configurations masses and occurrences Therefore the available

WIM the of tile study are

(i) To the magnitude of the load effects caused vehicles on structures in

South Africa as set out in RR 9100401 amp

To the assessmentdesign load derived in RR 91100402

(iii) To con finn the extent of the deficiencies in TMH7 Part 2 in regard to short tenn spans and

(iv) To the extent of overloading present 011 the National Route 3

(1-2)

12

In TMH7 Part 2 (1 judged that a of extreme truck events


and were to add a of that would invalidate the

made in the fonnulation of the fonnulas were therefore a

where pHingtpri was used to detennine combinations and

vehicles

In contrast the reports RR 9100401 amp 02 a in a live load

model The approach entailed the use of a Monte Carlo simulation to generate random vehicle streams

as researchers Bez (1991 and Moses and Venna (

FitzGerald (I EampltvU the level of dissatisfaction among South African

the of traffic within TMH7 Part 2

with

Ullman

(I stated that the live load model was cumbersome and that there was

room for its Given the deficiencies of TMH7 Part 2 and the of FitzGerald

(I and Ullman (1988) there is an need to the live load model contained within the

code The of traffic survey data removes the constraints listed

and adds to the

OBJECTIVES THE STUDY


the use of welgtj-I1l-miOUJn sensors Concessionaires are

collect vehicle data the axle and axle of individual trucks

The WIM data nrr1pc infonnation on vehicles on South African roads that was not

available when RR 91100401 amp 02 were drafted In those reports virtual simulations were used

to model masses and occurrences the available

WIM are

To the of the load effects caused vehicles on structures in


To the load derived in RR 9

To con finn the extent of the deficiencies in TMH7 Part 2 in to short tenn spans and

(iv) To the extent on the National Route 3

(1

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The following further objectives are set with the aim of contributing to the development of an

alternative live load model These objectives are taken from the review of research work referenced in

RR 91100410 I amp 02

(i) The identification of parameters that describe heavy vehicles

(ii) The review of the use of the Gumbel distribution to extrapolate extreme load effects and

(iii) The calibration of the design loads extracted from the probabilistic analysis of traffic survey

data

During the research period no references were found describing the derivation of the TMH7 Part 2s

NA loading curve for simulating nonnal traffic conditions Similarly no reference for its increase by

6kN in 1988 was found Liebenbergs (1974) assumed vehicle combinations were however referenced

in Ullman (1987) A further objective of the study was therefore to create a concise reference setting

out the basis of the NA loading curve It was considered that this reference was necessary in the future

revision ofTMH7 Part 2

13 SCOPE OF THE STUDY

The scope of the thesis includes the analysis of WIM data collected at Heidelberg on the National

Route 3 (N3) in February 2005 As shown in Figure 11 the N3 connects Durban and its port with

South Africa s commercial hub Johannesburg The route was chosen because of the high volumes of

heavy vehicles it experiences Heidelberg is situated on the N3 approximately 50km south of

Johannesburg For the month considered 106917 heavy vehicles were recorded by the WIM sensors

Figure 11 - Map of National Route 3 (Source Wikipedia Encyclopedia)

The load effects caused by the heavy vehicles on single span structures were calculated for the purpose

of verifYing the load effects generated in RR 91 00401 amp 02 Spans ranging from 5m to 30m were

considered

(1-3)



RR 9110040 I amp 02


(ii) The review of the use of the Gwnbel distribution to extrapolate extreme load effects and


data










South Africas commercial hub Johannesburg The route was chosen because of the high volumes of

heavy vehicles it experiences Heidelberg is situated on the N3 approximately 501an south of




of verifYing the load effects generated in RR 9100401 amp 02 Spans ranging from 5m to 30m were

considered

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14 METHODOLOGY

141 Review of Bridge live load Models

The thesis reviews the methods of formulating live load models that simulate traffic loading on bridges

structures This review was done for the purpose of critically reviewing TMH7 Part 2 The approaches

identified were

(i) The deterministic method using engineering judgement to deal with the unknowns associated

with the random nature of traffic loading and

(ii) The probabilistic method deriving and calibrating a live load model from actual traffic data

The reviewed codes include the American Load Resistance Factor Design (LRFD) Bridge Design

Specifications (1994) and the CANCSA-S6-00 Canadian Highway Design Code (2000) These

codes are proponents of the rationally based probabilistic derivation of load models and partial design

factors The Eurocode ENVI991-32000 Basis of design and action on structures - Part 3 Traffic

loads on bridges was also reviewed as the current forerunner in the probabilistic approach TMHTs

close relatives the British code of practice BS5400 Steel Concrete and Composite Bridges Part 2

Specification of loads (1978) and the Department Standard BD 370 I Loads for Highway Bridges

(2001) are included as examples of codes that have developed from both deterministic and probabilistic

approaches

142 Analysis of Traffic WIM Data

(a) Processing of WIM Data

The traffic data collected from the WIM survey was utilised to create two separate vehicle populations

The first population consisted of the vehicles with the recorded axle masses and axle configurations

This population was known as the actual vehicles In the second population the recorded axle

configurations were assigned with the maximum permissible axle masses in terms of the National Road

Traffic Regulations (1999) Depending on the number of axles and their configuration the loads were

apportioned to produce the maximum load effects This population was known as the legal set of

vehicles Its purpose was to simulate the maximum legal load effects that could be generated by an

individual vehicle thus creating a benchmark to measure the impact of overloading

The maximum load effects caused by the vehicles from both population sets were calculated for simply

supported spans ranging from 5m to 30m A Visual Basic (VB) program was written for this purpose

The program also ranked the results and calculated the statistical properties of the data

(1-4)

14 METHODOLOGY

141 Review of Live Load Models

142

The thesis reviews the methods of live load models that simulate traffic on bridges

structures This review was done for the purpose

identified were

TMH7 Part 2 The

(i) The deterministic using

with the random nature of traffic

UU1~CIUClll to deal with the unknowns associated

and

The and a live load model from actual traffic data

The reviewed codes include the American Load Resistance Factor

( I Code These

codes are proponents of the based derivation of load models and

factors The Eurocode ENV1991-32000 Basis of design and action on structures - Part 3 Traffic

loads on

close

was also reviewed as the current forerunner in the probabilistic approach TMHTs

the British code of Concrete and Part 2

ofJoads (1 and the Standard BO 370 I Loads for

(2001) are included as examples of codes that have from both deterministic and probabilistic

eo of Traffic WIM Data

rocessmg of WIM Data

The traffic data collected from the WIM survey was utilised to create two vehicle IJUIUIltlllUIJ

The first consisted of the vehicles with the recorded axle masses and axle configurations

This was known as the actual vehicles In the second the recorded axle

aou with the maximum

Traffic on the number of

the maximum load effects This

vehicles Its purpose was to simulate the maximum

individual thus a benclunark to measure the

axle masses in terms of the National Road

and their BW the loads were

was known as the legal set of

load effects that could be an

The maximum load effects caused the vehicles from both sets were calculated for simply

spans from 5m to 30m A Visual Basic program was written for this purpose

The program also ranked the results and calculated the statistical nrrmprtmiddot~ of the data

(1

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Population sets were further subdivided into subsets that grouped vehicles according to their total

number of axles As spans of 30m and less were considered the actions of a single heavy vehicle were

judged to be critical (Nowak 1991) Single heavy vehicles that could legally obtain a Gross Vehicle

Mass (GVM) of 500kN were therefore detennined to be of interest As a result vehicles containing

6 axles and more were studied

(b) Statistical Properties

The statistical properties of the recorded axle weights and calculated load effects of 30000 heavy

vehicles were extracted This data provides an insight into the nature and distribution of the heavy

vehicles travelling on the N3

(c) Statistical Distributions

As live loading due to traffic is a random time dependent variable a probability distribution function

may be fitted to the observed events This theoretical distribution can be used to predict extreme events

with a given non-exceedence probability The study analyses the load effects of both the actual and

legal vehicle populations and fits the appropriate statistical distribution to the results The maximum

load effects occurring within a 120 year period for spans ranging between 5m and 30m are

extrapolated from the theoretical distribution

The study considers two separate approaches for extrapolating extreme events The first of these was

developed by Nowak (1991) in the calibration of the LRFD (1994) and assumes that a nonnal

distribution best fits the load effects derived from a surveyed population of overloaded trucks The

second method used in RR 9110040 I amp 02 (1994 1995) involves the application of an extreme

distribution to a set of extreme events The study assesses the most appropriate extreme distribution in

describing the characteristic properties of the extreme events A comparison of the results generated by

both methods is given

143 Critical Assessment of TMH7 Part 2

(a) Background and Development of TMH7 Part 2

A literature search was carried out to investigate the basis of TMH7 and its development since its

introduction in 1981 As literature to the derivation of the TMHTs NA loading curves was not located

the thesis attempts to replicate the loading curves using Liebenbergs (1974) vehicle combinations and

those fonnulated by Henderson (1954) The combinations were used to calculate the maximum bending

moments and shear forces in simply supported spans ranging from 10m to 900m A VB program was

written to calculate the dynamic and static load effects of the vehicles in combination with an assumed

lane load An equivalent lane load was then derived to simulate the maximum bending moments in each

span increment and the results plotted to obtain the loading curve

(1-5)

sets were further subdivided into subsets that vehicles to their total

number of axles As spans of 30m and less were vvvu the actions of a vehicle were

judged to be critical 1991) vehicles that could obtain a Gross Vehicle

Mass (GVM) of 500kN were therefore determined to be of interest As a


Statistical

vehicles

The statistical nrrn~-tc of the recorded axle and calculated load effects of heavy

vehicles were extracted This data an insight into the nature and distribution of the

vehicles on the N3

Statistical Distributions

As live due to traffic is a random time a distribution function

may be fitted to the observed events This theoretical distribution can be used to extreme events

with a non-exceedence The the load effects of both the actual and

vehicle

load effects

and fits the

within a 120 year

statistical distribution to the results The maximum

for spans between 5m and 30m are


The considers two separate for extreme events The first of these was

Nowak (I 991) in the calibration of the LRFD ( and assumes that a normal

distribution best fits the load effects derived from a of overloaded trucks The

second used in RR 9100401 amp 02 (I involves the

distribution to a set of extreme events The assesses the most n rnnr

the characteristic nrrnp-t~ of the extreme events A

both methods is


and ~ of TMH7 Part 2

of an extreme

extreme distribution in

of the results OPprmiddotltgtmiddotrl

A literature search was carried out to the basis of TMH7 and its since its

introduction in 1981 As literature to the derivation of the TMHT s NA curves was not located

the thesis to the curves ( I vehicle combinations and

those formulated Henderson (I The combinations were used to calculate the maximum

moments and shear forces in spans ranging from lam to 900m A VB program was


lane load An equivalent lane load was then derived to simulate the maximum moments in each

span increment and the results to obtain the curve

(1

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(b) Critical Assessment

The load effects generated from the analysis of the WIM data are compared those

calculated TMH7 Part 2 and a critical assessment is A between the WIM

datas results and those derived in RR 9100401 amp 02 is also done

(c) Overloading

The extent of overloading was quantified by comparing the predicted 28 day event of the actual

vehicle population set against the legal vehicle population set This approach uses the statistical

of the data sets rather than individual results Due to the inherent inaccuracies associated

with the WIM data the comparison of individual maximum results will not provide conclusive results

Cumulative distributions of vehicle are however plotted to indicate the percentage of

overloaded vehicles travelling on the N3 in a month

15 ALTERNATIVE LIVE LOAD MODEL TO TMH7 PART 2

Alternative live load models that simulate the load effects calculated from the WIM data are reviewed

A live load model that may the NA curve in TMH7 Part 2 is recommended

16 CONCLUSIONS AND RECOMMENDATIONS

The conclusion of the thesis recommendations for the revision of the live load model in TMH7

Part 2 using the probabilistic analysis of traffic data Additional research to calibrate an

alternative load model as proposed in RR 9100402 is detailed The option ENV 1991

by a National Document is discussed

(1-6)

Critical Assessment

The load effects from the of the WIM data are

calculated TMH7 Part 2 and a critical assessment is A


The extent of

vehicle set

was UQIUJ pnnmna the 28

vehicle set This

those

between the WIM

event of the actual

uses the statistical


with the WIM the of individual maximum results will not conclusive results

Cumulative distributions of vehicle are to indicate the of

overloaded vehicles on the N3 in a month




16 CONCLUSIONS AND REICOM

The conclusion of the thesis recommendations for revision of the live load model in TMH7

Part 2 the of traffic data Additional research to calibrate an

alternative load nTronAopel in RR 9 is detailed The ENV 1991

a National r1l1vu allvll Document is discussed

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1~ REPORT STRUCTURE

Chapter 1 provides the of the development of bridge live load models in South Africa It

describes the of the relevant codes of practice TMH7 Part 2 and references the

subsequent research work carried out in RR 9110040 I amp 02 The objective of the referenced

live the collected WIM data is described The further of quantifying the

extent of on the National Route 3 and the review of the statistical distributions associated

with the extrapolation of extreme traffic events are also described A summary of methods used in

achieving these rhPItnJltlt is rnrt

Chapter 2 is concerned with the different approaches used in riPgt live load models The

chapter documents the deterministic approach where en~mjeermg JU(Jlgelmelilt is used to deal with the

unknowns associated with the random nature of traffic The approach involving

the analysis of actual traffic data to derive and calibrate live load models is also described The

differing methods developed in Canada the United the United Kingdom and Europe are

reviewed in detail

Chapter 3 deals with the of the WIM data The methods adopted in sorting and analysing the

WIM data are desclibed in detail The statistical of a of 30000 vehicles are also

given to nrrl(l into the nature of all vehicles on the National Route 3 For lane

spans from Sm to 30m the load effects caused the WIM data are

calculated In extreme events from these the chapter the use of

alternative statistical distributions and return periods The of overloading is also

the of the load effects generated by the WIM data

Chapter 4 a critical assessment of the live load models in TMH7 Part 2 and RR 91100401

amp 02 The and development of these live load models is reviewed in detail A I

assessment of each live load model is given the load effects calculated from the WIM data

Comment on the methods used in TMH7 Part 2 and RR 9100401 amp 02 is also with

reference to the codes ofpractice reviewed in -HaUl 2

S the development of an alternative live load model to the one in TMH7

Part 2 Various models are considered and their to simulate the load effects by the

WIM data is quantified From these recommendations for an alternative live load model are

VUY 6 presents recommendations for the future development of the live load model in TMH7 Part 2

in of the development of the probabilistic techniques described in Chapter 2 and the results of the

of the WlM data (Chapter 3)

(1

1~ REPORT STRUCTURE

the of the of live load models in South Africa It


research work carried out in RR 9110040 I amp 02 The of the referenced

live

extent of

with the

the collected WIM data is described The further of the

on the National Route 3 and the review of the statistical distributions associated

~~alLV of extreme traffic events are also described A summary of methods used in

these nhPlitnfltlt is rgtltn

2 is concerned with the different -f) I used in rtpna live load models The

where en~mjeermg IU(Jlgelmelilt is used to deal with the documents the deterministic lnrr)i~cn

unknowns associated with the random nature of traffic The

the of actual traffic data to derive and calibrate live load models is also described The

methods in the United the United and are

reviewed in detail

deals with of the WIM data The methods

WIM data are desclibed in detaiL The statistical of a

In and the

of 30000 vehicles are also

into the nature of all vehicles on the National Route 3 For lane

spans from 5m to the load effects caused the WIM data are

calculated In extreme events from these the

alternative statistical distributions and return The is also

the of the load effects the WIM data

-ua~ 4 a critical assessment of the live load models in TMH7 Part 2 and RR 91100401

amp 02 The and of these live load models is reviewed in detail A I

assessment of each live load model is the load effects calculated from the WIM data


reference to the codes htp reviewed in -HaUl 2

5 ___ ____ of an alternative load model to the one

Part 2 Various models are considered and their to simulate the load

WIM data is From these recommendations for an alternative

in TMH7

the

load model are

VUUY 6 presents recommendations for the future relclpmlent of the live load model in TMH7 Part 2

in of the of the described in 2 and the results of the

of the WlM data

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DEVELOPMENT OF BRIDGE LIVE LOAD MODELS

21 INTRODUCTION

Although vehicles have changed substantially since the development of the first live loading

curves in 1931 (Ministry of Transport) the basic form of the live load models used design engineers

has remained relatively unchanged This is because traffic loading may be simulated with reasonable

accuracy by the use of a uniformly distributed load and point loads 1978) The historical

velltoprnellt of live load models has therefore concentrated on the and calibration of

these loads

The gross vehicle mass (GVM) and the axle of heavy vehicles vary from country to country

jILUULa on the legal requirements As a different live load models have developed for

in the United States Canada and the United Kingdom The live load model in TMH7 Part 2

is also unique and a product of South Africas road traffic in 1974 Although the

aforementioned live load models vary in form and magnitude common methods were applied in their

derivation For the purpose of TMHTs live load the methods used to derive

the live load models in the codes were researched

(i) BS 153 1958 Specification for Steel Girder Bridges British Standards Institute

BS5400 1978 Steel Concrete and Composite Part 2 of loads

British Standards Institute

Department Standard BD 3788 amp 01 Loads for Highway I-lrriopo British

Transport (19882001)

(iv) American Association of State onAAn Officials (AASHTO) Load Resistance

Factor Design Design -f_n_uvbullbull ( I

(v) CANCSA-S6-00 Canadian Highway Code (2000) and

(vi) Eurocode ENV 1991-32000 Basis of and action on structures Part 3 Traffic loads

on bridges

Since the last revision ofTMH7 Parts I and 2 in 1 developments in engineering

have taken place These include

0) The IAmpt of limit state design IJIU~Jl and the use of safety

factors that are derived from the probabilistic of the given variable

(ii) The use of WIM sensors that have allowed the collection of a huge amount of traffic survey

and

21 INTRODUCTION

vehicles have 1511 since the of the first live

the basic fonn of the live load models used curves in 1931

has remained This is because traffic

distributed load and

may be simulated with reasonable

accuracy the use of a loads The historical

velltoprnelU of live load models has therefore concentrated on the and calibration of

these loads

The gross vehicle mass

lIllUlLla on the

and the axle of vehicles vary from country to country

As a different live load models have for

in the United Canada and the United The load model in TMH7 Part 2

is also and a of South Africas road traffic in 1974 the

aforementioned live load models vary in fonn and common methods were in their

derivation For the purpose of TMH7s live load the methods used to derive

the live load models in the were researched

BS 153 for Steel Girder British Standards

BS5400 1978

British Standards

Concrete and Part of loads

Standard BD 3788 amp 01 Loads for Hrriopo British

American Association of State onrHITIn Officials Load Resistance

Factor ( I

Code and

Basis of and action on structures Part 3 Traffic loads

on

Since the last revision ofTMH7 Parts 1 and 2 in 1

have taken These include

0) The Imiddotmpt of limit state 1J111V and the use of

factors that are derived from the of the

The use of WIM sensors that have allowed the collection of a

and

m

amount of traffic survey

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(iii) The advent of modem computers and the increased ability of engineers to process and analyse

large amounts of data

There is no doubt that the updating of THM7 Part 2 requires investigation when considering the above

facts TMHTs traffic loading is a nominal load derived from deterministic methods rather than a

characteristic load derived from the statistical analysis of traffic survey data The partial factors used in

TMH7 were calculated using engineering judgement taking into account the intention of the ultimate

limit state Probabilistic theory was not used to determine acceptable probabilities of achieving a

particular limit state (Dawe 2003) The following section therefore summarises the derivation of

bridge live load models in Europe and North America to provide recommendations for the revision of

the TMH7 Part 2

22 DETERMINISTIC AND PROBABILISTIC DERIVATIONS

The probabilistic analysis of actual traffic data was used to derive the bridge live load models in all of

the reviewed codes of practice issued since 1988 The traffic data included information on the volumes

and composition of traffic flows the frequency of traffic jams and the actual weights and spacing of

vehicles axles Statistical methods were used to calculate characteristic loads and to calibrate the partial

safety factors used in limit state design This method provided a more scientific approach that

researched the actual events rather than creating idealised events Data was collected by either

conducting traffic surveys of by the use of weigh-in-motion sensors

The deterministic method used in TMH7 and BS 5400 uses engineering judgement to deal with the

unknowns associated with the random nature of traffic loading Idealised combinations of vehicles

representing an extreme event are used to derive the live load models Historically these combinations

were chosen using engineering judgement More recently computer programs were used to find the

most onerous combinations of fully loaded legal vehicles The partial factors applied to the extreme

events are also based on engineering judgment rather than a rational approach Allowances for

overloading and dynamic loads are incorporated by factoring the vehicle axle weights

23 DETERMINISTIC APPROACH

The deterministic approach was developed in the United Kingdom (Henderson 1954) and has fonned

the basis of the live load models used in BS 153 and later on in BS 5400 A review of these codes is

pertinent as the TH MTs live load model is largely based on the methods developed by Henderson

(1954) to derive BS5400s live load model

The first modem loading model derived in the United Kingdom consisted of a 229m (75 feet) long

loading train that consisted of a tractor and four trailers The tractor contained a major axle of 219kN

with the following trailers having a series of 100kN axle loads The standard Ministry of Transport

Loading curve issued in 1931 was largely based on this design vehicle Details of the design vehicles

are shown in Figure 21

(2-2)

(iii) The advent of modem COlnpluters and the increased ability of


to process and

There is no doubt that the of THM7 Part 2 when the above

facts TMHTs traffic is a nominal load derived from deterministic methods rather than a

characteristic load derived from the statistical of traffic survey data The factors used in

TMH7 were calculated into account the intention of the ultimate

limjt state Probabilistic theory was not used to determine of a

limit state 2003) The section therefore summarises the derivation of

live load models in

the TMH7 Part 2

and North America to nrruujp recommendations for the revision of


The Vlnu~ analysis of actual traffic data was used to derive the bridge live load models in all of

the reviewed codes of issued since 1988 The traffic data included information on the volumes

and COlmpOSlltlOn of traffic the of traffic jams and the actual weights and spacing of

vehicles axles Statistical methods were used to calculate characteristic loads and to calibrate the

factors used in limjt state This method a more scientific that

researched the actual events rather than

conducting traffic surveys of by the use of

idealised events Data was collected either

- u- sensors

The deterministic method used in TMH7 and BS rlOImnl to deal with the


an extreme event are used to derive the live load models these combinations

were chosen More programs were used to find the

most onerous combinations of

events are also based on

and loads are Innrrn


vehicles The

rather than a rational

by the vehjcle axle

to the extreme

Allowances for

The detennirustic was in the United and has fonned


-- as the TH MTs live load model is largely based on the methods by Henderson

(I to derive BS5400s live load model

The first modem model derived in the United consisted of a 229m


with the trailers a series of 100kN axle loads The standard

curve issued in 1931 was based on this vehicle Details of the vehjcles

are shown in 21

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305 366 244 305 244 305 244 m

- E middot1- r -r----T-i--n ~o~[cg ~ I ~ I -[ rill

80 219 100 100 100 100 100 100 kN Axle loads (kN)

Ca)

7 x 305 IT = 213 m 0 ~----- -------__--- ___---

~[I ~[JJ 1 I 1 I 1 I] 70 B 96 896 896 896 8 96 896

1992 kN Axle loads (kN)(2 Tons)

(bJ

Figure 21 - (a) Ministry of Transport Standard Loading Train (1922) (b) BS 153 Unit Loading Train

(1923) (Source OConnor c 2001)

In constructing the loading curve the 100kN axles were assumed to act over a 305m by 305m area

giving a uniformly distributed load of 1O7kPa This value was rounded down to 1O5kPa and assumed

to act from 305m to 22 9m the length of the loading train The difference between the major 219kN

and the 100kN axles ie 119kN was then applied as a knife-edge load across the design lane An

impact factor of 15 was used for spans less than 229m reducing to 115 for spans at 122m and to zero

for spans greater than 762m (O Connor c 200 I)

The concept of normal and abnormal traffic was introduced in the revision of BS 153 10 1958 The

normal load was based on a so-called credibility approach which used judgement to determine the

most onerous combination and arrangement of trucks complying with the legal axle weights A design

truck with four axles spaced at 122m 305m and 122m was considered For a loaded length of 229m

three trucks with a total weight of 219kN each were used as shown in Figure 22 In longer spans five

trucks interspersed with lighter vehicles were utilised Equivalent loads were then derived from these

combinations for various loaded lengths and factored up to take into account impact loads For a

loaded length of 229m and a notional lane width of 305m a uniformly distributed load of 105kPa

resulted This load was identical to that derived in the previous MOT loading However for longer

spans the specified uniformly distributed load was much smaller For example at a span of 152m

BSI53 specified a distributed load of 48kPa in comparison to the MOT distributed load of 67kPa

(OConnor c 200 I) The new KEL of l20kN was similar to the MOT loading

LONGITUDINAL AflRNGEt-tENT FOR sPAN S IIP TO 1~middotmiddot1)middot

Figure 22 - Hendersons Vehicle Combination (Source Henderson 1954)

(2-3)

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The United Kingdoms first limit state code was introduced in 1978 in the form of issued in

ten parts As with BS 153 traffic was classified as normal loading (HA or abnormal

(HB loading) The HA did not differ significantly from the BS 153 loading other than at

longer spans it did not permit the distributed load to fall below 90kNm This increase was

necessary because of the decrease of the dead load partial safety factor from 14 to 12 2003)

the HA was based on a approach In BS 5400 HA loading was derived from

the load effects of various combinations and arrangements of 235kN vehicles with

additiona198kN and 49kN vehicles for 1954) A 25 allowance on

one axle group was also included The of the HB vehicle was revised to allow for the

increased lengths of abnormal loads on British roads A that is that

of the current TMH7 Part 2 NB live load model was adopted

The methods used in the live load model in BS 5400 issued in are similar to those

used to develop the bve load model for normal traffic conditions (NA loading) in the current revision of

TMH7 Part 2 BD 3788 has since superseded BS 5400 TMH7 Part 2s loading model has

remained It was in the United Kingdom that the live load model for normal

traffic conditions should simulate actual traffic events The deterministic method of using a

small number of vehicles was not considered to accurately simulate these events (Dawe 2003)

The probabilistic of traffic survey data was therefore used in BD 3788 Randomly

generated streams of vehicles were also developed Monte Carlo simulations Although

these were used in RR 91100401 amp 02 South African still use a live load

model based on the vehicles of 1974 There is an urgent need to translate the research work

carried out in RR 91100401 amp 02 into a revised loading model in TMH7 Part 2

24 PROBABILISTIC APPROACH

The basis of analysis is fitting a mathematical distribution to the random nature of traffic

In the section the various methods are reviewed that were developed in Canada the

United the United Kingdom and Europe

241 BD 3788

In the United a full review of traffic on both short and long span bridge IIIIVlaquoUlll5

1980 The British Department of considered that a live load model was

required that was based on limit state principles and the actual vehicles travelling on the

In the use of 30 units HB to derive the load effects on short spans for

normal traffic conditions was considered illogical The aim was therefore to revise HA to

simulate normal traffic conditions for both short and spans

The outcome of the review was the issue of BD 3788 in 1988 with revised HA loading curves for

normal traffic conditions The issue of BD 3788 was seen as an interim measure during a Irmo_tfnYI

review of BS 5400 cognisance of the of the Eurocodes The method of a

lane load and a KEL was continued In to BD3788 resulted in an increase of

24

The United first limit state code was introduced in 1978 in the fonn of issued in

ten parts As with BS I traffic was classified as nonnal or abnonnal

The HA did not differ from the BS 153 other than at

spans it did not the distributed load to fall below 90kNm This increase was

necessary because of the decrease of the dead load factor from 14 to 12

the HA was based a In BS HA was derived from

the load effects of various combinations and of 235kN vehicles with

additional 98kN and 49kN vehicles for A 25 allowance on


increased of abnonnalloads on British roads A that is that

of the current TMH7 Part 2 NB live load model was aw)prea

The methods used in the live load model in BS

used to lprpr the bve load model for nonnal traffic conditions

TMH7 Part 2 BD 3788 has since

are similar to those

IUDUU in the current revision of

TMH7 Part 2s model has

remained It was in the United that the live load model for nonnal

traffic conditions should simulate actual traffic events The detenninistic method of a

small number of vehicles was not considered to simulate these events

The of traffic survey data was therefore used in BD 3788 Randomly

vehicles were also r1PlPnl Monte Carlo simulations

these U1gt were used in RR 9100401 amp South African still use a live load

model based on the vehicles of 1974 There is an need to translate the research work

carried out in RR 911004101 amp 02 into a revised model in TMH7 Part 2

APPROACH

The basis of is a mathematical distribution to the random nature of traffic

In the the various methods are reviewed that were 111 the

United the United n )UVHI and

241 BD 3788

In the United a full review of traffic lvaUW5 on both short and span 111

1980 The British of considered that a live load model was

that was based on limit state and reJgtreented the actual vehicles on the

In the use of 30 units HB

nonnal traffic conditions was considered URI

simulate nonnal traffic conditions for both short and

to derive the load effects on short spans for

The aim was therefore to revise HA to

spans

The outcome of the review was the issue of BD 3788 in with revised HA -6 curves for

nonnal traffic conditions The issue of BD 3788 was seen as an interim measure a Irmo_tfnYI

review BS 5400 of the of the Eurocodes The method of a


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10 in the applied HA distributed load for loaded between 25m and 60m and as much as 56

for loaded of 150m (OConnor 2001) As shown in Figure for spans of less than 30m

the distributed load for normal traffic conditions was increased substantially The application of 30

units of the HB loading in conjunction with HA loading was no The revised HA

loading curves therefore provided a live load model for normal conditions BO 3788 also

increased the units ofHB loading to be carried structures on the various classifications of roads

Reised short-span loading

W= 260 kNfm

BS 153 Part SA 0 ltI) 0[g 50

J

BS 5400 Part 2

OL------~------~middotmiddotmiddotmiddotmiddotmiddot~----~----~~----~ o 10 20 30 40 50 loaded length L (m)

23 - Revised HA curve (Source Oawe

The HA loading curve published in BO 3788 was based on two separate live load models derived for

short and span bridges Both detenninistic and methods were used

In 1982 BS 5400s HA curve was revised using research work carried out by Flint amp Neill

(1986) on long spans 2003) These revisions were carried through to BO 3788 The

research work was a milestone because actual traffic data was used rather than a combination of

idealised vehicles In lVY the loading curves the collected traffic data was fJU using

statistical distributions to calculate the characteristic load effects that might occur in 120 years The

characteristics of traffic were modelled using random sequences of vehicles Each of vehicle

was chosen relative to its recorded average proportion

BO 3788s HA curves for short spans was derived from extreme combinations of legal

vehicles The of the vehicle convoy the most extreme load effects was identified

using a computer programme All vehicles in a convoy were assumed to be laden to the limits

Allowances for TIfn impact and lateral were included by the

legal axle loads An factor of 18 was applied to a axle The overloading factor was set at

14 for spans up to 1 Om ULvU1 linearly to unity at 60m span In the case of lateral UUll1vUJ1Je a factor

of 146 was for slow moving traffic on spans up to 20m reducing to unity at 40m span The

approach used was UUJlll using computer to fmd the most onerous combination

rather than engineering judgement

(2-5)

10 in the

for loaded

HA distributed load for loaded between 25m and 60m and as much as 56

200 As shown in for spans of less than

the distributed load for nonnal traffic conditions was increased The UIJIJvUVU of 30

units of the HB in ~~~h was no The revised HA

lVQUWjlt curves therefore nrrPEI a live load model for nonnal conditions BD 3788 also

increased the units ofHB

lt11 C l 0

150

E 100 lii CL

s

to be carried structures on the various classifications of roads

Revised short-span loading

W= 260 kNfm

BS 153 Part SA

BS 5400 Part 2


23 - Revised HA curve

The HA curve inBD was based on two separate live load models derived for

short and span Both detenninistic and methods were used

In I BS 5400s HA curve was revised research work carried out Flint amp Neill

on spans These revisions were carried UilJU to BD 3788 The


idealised vehicles In lVlI the curves the collected traffic data was

statistical distributions to calculate the characteristic load effects that occur in 120 years The

characteristics of traffic were modelled random sequences of vehicles Each of vehicle

was chosen relative to its recorded average

BD 3788s HA curves for short spans was derived from extreme combinations of


a computer programme All vehicles in a convoy were assumed to be laden to the limits

the Allowances for CnlltTIfn

axle loads An

14 for spans up to I

of 146 was

~nrn)~h used was

rather than elll~ml~en

and lateral

factor of 18 was

to

were included

to a axle The factor was set at

at 60m span In the case of lateral UUllAvUHle a factor

traffic on spans up to 20m IJUCvH1jlt to at 40m span The

to fInd the most onerous combination

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The loading model in BD3788 is derived from the basic asswnption that the most extreme traffic

loading can reasonably be expected to occur in the 120 year design life of a bridge (Dawe 2003) In

design tenns the extreme event was taken as 15 x the nominal loading Work carried out in calibrating

the partial factors (Flint and Neill 1980) showed that the value of the partial factor was relatively

insensitive to the return period assumed For this reason it was considered that the HA design load

could be based on the most extreme traffic load even though it had a very low probability of occurring

in practice When considering the design load against actual traffic survey data it was shown that the

ultimate design loading would occur approximately once in 200000 years and the nominal un-factored

load would occur once in 120 years

In conclusion BD 3788s live load models were derived from both the probabilistic analysis of actual

traffic data and the detenninistic analysis of convoys of legal trucks crossing short spans However the

method used in deriving the short spans load effects is not proposed in the revision of TMH7 Part 2

The use of a convoy of fully laden bumper to bwnper vehicles leads to the finding that multiple vehicle

loads are critical for spans 25-40m This finding is in contradiction with the findings of Nowak (1991)

that the effects of a single vehicle are dominant for spans up to 40m

(2-6)

The model in BD3788 is derived from the basic that the most extreme traffic

can be to occur in the 120 year In

terms the extreme event was taken as 15 x the nominal Work carried out in

the partial factors showed that the value of the

insensitive to the return assumed For this reason it was considered that the HA load

could be based on the most extreme traffic load even it had a very low of

III When the load actual traffic survey data it was shown that the

ultimate loading would occur once in 200000 years and the nominal un-factored


In conclusion BO 3788s live load models were derived from both the of actual

the traffic data and the deterministic of convoys of legal trucks

method used in the short spans load effects is not in the revision of TMH7 Part 2

The use of a convoy of to vehicles leads to the that vehicle

loads are critical for spans 25-40m This is in contradiction with the findings of Nowak (1991)

that the effects of a vehicle are dominant for spans up to 40m

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242 AASHTO lRFD

Bridge design in the United States is currently carried out in accordance with the probabilistic limit

state code of practice the AASHTO Load Resistance Factor Design (LRFD) Bridge Design

Specifications (1994) This specification has replaced the allowable stress code of practice the

AASHTO Standard Specification for Highway Design The impetus for the review came from the

inconsistencies in the AASHTO Standard Specification which resulted from its many revisions and the

advent of limit state codes of practice such as the Ontario Highway Bridge Design Code (1979)

Traffic loading in the LRFD is simulated by the use of a design truck and a design lane load of

93kNm The design truck is known as the H20 truck and has its origins in the first issues of the

AASHTO specification prior to 1931 In 1931 a uniformly distributed lane load was introduced for use

in conjunction with a combination of point loads Although state legal axle limits and bridge formulas

were in place many States drafted exclusions into their regulatory policies These exclusions allowed

vehicles in excess of the prescribed legal limits to operate on the roads Increasingly it was recognised

that the loading model for normal traffic conditions did not bear a uniform relationship to many vehicles

that were present on the roads

The State Bridge Engineers (National Highways Institute 1995) decided that a live load model

representative of the legal vehicles permitted on the highways was needed A population of probable

legal trucks was therefore created their load effects on bridges structures were then calculated The

results showed that the existing H20 load model was significantly underestimating the load effects

caused by legal vehicles on the highways A series of alternative load models including the H20 truck

in combination with a lane load were therefore proposed The legal vehicles maximum force effect

envelopes were compared with those simulated by the proposed load models The combination of the

H20 truck and of a lane load of 93kNm was found to produce the nearest fit Figure 24 shows the

characteristics of the design H20 truck

35 000 N 145 000 N 145000 N

1 4300mm 1~300 to gOOomm1

SOOmm General 1800mm 300mm Dock Overhang

Design Lane 3600 mm

Figure 24 - Characteristics of H20 Design Truck (Source LRFD 1994)

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The limit state partial factors used with the load were derived (Nowak 1995) from the

ulIngt analysis of actual truck survey data collected the Ontario Ministry of Transport in 1975

About 10000 trucks that appeared to be heavily loaded were measured and included within the survey

data base For simple spans from 90m to 60m the maximum moments and shears were then

calculated The resulting cumulative distribution functions (CDF) of these load effects were then

on normal probability paper The vertical z is a product of the inverse standard normal

distribution function

z [F(M)] (21)

Where

M Moment

F(M) CDF of the moment M

inverse standard normal distribution function

the the maximum truck moments and shears were extrapolated for each

span It was assumed that the survey data gave a population set of two weeks of heavy

traffic on the Interstate It was therefore concluded that for a 75 year time the population of

trucks would be about 2000 (522 x 75) times larger than in the survey The corresponding value of

inverse normal distribution Z was then calculated for the occurrence of the 1 in HUVaL

20000000 (2000 x 10000) truck The extrapolation of the cumulative distribution functions is shown

in Figure 25 this the maximum truck event in the life of the structure can be

predicted The ratio of the load effects of the extreme event against the loads were then used to

derive the factors used in ultimate limit state design

Partial factor Extreme load effect 1Design load effect (22)

The limit state factors used with the load were derived

of actual truck survey data collected the Ontario

from the

in 1975

About trucks that to be loaded were measured and included within the survey

data base For

calculated The

spans from 90m to the maximwn

UHlJI5 cwnulative distribution functions

on normal


paper The vertical is a

moments and shears were then

of these load effects were then

of the inverse standard normal

z

Where

M Moment

CDF of the moment M


the the maximum truck moments and shears were HHfV for each

span It was assumed that the survey data gave a pUJUIltlllU1l set reJlreentatlve of two weeks of

inverse normal distribution Z was then calculated for the occurrence IJVVULm

x truck The of the cumulative distribution functions is shown

in the maximum truck event in the life of the structure can be

the load effects the extreme event the loads were then used to

derive the factors used in ultimate limit state

Partial factor Extreme load effect load effect

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5~---------+--------~~~~----~ II NGntbs

I ~

j O~--------~~~-------------+------~

~------+ri~----------------+------~

~~--~~------~-------------+------~

Jr---~--------~-------------+------~

~~------------~------------~------~ o

Truck Moment H20 Moment

Figure 25 - Extrapolated Moments from Cumulative Distribution Functions (Source Nowak 1991)

In summary the LRDF uses a uniformly distributed load and series of knife edge loads to simulate the

load effects of a set of legal vehicles Using the probabilistic analysis of actual traffic survey data the

load model was calibrated so that the factored ultimate limit state design load represented the 1 in 75

year event This approach differs significantly from BD 3788 where the ultimate limit state design

load represents a I in 200000 year event

243 CANADIAN CODE

In 1979 the Ontario Highway Bridge Design Code (OHBDC) was published becoming the first limit

state code of practice for bridge design The code was a forerunner to the LRFD and developed the

probabilistic analysis of truck survey data to derive a live load model The OHDBC was superseded by

the CANCSA-S6-00 Canadian Highway Bridge Design of Code (2000)

CSA-S6-00s live load is formulated to represent actual vehicle loads and has a direct relationship to the

legal loads pel11lltted on Canadian highways A design truck the CL-625 is therefore used to simulate

the effects of heavy vehicles A lane loading CL-W is used to represent loading from lighter traffic

The magnitude and arrangement of these loads is shown in Figure 26 and 27

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1 2 3 4 5 AXLE NO O04W O1W O1W O14W O12W WHEEL lOADSCL-W - O08W O2W O2W O28W O24W AXLE LOADS

25 625 625 875 75 WHEEL LOADS ktlCL-625-[ 50 125 125 175 150 AXLE LOADS kf~

~ -i 1 3igtm

112ml

SSm 66m ltI ~Imiddot

Imiddot 18 m

~ ~P) =~-----ffi--tB------ -~---- ----8t------shy

t J-----ffi-----ffi-ffi------ --ffi---- -----~------

_110 25m _lto25m 240n 1BOm ~ (TYP) (TYP) (TW)

ClaHance Errvelope

300 m

~bcenturo OS m~1 I 18 m I 106m

Figure 26 - CL-W Truck (Source CANCSA-S6-00)

UNIFORMLY DISTRIBUTED LOAD 9 kNm

QQ32W (iOSN Q08W O096W WHEEL LOADS OQfgt4W Ol6W O16W O192W AXLE LOADS

So6m 6ampm

180 m

66m

Figure 27 - CL-W Lane Load (Source CANCSA-S6-00)

At the time the OHBDC was drafted there were a plethora of heavy vehicles operating on Canadas

provincial roads Engineers who were drafting the code were interested in the critical vehicles causing

the most onerous load effects on a bridge structure A means assessing the common dimensional

properties of these critical vehicles was considered necessary in deriving an equivalent load that

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modelled the maximum load effects The concept of the Ontario Equivalent Base Length was therefore

developed as a means of assigning two dimensional properties to a truck (OConnor c 1981) These

properties were then used to derive an equivalent design vehicle from a surveyed population of trucks

The two properties assigned were those of the total weight of the vehicle W and the vehicles

equivalent base length

The equivalent base length Bm was defined as

An imaginary finite length on which the total length of a given set of sequential set of concentrated

loads is uniformly distributed such that this unifonnly distributed load would cause load effects in a

supporting structure not deviating unreasonably from those caused by the sequence themselves

A set of values Wand Bm were found from the set of concentrated loads in the surveyed population

The set of values included both complete vehicles and subsets of adjacent loads In analysing the

properties of a set a histogram of W against Bm was created as shown in Figure 28 (OConnor c

1981) A curve was then fitted to points some distance above the upper bound of the survey This

curve was called the Ontario Bridge Formula Subsequent vehicles surveys were then undertaken to

establish and confirm a virtual upper bound of vehicles creating a curve know as the Maximum

Observed Load (MOL) This curve was then used to select a design vehicle whose Wand Bm values

followed its signature

The above method demonstrated a means of assigning properties to vehicles that could be used to

derive an equivalent design vehicle It was accepted however that it was not possible to describe

accurately the full range of variables associated with a complex truck by two properties alone The

value of the concept was recognised as the ability to defme a vehicle in WBmspace for the purpose of

observing those properties that should be incorporated into a design load model

IIgt

IIIQ

to

ro

to

IQ

~

0

j I_ ~t- - 4 I I IJ 1 bull J~plusmnlplusmn-l~ ~ r shy - J bull -4~ I i-II

I I ~ bull I bull II I 1 l l 1r-shy I ~ IIIr-fshy -0 -uA 1 r shy bull ~ bull bull I bullI-shy - 1 --+ shy - - ~ 1-rfILTlO 2071middot0007 r- I S I i

V-I - - ~~+-- bull 4 I I I I - t bull bull

I bull bull a bull bull I l

I j ~ l middot I Ion t bull bull bull I - JS bull iO

bull n ~ j ~- I ~ OS I ~t l Sr- - shy

J~ 1 i~ -_ bull 1 plusmn~~~ amp5 111 ~ bull- 1shy - - t-shy-~ ) lltgt ~~ J4 ~~ ~ ~ IA 1 U bull bullr-t Iii ~ t ~ci ~4t a to ~ 10 q

bull bull ~ ~- _- _~ n N 0)

ri ~ 0 U middot11 t4 ~ n 11

I - ~~ ~ ~ r=r -~ iOj 5 ~ bullbull tit II 1 bull bull

I ~ ii t4 11 II ~ -I I7 l n I II 4 bull ~bull bull ii no_ itmiddot ~t ill~~ ~~ bullbull II IJ bull I I I

~ i+~rOt~ r-iz I II 11 ~ 1amp M Jl P II bull I T

~~Jtli ~ -~ Rf

lshyi Ir Ti l l IP IiO l ii 1M U I 0 IP II J 1

10 I- shy7shy sI i ~ fq t~ I- ~ ~~ - 70 U I Il r I bull

L~ M I ii 11011

H ~~ II 11

_ r _ t

t7 ~ zo ~ n ~i -ii41 1 II

~ ~ to bull - bull bull

1M iiF-~ ~i~ I~ ii~ I middot~ I

I IJN ~ ~ 4 1 ) bull ~ 1 r-

I10shy --- ~- - shy - j middot ~rmiddot_Ie -rr r ILl ~

o Equivalent Base Length Bm in Feet

Figure 28 - Histogram in W IBM Space Ontario 1967 Census Data (Source OConnor c 1981)

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The CL truck is based on a set of regulations for interprovincial transportation that is all

Canadian It is a legal truck with axles weights and spacing that meet the Ontario

Formula and whose properties follow the signature of the MOL curve

The lane loading CL-W is based on the traffic loading for long span bridges recommended the

American for Civil Conunittee on Loads and Forces on 1978)

These reconunendations are derived from the survey of trucks crossing the Second Narrows in

the Greater Vancouver area For the purpose of the study trucks were and the overall hllfnYr

to measured

The CL-625 truck was used for the calibration of load factors load combinations and resistance factors

The used in calculating these factors was similar to that used in the LRFD

in the CL-625 truck a Gumbel distribution was used to the loading

from a set of independent truck samples Loadings associated with a return period were

calculated From the ratio of extreme loads and design loads the bias coefficients and standard

deviations were found and the live load factors calculated

As described the use of a rational method to calibrate the chosen live load model is

similar to that of the LRFD However CSA-S6-00s takes the rational method a further in using

the Ontario Equivalent Base Length to derive a vehicle that the most extreme load

effects caused by normal traffic conditions The aml1gt used in the calibration of the load

load combinations and resistance factors is considered a more rMrpnt r h than tha t used in

BD 3788

244 EUROPEAN CODE

The need for a common loading code in is a pnlCtlcal ne(esitty the volumes of cross

border traffic Since 1975 and the Treaty of the has embarked on a

programme to harmonise technical The specification for the loads on

bridges is ENV 1991-32000 Basis of and action on structures Part 3 Traffic loads on

bridge

The interesting aspect of the ENV 1991-3 is that it has to cover all eventualities and idiosyncrasies of

traffic loading sams from each of its member states Parallels may be drawn within Southern

Africa where uau cross border trade takes place by means of the road networks It should be

noted that it is that each member of the European Union will qualify the code for its localltVltftltro

circumstances This will ensure that existing levels of safety are maintained In the United

a National Document (NAD) for ENV 1991-3 was published in 2000 setting out

aUllu~_ factors for the loads and the factors

The ENV 1991-3 code two load models for normal traffic loading The first consists of a

uniformly distributed load in with a double axle or tandem set of point loads as shown in

Figure 29 These loads are to the notional lanes named Lane 1 Lane 2 and so on Lane 1 is

classified as the lane in which the loads will produce the most unfavourable effects and Lane 2

2)

The CL truck is based on a set of for that is all

Canadian It is essl~ntiallv truck with axles and Cl that meet the Ontario

Formula and whose orr)oprt follow the of the MOL curve

The lane CL-W is based on the traffic loading for span recommended the

American for Civil Committee on Loads and Forces on

These recommendations are derived from the survey of trucks the Second Narrows in

the Greater Vancouver area For the purpose of the trucks were and the overall k11rYln

to measured

The CL-625 truck was used for the calibration of load load combinations and resistance factors

The used in these factors was similar to that used in the LRFD

in a Gumbel distribution was used to the

from a set of -V~V associated with a return were

calculated From the ratio of extreme loads and the bias coefficients and standard


As the use of a rational JUaVUl method to calibrate the chosen live load model is

similar to that of the LRFD CSA-S6-00s takes the rational method a further in

the Ontario

effects caused

Base

normal traffic conditions

vehicle that the most extreme load

used in the calibration of the load

load combinations and resistance factors is considered a more rPTrpntl

BD 3788

lr)T)rnrh than that used in

244 EUROPEAN CODE

The need for a cornmon code in

border traffic Since 1975 and the

programme to harmonise technical

is ENV 199

is a the volumes of cross

the has embarked on a

The for the loads on

and action on structures Part 3 Traffic loads on

The

traffic

of the ENV 1991 is that it has to cover all eventualities and of

5UU05 from each of its member states Parallels may be drawn within Southern

Africa where cross border trade takes means of the road networks It should be

noted that it is that each member of the Union will the code for its local

circumstances This will ensure that levels are maintained In the United

a National Document for ENV 1991-3 was in out


The ENV 1991-3 code models for normal traffic The first consists of a

distributed load in IUH~1U with a double axle or tandem set of point loads as shown in

to the notional lanes named Lane 1 Lane 2 and so on Lane 1 is 29 These loads are

classified as the lane in which the loads will the most unfavourable effects and Lane 2

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the second most unfavourable effects The magnitude of the applied loads is reduced from Lane I to

Lane 2 as shown in Table 21 A second load model is intended to simulate the dynamic effects of

traffic loading on short structural elements and consists of a single 400kN axle The effects of dynamic

amplification are included within the specified applied loads

A further load model exists to cater for abnonnal loads This load model is only applied to structures

on specific routes designated for abnonnal loads

Tandem UDL System system

Location

Axle loads Qik

(kN) qik

(kNm2 )

Lane number I 300 9 Lane number 2 200 25 Lane number 3 100 25 Other lanes 0 25 Remaining area 0 25

Table 21 - Basic Values ofENV 1991-3 Load Modell (Source ENV 1991-3)

o

Q

~~H-050 200

-iti--Hl-fosomiddot

-f+l--++++Obull5O Lane No 2 200 Q2 =200 kN q2i= 25 kNm2

-iH----H1-gtI-O50

1m2

-ttl--Bf--I-050middot 200

050 120

2 00

For IV 300 m

Figure 29 - ENV 1991-3 Load Model I (Source Dawe 2003)

The derivation of the nonnalload models I and 2 is taken directly from traffic data recorded on the A6

dual carriageway in France Due to the number of international vehicles using this route it was judged

to provide a representative sample

Initially the load effects generated by the actual traffic loads were analysed and extrapolated to

correspond to a probability of exceedence of 5 in 50 years this represents a return period of 1000

years This extrapolation allowed the detennination of target values for the extreme load that were used

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to calibrate the live load model The approach adopted involved the extrapolation of the following

three traffic parameters

(i) Axle and Gross vehicle masses

(ii) Extreme total loads on the span and

(iii) Extreme load effects

In the case of axle weights and GYM the data was judged to fit a normal distribution and ultimate limit

single double and triple axle loads were predicted for the extrapolation of the sample data These

values were important for establishing the design loading for shorter spans

The prediction of the extreme total loads on the bridge involved five separate statistical approaches that

were then compared These approaches involved the use of differing distributions (Gaussian Poisson

and extremal distributions) for varying return periods Dawe (2003) stated that by and large there was

reasonable agreement between the approaches when comparing the maximum total loads for different

spans and different return periods The following three traffic situations were considered in the review

of the total loads

(i) Free flowing

(ii) Congested traffic including cars and

(iii) Congested traffic with only trucks

Monte Carlo simulations were used to generate random traffic streams from a sample of selected

vehicles As expected the congested traffic with only trucks produced the most onerous total loads

In predicting the extreme loads effects similar extrapolation techniques as described above were used

For a 1000 year return period reasonable correlation was found for the predicted equivalent uniformly

distributed load In conclusion it was found that the different methods of extrapolation produced

similar results This meant that theoretically any of the methods developed could be used

The development of ENV 1991-3 has involved the most extensive use of probabilistic methods in

deriving the live load models which are specified within the code of practice Of particular relevance is

the sensitivity analysis of the results using different extrapolation parameters and techniques This

analysis effectively provides a level of confidence in the methods used A great strength of the ENV

1991-3 is that it may be calibrated by each member state This calibration is based on the probabilistic

analysis of the states traffic characteristics Through the publication of a NAD a loading model

appropriate to each country is easily derived This calibration would not be possible if the live load

model was derived by a deterministic method

(2-14 )

to calibrate the live load model The approach


Axle and Gross vehicle masses


Extreme load effects

involved the of the

In the case of axle

double and

values were

and GYM the data was to fit a normal distribution and ultimate limit

axle loads were for the extrapolation of the data These

for the loading for shorter spans

The of the extreme total loads on the involved five separate statistical approaches that

were then (()mnrgtrI These involved the use of distributions Poisson

and extremal Dawe stated that and there was

reasonable between the when the maximum total loads for different

spans and different return

of the total loads

The following three traffic situations were considered in the review

(i) Free

(ii) traffic cars and

traffic with only trucks

Monte Carlo simulations were used to generate random traffic streams from a of selected

vehicles As the traffic with trucks the most onerous total loads

In the extreme loads similar v as described above were used

For a 1000 year return reasonable correlation was found for the

distributed load In conclusion it was found that the different methods of produced


The Irrrgtnt of ENV 1991-3 has involved the most extensive use of

deriving the live load models which are specified within the code

the of the results different eXlrarlOIatIClI1

a level of confidence in the methods used A

methods in

relevance is

This

nnmrn of the ENV

1991-3 is that it may be calibrated by each member state This calibration is based on the

of the states traffic characteristics Through the of a NAD a loading model

nt~r()nntp to each country is easily derived This calibration would not be if the live load

model was derived a deterministic method

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25 CONCLUSIONS

The review of the listed codes of practice ~ the extent of research and development W1dertaken

in recent years in the field of bridge live In each case deterministic methods of deriving live

load models have been replaced by methods Deterministic methods were developed

because of a lack of statistical data and the complexity of the variables associated with traffic

movements WIM sensors and traffic surveys have now a wealth of traffic data that has

removed this constraint

The modem philosophy developed in B03788 and ENV 1991-3 was to derive live load models that

accurately simulate actual traffic conditions As a rationally based probabilistic methods that

actual traffic survey data were used In the deterministic methods only models an

extreme event using a small number of virtual vehicles derived from engineering judgement This

leads to conservative results (0

South Africa has yet to progress to a live load model that is developed using probabilistic

methods Although research 1I111UaLlll in the RR 9110040 I amp 02 was carried between

1994-1995 in South TMH7 Parts 1 and 2 remains unaltered since 1998 Its closest relative

BS5400 was supierSeOta by BD 3788 in 1988 The advent of the ENV 1991-3 in Europe further dates

the deterministic derivations ofTHM7 Part 2s live load models

The review of BO 3788 also a number in the practice live load

models that have yet to be OJ in South Africa These developments include the derivation of

loading curves that do not the use of abnormal load models in short spans and the of

lateral bunching It is recommended that both developments be researched in the future revision of

TMH7 Part 2

The great advantage of live load models and their calibration on the probabilistic analysis of

traffic survey is load models may be easily derived In as the

properties of traffic for technical and economic reasons it is relatively to the live

load model

Of the codes ENV 1991-3 provides the most recent and extensive use of probabilistic

methods to derive a live load model For this reason the approach used in ENV 1991-3 provides an

excellent reference for the of the live load model contained with TMH7 As in the case of the

member states a NAO based on the probabilistic of local truck survey

data may be in South Africa and other southern African countries YICUUU

In the chapters that follow the probabilistic analysis of WIM data collected in South Africa is used to

provide a critical assessment of the loading model contained within TMH7 Part 2 Methods of

and an alternative load model are also

(2-15)

25

The review of the listed codes

in recent years in the field of

load models have been

n-hrmiddot bull bullbullbull O ~ the extent research and 1pJPlrnnpn

In each case deterministic methods of

pf()babIllstJIC methods Deterministic methods were

W1dertaken

live

because of a lack of statistical data and the the variables associated with traffic

movements WIM sensors and traffic surveys have now nrrvl1pl a wealth of traffic data that has


The modern philosophy r1Ir1 in BD3788 and ENV 1991-3 was to derive live load models that

simulate actual traffic conditions As a based

actual traffic survey data were used In the deterministic methods

methods that

models an

extreme event a small number of virtual vehicles derived from em~mc~ermg JudgerneIlt This

leads to conservative results

South Africa has to progress to a live load model that is

methods 111I1U 111 in the RR 91100401 amp 02 was carried between

1994-1995 in South TMH7 Parts 1 and 2 remains unaltered since 1998 Its closest

Ih~JwassuJerSe(lea BD in 1988 The advent of the ENV 1991-3 in further dates

the deterministic derivations ofTHM7 Part 2s live models

The review of BD 3788 also IHlgtUl~U a number oeifeloplrnems in the nrrrup live load

models that have to be in South Africa These include the derivation of


lateral It is recommended that both be researched in the future revision of

TMH7 Part 2

The of live load and their va1W1aWJU on the of

traffic survey is load models may be derived In uV as the

for technical and economic reasons it is to the live

load model

Of the codes ENV 1991-3 the most recent and extensive use of

methods to derive a live load model For this reason the used in ENV 1991-3 an


member states a NAD based on the of local truck survey

data may be YUl in South Africa and other southern African countries

In the the of WIM data collected in South Africa is used to

a critical assessment of the loading model contained within TMH7 Part 2 Methods of


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ANALYSIS OF WEIGH-iN-MOTION DATA

31 INTRODUCTION

The use of (WIM) sensors to collect traffic survey information on South African Toll

Roads has taken place on the National Route 3 at Heidelberg since 2000 This data an

into the complex random nature of traffic The National Route 3 was chosen because of the

volumes of heavy vehicles that regularly travel between and Durban In the

of the live load models in TMH7 Part 2 (1981) and the that reviewed it (RR

91100401 amp 02 1994 amp 1995) traffic survey information was not directly used It is considered that

the data now available provides the opportunity to research the actual load effects caused by heavy

vehicles on structures This research can be used to the earlier of the

deterministic approach of TMH7 Part 2 and the Monte Carlo simulation undertaken in Reports RR

9100401 amp 02

It is documented that the most onerous load effects in spans up to 40m are caused by a single heavy

vehicle (Nowak 1991) Given that over 90 of in South Africa (RR 911004101 1994) have a

span of less than 40m the research of the vehicles is fundamental In review of the

WIM data the following objectives were set

(i) To verify the magnitude of the load effects caused vehicles on bridge structures in


(ii) To verify the assessment load derived in RR 911004102

(iii) To confirm the extent of the deficiencies in TMH7 Part 2 with regard to short spans and

(iv) To quantify the extent on the National Route 3

32 ANALYSIS OF WEIGH-IN MOTION DATA

The population of heavy vehicles reviewed in the following section was recorded by WIM sensors on

the National Route 3 in 2005 Although WIM sensors collect a range of data only the

recorded vehicles axle and axle were used in this study

In the WIM sensors recorded 106917 heavy vehicles In order to manage process

this amount of data it was necessary to sort the vehicles into separate subsets Two means

vehicles were considered The first was the Van Wyk amp Louw Vehicle Classifications (1991) used in

Reports RR 91100401 amp as shown in Appendix A The second was simply classifying the vehicles

in terms of their total number of axles

(3-1 )

31 INTRODUCTION

32

The use of sensors to collect traffic survey information on South African Toll

Roads has taken on the National Route 3 at since 2000 This data an

into the random nature of traffic The National Route 3 was chosen because of the

volumes of vehicles that travel between and Durban In the

of the live load models in TMH7 Part 2 I) and the that reviewed it

9100401 amp 1994 amp 1995) traffic survey information was not used It is considered that

the data now available the to research the actual load effects caused

vehicles on

deterministic

9100401 amp 02

structures This research can be used to the earlier of the

nnT(h of TMH7 Part 2 and the Monte Carlo simulation undertaken in ~~~r~ RR

It is documented that the most onerous load effects in spans up to 40m are caused a

vehicle 1991 Given that over 90 in South Africa 91100401 1994) have a

span of less than the research of the vehicles is fundamental In review of the

WIM were set



To the assessment load derived in RR 9

(iii) To confirm the extent of the deficiencies in TMH7 Part 2 with to short spans and


ANALYSIS OF WEIGH-IN DATA

The of vehicles reviewed in the section was recorded WIM sensors on

the National Route 3 III 2005 WIM sensors collect a range of the

recorded vehicles axle and axle were used in this

In the WIM sensors recorded 1 17 vehicles [n order to manage process


vehicles were considered The first was the Van amp Louw Vehicle Classifications (1991) used in

RR 91100401 amp as shown in nVI A The second was simply the vehicles


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In review of the data it was identified that not all vehicles complied with the Van Wyk amp Louw Vehicle

Classifications (1991) hpr~t()rp to ensure that a critical vehicle was not excluded the classification in

terms of the total nwnber of axles was adopted

The of the WIM data took two forms the WIM data was to calculate the load

effects associated with the recorded actual across a range of simply supported

spans In the second stage a set of so-called vehicles was created by or decreasing

the axle masses of the actual trucks to the maximum values permitted the National Road Traffic

Regulations (1999) on the number of and their configuration the loads were

apportioned to produce the maximum load effects The load effects caused these legal vehicles

crossing the set range of simply supported spans were then calculated

The purpose of the vehicles was to simulate the maximum load effects that could be

generated by the individual vehicles In the distribution of the load effects of both the

actual and the legal the extent of overloading for various spans could be quantified

When analysing the actual load effects against the synthesised loads effects only static

conditions were considered This approach was considered valid given that the purpose of the study

the variance between the two sets of vehicleswas to

321 Actual Vehicles

The raw data from the WIM was into a Sprea(lSneer and the vehicles grouped in terms of the

total number of axles As spans of 30m and Jess were considered the actions of a heavy vehicle

are known to be critical 1991 ) heavy vehicles that could obtain or come close to

the maximum legal Gross Vehicle Mass (GYM) of 560kN (National Road Traffic

1999) were therefore determined to be of interest As a only vehicles containing


In the analysis of the WIM data the details of over 200 9-axle vehicles were extracted from the vehicle

population set The majority of these vehicles contained four axle axle-sets Given the number of axles

in the OA-Ol these vehicles were considered as abnormal loads and outside the scope of the study

Any 6 7 or 8 axle vehicle containing a four axle axle-set was also considered as an abnormal load and

extracted from the vehicle population set The remaining 6 7 or 8 axle vehicles were to

represent normal traffic The total number of vehicles used in vu the load effects is shown in

Table 31

6 Axle 7 Axle 8 Axle Vehicles Total

Vehicles Vehicles

No of Recorded

Vehicles 24901 34951 2587 62079

Table 31 - Nwnber of Recorded Vehicles

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F

of the a VB program was written to calculate the maximum bending moments

and shears caused by each vehicle moving across a supported span ranging from 5m to

30m were considered as per RR 91100401 amp 02 From these results the statistical distribution of the

UUll~ moments and shears forces for each span was found The results obtained are shown in Table

In the

32 and 33 The VB programs written are listed in -1TllltOm

5 to 15 20 30 6 Axle Veh Mean 1040 2801 4734 7507 14319

Std Dev 334 887 1458 2426 4618 7 Axle Veh Mean 1084 2838 5181 8474 17046


Std Dev 345 915 1701 2794 5865

Table 32 - Actual Vehicle Moments Statistical Properties

5 to 15 20 30 6 Axle Veh Mean 952 1224 1500 1782 2115



Std Dev 324 418 546 654 815

Table 33 - Actual Vehicle Shear Forces Statistical Properties

322 Legal Vehicles

The intent of the set of vehicles was to a set of vehicles fully laden to the limits allowed

by the National Road Traffic Regulations (1 Previous research 9100401 amp 1995) used

a garage of 28 vehicles that adhered to the Van Wyk amp Louw Classifications (1991) It is

proposed that the creation of a set of legal vehicles whose axle spacing and vVI~Ia are

truly representative develops this approach further It is evident that the size of the

a more rpnrppnlt sample than the smaller hand picked garage of vehicles

A VB program was written to first the maximum allowable axle mass to the vehicles The gross

vehicle mass was then checked the maximum allowable of 56 tonnes

the bridge formula was also checked If the vehicles did not comply with the GYM or the bridge

formula the axle masses were reduced till compliance was achieved In reducing the axle masses the

maximum 111100 mass of the central tandem or tridem axle set was retained the balance of the

vehicle mass was then proportionally allocated to the axles This method was aimed at

producing the maximum load effects from each legal vehicle For the span

important the critical axle sets were loaded to their limits (OConnor 198 If this was not

done the maximum legal load effects would be underestimated and the overloading factor

overestimated

it was

(3-3)

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In order to correctly assign the axle masses it was necessary to identify the various configurations of

vehicles that were present on the N3 The recorded vehicle configurations with the assigned maximum

axle masses are shown in Appendix A

As in the case of the actual vehicles the statistical distribution of the bending moments and shears

forces caused by the legal vehicles was calculated The results obtained are shown in Tables 34 and

35 The results represent the legal maximum load effects and as a result have a relatively small

standard deviation

Bending Moments (kNm) S[lans (m)

5 10 15 20 30

6 Axle Veh Mean 1677 4561 7644 12472 24242 Std Dev 65 214 252 481 620



Table 34 - Legal Vehicle Bending Moments - Statistical Properties

5 10 15 20 30




Table 35 - Legal Vehicle Shear Forces - Statistical Properties

323 National Road Traffic Regulations

The National Road Traffic Regulations (1999) limit the GYM and individual axle masses of heavy

vehicles on South African roads The set of legal vehicles created complies with the following

regulations

(i) The axle massload of an axle fitted with two or three wheels that is a steering axle shall not

exceed 7700 kilograms

(ii) The axle massload of an axle fitted with two or three wheels that is not a steering axle shall

not exceed 8000 kilograms

(iii) The axle massload of an axle fitted with four wheels shall not exceed 9000 kilograms

(iv) The axle massload of an axle unit that consists of two axles each of which are fitted with two

or three wheels that is not a steering axle shall not exceed 16000 kilograms

(v) The axle mass load of an axle unit that consists of three or more axles each of which are fitted

with two or three wheels that is not a steering axle shall not exceed 24000 kilograms and

(3-4)

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(vi) The bridge fonnula states that total axle massload of any group of axles of a vehicle shall not

exceed a mass detennined by multiplying the dimension of such group by 2 I 00 and

18000

(3-5)

The fonnula states that total axle massload of any group of axles of a vehicle shall not

exceed a mass detennined by the dimension of such group 2 I 00 and

Univers

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33 STATISTICAL APPROACH

Accuracy of Data

Weigh-in-motion sensors estimate static axle loads from the measurement of dynamic tire loads

Obtaining accurate results requires the careful calibration of the WIM sensors considering the type and

condition of the calibration truck the drivers nprtnrm and the condition of the road surface in the

of the sensor Between the calibration there are many variables that can lead to

inaccurate results These include the behaviour of drivers on the road the eccentricity of loading and

environmental factors such as and wind A further factor is the magnitude of the axle

spacing threshold If the threshold value is the programme records a separate vehicle

Therefore if the headway distance between two vehicles is less than the axle threshold the programme

will record two vehicles as a single vehicle

The WIM system that is used to collect the data on the National Route 3 is set to meet the International

Standard Specification for (WIM) Systems with User Requirements and Test

Methods E1318-02 This that the error in the estimated static wheel load should

not exceed 25 Given the number of variables achieving this target requires the daily

monitoring of the recorded WIM data

It is recognised that the of the recorded axles loads used in this study may be 25 more or

less than the actual vehicles axle loads on the road The for erroneous results that do

not represent actual vehicles on the road is also noted Given the level individual results

are not used to derive definitive conclusions regarding the extreme loading produced vehicles

The statistical properties of a of vehicles are rather used to extrapolate extreme load effects In

using this approach a erroneous result will not significantly skew the overall results

It is pertinent to note that the calibration of the live load model in ENV 1991-3 was in part carried out

using WIM data et 200 I) In that instance the accuracy of the WIM data was set at 5

of the static values as the European specification on weigh-in-motion road vehicles

(COST 323 1997)

In proces~mJ1 the WIM erroneous vehicles were removed from the These vehicles were

identified either low axle mass readings or by axle spacings that could not represent an

actual vehicle

(3-6)

33 APPROACH

of Data

sensors estimate static axle loads from the measurement of tire loads

accurate results the careful calibration the WIM sensors vVJlUIl the and



inaccurate results These include the behaviour of drivers on the the of and

envirorunental factors such as and wind A further factor is the of the axle

threshold If the threshold value is the programme records a separate vehicle

hrtr if the distance between two vehicles is less than the axle the programme

will record two vehicles as a vehicle


Standard with User and Test

E 1318-02 This that the error in the estimated static wheel load should

not exceed 25 Given the number of variables this target the

of the recorded WIM data

It is that the of the recorded axles loads used in this

less than the actual vehicles axle loads on the road The IJV0HUUi

not represent actual vehicles on the road is also noted Given the level

may be 25 more or

for erroneous results that do

individual results

are not used to derive definitive conclusions the extreme vehicles

The statistical of a of vehicles are rather used to extreme load effects In

this erroneous result will not skew the overall results

It is to note that the calibration of the live load model in ENV 1991-3 was in part carried out

of the static values as

323 1

In proces~mJ1 the WIM

identified either low

actual vehicle

et 200 In that instance the accuracy of the WIM data was set at 5

the road vehicles

erroneous vehicles were removed from the These vehicles were

mass VU i~ or axle that could not an

Univers

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332 General Statistical Properties of WIM Data

The following section provides an overview of the general statistical properties of heavy traffic vehicles

travelling on the National Route 3 For this purpose all heavy vehicles including 2 to 5 axle vehicles

were considered The first 30000 vehicles logged during February 2001 were analysed The sample

set was limited to 30000 vehicles for the purpose of analysing the data in Excel

The count of the vehicles axle masses shown in Table 36 reveals a significant number of axle masses

above the legal limits (90kN) for all axles other than the steering axle This may be considered

indicative rather than representative given the possible errors in the estimated static axle loads The

results showed that overloading to be particularly prevalent on axles 2 and 3 Whether this trend is due

to the overloading of 2 and 3 axle vehicles requires further research

940 1300 1500 1460 1180 1200 122 0 383Max 442 519 507 470 489 47 5 48 2 196Mean 100 207 208 216 207 213 207 870Std Dev

Tonnes Axle 1 I Axle 2 I Axle 3 I Axle 4 I Axle 5 I Axle 6 I Axle 7 I Axle 8 0 22 79 122 66 85 65 325 0 150 231 525 214 465 146 2710 0 502 431 1192 676 1007 513 4615

272 1267 1062 1535 1339 1190 831 8820 1476 2026 1734 1464 1522 1083 679 4725 1776 2242 1948 1260 1247 899 485 5430 2051 2146 1654 1128 1119 805 422 4835

40 3662 1796 1360 1119 1068 824 464 63 5976 1722 1342 1183 1061 943 535 4945 6436 1769 1304 1301 1233 1135 633 7350 4961 1775 1454 1476 1489 1375 864 7255 2460 2291 1850 1803 1788 1672 1195 6760 794 2747 2328 2117 2026 1805 1200 4565 144 3033 2590 2039 2046 1658 1080 3670 24 2694 2107 1528 1571 1218 705 1375

80 4 1976 1376 928 933 716 388 9 85 2 1019 719 394 423 275 151 4 90 0 487 __- 305 164 _ 170 __ 127- 51 _-- 1 ___ _ - _ _-_ _shy

95 I 213 112 58 47 47 18 0 100 0 80 43 31 23 19 6 0 105 0 43 14 8 5 5 3 0

0 17 8 4 2 2 2 0110 0 II 9 2 0 3 0 0115

120 0 3 3 0 2 2 0 0 125 0 6 1 I 0 0 I 0

More 0 2 1 I 0 0 0 0 30039 30039 24065 21383 20070 17360 10437 774Sum

Table 36 - Counts of Axle Mass Distributions

(3-7)

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A histogram of the gross vehicle masses Figure 31 shows a twin peaked bimodal distribution of

GVMs from 10 tOlmes through to 50 tonnes This fonn of distribution is typical for gross vehicle

weights (Hannan and Davenport 1979 OConnor et aI 200 I) The first mode contains the partially

loaded 4 to 7 axle vehicles and the fully loaded 2 and 3 axle vehicles The second mode involves the

fully loaded 5 to 7 axle vehicles Knowledge of the frequency of GVMs is off use in Monte Carlo

simulations that employ vehicles that reflect actual traffic flows (OConnor et aI 200 I)

2500 12000

c 0c10000 ltI2000 C I ~

8000 c ~

1500 IltI

~H-I-t++-f-++-+ 000

-=e

~C qj 6000 iI a Q~ 1000

qj~ 4000 ~ ~ ~

500 20 00 I

U

o

Bin

_Frequency Cumulative Distribution Function

Figure 31 - Histogram of Sample GVMs

The probability density function of the gross vehicle mass was observed to follow a nonnal distribution

as shown in Figure 32 As shown in Figures 33 and 34 the maximum bending moments caused by

vehicles crossing a 5m and 30m span also follows a nonnal distribution This confinns Nowaks (1991)

approach and the distributions found in derivation of the live load model in ENV 1991-3 (Dawe 2003)

(3-8)

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00030 -----------r-------------------r--------

o 00025 JI ~ 00020 i-----I~--_I_---t_-~--+---+-----f----I lIi i~ 00015 ~

] 00010 to

ampJ o ~ 00005 +----+----+----~-------_IIoc__

00000 +----+----+----j----i----+----+---

o 100 200 300 400 500 600 700

Weight(kN)

Figure 32 - Probability Density Function ofGVMs - 6 Axle Vehicles

001200

sa 001000 v

~ 000800pound

000600 ~ 15 000400 ~ to ~ 0

000200 ~

000000

0 50 100 150 200 250

Bending MOIntnt (kNm)

Figure 33 - Probability Density Function of Bending Moments - 30m span

000080

000070

ll 0

000060 ~ 000050 ~

fshy 000040 S ~ l- 000030 g ampJ

000020

0

D

p 000010

000000

i-~-I- ---- __ ~

o 500 1000 1500 2000 2500 3000

Bending rvIoment i kNm

Figure 34 - Probability Density Function of Bending Moments - Sm span

(3-9)

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34 STATISTICAL DISTRIBUTIONS

the WIM data the main objective of the study was to predict the extreme bending moment and

shear forces that would be experienced by a bridge structure during its design life Given that live

due to traffic is a random time dependent variable a probability distribution function may be

fitted to the observed events This theoretical distribution may then be used to predict extreme events

with a probability of exceedance Similarly for a given time period the exceedence Pf()0810111t

may be and the extreme event predicted

In review of current research two distinct approaches for extrapolating extreme events were identified

The first of these was developed by Nowak (1991) in the calibration of the LRFD (1994) The method

assumed that a normal distribution best fitted the load effects derived from a of

trucks identified as overloaded The second method used in RR 910040 I amp 02 (1994 amp

involved the use of the Gumbel extreme distribution to extrapolate a set of extreme events obtained

from a Monte Carlo simulation A similar approach was in the calibration of the live load model in

ENV 1991-3 (OConnor et aI 2001)

The present study undertakes to review both aPl)[oaCltles for the purposes In the case of

the application of an extreme distribution the further aims to

(i) Assess which extreme distribution best describes the characteristic properties of the extreme

events and

(ii) Investigate the sensitivity of the in relation to the size of the extreme event

In RR 9100401 the load effects of the traffic streams were to the total number

of traffic streams expected in a 50 year return This was amended in RR

where the load effects were extrapolated to a level that had a 5 of being exceeded within a

120 year design life The resulting return of 2976 years is more onerous than the 120 year and

1000 year return periods associated with the live load models in BD 3701 and ENV 1991-3

respectively

For the purposes of the it was considered that characteristic loads are those appropriate to a

return period of 120 years as per the recommendations of BD 3701 (200 l) This assumption was

considered valid that the results are relatively insensitive to variation in the return

periods (Dawe 2003)

0)


the WIM the main of the study was to the extreme moment and

shear forces that would be a structure its life Given that live

due to traffic is a random time a distribution function may be

fitted to the observed events This theoretical distribution may then be used to extreme events

with a of exceedance Similarly for a time the exceedence Pf()0810111t

may be and the extreme event

In review of current two distinct for extreme events were identified

The first of these was tlPpnnp by Nowak (1991) in the calibration of the LRFD (I The method


trucks identified as overloaded The second used in RR 910040 I amp 02 (1994 amp

involved the use of the Gumbel extreme

from a Monte Carlo simulation A similar

to a set of extreme events obtained

was in the calibration of the live load model in

ENV 1991-3 et 200

The

the

(i)

undertakes to review both aPllroaCltles for the purposes

of an extreme distribution the further aims

Assess which extreme distribution best describes the characteristic

events and

In the case of

of the extreme

the oflhe in relation to of the extreme event


of traffic streams in a 50 year return This was amended in RR

where the load effects were to a level that had a 5 of exceeded within a

120 year return of 2976 years is more onerous than the 120 year and

1000 year return associated with the live load models in BD 3701 and ENV 1991-3

For the purposes of the it was considered that characteristic loads are those to a

return of 120 years as per the recommendations of BD 3701 This was

considered valid that the results are insensitive to variation in the return

Univers

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341 Normal Distribution

Nowaks (1991) method of using a normal distribution to extrapolate the load effects from a set of

trucks was carried out using the recorded 6 7 and 8 axle vehicles Each class of vehicle was

considered with the bending moments and shears forces being calculated for

20m and 30m spans The mean and standard deviation of the load effects was calculated for each span

and for each class

As in case of Nowak (1991) the number of vehicles was assumed as of the survey

For the 24901 recorded 6 axle vehicles were taken as characteristic of a one month

For the 120 year return period the total population of 6 axle vehicles was

assumed to be 1440 (120 x 12) times larger This gave a total number of 6 axle of

The IJAUWIAY level corresponding to the maximum truck event was then calculated as

lIN

In calculating the standard normal distribution value Z the intermediate W was first calculated

and inputted into the formula estimating Z 1988)

(31)

2515517 + 080853w+ 0010328w2

z=w- 2 (32)1+ 1432788w+ 01 89269w + 0001

Where

p exceedence probability

W intermediate variable

Z standard nonnal distribution value

Given that a normal distribution was llHltU the frequency factor Kr was equal to z The magnitude

of an event at given time T was therefore calculated the formula

=x+Krs (33)

Where

Xr Event at time T

x Mean of events

Kr rPllHPU factor

1)

Univers

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s Standard deviation of events

The results of the analysis are shown in Table 37 and 38 For spans of less than 15m the results are

consistent for each class of vehicle For the 20m and 30m spans the load effects of the 6 axle

vehicles are lower than those of the 7 and 8 axle vehicles These load effects are lower because for 20in

and 30m spans the effects of a complete vehicle are dominant The average GVM of a 6 axle vehicle is

less than its 7 or 8 axle COtll1tfrmlrts as shown in Table 39 The load effects are therefore

lower In the case of the 10m and 15m span individual axles and axle sets are the dominant

Overloaded axle sets were observed in each of the vehicle classes and the predicted load effects are

therefore similar

6 Axle 7 Axle 8 Axle

5 285 290 278 290 10 762 739 743 762 15 1266 1365 1372 1372 20 2069 2262 2242 2262 30 4740 4638 4740

Table 37 - using the Normal Distribution

6 Axle 7 Axle 8 Axle Veh Veh Max

5 263 261 258 263 10 323 343 339 343 15 417 439 436 439 20 495 522 537

653 675

using the Normal Distribution

Maximum Average Vehicle GVM GVM Standard

6 Axle 533 281 91 -021 7 Axle 653 367 118 -073 8 584 122 -056

Table 39 - Statistical Properties of Recorded Vehicle Classes

In Nowaks method is intended for the review of a set of heavy vehicles rather

than subsets of that data the load effects of each class were observed to follow a normal

distribution and the maximum pvtr()1 values (7 amp 8 axle vetucl~s are considered rep1resenlatlve of

the total surveyed IJI)V Due to the sample set the 95 confidence limits gave a very

small range for the true event magnitude about the extrapolated 120 year event For 6 and 7 axle

vehicles a variance of 04 about the predicted event was calculated In the case of 8 axle vehicles a

variance of 12 was found A comparison of the extreme events predicted Nowaks method

with those obtained the extreme distribution is given in Section 35

(3-12)

Univers

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342 Extreme Distributions

For independent events such as traffic loading it is often the case that the distribution of maximum

extreme events is relatively insensitive to the distribution of the common events The method

developed in RR 9100401 amp 02 of a set of extreme events from the set of common events

was therefore undertaken In this extreme events were selected from the visual inspection of

the load effect distribution The extreme distribution best describing the characteristics of those

events was then used to the results

The practice of plotting the of an event against a linearised exceedence probability was used

to visually identifY the distribution of the load effects for each class of for each span Having

sorted and ranked the load the exceedence probability of the value Xm was calculated

using Cunnanes fOlmula 1978)

m 04P(Xgtx ) =--- (34)

n+

Where

P(X) Exceedence probability of event x

n Total number of values

m Rank of value in a list ordered by aescerlG value

Cunnane (1978) derived the formula from the study of the criteria of

unbiasedness and minimum variance An unbiased gtlVlaquo method is one that will cause the average of

the plotted points of each value of m to fall on the theoretical distribution line

For the purpose of the distribution graph of the load the reduced variate y of the

exceedence gtl~LJltY was calculated using the formula below (Chow 1988) The distribution graph

of the vvuWF moments and shear forces associated with a 6 7 and 8 axle vehicle on a 30m span is

shown in 35 and 36 The complete set of the distribution graphs for all spans is contained

with B

Where

1 T Return Period where T shy

342 Extreme

For events such as traffic it is often the case that the distribution of maximum

extreme events is insensitive to the distribution of the common events The method

i1ppl()npi1 in RR 9100401 amp 02 of a set of extreme events from the set of common events

was therefore undertaken In this

the load effect distribution

extreme events were selected from the visual of

The extreme distribution best the characteristics of those


The of of an event a Iinearised exceedence was used

to the distribution of the load effects for each class of for each span

sorted and ranked the load the exceedence of the value Xm was calculated

Cunnanes formula

gt

Where

Exceedence of event X


m Rank of value in a list ordered value

Cunnane (1 derived the formula from the of the criteria of

unbiasedness and minimum variance An unbiased method is one that will cause the average of

the of each value m to fall on the theoretical distribution line

For the purpose of the distribution of the load the reduced y of the

exceedence IJ~LJltY was calculated the formula below The distribution

of the UU) moments and shear forces associated with a 6 7 and 8 axle vehicle on a 30m span is

shown in 35 and 36 The set of the distribution for all spans is contained

with B

Where

T Return where T 1

Univers

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--

- - -_--_- _ shy3000

2800+------I----+----+----~--~---~f- shy

S ~ 2600+----~---r_----~----~~~--4----~

ir j 2400+----+---1-------1~~---~---r---~ ~ ~~ ~b

~ 2200 +---~---~~~--1---~---+-------1

jJl

2000+---~~--1-----I---~---r---~

1800 -------1f----+-----t-- Plot Area Ir------+-----I

o 2 4 6 8 10 Redlfed Variate

--6 Axle

----- - -------- - - ------- __- -----shy3200

3000

e ~ 2800 i S 2600 ~ ~I Vsect 2400 ai

jJl 2200

2000 o 2 4 6 8 10 12

Reduced V ruiate

-+-7 Axle

3000

I 2800

2600 ~

I~ 2400 I

I2200

Chart Area

2000

o 2 4 6 8

Reduced Vuiate

1-+-8 Axle I

Figure 35 - Distribution of Bending Moments - 30m span

(3-14 )

12

10

Univers

ity of

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n-- __ ___shy480

460

440

~ 420

400 ~

380ie (I)

u 360

340

320

300

380

360

340

~ 320 300 ~

280lt Vol

260

240

220

J -~

V ~

~ v

_ _

j~

~

- V

o 2 4 6 8 10

Reduced Variate

--6 Axle

o 2 4 6 8 10

Reduced Variate

--+-7 Axle

440

420

400

~ 380 i 360 ~

ie 340 -= ~ 320

300

280

V

1

Ir

~

V

o 2 4 6 8

Re(luced Variate

-+- 8 Axle

Figure 36 - Distribution of Shear Forces - 30m span

(3-15)

12

i

12

10

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ity of

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From the plotted graphs it was possible to identifY the cases where the maximum events deviated from

the POTP~ltI(n of the general population The distribution for each span for each vehicle class

was reviewed and the set of extreme events extracted A analysis was undertaken to assess

the impact of varying the population size of the extreme events This was done by calculating the mean

standard deviation and skewness of the extreme events and the Gumbel distribution to extrapolate

a 1 in 120 year event The predicted 1 in 120 year events for the various population sizes were then

compared The results of this sensitivity for the extreme vp moments caused 6 Axle

are shown in Table 310 Where a line was easily regressed it was confirmed that the

distribution was relatively insensitive to the population size In the case where distribution of the

extreme events deviated substantially from the distribution the distribution was

sensitive to the size of the population assumed In these cases the final decision on the population size

was done by the visual of the distribution graph

No of Reduced Event

5m Spans

10m Spans

15m Spans

20m Spans

30m

22 28 42

22 28 42

22 28 42

22 28 42

22 28

2024 2000 1961

5448 5379 5254

8937 8835 8659

13728 13572 13313

25468

25224

99 99 98

267 271 285

376 387 405

583 597 611

969

979

31680 40320 60480

31680 40320 60480

31680 40320 60480

31680 40320 60480

31680

40320

751 727 687

751 727 687

751 727 687

751 727 687

751

727

763 782 813

763 782

813

763 782 813

763 782 813

763

782

278 277 276

749

750 757

1181 1186 1195

1818 1824 1828

3285

3288

In RR the extreme set of results was assumed to be the top 15 of the sample set A

this to the graphical POTP~ of each distribution The results

shown in Table 311 demonstrate that the method used in RR 9100402 results up to 22 lower

For this reason the extreme events are defmed from the rpop~i of each distribution rather than

from an assumed percel1tal~e of the total sample set

(3-16)

Univers

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5 301 238 -21 10 812 631 -22 15 1364 1129 -17 20 2097 1756 -16 30 3631 3380 -7

Table 311 - of Predicted Moments for 6 Axle Vehicles to Sample Size

isolated the set of extreme events the statistical nrmiddotrtilaquo of the events were used to fit an

appropriate theoretical distribution As for the general set the extreme events were

ranked and an exceedence probability was calculated The graph of the magnitude of the event versus

the reduced variate was then plotted This was used to fit the various theoretical distributions

to the distribution of the plotted

Given the nature of the data the extreme distributions were considered It has been shown that the

distributions of extreme events converge to one of three forms of extreme value distributions

EVI and EV2 are also known as the Gumbel and Frechet distributions respectfully If a variable x is

described the EV3 then -x is said to have a Weibull distribution Given the positive

skewness of the data the Wiebull distribution was not considered further In addition to the extreme

distributions the Normal and the Normal distributions were considered for the purposes of

comparison The distribution of the load effects for 6 7 and 8 axle vehicles on a 15m span togethi~r

with the various theoretical distributions are shown in 37 to 39 A ffwYlnlpt set of the

distribution for each vehicle class and span is included within Appendix B

(3-17)

Univers

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1500 -------------------------------------------

1400 - S ~ 1300 -

~ 1200 S o ~ 1100 OJ)

=g 1000 ClJ

=l 900

800 +-----~----~----_r----~----~------~--~

-100 100 300 500 700 900 1100 1300

Reduced Variate

~ Plotted Points - 15m Span logNormal-+-Normal Gumbel -tt- F rechet

390

370

- 350 ~ - ClJ ~ 330 0 ~

~ 310 ClJ

c rJ)

290

270

250

Reduced Variate

-100 100 300 500 700 900 1100 1300

-ltgt- Plotted Points - 15m Span -f- Log Normal

-+- Normal -m- Gumbel

Figure 37 - Fit ofTheoretical Distributions to Plotted Points - 6 Axle Vehicles on 15m spans

(3-18)

Univers

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1450 -----------~--------------------------_

1350

1250

1150

1050

950

-

~ - ltI) tI I 0 ~ I eIS ltI)

Q rJ1

850 +-----~----~----~----~----~----~----~

-100 100 300 500 700 900 1100 1300

Reduced Variate

~ Plotted Points - 15m Span Log Nonnal

-Nonnal Gwnbel

360

350

340

330

320

310

300

290

280

270

260

-100 100 300 500 700 900

Reduced Variate

1100 1300

~ Plotted Points - 15m Span Log NannaI

Nonnal Gwnbel


(3-19)

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1200

1150 --

3 1100

~ - 1050 ~

3 = 1000 0

~ 950 OJ)

0 = 900 ~ = ~ 850

800

750

-l00 l00 300 500 700 1100 l300

Reduced Variate

900


--Nonnal Gwnbel

370

350

-Z ~ - ~ (j 0 ~

11 ~ -= 00

330

310

290

270

250

230

-100 100 300 500

Reduced Variate

700 900 1100


-- Nonnal Gumbel


(3-20)

Univers

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In plotting the the frequency KT was calculated for the Normal and Gumbel

distributions In the case of the Normal distribution the frequency factor was taken as z the standard

normal distribution variable In the case of the Gumbel distribution the following formula was used

Where T = Return Period

In considering the effective return it was necessary to note the -VIJLLRU size of the extreme

events and the fact that survey data reoresenlted a single month of traffic flow Each event was set to

represent an riPPt1riPlnt period within the month Where 28 extreme events were identified 28

effective periods were judged to have occurred within the month In considering a return period of 120

years 40320 x 12 x 120) effective were considered to have occurred In the case where

only 16 extreme events were found for a return period of 120 years 23040 (16 x 12 x 120) effective

periods were considered to have occurred

In review of the distribution the plotted points did not extend sufficiently to allow a conclusive

comparison with the various distributions Although a number of vehicles were analysed a

limited number of extreme events were identified these events had a return period of I

It is apparent that extreme events reIlrelsenltlOg a larger time are to

the distribution of events up to a return period of 120 years

In review of the Normal and the Normal distributions it was noted that for the shorter spans a

number of the plotted events were within 5 of the eXlrralJOlareO 120-year event A variance of 5

between the 28 events and the 120 year events was UllltlCCeOIaDlle and the use of the Normal

and the Normal distributions was discounted

the extreme the datas skewness points to the use of the Frechet and

the Gumbel distributions In the majority of cases the Frechet Distribution predicted events far in

exceedence of those of the Gumbel distribution as shown in Figure 37

In the of bridge structures a high of confidence is required given the human and

economic cost of a structures failure Although the Frechet Distribution provided the most

conservative the uubullwu~ of the events was considered that expected from traffic

live The Gumbel distribution was therefore chosen as a distribution that will

adequately cater for extreme events and potential outliers

In the the was calculated for the Normal and Gumbel

distributions In the case of the Normal the factor was taken as z the standard

normal distribution variable In the case of the Gumbel the formula was used

+


In the effective return it was necessary to note the size of the extreme

events and the fact that survey data a month of traffic flow event was set to

within the month Where 28 extreme events were 28

effective

years 40320

were to have occurred within the month In a return of 120

x 12 x were considered to have occurred In the case where

16 extreme events were for a return of 20 years 23040 (16 12 x effective

were considered to have occurred

In review of the distribution the did not extend to allow a conclusive

with various distributions number of vehicles were a

limited number of extreme events were identified these events had a return

It is that extreme events a are to

the distribution of events up to a return of 120 years

In review of the Normal and the Normal it was noted that for the shorter spans a

number of the

between the 28

events were within 5 of the eXlrralJOlareO event A variance of 5

umlcceplaDlle and the use of the Normal events and the 120 year events was


the extreme the datas skewness to the use of the Frechet and

the Gumbel distributions In the

exceedence of those of the Gumbel

of cases the Frechet Distribution events far in

lUUUV as shown in 37

In the of of confidence is

economic cost of a structures failure the Frechet Distribution

the human and

the most

IYPflp1 from traffic conservative the of the events was considered


cater for extreme events and At n outliers

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343 Confidence limits

In review of the events by the chosen statistical distribution the true event magniltucle may lie

within a range about the extrapolated value To this range confidence limits were found

the standard error of estimate The size of confidence limits are dependent on the confidence level fJ

and associated with the confidence level is a a given

a (37)

For v1UHlJlv for a confidence level of95 the level is 25 laquo I

For a of n and standard s the below tlV were used to calculate the

standard error of estimate Se for the Normal and Gumbel distributions

2 + Z2 Normal S = S (38)e

n

X Gumbel s = 1 1+11 + 11000Kn] 2 S (39)e

n

The confidence limits were calculated for a confidence level of 95 For an event XT the confidence

limits were taken as xrplusmnSez(J For a confidence level of95 the standard normal variable Z is 196

An of the plotted confidence limits is shown in Figure 310 In the case of the 7 axle Vv1vl

the confidence limits for the I in 120 year bending moments are plusmn 10 This error

COlrllPOWlaeQ with the inherent inaccuracies of the WIM data is The means of reducing it

include the use of a larger set ofextreme events

(3-22)

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---

4150

3950

3750

e 3550 ~ - 3350 = ~ e 3150 Q

~ 2950

2750

2550

2350

-100 100 300 500 700 900 1100 1300

Reduced Variate

~ Plotted Points - 30m Span -reg- Gumbel

- 0 - Upper 95 Limits --6- Lower 95 Limits

Figure 310 - Confidence limits for Gumbel Distribution for 7 Axle Vehicle on 30m Span

35 RESULTS

Using the Gumbel distribution the load effects of the actual vehicles were extrapolated to a I in 120

year event The results of that extrapolation are shown in Table 312 amp 313 The results are

characteristic load effects that represent serviceability loads using limit state principles as discussed in

Section 34 In combination with an impact factor the load effects generated from actual traffic data

may be compared to those calculated by TMH7 Part 2 and the design load derived by Reports RR

91 00401 amp 02

Bending Moments (kNm) 6 Axle 7 Axle 8 Axle

Span (m) Veh Veh Veh Max

5 276 301 231 301 10 757 812 624 812 15 1195 1364 1135 1364 20 1828 2097 1780 2097 30 3275 3631 3289 3631

Table 312 - Extrapolated Bending Moments

Shear Forces (kN) 6 Axle 7 Axle 8 Axle


5 297 233 201 297 10 320 314 279 320 15 369 350 349 369 20 431 433 392 433 30 489 542 481 542

Table 313 - Extrapolated Shear Forces

(3-23)

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The results show that the 7 axle vehicles produced the bending moments For the

spans of 15m and greater this was to be expected as

(i) The average GVM of7 axle vehicles is greater than the 6 axle vehicle as shown in Table 3

and

(ii) In complying with the formula and the GVM the 7 axle vehicle can achieve

axle masses in closer 111UA1IJUltY than its 8 axle counterpart

The 7 axle vehicles cause moments on the shorter spans because their axles and axle sets

are heavier than those of the 6 and 8 axle vehicles Table 314 that details the statistical

of the vehicles this statement No specific trends in the shear force results

were observed between the vehicle classes this is because the shear load effects are not as sensitive to

the vehicles axle

Axle Axle Axle Axle Axle Axle Axle I 2 3 5 6 7 8 GVM

Mean 467 529 518 423 429 441 2806 6 Axle

Std Dev 68 196 199 199 188 189 913Vehicles 006 -014 -009 012 001 -021

Mean 488 557 555 529 545 501 490 3665 7 Axle

Std Dev 67 201 191 215 224 205 1176Vehicles 16 -059

Mean 470 504 526 455 456 446 391 384 3632 8 Axle

Std Dev 67 200 198 197 187 197 189 186 1216Vehicles Skewness -020 -034 -028 -024 -025 -015 -006 -003

Table 314 - Statistical of Axle Weights and GVM

In review of the events it is important to that the true event magnitude probably

sits within a range about the events 95 confidence limits this range was calculated in

each case The ranges of plusmn 11 shown in Tables 315 and 316 are when considering the

possible error in the WIM data The results reinforce the need for a population of extreme

events

plusmn of95 Confidence Limits About

5 98 147 117 10 104 141 119 15 93 128 124 20 92 128 119 30 95

Table 315 Predicted Bending Moment Confidence Limits

(3-24)

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plusmn of95 Confidence Limits About the Predicted Shear Force Event

6 Axle 7 Axle 8 Axle Veh Veh

5 151 130 104 10 120 1l0 127 15 103 88 133 20 103 95 116 30 103 113

Table 316 - Predicted Shear Force Confidence Limits

It was observed that the load effects oprr~tri using Nowaks were than those

calculated by the Gumbel distribution to the set of extreme events The results of the

comparison are shown in Tables 317 and 31S It is observed that the variance in the bending moment

effects increases with the span The results suggest that the distribution of axle and axle set weights

differs from the distribution of the GVM Given that the deviation of the extreme events from the

common events Nowaks method of applying a single distribution to the total data set is not supported

Difference Span (m) Nowak Gumbel

NowakGumbel

5 290 301 -4 10 762 S12 -6 15 1372 1364 1 20 2262 2097 S 30 4740 3631

Table 317 - NowakGumbel Comparison - Bending Moments

Shear Forces

(m) Nowak Gumbel Difference

NowakGumbel

5 263 297 -11 10 343 320 7 15 439 369 19 20 537 433 24

542

Table 3IS NowakGumbel Comparison - Shear Forces

of the WIM also provided the to the sensitivity of the results to

the assumed return period The sensitivity of the rppound1Itpound1 events to the return periods assumed in

BD3701 ENV 1991-3 (1000 and RR 91100402 is shown in Table 319 The 10

variance between the assumed 120 year period and the 2976 associated with RR 91100402 is

when comparing the two set of results

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Predicted Moments (kNm) Spans

5m 10m 15m 20m 30m

120 year event 1 000 year event 2976 year event

276 292 (+59)

301 (+89)

757 804 828

1195 1262 1297

(+56)

1829 1930 1982

3275 3436 3519

(+49)

(+74)

Table 319 Moments for 6 Axle Vehicles with Varying Return Periods

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36 OVERLOADING

The overloading of vehicles was accounted for in TMH7 Part 2 and RR 9100401 amp 02 through the use

of an overloading factor applied to the GVM and axle sets In RR 9100401 amp 02 the factor was

derived from measurements taken in Switzerland by Bez (1989) because of a lack of data in South

Africa The final recommendation of RR 91100401 was however that the extent of overloading on

South African roads be verified using traffic survey data

In assessing the prevalence of overloading the GVM of each vehicle was reviewed in terms of the

maximum limit of 560kN and the bridge formula The results of this review are shown in Table 320

Over 99 of the 6 7 and 8 axle vehicles were found to be in compliance with the National Road

Traffic Regulations (1999) However only 40 of abnormal vehicles met the restrictions in terms of

the GVM The study indicates that the abnormal vehicles merit special attention from the law

enforcement agencies The cumulative distribution of vehicle GVM shown in Figure 311 graphically

indicates the percentage of9 axle vehicles that are overloaded

Total No of of Vehicle No of Illegal Illegal Class Vehicles Vehicles Vehicles

6 Axle 24901 19 008 7 Axle 34951 43 012 8 Axle 2587 15 057 9 Axle 45 27 6000

Table 320 - Number of Observed Illegal Vehicles

12

~ 08 D lte

D 0 shy 06p v ~

-a 04

8 02

o 100 200 300 400 500 600 700 800 900

Weight (lN)

I 6 axle [J i axle amp 8 axle Q 9 Axle 1

Figure 311 - Cumulative Distribution of Axle Weights

(3-27)

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The impact of individual axles and axle sets on short spans are well documented (Ullman

1988) A review of the extent of oVC~rl(ladmg associated with individual axles was therefore undertaken

The allowable axle mass was set at the permissible limits in the National Road Traffic

Regulations (1999) and those allowed by the bridge formula in terms of the vehicles length and axle

spacings The of this exercise are shown in Table 321

It was observed that a maximum of 25 of axles in 6 axle verucles were overloaded The second and

third axles of 7 and 8 axle vehicles were seen to be prevalent to In particular the trurd

axle of the 8 axle verucles was overloaded in 31 of the recorded events The greatest prevalence in

axle overloading was observed in the 9 axle vehicles Over 34 of the axles were observed to be

overloaded Due to inaccuracies of the WIM data these results are indicative rather than

representative

Vehicle Axle No Class 2 3 4 5 7 8 9

6 Axle 00 19 20 21 12 25 7 Axle 03 77 69 09 09 56 37 8 Axle 83 280 310 13 09 44 67 70

444

It is imlnArt to recogrllse that overloading is a time UCIJCllUClll variable The quantification of an

-IltgtrhnCJ factor is therefore dependent on the considered return In the case ofRR 91100401

factor was applied to the vehicle mass of the associated load the

effects This approach is considered valid however it is not followed in this study

In the calculation of the overloading factor cognisance of the approach is required The current

limit state codes are based on the use of partial factors that limit the exceedence probability ofan

event for a time period The objective of this thesis is to calibrate a load model based on the

of the collected traffic survey data Given that the traffic survey data is a product

of gt111 the need for a t factor was judged unnecessary the set

nhPltnp of quantifying the prevalence of within a specific period on the National Route 3

was retained

For the purpose of quantifying the increase in load effects an overloading factor is defined as the

increase caused by the actual vehicles in comparison to those of the vehicles As

stated the percentage error associated with the WIM results nrvP the use of individual

results to draw definitive conclusions The statistical properties of a set of results are used rather to

JVLLV events In the case of nv- a 1 in 28 day event was used The results therefore

the maximum overloading event within the 28 day period

In the 1 in 28 event two statistical approaches were used The first applied a normal

distribution to the complete population set of vehicles The second a normal

distribution to a set to extreme vehicles identified from the distribution as in the case of

(3-28)

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the actual vehicles These results were then compared with the I in 28 day events predicted using the

actual vehicles For the actual vehicles a normal distribution was also used as a means of

comparing similar statistical distributions

The normal distribution of the extreme population set was considered the more indicative set of results

The complete set of events did not always fit a single regression line In the case of 8 axle vehicles the

plotted points demonstrated a bimodal distribution The variance between the load effects calculated

using the complete set of events and the extreme set of events is shown in Table 322 In 80 of the

cases the results vary by less than 10 Although the calculated overloading factors results vary for

the two approaches similar trends develop in both cases

Bending Moments (kNm) Shear Forces (kN)

Difference Difference Total Pol Extreme POf Total Pol Extreme Pol

Span 6 Axle 7 Axle 8 Axle 6 Axle 7 Axle 8 Axle (m) Veh Veh Veh Veh Veh Veh

5 -2 -6 3 5 -1 7 10 6 -13 14 -9 -4 6 15 -11 -11 11 1 -6 5 20 -4 -7 6 5 -3 8

30 -4 -1 3 5 2 21

Table 322 - Variance of Load effects derived from Complete Set of Events and Extreme Set ofEvents

The results of the analysis shown in Tables 323 and 324 demonstrate the impact of overloading on

short span structures The obvious trend is that overloading is prevalent in 6 and 7 axle vehicles but not

in 8 axle vehicles In review of the bending moment effects overloading has a significant impact on

spans of 15m and less This finding indicates that the use of a blanket overloading factor is not

appropriate The results support the conclusion that the overloading of individual axle sets is more

prevalent than the overloading of a complete vehicle This fmding is consistent with work carried out in

the drafting ofBD 3788 (Dawe 2003) where a 14 overloading factor was applied for spans up to 10m

and then reduced linearly to WIlty at 60m spans

Bending Moments (kNm)

Legal Vehicles Actual Vehicles Difference Actual Legal

Span 6 Axle 7 Axle 8 Axle 6 Axle 7 Axle 8 Axle 6 Axle 7 Axle 8 Axle (m) Veh Veh Veh Veh Veh Veh Veh Veh Veh

5 197 195 196 216 220 181 10 13 -8 10 510 547 520 582 600 486 14 10 -7

15 968 1054 986 946 1034 875 -2 -2 -11 20 1504 1582 1537 1452 1599 1388 -3 1 -10

30 2767 2917 2899 2676 2944 2697 -3 1 -7

Table 323 - Overloading Results using Normal Distribution - Bending Moments

(3-29)

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6 ixle 7 ixJe 8 ixJe 6 ixle 7 ix]e 8 ixJe 6 ixle 7 ixle 8 ixle

5 182 183 184 210 197 164 15 8 -11 10 246 251 252 249 250 220 1 0 -13 15 295 308 302 298 293 272 1 -5 -10 20 337 347 337 349 358 316 4 3 -6 30 411 440

Table 324 - Overloading Results Nonnal Distribution - Shear Forces

The overloading factor with to the predicted 28 day shear forces varied with a similar trend to

those associated with the moments However the results showed that caused an

increase in the shear effects of the 7 ixle vehicles for spans of up to 30m For spans the shear

force effect is not as sensitive to the location of critical axle sets as the 1II ll1trIO moment effect

Overloaded axles will therefore still contribute significantly to the total shear forces on spans of 30m

The results thPTPtCTP the of the overloading of6 and 7 axle vehicles

As stated the load effects on short spans are dominated by the action of individual axle and axle sets

Overloaded axles on 2 and 3 axle trucks will therefore impact on calculated results for 5m and 10m

spans It is therefore recommended that future studies include a review of all regardless

of the vehicles number of axles

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37 CONCLUSIONS

In conclusion the probabilistic analysis of the truck survey data produced load effects that can be

compared with those calculated from TMH7 Part 2 and RR 91 00402 In addition the creation of a

legal set of vehicles allowed the quantification of the load effects due to overloading

In regard to the probabilistic analysis of the WIM data the study confirmed the use of the Gumbel

distribution (RR91 10040 I 1994) as the most appropriate means for extrapolating the load effects of

heavy vehicles on simply supported spans Nowaks (1991) application of a normal distribution to the

complete set of events was not favoured as the distribution of the extreme load effects was observed to

deviate from the distribution of the common load effects The use of the normal distribution produced

load effects up to 31 higher than those calculated by applying the Gumbel distribution to the extreme

set of events

In applying the Gumbel distribution it was shown that the extrapolated load effects are sensitive to the

population size of the extreme events For each vehicle class and span it was necessary to visually

identifY the population size of the extreme events from the distribution graphs RR 9100401s

assumption that the top 15 of load effects from a population set are extreme events is therefore not

supported In addition a sample of extreme events representing a larger time period is required This

will reduce the confidence limits of the predicted events

The probabilistic analysis of the WIM data was shown to be relatively insensitive to the return period

selected However the 2976 year return period used by RR 9100402 is conservative when compared

with ENV 1991-3 and BD 3710 I For the serviceability limit state a maximum return period of

1000 years as per ENV 1991-3 is recommended

The potential inaccuracy of the WIM data (plusmn25) raises a question over the validity of the results This

question should be answered in future research by quantifYing the impact of the potential error on the

predicted load effects ENV 1991-3 was calibrated (OConnor 2005) using WIM data with a

maximum error of 5 Similar standards are required in South Africa if WIM data is to be used in the

calibration of bridge live load models

The number of overloaded vehicles recorded on the National Route 3 was found to be low Their

occurrence however raises concerns for the serviceability and ultimate limit states of bridge structures

In particular the extent of the overloading associated with the abnormal vehicles requires the attention

of law enforcement agencies The results of the probabilistic analysis of the WIM data show that the

overloading of individual axles rather than of the overloading of complete vehicles is prevalent A

comprehensive survey of heavy vehicles using weighbridges is necessary to accurately quantifY

overloading on South African roads These survey results may be the used to calibrate the partial load

factors used with the chosen live load model Using this approach there is no longer the need to

calculate overloading factors

(3-31)

37 CONCLUSIONS


compared with those calculated from TMH7 Part 2 and RR 9100402 In addition the creation of a



distribution (RR9110040 I 1994) as the most appropriate means for extrapolating the load effects of





set of events



identifY the population size of the extreme events from the distribution graphs RR 9110040 I s

assumption that the top IS of load effects from a popUlation set are extreme events is therefore not





with ENV 1991-3 and BD 3701 For the serviceability limit state a maximum return period of


The potential inaccuracy of the WIM data (plusmn2S) raises a question over the validity of the results This


predicted load effects ENV 1991-3 was calibrated (OConnor 200S) using WI M data with a

maximum error of S Similar standards are required in South Africa if WIM data is to be used in the











(3-31)

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CRITICAL REVIEW OF TMH7 PART 2 amp SUBSEQUENT RESEARCH

The following chapter undertakes a critical review of the live loading model contained with TMH7

Part 2 using the load effects from the probabilistic analysis of the WIM data Also reviewed

are the load effects used to derive the alternative load model proposed in the of

(i) RR 9100401 The effect of an Increase in the Permissible Heavy Vehicle Loads on

June 1994

(ii) Report RR 9100402 The effect of an Increase in the Permissible Vehicle Loads on

- Assessment Code December 1995

In order to undertake a meaningful comparison of the various load a detailed appraisal of the

methods used by Liebenberg (1974) and RR 9100401 amp 02 is undertaken

The following chapter also reviews the used Liebenbergs deterministic methods

the statistical information provided by the WIM data The probabilistic methods used in RR 91100401

amp 02 are reviewed with reference to the latest research (OConnor et aI 2001) used in drafting ENV

1991-3 In both the used to calibrate the live load model for limit state is

examined

41 TMH7 PART 2

411 Background and Development

In 1974 the then National rltnrr Commission YV~~V~~ the need to create uniform standards for

design across South Africa that incorporated the latest theory and nrltlfhp the

Code of Practice ofthe Design of Highway and Culverts was issued in 1981 with a

number of errata and revisions being issued in 1988 Although the code was based on the

provisions of the BS5400 Steel Concrete and Bridges Part 2 Specification of loads

issued in 1978 TMH7 Part 2 (1981) differed significantly in regard to the application of live loads due

to traffic

The development of the live load models contained within TMH7 is largely based on research work

carried out by (1974) In tum the basis of his research was taken from the formula

developed by Henderson (1 for the inclusion within BS 153 (1954) and the subsequent issue of

BS 5400 (1978) Henderson (1954) a credibility approach where engineering judgement

was used to determine most onerous probable combinations and arrangements of heavy vehicles

Liebenberg ( favoured this approach versus the probabilistic of truck survey data The

lack of available statistical data and the of the variables associated with traffic movements

meant the approach was deemed the only feasible method The combinations of vehicles

chosen by (1974) and Henderson (I 954) are shown in Appendix C

(4-1 )

2 amp i) UD i)J ol

The

Part 2

undertakes a critical review of the live ~~ model contained with TMH7

the load effects from the of the WIM data Also reviewed

are the load effects used to derive the alternative load model orciDosed in the of

RR 9100401 The effect of an Increase in the Permissible

June 1994

Vehicle Loads on

(ii) The effect of an Increase in the Permissible


Vehicle Loads on

In order to undertake a H~UHUeUU (nrnn~n of the various load a detailed of the

methods used and RR 9100401 amp 02 is undertaken

The also reviews the used deterministic methods

the statistical information the WIM data The methods used in RR 911004101

amp 02 are reviewed with reference to the latest research et 2001) used in ENV


examined

41 TMH7 PART 2

411 and OAfAIIID

In I the then National rTIltnnrr Commission y~~v~ the need to create uniform standards for

across South Africa that Inlrtpmiddott1 Md the

Code of Practice ofthe and Culverts was issued in 1981 with a

number of errata and revisions issued in 1988 the code was based on the

of the Concrete and Part 2 of loads

issued in 1 TMH7 Part 2 (1981) differed in to the of live loads due

to traffic

The ae1elJornerlt of the live load models contained within TMH7 is based on research work

carried out (I In tum the basis of his research was taken from the formula

for the inclusion within BS 153 ( and the issue of

BS 5400 ( Henderson (I

was used to determine most onerous JluaUlv

favoured this

lack of available statistical data and the COlnplex

meant the was deemed the

chosen (1 and Henderson are shown in 1)JIA C

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TMH7 divides live loading due to traffic into the three categories of nonnal (NA) loading abnonnal

(NB) loading and superloads (NC) loading NC loading represents multi-wheeled trailer combinations

with controlled hydraulic suspension and steering For the purposes of this thesis only the live load

models associated with nonnal (NA) loading are considered

The original fonn NA loading was based on the existing legal loads in South Afiican in 1972 Two

traffic states were considered One of these cases was bumper-to-bumper traffic that modelled the static

load conditions and thus contained no allowance for impact loading The other case took account of

moving traffic at set following distances with allowances for impact based on the Swiss Impact

fonnula (1970)

cent = 5(100 + L) Swiss Impact Fonnula (1970) (41)10+L

Where

Impact factor

Equivalent span length

From the analysis of these two states a loading curve was derived that specified a unifonnly distributed

lane load as a function of the loaded length This lane load was applied as two line loads at a set

spacing within a notional design lane The lane load was applied in conjunction with a single knifeshy

edge load (KEL) to ensure that the maximum bending moments and shear forces were produced

Although a set of KELs are required to model both the bending moments and shears a single KEL

(Henderson 1954) was chosen for simplicity Although this approach correctly estimates the shear

forces it overestimates the bending moments Multi presence is taken as a function of the loaded length

as is the presence of critical axle loads

The application of the unifonnly distributed load (UDL) to obtain the maximum load effects is

somewhat complex In order to achieve the maximum load effects TMH7 Part 2 requires that

(i) The transverse position of the lane loads within the notional lanes is varied to derive the

maximum effects on the structural element under consideration

(ii) The intensity of the UDL in the longitudinal direction is varied on separate parts of an

influence line to produce the most onerous effects and

(iii) A correction factor k be used to cover the case where the partial loading of the base of any

portion ofan influence line creates the most onerous effects

The amount of computation required to correctly apply NA loading has caused dissatisfaction with

South African bridge engineers (Fitzgerald 1998) when compared with the simpler loading models in

BD 3701 LRFD and ENV 1991-3

(4-2)









fonnula (1970)

cent = 5(100 + L) 10+L

Where

Impact factor

L Equivalent span length

Swiss Impact Fonnula (1970) (41)
















portion of an influence line creates the most onerous effects




(4-2)

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They were deemed necessary by (1978) who stated

At first consideration the above may appear to increase the of

if the maximum effects are to be calculated These refinements cannot however be

F- as total discrepancies UlUf 50 can occur

The sections review the of TMH7 Part 2 in detail with the purpose of

mnlPnhna on the assumptions made in comparison to the latest research and development

412 NA loading Curves

The curve for NA Loading in TMH7 Part 2 is used by design for the

UHJlVU of the uniformly distributed loads that model normal traffic conditions on bridge and

culvert structures A of the methodology used in constructing this curve was undertaken to

comment on the assumptions made with reference to the characteristics of heavy vehicles recorded by

the WIM sensors

As Liebenberg (1978) used a credibility in determining the most onerous configuration

and arrangement of various of heavy vehicles to model live load effects In developing these

bumper-to bumper conditions and moving traffic conditions were considered

In the case of moving an allowance for the effects was included in the quantification of

the load effects The axle loads of the chosen vehicles were the pre 1972 South African legal loading

increased by 20 Direct reference to the derivation of the loading curve from these combinations was

not found during the literature search However the vehicle combinations assumed by Liebenberg

(1974) and Henderson (1954) were referenced in Ullman (1987) and are shown in C

The following into the development of the loading curve was taken for Ullman (19871988)

referencing Llfbel1bfrg earlier work

bull Short Span 40m) The combinations used by (l included a convoy of five

heavily loaded vehicles weighing up to 228kN These were orelcejed and followed a

combination of vehicles rpnrpltIPnltpn by a line load of 60kNm In the case of

vehicles a ~vu of 45m was assumed between vehicles and allowances were made for

impact the Swiss Impact Formula (1970) To allow for the eventuality of overloading a

20 was added to all axle or alternatively a 40 surcharge to a axle

group

bull Long (gt 40m) In the case of long spans identical vehicle combinations were

considered with stationary traffic condition being dominant No allowance for impact

was therefore made The blanket 20 surcharge to account for overloading was considered

excessive for the number of vehicles associated with spans Instead a 10

was to allow for the future increase in legal axle limits

(4-3)

were deemed necessary who stated

At first may appear to increase the vVU-1vnHy of

The

412 NA

The

if the maximum effects are to be calculated These refinements cannot nJ be

middotUlUf 50 can occur

sections review the cornDl)nents of TMH7 Part 2 in detail with the purpose of

Curves

curve for

UH1lUH of the no-m

made in to the latest research and

NA LVUUI in TMH7 Part 2 is used for the

distributed loads that model normal traffic conditions on and

culvert structures A of the used in this curve was undertaken to

comment on the asunlptIOfIS made with reference to the characteristics of vehicles recorded by

the WIM sensors

As

and

(I used a -__ bullbullbullbull J ~r rmiddoth In the most onerous

vehicles to model live load effects In these

conditions and traffic conditions were considered

In the case an allowance for the effects was included in the of

the load effects The axle loads of the chosen vehicles were the pre 1972 South African

increased 20 Direct reference to the derivation of the curve from these combinations was

not found the literature search the vehicle combinations assumed

The

and Henderson were referenced in Ullman (1987) and are shown in C

pound1 of the 1VYUUamp curve was taken for Ullman (1987 I

earlier work

Short The combinations used (I included a convoy of five

loaded vehicles up to 228kN These were orece(ted and followed a

combination of a line load of 60kNm In the case of

a ~vu of 45m was assumed between vehicles and allowances were made for

To allow for the of a

20

group

was added to all axle a 40 to a axle

In the case of spans identical vehicle combinations were

with traffic condition dominant No allowance for

was therefore made The blanket 20 to account for was considered

excessive for the number of vehicles associated with spans a 10

was to allow for the future increase in axle limits

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In 1988 the NA loading curve was revised to increase the unifonnly distributed load by an additional

6kNm for all loaded lengths No reference was found on the rationale for this increase It is proposed

however that the deficiencies in TMH7 Part 2 in both the short and long span cases motivated this

revision In particular the specified lane load of 6kNm was low in comparison to the 9kNm

recommended by comprehensive studies that Buckland (1978) carried out in the United States A

further factor for the increase was the inclusion of a 9kNm lane load for long span structures in

BS 5400 This was an increase over the 58kNm lane load in BS 153 The increase allowed for the

adoption of lower partial factors (12 in lieu of 14) for dead loads Previously the dead load partial

factor provided an increased factor of safety against an underestimation of the live load A similar

reduction in the dead load partial factor also occurred in South Africa

Using the original vehicle combinations the loading curves were replicated using a VB computer

program (Appendix F) The load effects from the Liebenbergs vehicle combinations and a lane

loading were calculated for static and dynamic conditions for spans ranging from 10m to 900m From

the calculated force effects an equivalent UDL was calculated using both the calculated bending

moment and shear load effects In the case of the long spans a lane load was assumed to precede and to

follow the vehicle combination The sensitivity of varying the assumed lane load was also reviewed

The results of this study are shown in Figures 41 and 42

40

-

sect ~ - C ~ 0

l C ~ I

Q

C 0is

5

0

10 100 1000

Loaded length (m)

~------------------------~~------------------------~

1-30

25

20 1-15

-- ------

TMH7 -ir-Trucks + 9kNm -+- Trucks + IOkNm

Figure 41 - Unifonnly Distributed Lane Loads Derived From Bending Moments

(4-4)

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---

___bull___ __ _- --- ---___bull _bull40

35

---E 30 -+ --+-shy

Z ~ - 25 ~ CI 0

l 20 ~ ltII c = 15 i 10Q

+5

0

10 100 1000

Loaded length (m)

TMH7 --r Trucks + 9kNm -+-Trucks +IOkNm

Figure 42 - Uniformly Distributed Lane Loads Derived From Shear Forces

The figures confirm Liebenbergs (1978) statement that the shear forces dictate the form of the loading

curve In order to simulate both bending moments and shears accurately at least two different knife

edge loads would be required Liebenberg therefore took the approach of fitting the loading curve to

the shear forces while overestimating the bending moments This approach greatly simplifies the

loading model The figures also confirm that the increase of the unifonnly distributed load in 1988 by

6kNm effectively provided for an increased lane loading of 10kNm This value is comparable to the

lane loads introduced into BS 5400 (1978) and the findings of Buckland (1978)

413 Review of Truck Combinations

Liebenbergs (1974) combination of vehicles was selected to represent an extreme event The

possibility of human manipulation in creating convoys of heavily loaded vehicles was taken into

account in selecting these combinations In review the static truck combinations JI and 12 are found

to be the most onerous events other than for very short spans These combinations contained five

heavily loaded short axle vehicles Liebenberg (1978) stated that one of the most important

requirements of a live load specification was that it should be a reasonable simulation of characteristic

traffic loading based on a non-zero but sufficiently low probability of occurrence during the useful

lifetime of the bridge The question arises how the probability of occurrence may be calculated when

the occurrence and sequence of the vehicles is selected using engineering judgement

Current design codes are based on a limit state approach In the case of the LRFD and CSA-S06-00

the live loads are factored with a partial factor based on a reliability index This index is derived from

the statistical evaluation of the probability of an event being exceeded within a given time frame The

approach uses of the statistical characteristics of an event to quantify a rational partial factor that

(4-5)

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provides the required level of serviceability It is considered that the use of the credibility approach

does not support the rationally based calculation ofpartial factors

In developing a consistent approach to limit state design of bridge structures it is proposed that the

statistical characteristics of traffic loading in South Africa require investigation Through this

investigation the development of a live load model that is calibrated to the required serviceability and

ultimate limits of a bridge structure can be derived

The collected WIM data provides the opportunity to assess the probability of occurrence of the truck

combinations selected by Liebenberg (1974) To calculate the probability of a specific convoy of

vehicles occurring the probability of one type of vehicle being followed by another was calculated

The results of this calculation are shown in Table 4 1 For example there is a 216 probability of a 2

axle vehicle being followed by another 2 axle vehicle The probability of a 3 axle vehicle being

followed by another 3 axle vehicle is 106

Following Probabili~ Vehicle

Type 2-Axle 3-Axle 4-Axle 5-Axle 6-Axle 7-Axle 8-Axle 9-Axle

2-Axle 216 204 195 190 183 186 184 196

3-Axle 97 106 94 86 82 82 82 165

4-Axle 48 43 51 43 43 42 45 82 5-Axle 86 86 85 101 91 90 87 103 6-Axle 223 220 221 233 251 231 22 8 124 7-Axle 307 314 328 321 326 343 328 258

8-Axle 23 25 25 24 23 25 45 41 9-Axle 01 01 00 01 01 01 02 31

Total 100 100 100 100 100 100 100 100

Table 41 - Following Probability

The following vehicle combinations assumed by Liebenberg were reviewed

bull Combination Jl - 2 axle vehicles Liebenberg assumed a GYM of five co-existent adjacent

vehicles of 197kN with axle spacing of 24m From the survey of 20086 2 axle vehicles it

was found that 00023 of vehicles have a GVM of 197kN or greater It was also observed

that only 002 of vehicles have an axle spacing of24m or less From the sequence analysis

on the WIM data it was calculated that there is a 005 chance of five 2 axle vehicle

occurring in sequence The probability that each of these vehicles would have the GVM and

1039axle spacing assumed by Liebenberg represents a 1 in 38 x year event Detailed

workings of this calculation are provided in Appendix C

bull Combination J2 - 3 axle vehicles From the survey of9000 3 axle vehicles it was found that

254 of vehicles have a GYM of 228kN and more It was also observed that only 49 of

vehicles have internal axle spacing between axle sets of28m or less The probability of five 3

axle vehicles occurring in sequence was calculated as 00016 in a given month

Liebenbergs assumption of five co-existent adjacent vehicles each with a GVM of 228kN and

an internal axle spacing between axle sets of 28m was calculated as a 19 x 1014 year event

Detailed workings of this calculation are provided in Appendix C

(4-6)

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The statistical analysis of the WIM data highlights the conservative assumptions made by Liebenberg in

formulating the truck combinations used to derive the design loading in TMH7 Part 2 The load effects

calculated by these combinations are further factored to give ultimate limit state effects In order to

prevent engineers designing for serviceability limits that will not occur within the design life of a

structure there is the need for a rational assessment of South African heavy vehicles

414 Comparison of Dynamic to Static Loads

Dynamic load effects result from the heavy vehicle travelling over irregularities on the surface of the

bridge deck The magnitude of the effect is dependent of the magnitude of the irregularities the natural

frequency of the bridge as well as the suspension of the heavy vehicle

TMH7 Part 2 uses the Swiss Impact formula specified in the SIA Specification 160 (1970) For

Liebenbergs combinations the dynamic load effects exceed those of stationary bumper-to-bumper

traffic for spans below 1 IOm (Ullman 1988) As shown in Figure 43 this fact was verified by

calculating the load effects of Liebenbergs vehicle combinations for both static and dynamic states A

Visual Basic program was written for this purpose The magnitude of the impact factor for various

spans is shown in Table 42

1600

1400

1200 middot 8 ~

1000 agt-= 8 0 800

~ = 600a =agt

co 400

200

0 4 6 8 10 12 14 16 18

Span m

~ Travelling Traffic Stationary Traffic

Figure 43 - Plot of Bending Moments Due to Travelling and Stationary Traffic

Impact Span (m) Allowance

5 35 10 28 15 23 20 20 30 16

Table 42 - Impact Allowance in TMH7

(4-7)

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The advent of 7 and 8 axle vehicles with a GYM of up to 560kN has led to a vehicle

Ul1lt the most onerous load effects in spans below 40m (Nowak 1991 Given

this dynamic loading becomes the dominant load case Considering the of TMH7 Part

2 the study of the dynamic effects of single heavy vehicles moving across spans up to 40m is

relevant

The impact allowance made within TMH7 was based on the Swiss formula from SIA 160

(1970) This impact formula has since been superseded in the SIA 160 (1989) and research

work has been carried out in the field of dynamic loading on structures and Nowak

1989) These developments were incorporated into the review camed out in RR 91100401 amp 02

415 Lateral Bunching

The of lateral bunching accounts for the event where Ivwu lanes of traffic are S4llCC~cu

together laterally For example three lanes of traffic may be into two lanes to pass a broken

down vehicle In the United the ofHA included with BD 3701 (2001)

was increased to take into account the effects of lateral A lateral bunching factor of 14 was

applied to spans up to 20m and then reduced linearly to at40m

TMH7 Part 2 makes no allowance for lateral This is also true for the LRFD and CSA-S06shy

00 Further consideration of this effect is tnritrl for the 120 year life of a bridge in the

South African metropolitan centres there is a reasonable prclbalolhty of lateral bunching occurring The

issue requiring further research is whether this event is concurrent with the maximum load effects

416 NB Loading

The impact on short spans of individual which is caused by rogue overloading was

recognised by Liebenberg (1978) in TMH7 Part 2 It was therefore specified that 24 units of NB

loading be applied to all highway This is not consistent with the latest codes of

practice In the case of the BD 3788 the HA curve was revised for the purpose ofcatering for

heavy point loads on short span structures In the case of the CSA-S06 and ENV 1991-3 the

live load model contains a axle group that simulates the load effects that develop on

the shorter spans It is proposed that any revision ofTMH7 Part 2 includes a single live load model that

adequately simulates normal traffic

(4-8)

The advent of 7 and 8 axle vehicles with a GVM of up to 560kN has led to a vehicle

Given

Ipvntv of TMH7 Part

aL bull ult the most onerous load effects in spans below 40m 1991

this

2 the

The

(1

of the

relevant

becomes the dominant load case

effects of vehicles

allowance made within TMH7 was based on the Swiss

This formula has since been in the SIA 160

the

across spans up to 40m is

formula from SIA 160

and research

work has been carried out in the field of on strucnITes and

were nCrtfrl into the review earned out in RR 9100401 amp 02

415 Lateral

The accounts for the event where U1Vw lanes of traffic are gt4lltt~tU

For ftIJ three lanes of traffic may be into two lanes to pass a broken


was increased to take into account the effects of lateral

to spans up to 20m and then reduced

A lateral

at40m

factor of 14 was

TMH7 Part 2 makes no allowance for lateral This is also true for the LRFD and CSA-S06-

00 Further consideration of this effect is pritrl the 120 year life of a

South African centres there is a reasonable prclbalolhty oflateral

issue further research is whether this event concurrent with the maximum load effects

416 NB

in the

The

The on short spans of individual which is caused rogue was

in TMH7 Part 2 It was therefore that 24 units of NB

to all This is not consistent with the latest codes of

practice In the case of the BD the HA curve was revised for the purpose for

heavy loads on short span structures In the case of the CSA-S06 and ENV the

live load model contains a axle group that simulates the load effects that on

the shorter spans It is that any revision ofTMH7 Part 2 includes a live load model that

simulates normal traffic

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42 RR 9100401 - PEI~MIISSIIB HEAVY VEHICLE LOAD RESEARCH

In the various bodies approached the Department of Transport with to increase the

load limits for vehicles contained within the then Road Traffic Act

As a result of those the Report RR 9100410 I The Effect of an Increase in the Permissible

Heavy Vehicle Loads on Road June 1994 was commissioned by the of

The aims of the were stated as

(i) To evaluate the limit in relation to past and present bridge codes and

international and

(ii) To quantify the effect of increased permissible loads on road bridges

The report is the most research on the effect of heavy vehicles on South African

bridge structures and represents an important body of The methodology adopted in

considering the load effects of structures draws on a wide body of current

international research Also bull rMrl was research work carried out into TMHTs shortcomings by

Ullman (1988) and Oosthezien et al

The report nrrp a valuable reference for further research into bridge live loads in South Africa

Cognisance was therefore taken of the UFYUE~H in the report as requiring further research

421 Problem Statement

The report begins with a problem statement that sets the optimum use of South Africas transport

infrastructure against the safety of its roads and It describes the current situation in the country

where overloading is commonplace and law enforcement is The report tasks itself

with developing a new set of truck mass restrictions that meet the

(i) Fair balance between increased massloads HU in increased revenue for the operator) and

additional costs associated with the ctrgtnothpnl or ret)la(~eni1erlt

Oi) Ease of understanding for the truck owner and and

(iii) Ease ofenforcement

In developing the mass restrictions RR91100401 considered 17 different variations to the

axle mass limitations These variations included increases to the axle amendments to the

v and the impact of disregarding the formula all together

422 Development of live Load Model

J n the live load 10 vehicles were chosen to represent the most common classes of

vehicle found on South African roads The likelihood of occurrence of each of these classes was

taken from surveys carried out by Van Wyk amp LDUW (1991)

(4-9)

42 RR 9100401 HEAVY VEHICLE RESEARCH

In the various bodies the of with to increase the


As a result of those the RR 9100401 The Effect of an Increase in the Permissible

Vehicle Loads on Road June 1994 was commissioned the of


To evaluate the limit in relation to and present codes and

international and

(ii) To the effect of increased pelmissilble loads on road

The report is the most research on the effect of vehicles on South African

structures and represents an nrt

the load effects of

international research Also

Ullman and Oosthezien aL

of trnrP The in

structures draws on a wide body of current

research work carried out into TMHTs by

The a valuable reference for further research into live loads in South Africa

VVEAUVv was therefore taken of the in the report as further research


422

The report

infrastructure

with a

the

statement that sets the use of South Africas trrl~rrt

of its roads and It describes the current situation in the country

where rIInr is and law enforcement is The report tasks itself

with

(i)

a new set of truck mass restrictions that meet the

laquoLa in increased revenue for the Fair balance between increased massloads

additional costs associated with the ctrnothpm or ret)la(~enr1erlt

Ease for the truck owner and and

Ease of enforcement

In the mass RR91100401 considered 1 different variations to the

and


V and the the formula all together

]orgtrorgtIClnl1l1orgtrllt of Live Load Model

J n the live load 10 vehicles were chosen to the most common classes of


taken from surveys carried out Van Wyk amp Louw (1991)

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The following variables were considered

(i) Overloading In the vehicle mass to each of the overloading ratios were

applied as derived from studies in Switzerland and 1989) The statistical

information associated with South African Vehicles was insufficient to derive a locally

applicable factor

Oi) Vehicle Spacing Vehicle for stationary and conditions were derived from

various sources from Switzerland 1989) and survey data collected in South Africa

Impact The dynamic interaction of a vehicle moving at and a deck of a given

surface profile and natural is known to create more onerous effects than those of a

stationary vehicle An of the report is the calculation of the impact factor as

shown below the recommendations of research work carried out in Switzerland (SIA

1989) This research work the Swiss Impact formula 160 1970) used in

TMH7 Part 2 A detailed review of the Swiss Impact formula (1989) is provided in

Appendix D

Swiss Impact Formula (1 (42)

Where

the final factor

the impact factor for the

the reduction factor for the vehicles mass

the speed reduction factor

pound the coefficient of variation

The report a approach by the Monte Carlo simulation technique to

generate different traffic streams A garage of 10 vehicles was used to generate random

stationary and traffic conditions All vehicles were assumed to be loaded to the p uUCv

limits with an ratio applied in line with the measured field distributions The load effects of

these 5000 vehicle combinations were then calculated for various spans of simply TI(middotrI one two

and three span continuous structures

To simulate the load effects on the bridge structure over its the results from the

vehicle streams were to a total of 18 million traffic streams In this regard research work

carried out by Grouni and Nowak (1984) and Moses and Verma (1987) was which

postulated the use of a return period for loads The number of critical static

occurrences was taken at 10 of the total vehicle streams within the 50-year period The extreme

events were assumed to follow a Gumbel distribution

(4-10)

The variables were considered

In the vehicle mass to each of the

as derived from studies in Switzerland and

information associated with South African Vehicles was

factor

ratios were

The statistical

insufficient to derive a

Vehicle Vehicle for and conditions were derived from

various sources from Switzerland and survey data collected in South Africa

interaction of a vehicle at and a deck of a

surface is known to create more onerous effects than those of a

thrnmiddotu vehicle An of the is the calculation of the factor as

shown the recommendations of research work carried out in Switzerland (SIA

This research work the Swiss formula used in

TMH7 Part 2 A detailed review of the Swiss formula (I in

D

Ismiddot +poundj Swiss Formula (1

Where

the final factor

the factor for the


the reduction factor


The report a the Monte Carlo simulation to


traffic conditions All vehicles were assumed to be loaded to the P UUH

limits with an ratio in line with the measured field distributions The load effects of

these vehicle combinations were then calculated for various spans of simply one two


To simulate the load effects on the structure over its the results from the

vehicle streams were to a total of 18 million traffic streams In this research work

carried out Grouni and Nowak and Moses and Verma which

the use a return for loads The number of critical static

occurrences was taken at 10 of the total vehicle streams within the The extreme


0)

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The above process was -L-Y the 17 alternative truck mass limitation criteria for a single span

The load effects were then to those ofTMH7 Part 2

423 Review

The following comments are made following the review of Report RR 91100401

Axle Loads The full permissible load was to each of the 10 vehicles in the simulation

As stated this load was then multiplied by an overloading ratio derived from the distribution of

observed axle loads The comment is made that the of individual axles is more

prevalent than the overloading of vVHtJ bull vehicles (Section The use of a convoy of

vehicles loaded to the legal limit and is considered conservative It is proposed that

an overloading factor that decreases as the span increases is more appropriate (Section 36

Dawe As stated in the RR 91100401 additional research is in quantifying the

extent ovcerI()aorng and its

(ii) Monte Carlo Simulation The scope of RR 91100401 was set to consider spans of up to

30m It is accepted that for spans of up to 30m a vehicle causes the

most onerous load effects (Nowak 1991 OConnor A 2005) The Monte Carlo simulation

assumed that the maximum effects were caused by a convoy of fully laden overloaded trucks

This event does not happen in of this fact was taken in the Monte Carlo

simulation used in the calibration of ENV 1991-3 where the simulation vehicles were

representative of recorded vehicle and weights et 200 I)

Extrapolation of Load effects The statistical approach used in extrapolating the load effects

is similar to that used in the calibration of the CSA-S06-00 (2000) However the vtrlotrI

load effects ultimate limit state events in CSA-S06-00 (2000) as opposed to

nominal load effects in the RR 91100401 The of the load effects the

Gumbel distribution is considered valid (Section the definition of extreme

events as the upper 15 of the set is not always valid It is considered that the

distribution of the extreme load effects is sensitive to span and class of vehicle 342)

(iv) Rational The live load model derived in SD 3788 followed a similar methodology

carried out on RR 9110040 l In the case of BD the results of the simulation of fully

loaded vehicles were judged to represent ultimate limit state events The nominal loads were

then calculated by dividing the extreme load events by 15 In RR 91100401 the

results of the Monte Carlo simulation are taken as nominal results and by a partial

factor of 15 to derive ultimate limit state load effects This approach is considered overly

conservative and not based on rational limit state principles

(4-11 )

The above process was LU

The load effects were

the 17 alternative truck mass limitation criteria for a

to those ofTMH7 Part 2

span

The

Review

comments are made the review RR 91100401

Axle Loads The full

As stated this load was then

to each of the 10 vehicles in the simulation

ratio derived from the distribution of


an

extent

than the of vVHIJ use of a convoy of

loaded to the limit and is considered conservative It is that

factor that decreases as the span increases is more

As stated in the RR 91100401 additional research is

OVC~rI()aatng and its

In f1nntltvmo the

Monte Carlo Simulation The scope of RR 91100401 was set to consider spans of up to

30m It is that for spans of up to a causes the

most onerous load effects 1991 The Monte Carlo simulation

assumed that the maximum effects were caused by a convoy of overloaded trucks

This event does not in of this fact was taken in the Monte Carlo

simulation used in the calibration of ENV 1991 where the simulation vehicles were

of recorded vehicle vVtlUF and et 200

of Load effects The statistical approach used in extrarlolitIrU the load effects

is similar to that used in the calibration of the CSA-S06-00 the vtrlotrI

load effects ultimate limit state events in CSA-S06-00 (2000) as to


Gumbel distribution is considered valid the definition of extreme

events as the upper 15 of the set is not valid It is considered that the

distribution of the extreme load effects is sensitive to span and class of vehicle

Rational The live load model derived in BD 3788 followed a similar HIltOUlUUUIIU

carried out on RR 9110040 I In the case of BD the results of the simulation of

loaded vehicles were

then calculated by

to ultimate limit state events The nominal loads were

the extreme load events 15 In RR 91100401 the

results of the Monte Carlo simulation are taken as nominal results and a

factor to derive ultimate limit state load effects This is considered

conservative and not based on rational limit state

1)

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In v the a probabilistic approach in the derivation of load effects a Monte

Carlo simulation to random traffic streams and a statistical distribution to predict extreme

events This differs from the detenninistic adopted in the derivation of

the live load model within TMH7 Part 2 a further is the use of truck survey data to

assign the simulation vehicles with a distribution of truck axle weights and GVMs This will

supersede the assumption used in the RR 9100401 that all vehicles are fully laden and overloaded It

will also allow the derivation of partial limit state factors based on the probabilistic of the truck

survey as in the case 0 f ENV ]99] -3 (Connor et aI 200 I )

(4-12)

In v the a in the derivation of load a Monte

Carlo simulation to random traffic streams and a statistical distribution to extreme

events This differs from the detenninistic in the derivation of


the simulation vehicles with a distribution of truck axle and GVMs will

~l1npr~rlp the used in the RR 9100401 that all vehicles are laden and overloaded It

will also allow the derivation of partial limit state factors based on the pn)babillstllc of the truck

survey as in the case of EN V 1991-3 et 2001)

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43 RR 9100402 bull DEVELOPMENT OF ALTERNATIVE DESIGN LOAD TO TMH7

As a result of the work carried out in Report RR 9100401 the Department ofTransport recommended

an increase in the allowable axle masses and the amendment of the formula Given the

shortcoming in TMH7 Part 2 (RR 91100401 1994) there was a requirement to derive assessment loads

that would model the load effects associated with the new traffic loads RR

9100402 The Effect of an Increase in the Permissible Heavy Vehicle loads on Road

Assessment Code was therefore commissioned and published in December 1995 The primary

stated within the executive summary of the were

(i) the recommendations of the task group concerning the increases in axle

masses to develop an assessment load that is simple in format and is easy to This load

should accurately predict the increased load effect produced

(ii) To substantiate theoretical work with full-scale load tests and

(iii) To develop a code procedure for the evaluation process

The of traffic streams of vehicles complying with the proposed new regulations

was undertaken using the same as in RR 91004101 In this case a set of 55 different

vehicles within 24 vehicle classifications were selected The extent of overloading was again

Bez (1989) The need to confirm the extent of on South African roads was

An component of the research was the attempt to correlate the measurement of deflections

and stress in three bridges in the field with those predicted by the theoretical live load model

The results of this research are in summarised in Section 433

431 Traffic loading

RR 9100402 comments that the formula complicates law enforcement The case of the

technical overloading of common classes of vehicles is highlighted The following example is in

the

In the case of a typical class 14 with an inter axle distance between the second and last axle of

the total load of 494 tonnes is 45 tonnes more than the 4895 tonnes allowed by the

formula

( 4-13)

43 bull DEVELOPMENT OF DESIGN LOAD TMH7

As a result of the work carried out in RR 9100401 the recommended

formula Given the an increase in the allowable axle masses and the amendment of the

in TMH7 Part 2 9100401 there was a to loads


9100402 The Effect of an Increase in the Permissible Vehicle loads on Road

Assessment Code was therefore commissioned and in December 1995 The nnlml

within the executive summary of the were

the recommendations of the task group the increases in

masses to an assessment load that is in format and is easy to

should the pVlhri increased load effect

To substantiate theoretical work with full-scale load tests and

To a code for the evaluation process

axle

This load

The of traffic streams of vehicles with the new

was undertaken the same as in RR 9100401 In this case a set of 55 different

vehicles within 24 vehicle classifications were selected The extent of was

An

and

The need to confirm the extent of frl on South African roads was

component of the research was the am~ml)[ to correlate the measurement of deflections

in the field with those the theoretical live load model

results of this research are in summarised in Section 433

431 Traffic

RR 9100402 comments that the formula tJVIIJIIL law enforcement The case of the

technical rl(lgt(1

the

of common classes of vehicles is IIampW The in

In the case of a class 14 with an inter axle distance between the second and last axle of


formula

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Figure 44 - Configuration of Class 14 Vehicle (Source RR 91 00402 1995)

A revision of the bridge formula that allows the most common classes of vehicles to be loaded to the

sum of the pennissible axle loads was therefore proposed It was postulated that the bridge formula be

changed to 16+30L for L lt 13 3 and 56 ton for 134 gt L lt 222m This change would eliminate the

technical overloading of the most popular classes of vehicles this proposal was then used in assigning

the axle masses to the vehicles used in generating the vehicle streams The revision of the bridge

formula is merited as it simplifies law enforcement that may effectively combat overloading

432 Impact Factor

The impact factor was calculated in accordance with the method set out in Appendix D However in

calculating the impact factor a reduced vehicle mass reduction factor fn is used in RR 9100402 For

a vehicle of mass T tons the following reduction factors for the vehicles mass fn were used

ForT lt 16t

For T gt SOt

This amendment significantly reduces the impact factor applied to the load effects on spans greater than

5m as shown in Table 43

ImEact Allowance

RR91 0041 RR910041 SEan (m) TMH7 01 02

5 35 37 36 10 28 26 18 15 23 17 12 20 20 13 9 30 16 9 6

Table 43 - Impacts Allowances

(4-14)

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433 Test loading

The methodology adopted in the of the three is not included within this document The

of the testing are however summarised below

(i) The correlation between measured and calculated strain was considered

(ii) The results confirmed that the present design practice is realistic with respect to load effects

under PTVi conditions

(iii) The correlation between the calculated crack widths and the spacing measured is poor Fewer

but cracks occur which exceed the code limits and

(iv) Some reserve strengths and stiffuesses are present in each bridge The amount of reserves was

considered on the restraint at the supports the actual constitutive behaviour of the

material and the global response of the bridge

434 Assessment amp loads

An important differentiation in the report is in the defmition of an assessment load and a design load

The assessment load is defined as the load that results in load effects equivalent to those produced by

the full range of vehicles under the present The load is then considered equal

to the assessment plus a contingency of 10

From the studies undertaken the proposes that neither TMH7 Part 2 nor BD 3788

provides suitable design loads for South African conditions in relation to their value and format An

assessment load was therefore derived from the maximum load effects produced by the

vehicle streams the adopted in the RR 91100401 the load effects were

extrapolated to a characteristic value with a 5 chance of being exceeded in 120 years

The assessment load derived by the report is shown in Figure 45 and was formulated to match the

VvY1gt moments and shears The use of a double axle concentrated load model in

vith a unifonnly distributed load (UDL) bears close resemblance to the live load model of

ENV 1991-3

(4-15)

433 Test

The melthoclolo in the of the three

are mpJPr summarised below

is not included within this document The

of the


The results confirmed that the nrlT1l-p is realistic with to load effects

under PTVi

The correlation between the calculated crack widths and the measured is poor Fewer

but cracks occur which exceed the code and

Some reserve and stiffuesses are present in each The amount of reserves was

considered vJv on the restraint at the the actual constitutive behaviour of the

material and the response of the

Assessment amp

An differentiation in the report is in the definition of an assessment load and a load

The assessment load is defined as the load that results in load effects to those

the full range of vehicles under the The load is then considered

to the assessment a cOlltmlgeJrlcy of 10

From the the proposes that neither TMH7 Part 2 nor BD 3788

nnHf1 suitable loads for South African conditions in relation to their value and format An

assessment load was therefore derived from the maximum load effects the

vehicle streams the in the RR 91100401 the load effects were

to a characteristic value with a chance exceeded in 120 years

The assessment load derived the report is shown in 45 and was formulated to match the

5 moments and The use of a double axle concentrated load model in

lith a distributed load bears close resemblance to the live load model of

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I

1J- 8

_______- - 1 ~ ~-- ~

--tf-fBT-1--+Or

I

I IPi t I

Figure 45 - Live Load Model Proposed in RR 91100402 (Source RR91100402)

In considering load models for multi-lane conditions the guidelines set out in the ENV 1991-3 were

adopted The design loads (11 x assessment loads) were applied to the notional lanes named Lanel

Lane2 and so on Lane I was classified as the lane in which the applied loads will produce the most

unfavourable effects and Lane 2 the second most unfavourable effects The magnitude of the applied

loads was reduced from Lane I to Lane 2 as shown in Table 44

Location Tandem Load UDL

Lane number I Lane number 2 Other lanes Remaining area

240 140 0

NA

6 4 3 3

Table 44 - Design Load Values

The load effects generated in RR 91100402 are compared to those from TMH7 Part 2 in Tables 45 and

46 The deficiency in NA loading to cover short spans is highlighted in the bending moment and shear

force results For spans of 15m to 30m the bending moments show reasonable correlation Because

the simulation vehicles used in the Monte Carlo simulation are assumed to be fully loaded a convoy of

vehicles is the critical load case for these span lengths Liebenberg (1974) made the same assumption

in formulating the NA loading curves in TMH7 Part 2 Although Liebenbergs (1974) convoy is

derived from engineering judgement the magnitude of load effects is similar to RR 91 00402

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RR 911 TMH71 Difference 00402 NA RRTMH7

5 415 293 42

10 949 810 17

15 1510 1553 -3

20 2442 2520 -3

30 5

Table 45 Moments RR 91100402 versus TMH7

The shear forces calculated from the reports load are consistently than TMH7 This

difference is in part due to the increase in axle masses and GVM since the 1978 As

expected the increase in axle masses on the short spans

RR 9J1 TMH71 Difference NA RRTMH7

most

5 378 10 413 15 506

20 576 30 739

234 324 414

504 684

62 27

22 14 8

Table 46 - Comparison of Shear RR 9100402 versus TMH7

435 Report Conclusions

In conclusion RR 9100402 states that short span bridges need to be assessed individually to ensure

their continued and under the increased permissible axle loads It was

recommended that the assessment and design load derived within the In addition it

was concluded that the design load provisions in TMH7 Part 2 require adjustment to eliminate

substantial deficiencies in the short span range With to overloading it was again concluded that

the assumptions made within the need to be verified traffic surveys

436 Critical Review

The comments are made following the review of Report RR 91100402

i) As in the case ofRR 9100401 the use ofa Monte Carlo simulation convoys laden

vehicles to simulate nominal load effects for spans up to 30m is considered conservative

ii) The form of the assessment and load is valid as is the process involved in quantifying the

ugtuvuuy distributed load and point loads to replicate the maximum actual load effects

As stated in the report a detailed review of the impact of ~~~ is required from traffic

surveys

The impact factor applied is less onerous than the factor used in theNA curves

in TMH7 Part 2

(4-1

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v) The design approach uses a characteristic load with a 5 probability of exceeded in 120

years This a return period of 1 in 2976 years This return is somewhat than

the I in 1000 years assumed in ENV 1991-3 and the 1 in 120 years used in BD 3788 (2000)

The key observation is that RR 91100402 extrapolates events that are extreme in their own

Using the same method BD 3788 considered the extrapolated events to an ultimate

limit state In RR 91100402 a factor was further applied to the extrapolated characteristic

values to an ultimate limit state event This factor was 15 as in the case of TMH7 Part 2

The factor is based on rather than a rational It is therefore

proposed that the logic used in RR 91100402 is extremely conservative In the case of ENV

1991-3 the Monte Carlo simulation used simulation vehicles with a range of GVMs The

events were therefore of normal traffic conditions rather than extreme

conditions This approach is recommended in future simulations

In the following the extreme load effects predicted in RR 91100402 are compared with those

from the WIM data

(4-18)

In the

The uses a characteristic load with a 5 of exceeded in 120

years This a return of 1 in 2976 years This return is somewhat than

the I in 1000 years assumed in ENV 1991-3 and the I in 120 years used in BD 3788

The observation is that RR 91100402 that are extreme in their own

the same BD 3788 considered the events to an ultimate

limit state In RR 9100402 a factor was further to the characteristic



trr r~11 that the used in RR 91100402 is conservative In the case ENV

199 the Monte Carlo simulation used simulation vehicles with a range of GVMs The


conditions This is recommended in future simulations

the extreme load effects nrp(htpj in RR 91100402 are 1r rI with those

from the WIM data

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44 COMPARISON OF DESIGN LOADS VERSUS ACTUAL LOADS

The main objective of the study was to compare the load effects generated by the WIM data with those

calculated using the live load models contained within TMH7 Part 2 and RR 9100401 amp 02 This

approach allows the assessment of theoretically derived live load models with the load effects of actual

trucks For the purpose of the comparison the static load effects extrapolated from the WIM data using

the Gumbel distribution were factored by the impact factors used in RR 911004102 The magnitude of

the load effects calculated from each source are shown in Table 47 and 48 A graphical comparison is

also given in Figures 46 and 47


WIM RR 911 TMH7 S2an m) data 00402 Part 2

5 409 415 293 10 957 949 810 15 1527 1510 1553 20 2284 2442 2520 30 3847 5397 5130

Table 47 - Bending Moments Results

6000 - shy

5000 - E

~ 4000-III= ~ 3000 ~ OJ)

= 2000a III= ~

1000

0

0

middotmiddotmiddot-_middotmiddotmiddotmiddotmiddotmiddot

5 10 15 20 25 30 35 Span (m)

--- Study -0- RR91100402 ~ TMH7 I

Figure 46 - Comparison of Bending Moments

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Shear Forces (kN)

WIM RR 911 TMH7 SEan (m) data 00402 Part 2

5 297 378 234 10 320 413 324 15 369 506 414 20 433 576 504 30 542 739 684

Table 48 - Shear Force Results

800

700

600 -

~ 500 QJ ~ 0 400 ~ ~ QJ 300

c C-J

200

100

0

0 5 10 15 20 25 30 35

Span (m)

__- -- - middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot 1 middotmiddot middotmiddotmiddot

Study -ltr RR91 100402 -fr- TMH7

Figure 47 - Comparison of Shear Forces

441 TMH7 versus Actual Traffic Measurements

It was observed that TMH7s bending moment effects are less than the studys effects for 5m and 10m

spans TMH7s NA loading is known to be deficient in catering for normal traffic conditions over short

spans (Ullman 1988) This is confirmed by the results of the study shown in Table 49 In drafting the

code it was intended that 24 units of NB loading be applied to all structures to cover this shortcoming

A normal design loading that covers all spans is considered more logical

Bending Moment (kNm)

WIM TMH7 Difference Span (m) data Part 2 WIM TMH7

5 409 293 39 10 957 810 18 15 1527 1553 -2 20 2284 2520 -9 30 3847 5130 -25

Table 49 - Bending Moment Comparison WIM data v TMH7

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The bending moment effects calculated on a 15m span are similar for the WIM data and TMH7 Part 2

This similarity is because a combination of axle groups are the critical load event for 15m spans The

results indicated that Liebenbergs (1974) vehicle axle groupings replicate those in the longer single

heavy vehicle on South African roads today

For spans of 20m and 30m TMHTs loads increase significantly above those found by the WIM data

TMHTs loadings for the 20m and 30m spans are derived from the static combinations of bumper-to

bumper fully laden vehicles These vehicles are taken to be overloaded by 10 This approach differs

to that taken by Nowak (J 991) and OConnor (2005) who judge a single dynamic vehicle loading as

dominant for spans up to 30m Nowaks approach is based on the fact that in practice the return period

associated with a convoy of fully laden overloaded trucks is extremely high (Section 413) Although

BD 3788 is based on a similar approach to TMH7 the results are judged to represent the ultimate limit

state Serviceability limit state effects are then calculated by dividing the ultimate limit state results by

15 In TMH7 Part 2 the loads effects derived from the overloaded convoy are further factored by a

partial factor of 15 This fact explains the difference between the WIM datas results and TMHTs

Although there are factors such as lateral bunching and multi-lane loading that are not covered in this

study the results expose the extremely conservative logic used by TMH7 Part 2 in deriving the static

nominal load effects on bridge structures

The results of the comparison of the shear forces generated in the WIM data and those of TMH7 Part 2

are shown in Table 410 Only in the case of the 5m spans does the WIM datas predicted shear force

exceed that ofTMH7 Part 2 This factor is due to the action of overloaded tridem and tandem axles on

the shorter spans Liebenbergs (1974) vehicle combinations do not adequately cater for such an event

For spans of 10m and greater Liebenbergs (J 974) JI-combination causes shear forces in excess of

those predicted by the WIM data This combination includes bumper to bumper 2 axle vehicles with a

rear axle weight of I 15kN This assumption is extremely conservative especially for 30m spans

(Section 413)

Shear Force (kN)


5 297 234 27 10 320 324 -1 15 369 414 -11 20 433 504 -14 30 542 684 -21

Table 410 - Shear Force Comparison WIM data v TMH7

442 RR 9100402 versus Actual Traffic Measurements

The WIM data and RR 91 00402 show close correlation of the bending moments for 5m 10m and

15m spans These are the spans for which a single vehicle is dominant in both approaches The

comparison of the results is shown in Table 411 Since RR 91100402 used a garage of legal vehicles

with a overloading factor this correlation is expected The reports bending moments increase above

(4-21)

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those of the for the 20m and 30m spans This is because the report considers a convoy of fully

Moment (kNm)

WIM RR 911 Difference data 00402 WIM

5 409 415 -2 10 957 949 1 15 1527 1510 1 20 2284 2442 -6 30 3847

Table 411 - Moment

5397

laden vehicles the most critical case as per TMH7 Part 2

The WIM datas results for the shear load effects are consistently lower than those predicted by

RR 91100402 as shown in Table 412 This difference is because the report assumes all axles are

loaded with an applied additional rlr factor The results of the study indicate that the

of axles and axle sets is more prevalent than the blanket overloading of a complete vehicle

No reference was found for the overloading ratios applied in RR 9100402 and whether or not it

varied with the span From the findings in Section 36 it is proposed that a overloading ratio

applied to all vehicles is conservative in the case of spans

Shear Force (kN)

WIM RR 911 Difference

5 297 378 -21 10 320 413 -23 15 369 506 -27 20 433 576 -25 30 542 -27

Table 412 - Shear Force Comparison WIM data v RR 9100402

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45 CONCLUSIONS

The load effects generated from the probabilistic analysis of the WIM data provide important reference

for the critical review of the live load models in TMH7 Part 2 and RR 9100402 They provide a

benchmark for the detenninistic and probabilistic methods used to simulate actual traffic loadings

In review ofTMH7 Part 2 the statistical analysis of the WlM data showed the detenninistically derived

vehicle combinations to be conservative in comparison with the recorded traffic flows Load effects

calculated using the WIM data substantiated this finding For 30m spans TMH7 Part 2s load effects

were 25 higher than those calculated using the actual vehicle data TMH7 Part 2s deficiency in

catering for the load effects on short spans was also confinned It is proposed that the detenninistically

derived vehicle combinations do not adequately cater for overloaded tridem and tandem axle sets A

further point of concern is TMH7 Part 2 s use of the Swiss impact fonnula from SJA 160 (1970) when

SIA 160 (1989) has significantly changed the fonn of the impact fonnula In conclusion it is proposed

that the detenninistic methods do not adequately simulate the load effects caused by actual vehicles on

the roads

The load effects calculated from the WIM data allow the critical review of the probabilistic methods

used in RR 91 00402 The results demonstrate that the use of a Monte Carlo simulation using fully

laden overloaded vehicles is conservative for spans greater than 20m It is recommended that future

simulations be based on a garage of vehicles whose axle weights and GYMs are distributed as in the

case of nonnal traffic conditions The above method was used in the drafting of ENV 1991-3

(OConnor et aI 200 I) The availability of WIM data from South African Toll roads now provides

sufficient data on which to base such an approach

The analysis of the WIM data indicates that the overloading of axles and axle sets is more prevalent

than the overloading of a complete vehicle As in the case of BD 3701 the use of an overloading

factor that decreases as the span increases is proposed

The un-factored design loads in RR90100401 and TMH7 Part 2 are fonnulated from the extrapolation

of events that are extreme in themselves This methodology is excessively conservative in comparison

to modem codes of practice such as ENV 1991-3 and BD 3701 It is recommended that the

characteristic load events be derived from nonnal traffic conditions occurring over a rationally-based

return period

In conclusion the load effects calculated from the WIM data reveal the conservative assumptions

associated with the detenninistic methods used to derive the live load model in TMH7 Part 2 In the

case of the probabilistic methods used in RR 91 00401 amp 02 they highlight the need to base

simulations on data derived from actual traffic surveys

(4-23)

45 CONCLUSIONS







were 25 higher than those calculated using the actual vehicle data TMH7 Part 2 s deficiency in





that the deterministic methods do not adequately simulate the load effects caused by actual vehicles on

the roads











The un-factored design loads in RR9010040l and TMH7 Part 2 are fonnulated from the extrapolation


to modem codes of practice such as ENV [991-3 and BD 3701 It is recommended that the


return period



case of the probabilistic methods used in RR 91100401 amp 02 they highlight the need to base


(4-23)

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ALTERNATIVE LIVE LOAD MODEL TO TMH7 PART 2

51 CALCULATION OF LOAD FACTOR

The development of any traffic live load model its calibration values In TMH7

Part 2 the values were taken from the deterministic review of truck combinations In ENV 1991

3 the probabilistic of actual truck survey data was used to calculate the target values

The WIM results an opportunity to review the live load model in RR 91100402 to

the NA loading curves in TMH7 Part 2 In out this the live load models

shown in 51 were calibrated the I in 120 year load effects calculated from the WIM

data

The proposed live load models take the form of a uniformly distributed load in combinations with a

series of point loads (Buckland 1 For each of the 8 live load models lane loads of

9kNm 18kNm and 27kNm were applied Equivalent load models 1 and 2 represent the

characteristics of actual 6 and 7 axle vehicles respectively Using the equivalent base length method

developed by OConnor (1981) the Wlbm values of the 6 and 7 axle vehicles causing the most onerous

load effects were identified I-DIDenOlX E) The equivalent load models 1 and 2 were created to replicate

these -0

The remainder of live load models take the form of a series of two or three axle sets in combination

with a uniformly distributed lane load The points loads are not chosen to any specific

vehicle ENV 1991-3s live load model and the load from RR 91100402 were

considered Variations to these load models were also included for the purposes of comparison

A VB program was written to calculate the bending moments and shear associated with each of the

design models Spans of 5m to 30m were considered

The method by Nowak (1995) in calibrating the LRFD is used to calculate the

load factors A full calibration of the partial factors considering the datas reliability index was not

carried out as the thesis does not include a review of the ultimate limit state targets values

(5-1 )

51

2

OF LOAD

The cevelC)prneIlt of any traffic live load model its calibration values In TMH7

Part 2 the

3 the

values were taken from the deterministic review of truck combinations In ENV 1991

of actual truck survey data was used to calculate the values

The WIM results nrcvPCl an to review the live load model prcposeC in RR 91100402 to

shown in

data

curves in TMH7 Part 2

51 were calibrated the

In out this the live load models

in 120 year load effects calculated from the WIM

The orcooseC live load models take the form of a distributed load in combinations with a

series of loads For each of the 8 live load models lane loads of

18kNm and 27kNm were load models and 2 represent the

characteristics of actual 6 and 7 axle vehicles the method

OConnor (I the values of the 6 and 7 axle vehicles the most onerous

load effects were identified The load models 1 and 2 were created to

these prlmiddoto


with a distributed lane load The loads are not chosen to any

vehicle ENV 1991-3s live load model and the nrrm()op(j load from RR 91100402 were

considered Variations to these load models were also included for the purposes

A VB program was written to calculate the moments and shear associated with each the

models of 5m to 30m were considered

The method Nowak ( the LRFD is used to calculate the

load factors A full calibration of the the datas index was not

carried out as the thesis does not include a review of the ultimate limit state values

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40 80 ~~~--------~~4~~------------~~

240

I

180

80 180 180 120 2 Equivalent 7 axle vehicle

20 20 ~ II~ ~

180 180 180 3 Equivalent load 1

80 80 80 4 Equivalent load 2 (Models a single tridem)


13 ~ ~

240 240

6 Equivalent load 4 model)

12 ~ II

150 150

7 1991-3 design

12 ~

200 200

8 Ul Valj load 6 (Variation to RR 9100402 model)

51 - Load Models

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Nowak s (1995) method involves the use of a bias factor calculated as the ratio of the target values

against the load effects from the live load model The bias factors for the range of spans were found

By calculating the mean standard deviation and coefficient of variation of the bias factor for a

particular load effect the load factor was calculated using the fonnula below

y = -(1 + kV)

load factor r

bias factor

v bais factor coefficient of variation calculated by dividing the mean by the standard

deviation

k constant k =2 (Nowak 1995)

52 RESULTS

The equivalent vehicle models 1 and 2 applied in conjunction with various distributed lane loads did

not produce consistent load factors As shown in Figure 52 for a lane load of 27kNm load factors

ranged from 21 at 50m spans to 09 at 30m spans

2300

2100 0-v 1900~ 0 1700~ 0

l 1500-=QI

E 1300 0

~ 1)1) ll00 = a 0900 = QI

tl

- - ~~- -- shy - shy - shy

I

I I--- L~- shy ~~t--==- -

r-shy

----r-=9 I

~ 0700

0500

- T - - shy -

o 5 10 15 20 25 30 35

Span (m)

Figure 52 - Bending Moment Load Factors - Models 1 amp 2

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The results indicated that the simple model containing a set of two or three axle sets spaced at less than

20m produced more consistent load factors across the spans A comparison of the load factors

calculated for these models is shown in Figure 53 and 54 In the case of model 8 with a lane loading

of90kNm the bending moment load factor varied by 65 and the shear force load factor by 247

This model and lane load was found to replicate the WIM target values with the least variance The

adoption of a load factor of 11 accurately modelled the maximum shear forces whilst it overestimated

the maximum bending moments by 48

1800

0 1600 (I

laquoI

1l laquoI 1400 0

l ltII = 1200 8 0

~ ~ 1000 = 0 = ~ 0800

0600

o

~ ~--shy -

~~ n

5 10 15 20 25 30 35

Span (01)

-0-3 6 -4-7 8

Figure 53 - Bending Moment Load Factors using WIM data- Models 3 6 7 amp 8

1600

14000 (I laquoI

1l laquoI 1200 0

l

ltII (I

0 1000 laquoI ltII

-= ~ 0800

0600

0 5 10 15 20 25 30 35

Span (01)

6 -4-7

Figure 54 - Shear Force Load Factors using WIM data - Models 3 6 7 amp 8

(5-4)

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The calibration process carried out in RR 91 00402 was replicated using the VB programs written to

undertake the calibration of the WIM data The results shown in Figures 55 and 56 confirm the

findings of the report that load model 6 in conjunction with a 18kNm lane load gives a close calibration

to the target values

1800

0 1600 v CltI ~ ~

CltI 1AOO 0

e ~ = 1200

0

~ ~ 1000 = a = ~ 0800 I=Q

0600

0 5 10 15 20 25 30 35

Span (m)

6 ~7

Figure 55 - Bending Moment Load Factors using RR 91 00402 - Models 3 6 7 amp 8

1600

IAOO 0 v CltI ~ ~ 1200CltI 0

v ~ 0 1000 ~

CltI ~ c 00 0800

0600

- - - shy - shy

~

0 5 10 15 20 25 30 35

Span (m)

-ltgt-3 6 ~7 -8

Figure 56 - Shear Force Load Factors using RR 9100402 - Models 36 7 amp 8

(5-5)

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Using Nowaks (1995) method the bending moment load factor varies by 40 and the shear force load

factor by 29 The adoption of a load factor of 12 accurately models both the maximum shear forces

and the maximum bending moments A full set of the results of the calibration process is shown in

Table 51 to 54

In conclusion the results clearly indicate that a load model containing two closely spaced point loads in

combination with a uniformly distributed load accurately simulates the load effects of South African

heavy vehicles This research work therefore supports the use of the load model proposed in RR

91100402 it also shows that ENV 1991-3s load model may be used in South Africa The probabilistic

analysis of the WIM data demonstrates the means by which ENV 1991-3s load model may be

calibrated to South African conditions Rather than revising TMH7 Part 2 a viable alternative is the

adoption of ENV 1991-3 and the drafting of a National Application Document (NAD) The significant

research and development carried out in developing the limit state principles and live load model in

ENV 1991-3 may be utilised in South Africa with limited expenditure

(5-6)




Table 51 to 54





analysis of the WIM data demonstrates the means by which ENV 1991-3 s load model may be





(5-6)

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Bending Moments

Lane Load 9 kNm

Model Mean SD V Load Factor y

1 124 012 010 154 162 155 145 125 2 133 029 022 240 225 179 166 141 3 091 018 020 171 123 ll1 ll4 114 4 1 56 017 011 223 193 177 180 173 5 172 037 022 339 247 219 219 208 6 084 002 003 091 087 085 090 091 7 123 004 003 139 132 127 131 8 097 002 002 105 101 098 103

Lane Load 18 kNm


1 105 015 014 153 151 138 126 106 2 112 029 026 228 202 158 144 119 3 080 019 023 166 ll7 103 104 099 4 126 023 018 223 183 160 157 141 5 138 039 028 318 224 190 184 164 6 074 004 006 091 084 080 081 079 7 103 010 010 143 130 ll9 119 ll1 8 084 006 007 106 099 092 093 089

Lane Load 27 kNm


I 091 017 018 150 141 125 ll3 093 2 097 029 029 216 182 141 127 103 3 072 019 027 160 ll2 096 095 088 4 107 025 024 216 170 144 138 120 5 ll6 038 033 294 203 167 158 136 6 067 007 010 093 083 077 077 072 7 090 0 14 015 144 126 lll 109 097 8 075 009 012 108 097 088 087 080

Best Fit

Table 51 - Calibration of Model Bending Moments to WIM Data

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Shear Forces

Lane Load 9 kNm

C

Model

1 2 3 4 5 6 7 8

Mean 102 114 081 144 1 53 075 11 1 088

SD 008 023 013 014 024 010 010 010

V

008 020 016 010 016 013 009 012

135 221 142 200 280 073 116 087

Load Factor y 127 ll3 ll3 164 144 145 099 099 107 159 160 171 200 196 206 069 075 083 106 ll2 122 08 ] 087 096

ll8 145 120 183 219 095 136 109

Lane Load 18 kNm

Model Mean SD V Load Factor y 1 087 011 013 134 ll9 103 102 102 2 097 024 025 210 150 129 127 123 3 072 013 018 139 095 093 097 104 4 ll6 017 014 199 151 145 148 149 5 123 026 021 266 182 171 173 173 6 066 005 008 073 067 070 076 082 7 093 005 006 120 105 106 111 116 8 076 005 007 089 079 082 087 093

Lane Load 27 kNm

Model Mean SD V Load Factor y 1 077 013 017 132 112 096 093 091 2 085 024 028 199 138 ll7 113 107 3 064 013 021 135 091 087 089 092 4 098 019 019 194 141 131 131 127 5 104 027 026 249 165 150 149 143 6 059 003 006 075 067 068 071 075 7 080 007 009 122 102 099 102 102 8 067 004 006 091 078 078 082 084

Best Fit

Table 52 - Calibration of Model Shear Forces to WIM data

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Bending Moments

Lane Load 9 kNm

Model

I 2 3 4 5 6 7 8

Mean 134 1A2

099 169 186 092 135 107

SD 008 020 020 023 036 017 021 019

V

006 014 020 014 019 018 015 017

1A6

218 174 237 333 119 172 136

Load Factor y 150 1A4 1A4

200 159 159 122 110 123 200 183 201 237 209 227 112 109 124 161 153 172 129 125 lAI

164 177 161 254 282 165 223 187

Lane Load 18 kNm

Model 1 2 3 4 5 6 7 8

Mean 113 119 087 136 lA8

081 112 092

SD 007

022 018 020 034

011 013 012

V

006 018 021 014 023 014 011 013

135 209 163 213 302 105 lA8

118

Load Factor y 130 119 118 180 1Al 138 112 099 107 171 lA9 158 208 176 184 095 089 099 131 120 129 107 100 110

130 150 134 187 215 126 158 138

Lane Load 27 kNm

Model 1 2 3 4 5 6 7 8

Mean

098 103 078 115 124 072 097 081

SD

009 023 017 021 033 008 011 009

V

010 022 023 018 027 012 012 011

133 199 154 202 278 096 138 108

Load Factor y 122 108 105 164 127 123 105 090 096 156 132 136 187 154 157 085 077 084 117 104 109 095 086 092

114 131 117 155 177 103 128 111

Best Fit

Table 53 - Calibration of Model Bending Moments to RR 9100402

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Shear Forces

Lane Load 9 kNm

Model

I 2 3 4 5 6 7 8

Mean

135 151 108 190 203 099 147 116

SD

007 026 0 15 017 027 015 017 016

V

005 017 014 009 014 015 012 014

202 250 179 285 325 118 138 105

Load Factor y 193 181 177 188 175 171 127 136 143 231 246 256 235 245 252 114 130 142 129 144 153 100 113 122

189 175 163 280 272 165 173 141

Lane Load 18 kNm

Model

1 2 3 4 5 6 7 8

Mean

115 128 095 154 163 087 123 101

SD 011 027 015 018 030 009 007 008

V

010 021 016 012 018 010 006 008

188 227 175 236 265 104 127 099

Load Factor y 170 157 150 164 150 144 122 126 130 182 185 185 184 183 181 097 107 113 113 121 124 090 099 103

154 142 141 190 184 125 131 112

Lane Load 27 kNm

Model 1 2 3 4 5 6 7 8

Mean 101 112 085 130 137 078 107 089

SD 014 028 015 021 031 005 007 005

V

013 025 018 016 023 006 006 005

178 216 172 206 236 097 118 094

Load Factor y 154 140 132 152 137 129 117 119 120 152 150 146 159 154 148 087 094 096 100 104 104 082 087 089

131 125 126 144 146 103 106 093

Best Fit

Table 54 - Calibration of Model Shear Forces to RR 9100402

(5-10)

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6 FINAL CONCLUSIONS AND RECOMMENDATIONS

This thesis was concerned with the review of the live load models specified in TMH7 Part 2 (1988) and

the alternative live models proposed in the Department of Transport Reports RR 91 00401 amp 02 (1994

1995) The review was carried out using the load effects calculated from WIM data recorded on the

National Route 3 at Heidelberg in February 2005 This route was chosen because of the high volumes

of heavy vehicles it experiences In support of the review the methods of deriving bridge live load

models were researched The methods used are

(i) The deterministic approach that uses engineering judgement to deal with the unknowns

associated with the random nature of traffic loading This method was used by Liebenberg

(1974 1978) in the drafting ofTMH7 Part 2

(ii) The probabilistic approach that fits a mathematical distribution to recorded traffic events This

method was used in drafting Eurocode ENV 1991-3 2000 Basis of design and action on

structures - Part 3 Traffic loads on bridge

The basis of the live models in following bridge design codes was investigated


(ii) BS5400 1978 Steel Concrete and Composite Bridges Part 2 Specification of loads


(iii) Department Standard BD 3788 amp 01 Loads for Highway Bridges British Department of

Transport (1988 2001)

(iv) American Association of State Highway Transportation Officials (AASHTO) Load Resistance

Factor Design (LRFD) Bridge Design Specifications (1994)

(v) CANCSA-S6-00 Canadian Highway Bridge Design Code (2000) and

(vi) Eurocode ENV 1991-32000 Basis of design and action on structures - Part 3 Traffic loads

on bridges

In each case reviewed the deterministic methods of deriving live load models were replaced by

probabilistic methods Deterministic methods historically developed because of a lack of statistical data

and the complexity of the variables associated with traffic movements WIM sensors and traffic surveys

have now provided a wealth of traffic data and have effectively removed this constraint In review of

TMH7 Part 2 the statistical analysis of the WIM data showed the deterministically derived vehicle

combinations to be conservative in comparison with the recorded traffic flows Load effects calculated

using the WIM data substantiated this fUlding It was therefore concluded that the deterministic

methods do not adequately simulate the load effects caused by actual vehicles on the roads

(6-1 )



the alternative live models proposed in the Department of Transport Reports RR 9100401 amp 02 (1994
















Transport (1988 200 I)





on bridges









(6-1 )

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South Africa has yet to progress to a live load model llPpnpr methods

Although research work culminating in the RR 9100401 amp was carried out between 1994

and 1995 in South Africa TMH7 Parts I and 2 have remained unaltered since 1988 Its closest rpTIrp

BS5400 was by BD 3788 in 1988 The advent of the ENV 1991-3 in Europe further dates

the deterministic derivations ofTHM7 Part 2s live load model

The review of BD 370 I also a number of in the of deriving live load

models that are yet to be adopted in South Africa These include the derivation of

curves that do not the use of abnormal load models in short spans and the of


TMH7 Part 2

Of the codes reviewed ENV 1991-3 provides the most recent and extensive use of probabilistic

methods to derive a live load model For this reason its n provides an excellent reference for

the live load model contained within TMH7 Part 2 As in the case of the

member states a National Application Document (NAD) based on the

of local truck survey data may be developed in South Africa and other South African countries

The advantage of live load models and their calibration on the probabilistic analysis of

traffic survey data is that load models may be derived In addition as the properties

of traffic change for technical and economic reasons it is relatively simple to the live load

model

In to the probabilistic of the WIM the confinned the use of the Gumbel

distribution (RR9100401 1994) as the most n~rArr means for extrapolating the load effects of

vehicles on simply supported spans In applying the Gumbel distribution it was shown that the

exltral)olate(I load effects are sensitive to the population size of the extreme events It was however

concluded that a than one month was required to narrow the confidence limits of

the predicted events

The probabilistic of the WIM data was shown to be relatively insensitive to the return


with ENV 1991-3 and BD3701 For the limit state a maximum return period of

1000 years as per ENV 1991 is recommended

The potential of the WIM data raised a question over the of the results

ENV 1991-3 was calibrated (OConnor et 200 I) using WIM data with a maximum error of 5

Similar standards are required in South Africa if WIM data is to be used in the calibration of future

bridge live load models

The analysis of the WIM data indicates that the overloading of axles and axle sets is more

than the n~rlfpound1 of a complete vehicle As in the case ofBD3788 the use of an overloading factor

that decreases as the span increases is therefore oroooed

South Africa has to progress to a live load model IlPmiddotpnpmiddot11 methods

research

and 1995 in South

in the RR 9100401 amp was carried out between 1994

TMH7 Parts I and 2 have remained unaltered since 1988 Its closest rplTIrp

UJ)tVV was BD 3788 in 1988 The advent of the ENV 1991-3 in further dates

the deterministic derivations ofTHM7 Part live load model

The review of BD 370 I also a number of in the of live load

models that are to be in South Africa These include the derivation of

curves that do not the use of abnormal load models in short spans and the COflCe1Jt


TMH7 Part 2


methods to derive a live load model For this reason its an excellent reference for


member states a National Document based on the

of local truck survey data may be in South Africa and other South African countries

The of live load models and their calibration on the of

traffic survey data is that load models may be derived In

of traffic for technical and economic reasons it is to the live load

model

of the WIM the confinned the use of the Gumbel In

distribution as the most rrnr means for the load effects of

it was shown that the ltHr t~middotrI spans In the Gumbel

exltral)olated load effects are sensitive to the size of the extreme events It was h()1vvpr

concluded that a than one month was to narrow the confidence limits of

the events

The of the WIM data was shown to be insensitive to the return

selected the 2976 year retmn used RR 9 is conservative when cOlmpared

with ENV 1991-3 and BD3701 For the limit state a maximum return of


The of the WIM data raised a over the of the results

ENV 1991-3 was calibrated et 2001) WIM data with maximum error of 5

Similar standards are reOluued in South Africa if WIM data is to be used in the calibration of future

live load models

The of the WIM data indicates that the nfl~rI of axles and axle sets is more

than the ~rlfrI of a cornplete vehicle As in the case the use of an factor


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The load effects generated from the probabilistic analysis of the WIM data provided an important

reference for the critical review of the live load models in TMH7 Part 2 and RR 91100402 The

following conclusions were reached

L) The of TMH7 Part 2s NA to cater for normal traffic load effects on shorts

spans was proven The use of NB loading to derive load effects due to normal traffic is not

coherent with a rationally based live load model

The use of a Monte Carlo simulation to target values that are required in formulating a

load is considered a valid approach (ENV 1991-3) The assumption used in RR

9100401 amp 02 that all vehicles are fully loaded is considered to be conservative It is

recommended that future simulations be based on a garage of vehicles whose axle and

GYMs are distributed as in the case of normal traffic conditions This method was used in the

ofENV 1991-3 (OConnor et aI 2001) The use ofWIM sensors on South

African Toll roads now provides sufficient data on which to base such an approach

iii) The un-factored design loads in RR 911004101 and TMH7 Part 2 are formulated from the

extrapolation of events that are extreme in themselves This methodology is

conservative in to modern codes of such as ENV 1991-3 and BD 3701 It

is recommended that characteristic load events be derived from normal traffic conditions

occurring over a rationally-based return period

iv) The form of the live load model proposed in RR9100402 was verified by the of the

thesis A method of calibrating this Jive load model is demonstrated in the thesis The form of

the proposed live load model is almost identical to that used in ENV 1991-3 The adoption of

ENV 1991-3 and the issue of a South African NAD is therefore a viable alternative to TMH7

Part 2

The thesis considers alternative live load models to TMH7 Part 2s NA loading curve A load model

two spaced point loads in combination with a constant uniformly distributed load was

found to accurately simulate the load effects of South African heavy vehicles This supports the

use of the load model in RR 91100402 it also shows that ENV 1991-3s load model may be

used in South Africa The probabilistic analysis of the WIM data demonstrates the means which

ENV 1991-3s load model may be calibrated to South African conditions As opposed to the future

revision of TMH7 a viable alternative is the adoption of ENV 1991-3 and the of a National

Application Document (NAD) The research and development carried out in developing the

limit state principles and live load model in ENV 1991-3 may then be utilised in South Africa with

limited expenditure

The derivation of a complete load model is a task beyond the scope of this thesis There are many

factors such as dynamic lateral bunching and multi-lane loading that must be considered in

uUraquoS a live load modeL The aim of the study was to review current international with

the aim of critically reviewing the live load models in TMH7 Part 2 and RR 91100402 This review

(6-3)

The load effects opnpr~ltpl1 from the of the WIM data rwr1pn an


conclusions were reached


spans was proven The use of NB to derive load effects due to normal traffic is not

coherent with a based live load model

The use of a Monte Carlo simulation to oPtprMp target values that are in a

load is considered a valid The used in RR

9100401 amp 02 that all vehicles are loaded is considered to be conservative It is



ofENV 1991-3 et The use ofWIM sensors on South

African Toll roads now ~rr~ sufficient data on which to base such an

iii) The un-factored loads in RR 911004101 and TMH7 Part 2 are formulated from the

of events that are extreme in themselves This is



over return

iv) The form of the live load model nraquon in RR9100402 was verified the of the

thesis A method of this live load model is demonstrated in the thesis The form of

the live load model is almost identical to that used in ENV 1991-3 The of


Part 2

The thesis considers alternative live load models to TMH7 Part 2s NA curve A load model

two loads in combination with a constant distributed load was

found to simulate the load effects of South African vehicles This the

use of the load model in RR it also shows that ENV 1991-3s load model may be

used in South Africa of the WIM data demonstrates the means which

ENV 1991-3s load model may be calibrated to South African conditions As to the future

revision of a viable alternative is the of ENV 1991-3 and the of a National

The research and carried out in the

limit state and live load model in ENV 1991-3 may then be utilised in South Africa with

limited

The derivation of a cornolete load model is a task the scope of this thesis There are many

factors such as lateral and multi-lane that must be considered in

US a live load model The aim of the was to review current international with

the aim of the live load models in TMH7 Part 2 and RR 91100402 This review

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has highlighted the fact that further development of live loading in South Africa must be based on the

rational assessment of the traffic events on the roads The use of the WIM data to derive characteristic

load effects demonstrates one way of this

(6-4)

has the fact that further of live in South Africa must be based on the



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BIBLIOGRAPHY

American Association of State and ransportatlOll Officials (1994) LRFD Bridge

ASTM ntelnatioDltll (2000) Standard )lJCTICUilnn for nI2nW1V Weigh-In-Motion (WIM)

with User Xe711renlenlS and Test Methods EI318-02

Benjamin J R and Cornell (1970) Probability statistic and decision civil engineers

McGraw-Hill Book Co New York

(1989) Modelisation des dues au Traffic Routier These No 793 Ecole Polytechnique

fedrale de Lausanne

Bez Hirt MA (1991) Load Models of HU~lla Traffic Structural

British Standards lnstitution (2000) DD ENV-1991-3-2000 Eurocode IBasis of design and action

on structures - Part 3 Traffic loads on bridges

Bruls A Calgaro J Mathieu Hand Prat M (1996) ENV 1991-Part3 The main models of traffic

loading on road bridges IABSE report 74

BD 3788 amp 01 (19882001) Department Standard BD 3788 Loads for Highway Bridges British Department ofTransport

BS 153 (1 1958) Specification for Steel Girder RrJt1fT~ British Standards Institute

BS 5400 (1978) Steel Concrete and Composite British Standards Institute

1 (1978) Traffic loading of span TransportationlJU-JUltU P G and

Research Record 655 -D Vol 2 146-154

Calgaro J-A (1998) Loads on ~~h~~ Progress in Structural and Materials Vol 1(4)

452-461

CANCSA-S6 (2000) Canadian Highway Bridge Code Canadian Standards Association

Committee on of the Structural Division (1981) Recommended Loads For Bridges By

the Committee on Loads and Forces on ASCE Journal of Structural Division pp1161-1213

July 1981

Univers

ity of

Cap

e Tow

n

Chow V Maidment D R and Mays L W (1988) Applied Hydrology McGraw-Hill International

Cunnane (1978) Unbaised plotting positions - a review Journal Hrtlrr Vol 205-222

Dawe P (2003) Research Perspectives Traffic loading on highway nrlnmgt~ Thomas Telford

of Transport 1994) Report RR 911004101 The effect an Increase in the

Permissible Heavy Vehicle Loads on Bridges

Department of Transport (December 1995) Report RR 911004102 The effect of an Increase in the

Permissible Heavy Vehicle Loads on Bridges - Assessment Code

Grouni R K and Nowak AS (1984) Calibration of Ontario Design code 1983 edition

Canadian Journal ofCivil Vol 11 760-770

Harman D amp Davenport (1979) A statistical to the traffic loading on

Canadian Journal ofCivil Engineering 6494-513

Henderson W M (1954) British Highway tnlceeallffs of the Institution of Civil

Engineers Part lJ Vol 3 No2 June 1954

Honda Kobori T and Yamada Y (1986) Factor of Steel Girder Bridge

IABSE Proceedings P9886 57-75

H E and Nowak A S (1989) Dynamic Analysis of Girder Bridges Transportation

Research Record 1223 pp88-92

P (1998) The Status LVltUilJ in South Africa Proceeding ofthe South African

National Conference on Loading J998

Flint and Neill and Imperial vm (1980) Derivation ofsafety factors for BS 5400 Part

3- Final and appendices for the

Flint and Neill and Imperial vv (1986) Transport and Road Research Laboratory

contractor report 16 Long span bridge Crowthorne TRRL

Liebenberg A (1974) for a Uniform Specification of Live Due to Traffic on

National Road Bridge National Transport Commission amp Stander Consulting hlll~me~ers

V Maidment D R and L W wC_ MUmrlgt McGraw-Hill International

Unbaised OlOlttlIll

P Research I-p~mrf1vplt

Permissible Vehicle Loads on Hnr1a~~

Permissible Vehicle Loads on N iAnao

- a review Journal Hrtrr Vol 205-222

on hlaf1wfm nrlfluPlt Thomas Telford

RR 911004101 The

RR 911004102 The

Assessment Code

an Increase in the

an Increase in the

R K and

Canadian Journal

Calibration of Ontario

npmiddotmlIrzrp Vol 11 760-770

code 1983 edition

D amp uaveIlDon

Canadian Journal

W British

fnOlnPPlrs Part Vol 3 No2 June 1954

AlVUUl T and

lABSE Proceedim~s P9886 57-75

A S (

Research Record

National 1998

Flint and Neill pmPTlthm

Final

UCOUll- and Flint and Neill

contractor report 16 span

( a

A statistical

6494-513

to the traffic on

the Institution of Civil

Factor of Steel Girder

of Girder

LVUilJ in South Africa South

Derivation BS 5400 Part

Frllnltrlflrt and Road Research 1J1IJnr(1tflgt1J

Crowthorne TRRL

Live LU(lUjU~ Due to on Llebenberg A

National Road National Frnnltnnrt Commission Lleberlbelrg amp Stander

Univers

ity of

Cap

e Tow

n

Liebenberg A c (1978) The formulation of a New Code of Practice for the Design of Highway

Bridges with Specific Reference to Live Loading due to Traffic Liebenberg amp Stander Consulting

Engineers

Ministry of Transport (1931) Standard load for highway bridges (single sheet) London Ministry of

Transport

Moses F Verma D (1987) Load Capacity Evaluation of Existing Bridges NCHRP Report 30

TRB December 1987

National Highway Institute (1995) Load and Resistance Factor Design of Highway Bridges shy

Participant Notebook NID Course No 13061

National Road Traffic Regulations (1999) Chapter 6 - Fitness of Vehicles

Nowak A S and Hong Y -K (1991) Bridge Live Load Models American Society ofCivil Engineers

Journal ofStructural Engineering 117 (9) 853-867

Nowak A S (August 1995) Calibration of LFRD Bridge Code American Society ofCivil Engineers

Journal ofStructural Engineering 1245-1251

Nowak A S and Ferrand D M (1995) Truck load models for bridges American Society of Civil

Engineers Journal ofStructural Engineering

OConnor A Jacob B OBrien E and Prat M (2001) Report of current studies performed on

normal load model ofECI-traffic loads on bridges Revue Francaise du Genie Civil (RFGC) Hermes

Science Publications 5(4) 411-434

OConnor A and OBrien E (2005) Traffic load modelling and factors influencing the accuracy of

predicted extremes Canadian Journal ofCivil Engineenng Vo132 270-278

OConnor c (1981) Ontario Equivalent Base Length An Appraisal American Society of Civil

Engineers Journal ofStructural Engineering 107 (1) 105-127

OConnor C and Shaw P (2001) Bridge Loads Brunner-Routledge

Oostehuizen APC Mein~ies C J Trumpelmann V Peters D Ullman KKAB and Opperman

G H P (1991) Proposed substitution ofsection 26 TMR7 Part 2 Ref noNI29-2-EOO-000-671

Department of Transport

Republic of South Africa Committee of State Roads Authority (1977) Code ofpractice for the Design

ofHighway Bridges Interim Specification with Explanatory Notes and Appendix

Univers

ity of

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e Tow

n

Swiss Loading Code SIA 160 (1970 1989) Einwirkungen auf Tragweke Swiss Society of Engineers

and Architects

Ulhnan K K A B (1987) Investigation ofBridge Loading Limits NRD R9936

Ullman K K A B (1988) Proposal for a Revision of Traffic Loading of TMH7 Part2 (Unpublished

Report)

Van Wyk amp Louw Inc (1991) Consequences of increasing heavy vehicle load restrictions transport

saving against additional pavement cost Report 370811

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ity of

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A-1

APPENDIX A

A-1

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nAppendix A

Vehicle Configurations amp Classifications

Appendix A


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bull bull bull bull bull bull




bull bullbull

Recorded 6 Axle Vehicle Confi urations Configuration 1

77 90 90 80 80 80

o 00 000 Max W = 497kN

Configuration 2

77 90 90 90 90 90

00 00 00 Max W = 527kN

Configuration 3

77 90 9090 90 90

o o 00 00 Max W =527kN

Configuration 4

77 90 90 80 80 80

o o o 000 Max W =497kN

Configuration 5

102 102

o 00 Max W =560kN

C1My OocumentsMSClFinai DocumenlAppendiceslAppendlx A - Vehide CombinaUonslAxle Configura~onsdocldlO6lO2I12

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bull bull bull

3

Configuration 7

80 80 80

000 MaxW = 560kN

C1My OocumentsMSCFinal OocumenMppendlceslAppendix A - Vehicfe CombinaUonslAxle ConfigurationsdocIdl12102l2OO6

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nbull bull bull

bull bull bull

Recorded 8 Axle Vehicle Confi urations

Configuration 1

80 80 80

Max W = 560kN

Configuration 2

80 80 80

eee Max W = 560kN

Configuration 3

80 80 80

eee MaxW = 560kN

Configuration 4

90 90

MaxW= 560kN

CIMy DocumentslMSCFinel DocumentlAppendlceslAppendlx A - Vehide CombinationslAxie ConfiguraUonsdocldlO6l02l12

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bull bull bull bull bull bull bull bull bull

bull bull bull

bull bull bull bull bull

5

Recorded 9 Axle Vehicle Confi urations Configuration t

77 60 60 60 60 60 60 60 60

o 0000 0000 MaxW = 557kN

Configuration 2

80 80 80

000 MaxW = 560kN

Configuration 3

80 80 80

bull bull bull 000 60 60 60 60

bull bull bull bull 0000 MaxW = 557kN

Configuration 4

48 48 48 48 48

00000 MaxW = 557kN

C1My DocumentslMSCFinai OocumentlAppendlcaslAppendix A - Vehlde CombinationslAxie Configuratlonsdocldl12J0212006

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bullbull bull

bull bull bull

bull bull bull

APPENDlXC

s Ii

~ [I $

~ 1- fl~


Configuration 1

90 90

Max W =560kN

Configuration 2

80 80 80

MaxW = 560kN

Configuration 3

90 90

00 0 MaxW = 560kN

Configuration 4

80 80 80

000 MaxW = 560kN

Configuration 5

80 80 80

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nAppendix B


bull

Appendix B


bull

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APPENDIXB

Frequency Distribution of Bending Moments of Actual Vehicles

6 Axle Vehicles

2~ ------------------------------------

220+------+------+_----_+------+_--~~~--~

e ~200+------+------+------+----~~-----+----~

5 ~ 180 +_----_+------r---~~~----+-----_+----~ s =i 160 +_-----r----~~----_+------+_----_+----~ = I~+-----~------+------+------+------+----~

120 r------+------r-----+-----+------+--~ o 2 4 6 8 10 12

Reduced Variate

---6 Axle

Figure B I Sm span

o 2 4 6 8 0 12

Reduced Variate

-6 Axle

Figure B2 10m span

650

600

~ 550 o ~ 500 8 Q

~ 450 CgtII S 0 ~400 =

350

300

I

~

~

~

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APPENDIX B

1050

1000

9508 ~ 900

-= 850e Q

~ 800 c ~

a 750 ~ ~ 700

650

600

o 2 4 6 8 10 12

~

p y

r

V

Reduced Variate

--6 Axle

Figure B3 15m span

1600

1500 middotLL7 8 ~ 1400 r ~ ~ 1300 e Q

Ishy ~ 1200 ~ c V] 1100 ~ V ~ 1000

900

o 2 4 6 8 10 12

Reduced Variate

--6 Axle

Figure B4 20m span

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APPENDIXB

3000

2800

8 ~ 2600 sect ~ 2400

E OIlca 2200 ==GI

=I

2000

1800

V

_V

Ijj

o 2 468 Reduced Variate

10 12

--6 Axle

Figure B5 30m span

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APPENDIXB

Frequency Distribution of Shear Forces of Actual Vehicles

6 Axle Vehicles

24)

220

~ 200 180~ ca

c IIl 160

14)

120

0 2 4 6

Reduced Variate

8 10 12

---- 6 Axle

Figure B6 5m span

290

270

__ 250 Z ~ 2l 230 ~ 1 210

c IIl 190

170

150

~ b V

~

~ I

I o 2 4 6 8 10 12

Reduced Variate

--6 Axle

Figure B7 10m span

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APPENDIXB

330

310

~ 290 Z ~ 270 Q

r 250 ~

c (IJ

230

210

190

o 2 4 6 8 10 12

V

J1V

I ~ I l

Reduced Variate

Figure B8 15m span

o 2 4 6 8 10 12 Reduced Variate

6 Axle

Figure B9 20m span

380

360

340

Z ~ 320 300 ~

01 280

c (IJ

260

240

220

--

V ~

~

)1

~

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APPENDIXB

430

410

390 Z 370 ltJ ~ =gt 350 ~ ~ 330c

00

310

290

270 o 2 4 6 12

r V

V ~

~V 1

8 10

I I

I I

1

I I I

i

I I i I

Reduced Variate

--6 Axle

Figure B 10 30m span

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APPENDIXB

Frequency Distribution of Bending Moments of Legal Vehicles

6 Axle Vehicles

200

195

e Z ~

190

-= S 185 ~

~ 011 9 180 0

= Ql

175

170

0 2 4 6

Reduced Variate

8 10 12

--6 Axle I

Figure B 11 5m span

530

520

e ~51O -= ~ 500 ~ 011

=a 490 =

Ql

480

470

V ~

~V ~

o

r

2 4 6 8 10 12

Reduced Variate

I --6 Axle I


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APPENDIXB

1000

950 5 ~ c 900 OJ e Q

~ C)I) 8509 -g c OJ = 800

750


o 2 4 6 8 10 12

Reduced Variate

--6 Axle I


0 122 4 6 8 10

Reduced Variate

--6 Axle

1550

1500

5 ~ 1450 a OJ

C 1400Q

~ C)I)

a a 1350 OJ =

1300

1250

~7

shy

~ V

-~

~

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APPENDIX B

- ~

V d ~

AV V

I

-i

V

2 4 6 8 10 12

Reduced Variate

--6 Axle

2850

2800

e 2750 Z 0 2700 Se2650 Q

~ 2600 ~

5 2550-g ga 2500

2450

2400

o


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APPENDIXB

Frequency Distribution of Shear Forces of Legal Vehicles

6 Axle Vehicles

185

180

~ 175 cJ ~

170~ -= en

165

160 0 2 4 6

Reduced Variate

I --6 Axle

8 IO 12

Figure B 16 5m span

250

245

240

235

~ 230

~ 225 ~ ~ 220 -= en

215

210

205

200 -

f

- I

~ ~

7 V

2 4 6 Reduced Variate

I --6 Axle I

12 o 8 IO


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APPENDIXB

305

300

295

290 ~ 285 0 ~ 280 ~

275 270

265

260 o

2

~

~ r It

V

4 6 8 10 12 Reduced Variate

--+-- 6 Axle I

FigureBl8 15m span


--+-- 6 Axle I


340

335

~ 330

u 3250 ~ 01

320

315

310

~ V V

J ~

~

L V

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APPENDIXB

405

400

395 -

~ 390

QI OJ

Q 385 ~

eo QI 380

c en 375

370

365 o 2 4 6 8 10 12

--~

V

~ V

~

-~

i I

I i i

l Reduced Variate

-+- 6 Axle I

Figure B20 30m span

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e Tow

n

APPENDIXB


7 Axle Vehicles

240

220 a ~ 200

= ~ 180 sIgtIl shytI 160 =

CQ

140

120 0 2 4 6

Reduced Variate

--+---7 Axle

Figure B21 Sm span

700

650

~ 600

- 550 ~

~ 500 ~ 450a = ~400

350

300 12o 2 4 6 8 10

4~

h 1

~

I t

I

I

~ -I I

I I I I

Reduced Variate

--+---7 Axle

Figure B22 10m span

8 10 12

Univers

ity of

Cap

e Tow

n

APPENDIXB

1200

1100 e z 0 1000 C a Q 900 1gt11 CIa 800 CI

cQ

700

600

0 2 4 6 Reduced Variate

-+--7 Axle

Figure B23 15m span

1800

1700

Le 1600

~ C 1500 sect 1400 ~ ~ 1300a ~ 1200cQ

1100

1000

o 2 4 6 8 10 12

~

d ~

~

7 bull

Reduced Variate

-+--7 Axle

Figure B24 20m span

8 10 12

Univers

ity of

Cap

e Tow

n

APPENDIXB

3200

3000 e 2 2800 CI OJ

e 2600Q

t CG CIa 2400 I OJ =

2200

2000


8 IO 12

--7 Axle

Figure B25 30m span

Univers

ity of

Cap

e Tow

n

APPENDIXB


7 Axle Vehicles

240 ----------- ----- ---------------------

220 +---~r_--_+----r----+_---r_--~

~200 +-----4------+----~------+-----~~~~ ~ ~ ~ 160+----~r_---_+-----_b~--+_-----r_--~

140 +----~r_-~~~---r------+-----r_--~

180 +---~r_--_+-----r----~~---r_--~

120+-----r_--_+---~---+------r_---_4

o 2 4 6

Reduced Variate

-+--7 Axle

8 10 12

Figure B26 5m span

270----~------_-------_----~

250+----~----+---~---~--~~--~

Z 230 +---middot~~---+---~----~~--~----~ C ~ 8 210 +-----4-----~---~~~-+---~---~ r ~ ~ 190 +------I-------t~---_t__----+_---__t---_i

170+---~~--~---_t__---+-----__t---_i

150+----~------_+------~------+-----_4-----~

o 2 4 6

Reduced Variate

-+--7 Axle

8 10 12

Figure B27 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

320

300

~ 280 - 41 OJ ~ 260 41

~ 240

220

200

V

V

V

~~

~ f7

I i I I I i

I i 1

o 2 4 6

Reduced Variate

--+-7 Axle

8 0 12

Figure B28 15m span

390

370

~ 350 Z 0 41 330OJ C ~

30 41

c (J 290

270

250

o

h pound

7 6A V I

~

V

4V 2 4 6 8

I r

I I I

I i I

i I

0 12 Reduced Variate

--+-7 Axle

Figure B29 20m span

Univers

ity of

Cap

e Tow

n

APPENDrxB

480

460

44)

Z 420 ~ ~ 400 0

380 os

CI 360(I)

340

320

300

~

)~

d ~ ~

~

k

o 2 4 6

Reduced Variate

-+-7 Axle

8 10 12

Figure B30 30m span

Univers

ity of

Cap

e Tow

n

APPENDIX B


7 Axle Vehicles

200

~ 195

e Z 190 e Jif75 185

8 Q 180 CD

a fS 175 =I 170

~ 165


I ---7 Axle

Figure B31 5m span

o 2 4 6 12

Reduced Variate

580

560

e 54)

~ 520

il 500 01

sect 480 ~ 460

]44) 01

=I 420

400

380

-

I

j ~

--~ ~ ~

I

L

4

8 10

I

I

I

i

---7 Axle

Figure B32 10m span

Univers

ity of

Cap

e Tow

n

APPENDIX 8

1100

1050

e ~ 1000

C 01 e 950 Q

011

= 900a I 01 ~

850

800 0 2 4 6 8 10 12

Reduced Variate

--7 Axle

Figure 833 15m span

1700

1650

e 1600

L ~ 1550 01= e f1500Q

011

= 1450 rIIa 01= ~ ~ 1400

~

1350 ~~

1300 o 2 4 6 8 10 12

Reduced Variate

--7 Axle

Figure 834 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

3000

2950

ez 2900 ~ 2850 e ~

~ 2800 = a ~ 2750 =

2700

2650

o 2 4 6 middot 8 10 12 Reduced Variate

-+-7 Axle

4

v

- V

Figure B35 30m span

Univers

ity of

Cap

e Tow

n

APPENDIXB


7 Axle Vehicles

~ ltI ~ 1 -= C-I

190

185

180

175

170

165

160

155

150

145

140

--shy

J r

) -

i-~

~ J1V


I ---7 Axle I

Figure B36 5m span

260

~V250

Y240 ~ ~ 230 -~ 5 ~ -= C-I 220

~

210 ~

200 o 2 4 6 8 10 12

Reduced Variate

I ---7 Axle I

Figure B37 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

320

~ 310

~ 300 r ~ 290 1

~

280 ~

~ ~ CI 270 (I) 260 -

250

240


--+-7 Axle

Figure B38 15m span

355

350

345

340

~ 335 330 ~ 325 ~

CI 320 (I)

315

310

305

300


--+-7 Axle

~

( L

l

~ ~

gt

~ ~

L

~

Figure B39 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

420

415

410

~ 4tl5

tJ

or 400

z (Il

395

390

385


I --7 Axle

Figure B40 30m span

t ~ i-

~~

1pound J

Univers

ity of

Cap

e Tow

n

APPENDIX B


8 Axle Vehicles

o 2 3 4 5 6 7 8 9

Reduced Variate

--+- 8 Axle

Figure B41 Sm span

o 2 3 4 5 6 7 8 9

Reduced Variate

1 --+-8 Axle I

Figure B42 10m span

e 3

550

500

- 450 c e c ~400 OIlca ~

CQ 350

300

V V ~

~--shy V

~ V~

8 ~

550

500

- 450 c a V

V r shy --

V -c ~400 ~

-V a c=350

300

~ V

Univers

ity of

Cap

e Tow

n

1050

1000

8 950

Z 900~

C 850a 0

~ 800 Oilc

750ac =I 700

650

600

o 2 3 4 5

Reduced Variate

1 --+-8 Axle

Figure B43 15m span

1600

1500

e Z 1400 ~ C a 1300 0

~ Oilc 1200ac

=I 1100

1000

o 2 3 4 5

Reduced Variate

--+- 8 Axle

Figure B44 20m span

I

-~ ~

shy

~ ~

~ ~ shy

V

I

~ ~~

- ~

~ ~

~ ~

V III

~

6 7 8

APPENDIXB

9

6 7 8 9

Univers

ity of

Cap

e Tow

n

APPENDIXB

I 17 I

7 ~ ~ I-

I

1

-e ~ i i

~ shy I- I

~ ~ 1

f

~ ~

i

I 2 3 4 5 6 7 8 9

Reduced Variate

1 -+--8 Axle I

3000

2900

2800 8 2700 ~

2600 -= 8 ~

2500 = ~ 2400 0laquo1 = a 2300 = ~

~ 2200

2100

2000 o

Figure B45 30m span

Univers

ity of

Cap

e Tow

n

APPENDIXB


8 Axle Vehicles

260

240

~ 220

~

~V ~ 200 ~ c

IIl 180

160

140

~

~

V ~V

V-

~

o 2 3 4 5

Reduced Variate

I --8 Axle I

6 7 8 9

Figure B46 5m span

250 I

240

~ ~~

~

~

~ ~ I

~

~ I

I I

230

220

~ 210 ~ ~200

I 190 ~ IIl 180

I 1170

J160

150

o 2 3 4 5 6 7 8 9

Reduced Variate

I --8 Axle I

Figure B47 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

310

290

~ 270

0 250

gj I 230rJl

210

190 o 2 3 4 5 9

Reduced Variate

-+-- 8 Axle I

Figure B48 15m span

r-- i I

L i v

v ~

I

~ ~ I

-11 I

~ i j

6 7 8

V

I

360

340

320 Z o 300 ~ ~ 280

c rJl 260

240

220

10-shy

-~

-V

- ~

o 2 3 4 5

Reduced Variate

-+-- 8 Axle I

6 7 8 9

Figure B49 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

440

420

400

~ 380 Q 360 ~ ~ 340 c CIl

320

300

280 o 2 3 4 5 6 7 8 9

~ ~

---~VIII

~

I

L Y I

~ ~ I

~ ~- I

i I I I

1

I I i

Reduced Variate

-+- 8 Axle I

Figure B50 30m span

Univers

ity of

Cap

e Tow

n

APPENDIX B


8 Axle Vehicles

I

I

570

550

a ~ 530

-= ~ ~ 510 ~ 01)

9 ~ 490 OJ

I=Q

470

450

L

I

I i

~- ~

~

-~ shy i

~

I

I j i

o 2 3 4 5 Reduced Variate

--8 Axle I

6 7 8 9

Figure BS I Sm span

570

550

e ~ 530 -

~ -= E lt) 510 ~ 01)c 490ac ~

I=Q

470

~V

-~ ~ ~

~ shy-shy

~

450


I -shy 8 Axle I

6 7 8 9

Figure B52 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

1030 1 i1010

I990e IZ e 970 c ~ 95013 Q

~ 930 OIl

Is= 910 = I= ~

890 1

870 i

850

V ~

[i i

~ V I

~~ I I

~ ~ I I

I

I I

V

I

o 2 3 4 5 6 7 8 9

Reduced Variate

1 -+-8 Axle

Figure B53 15m span

1600 I

~ 15508 ~ z e ~ -c 1500 shy8 ~

~ Q OIl 1450 s= ~ =

V = 1400

1350 o 2 3 4 5 6 7 8 9

Reduced Variate

-+-8 Axle I

Figure B54 20m span

Univers

ity of

Cap

e Tow

n

APPENDIX 8

3000-----r-------------~----~----r---~----~----~

e ~ - 2900 E 8 Q

~ ~

aI 2800 I =

2700+---~~--~----~----~---+----~----~---+--~

o 2 3 4 5

Reduced Variate

-+-8 Axle

Figure 855 30m span

6 7 8 9

Univers

ity of

Cap

e Tow

n

APPENDIX B


8 Axle Vehicles

260

255

250

Z 245

~ ~

240 235= ~ 230~

c CIl 225

220

V

215

210

~ I

~~

~r V

~

~ ~r

I i I

l i

I

o

Figure 856 5m span

2 3 4 5

Reduced Variate

-+- 8 Axle

6 7 8 9

3000

~ --~ ~ 2900 V ~ V

~ V 01 41 ~c

CIl 2800

V ~

2700

o 2 3 4 5 6 7 8 9

Reduced Variate

1 -+-8 Axle I

Figure 857 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

-

o 2 3 4 5 6 7 8 9

Reduced Variate

-+- 8 Axle

Figure B58 15m span

305

300

295

~ 290 III ltJ 285Q ~ ~ 280 c rI)

275

270 I 265

L ~

~ ~

tr V

~

I-shyi-shy

I

I i I

I I I i i I

I

345

340

335

Z 330 ~ III 325 Qr 320 =OJ c 315IJ)

V

~

-U i-

~

310

305 V-300

shy

i I

I I I

I i i

i I


1 -+-8 Axle

6 7 8 9

Figure B59 20m span

Univers

ity of

Cap

e Tow

n

I

APPENDIXB

415

40

405 Z ~ 400 0 ~ 395 gJ

c (I)

390

385

380

o 2 3 6 7 8 9

I

~ V

~

~ ~

~ ~

~

4 5 Reduced Variate

I --8 Axle

k I L

-I

i

I i

i

i

i I

Figure B60 30m span

Univers

ity of

Cap

e Tow

n

APPENDIX B

Distribution Graphs of Bending Moments of Actual Vehicles

6 Axle Vehicles

295---------~----------~----------~--_

275

e 255

~ lt11

C 235 e ~ Q

~ 215

195

--t-- i

i-----i---

175 +-----r-----r-------------------r----~

-100 100 300 500 700 900 1100 1300

Reduced Variate

Figure B61 5m span

-0- Plotted Points - 5m Span -ift- Log Normal

--- Normal --Gumbel Frechet

bull

Univers

ity of

Cap

e Tow

n

APPENDIX 8

1500~----~----------~----r---~~--------~

I I I1400 -1 shy --+-__--_1shy

~ 1300 --~-~---j---+I -

i 1200 -1-shy - -+-shy - -+-shy8 Q

1100 -+--shy - +shyell 5 C 1000 ----i--shy --i

~ ~~~-- I I I 900 r-- ---t---T 800+-----+-----~----r_----r_----r-----~--~

-100 100 300 500 700 900 11 00 1300

Reduced Variate

-0- Plotted Pointsmiddot 15m Span -- Log Normal -- Normal Gumbel -+-Frechet

Figure 863 15m span

2200

2100

~2000 a ~ 1900

i 1800 g1700

~1600 = i 1500

11 1400

1300

1200

I 1

-1 I I

I I I

L---shyI

___shy---- shy

-100 100 300 500 700 900 1100 1300

Reduced Variate

-0- Plotted Points - 20m Span Log Normal -- Normal Gumbel -k- Frechet

Figure 864 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

3800

3600

e 3400Z e I 3200 QI e

3000Q

~

2800a QI 2600=

2400

2200

-100 100 300 500 700 900 1100 1300

Reduced Variate

~ Plotted Points - 30m Span -+- Log Nonnal -- Normal --Gwnbel Frechet

Figure B65 30m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

Distribution Graphs of Shear Forces of Actual Vehicles

6 Axle Vehicles

300

280

Z 260

0 240 ~ 220i ~ fIJ

200

180

160

I--I-shy

I --shy

i

I

-100 100 300 500 700 900 1100 1300

Reduced Variate


--Nonnal Gumbel

Figure B66 5m span

340

~ - Q CIS ~ fIJ

200

Reduced Variate

320 ~-l--middot- 1 --300

280

260

240 i

220 I T

I

-100 100 300 500 700 900

-I 1100 1300

~ Plotted Points - 10m Span - Log Normal

--Nonnal Gumbel

Figure B67 10m span

Univers

ity of

Cap

e Tow

n

390

370

350

~ 330 r 0

310 ~

CI rJl

290

270

250

i -i----~--~middot~--- -+ -- ---~-- ----~--shy

=shy-+------shy 1- -shyI

i q-shy 1 -1shy -1 1-- shy

-djr-+----4-middot-shy-1shy-- --shy-+-- 1 I l

-100 100 300 500 700 900 1100 1300

Reduced Variate

-0- Plotted Points - 15m Span - Log Normal

-- Normal Gwnbel

Figure B68 15m span

440

420

400

~ 380 0 r 01 360

CI rJl

340

320

300

-100 100 300 500 700 900 1100 [300

Reduced Variate

-0- Plotted Points - 20m Span -ill- Log Normal

--Normal Gwnbel

Figure B69 20m span

APPENDIXB

Univers

ity of

Cap

e Tow

n

APPENDIXB

510

490

470

~ 450 Ol _ e

430~ 01 41 410

CIl

390

370

350

-100 100 300 500 700 900 1100 1300

Reduced Variate

-0- Plotted PoinlS - 30m Span -+- Log Normal

-- Normal - Gumbel

1 _ - --1-

j ---+--~~I i

-1----1-----

-+-------tli

- -+---~ I - i - --L-- -l- - -l

-I -+---1-- 1


Univers

ity of

Cap

e Tow

n

APPENDIXB

Distribution Graphs of Bending Moments of Legal Vehicles

6 Axle Vehicles

220

215

e 210Z e l 205 I ltI e I

ltgt 200 I~ ~

1955 ---shyt) i -I ltI 190= ~---imiddot----middot-

I 185 19----1----1- -------------r

180

-100 100 300 500 700 900 1100

Reduced Variate

~ Plotted Points - 5m Span Log Normal

Normal -It- Gwnbel

Figure B71 Sm span

670

650

e 630 Z e 610 7 ltI 590S ltgt ~ 570

cI ~

550 I ltI

cQ 530

510

490

I +---+--+---shy- T - shy -

1 ------

-100 100 300 500 700 900 1100

Reduced Variate


-- NonnaJ -It- Gwnbel

Figure B72 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

1450 -r------------------------

e z 13502 1250

ltII

C e 0 1150 5 ~

1050 c CQ

950

I

~-+_____ I

850+----r---r----~--~---+----~

-100 100 300 500 700 900 1100

Reduced Variate


-- Normal --- Gwnbel

Figure B73 15m span

1910

1860

e 1810 Z 2 1760l c

1710e 0

1660

5 ~

1610 c CQ 1560

1510

1460

-100 100 1100

--------1 ---

~-r---~-- ----shy- 1- --1-- - -I-

I i

300 500 700 900

Reduced Variate

~ Plotted Point~ - 20m Span -e- Log Normal

-- Normal --- Gumbel

Figure B74 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

3150 ----------------------------

3100

3050

3000

2950

2900

2850

2800

Ii I ~--l-middot -+_ -1-- shyI I

-1- I Ii+ --shy__- -shy --shy--shy

i I I i -

- i

i

I--I - - -1-shy

I -LOO 100 300 500 700 900 1100

Reduced Variate

-ltgt- Plotted Points - 30m Span Log Normal

-- Normal --Gumbel

Figure B75 30m span

Univers

ity of

Cap

e Tow

n

190

APPENDIXB

Distribution Graphs of Shear Forces of Legal Vehicles

6 Axle Vehicles

Z 186 Cshy Ol

184 01 Olc 182

CIl

180

178

-100

I 188 +---1-shy

t-+----shy

100 300 500 700 900 1100 1300

Reduced Variate

-0- Ploued Points - 5m Span ~ Log Normal

-- Normal ~Gumbel

Figure B76 5m span

290

280

270Z e ~ 260 lt=

250 ~ c

rJ)

240

230

220

-100 100 300 500 700 900 1100 1300

Reduced Variate

-0- Plotted Points - 10m Span -6- Log Normal

--Normal ~Gumbel

Figure B77 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

325 i

--------------t------~t__-__I320

315

Z 310cshy 305 Q

300 = c (JJ 295

290

285

280

-100 100 300 500 700 1100 13 00

+--------+--- +-----i---Le----+- -I

=---=------- ------I

j-__+--_ - i___ __ I

900

+-_-I- shyI

Reduced Variate

-0- Plotted Points - 15m Span -- Log Normal

-- Normal --Gumbel

Figure B78 15m span

355~----~----~----~--~~--------------~

350 +shy

345

340 -Jshy

335

- -I I II

--J---- t---j---- k-- ------------I_____I

---l-

330~~--T----r-----~--~~--~----_----__t

-100 100 300 500 7 00 900 1100 13_00 Reduced Variate

-0- Plotted Points - 20m Span -iI- Log Normal

-- Normal Gumbel

Figure B79 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

420

415

410

~ 405 ~ 400 ~ c CIl 395

390

385

-100 100

---1shy--T

I 3_00 500 700 900 11 00 1300

Redoced Variate

-ltgt- Plotted Points - 30m Span -e- Log Normal -- Normal Gumbel

Figure B8D 30m span

Univers

ity of

Cap

e Tow

n

APPENDIXB


7 Axle Vehicles

310

--L290

e 270Z ~ l 250c a 230Qa 01)

210 I cac 190 - - -shy -L--shy ---i-shy== i I

170 I I i

150

-100 100 300 500 700 900 1100 1300

Reduced Variate

- Ploned Points - 5m Span Log Nonnal

--Normal Gwnbel

Figure B81 5m span

i

600 +----

850~----~--~----~----------------T_--~

800

750 ----1 -1-1-1 -+1-----gt+-1 700 --------I----b---i------ -t-- i_ _ 650 -I- ----+---- +- - -- - --=L--+---tI

~ ac ~ 550

500

450+-----r---~----_+----_r----~----~--~

-100 100 300 500 700 900 1100 1300

Reduced Variate

- Plotted Points - 10m Span -II- Log Normal

-- Nonnal Gwnbel

Figure B82 10m span

Univers

ity of

Cap

e Tow

n

1350 ~-+ ~ -1250 - i - ishy1150

I 1050 I 950 I

APPENDIX B

1450 ~--~------------------r----------

850+----r---~----_r---4_----r_-~---~

-100 100 300 500 700 900 1100 1300

Reduced Variate


Normal --Gwnbel

Figure B83 ISm span

2150

2050

E 1950 z ~ 1850 l I 1750S ~

~ 1650 toll

aI 1550 I = 1450

1350

1250

-100 100 300 500

Reduced Variate

__1__ _

i ~~----- --~I -----

700 900 1100 1300


Normal --Gwnbel

Figure B84 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

I middot---1shy 1 -shyI -shy-r- - t- -tshy I

2650 f----i~-_+---r---i---+---ir-----l

-100 100 300 500 700 900 lUXgt 13 00

Reduced Variate

-lt)- Plotted Points - 30m Span Log Nonna

-shy Normal --Gumbel

Figure B85 30m span

3850 ------1----------------------

3650

3450

3250

3050

2850

Univers

ity of

Cap

e Tow

n

APPENDIXB


7 Axle Vehicles

~ Qj e r ltII Qj

-= CIl

280

260

24)

220

I I +---+-----l-- -+_-+--~I- --

I---shy-1shy-tshy --+shy--shy -shy - -shyL

200

180 -l--~_-__+- ------L--__+------ shyt----shy160+-----r---------+-----r-----r----~--~

-100 100 300 500 700 900 1100 1300

Reduced Variate

-0- Plotted Points - 5m Span Log Normal

Normal -+-Gumbel

Figure B86 5m span

320 I

300 1___

I I ~ 280 I Qj

--t-~-- - e 260r g

-= 24) -CIl

220

200

-100 100 300 500 700 900 1100 1300

Redoced Variate

-0- Plotted Points - 10m Span ~ Log Normal

--- Normal -+- Gwnbel

Figure B87 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

360

350

340

~ 330 - 320~ ltJ ~ 310 01 300 -= rIl

290

------tlshy-middot - 1shy

280

270

260

-100 100 300 500 700 900 1100 1300

Reduced Variate

-0- Plotted Points - 15m Span -+- Log Normal

Normal Gwnbe1

Figure B88 15m span

450r-----~----r_----~----~----~--~----_

430 ~---+_---+_--_+_--_+_--_+--_=_+--_l

Z 410

0 ~ 390ltJ ~ 37001 ~

-= rIl 350

330

i------shy--shy--shyL

310

-100 100 300 500 700 900 1100 1300

Reduced Variate


Normal Gwnbel

Figure B89 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

~ y Q ~ CII d rJJ

560

540

520

500

480

460

440

420

400

380

360

I I

-t-------i~----+l --- middot middot f=-f~~~----+---l shy -I--r--r--~---~~_ i--I-

-9~-middott=-t-- - I- 1shy -shyi--~t -+- -shy - --shy

+----+ishy - ---- -+------L shy-shy-----~--___l I I -

-100 100 300 500 700 900 1100 1300

Reduced Variate

-ltgt- Plotted Points - 30m Span -iIt- Log Normal

Normal --- Gwnbel

Figure B90 30m span

Univers

ity of

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APPENDIXB

Distribution Graphs of Bending Moments of legal Vehicles

7 Axle Vehicles

210

205 5 z e 200 ~ c e ~ 195

E till ca 190 c

=

185

180

-100 100 300 500 700 900 11 00 1300

Reduced Variate

I r----+-I-- ---~-------+---t---I I

~ Plotted Poinls - 5m Span Log Normal

Normal Gumbel

Figure B9 I Sm span

5 Z e l c e ~

E

aC till

c =

535

530

525

520

515

510

505

500

- Ploued PoinlS - 10m Span -II- Log Normal

Normal Gumbel

I i I I I ---+----l-- -l--shy middot-- shy T --i 4 shy-I

-100 100 300 500 700 900 1100 1300

Reduced Variate

Figure B92 10m span

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1150

1100 - middot 1050

1000 r --

950

900

-i -t l_-lshyI~-fshy----+ 1-shy ishy

i I

- 1i

APPENDIX B

1200 -------~----____--____----_

850+---r-----r--~--~---~--_T----~

-100 100 300 500 700 900 1100 1300

Reduced Variate

-0- Plotted Points - 15m Span -it- Log Nanna]


Figure 893 15m span

e

1650

1630

1610

~ 1590 ~ c 1570 e Q 1550 ~ ell 1530= a c 1510 = 1490

1470

1450

I I -~-t-shyI

i il )

l--shy

-100 100 300 500 700 900 1100 1300

Reduced Variate


-shy Normal --- Gumbel

Figure 894 20m span

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APPENDIXB

I i I

-~-+--1-1 ~ I-1--

2820+-----r---~~--~----~----_+----_+----~

-100 100 300 500 700 900 1100 1300

Reduced Variate

-0- Plotted Points - 30m Span -It-- Log Normal

-- Normal Gumbel

Figure B95 30m span

2940

2920 e Z 2900ltII

I -OJ

8 ltgt 2880 ~ OG Ia 2860 I OJ

CQ

2840

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APPENDIXB


7 Axle Vehicles

210

205 +---f---l----I I---r----f-----

----- -JbI~__+ - I

--~-l ---- - ---+----+-- i

200 -J-- -+- - - j--shy

~ 195 -- ---1- -+----

ltj 41 190

ri I II i __ J ---r--shy 185

41 -= I ~ I - I ~+---r---rIl 180

175 +-ltSgt---- - +-i--i---T --+--shy i

170

-100 100 300 500 700 900 1100 1300

Reduced Variate

-0- Plotted Points - 5m Span -a- Log Normal

-- Normal --Gumbel

Reduced Variate

-0- Plotted Points - 10m Span -j- Log Normal

--Normal --Gumbel

Figure B97 10m span

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360

+ JiUO--t---

-j---t----+--- -~-- - T -3S0

-340 r- -r- I ~- -1- -shy~ 330 ltJ ~ Q 320 +---h-=-~~--1 ~~-Ib~01

310c ~ -- I-- r-----1-shyen

300 -I ------ middot-middot -middot-middot--middotmiddotmiddot middot middot middot--middot-middotmiddot~Imiddot ---i I I 290 - ---1------- shy

280

-100 100 300 Soo 700 900 1100 1300

Reduced Variate

-0- Plotted Points - ISm Span -- Log Normal

-- Normal Gumbel

Figure B98 ISm span

390r---~----~----~-----1

~ 370

~

----------~--~

380 +--------- I - ---r ---+- - - - ------- ---+-- - - - - --1

I - +1--- -+-

3S0 +----+

330+-----r---~----_+---_r----~----~-~

~ 360 +--shygj t3

340

-100 100 300 SOO 7 00 900 1100 1300 Reduced Variate

1-0- Plotted Points - 20m Span -- Log Normal --Normal --Gumbel

Figure B99 20m span

APPENDIXB

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APPENDIX B

423

421

419

417Z 415 Q

413 ltlI c 411 (IJ

409

407

405

-100 100 300 500 700 900 1100 1300

Reduced Variate

-0- Plotted Points - 30m Span - Log Normal --Normal --- Gumbel


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APPENDIXB


8 Axle Vehicles

240

230

e 220

~ - 210 -= 200e 0

E 190 011c a 180 c = 170

160

150

-100

-I----tl ---+shy

I

-r I i-----1L-~II --_t_

_ -+shy _ _ i

100 300 500 700 900 1100 1300

Reduced Variate

~ Plotted Points - 5m Span -3t- Log Normal

Normal Gumbel

Figure BIOI Sm span

650

8 600 z -I - I c 550 e 0

E 011 500ca I = 450

4OO+-----r---------+-----r-----r----~--~

-II

-100 100 300 500 700 900 1100 1300

Reduced Variate

~ Ploned Points - 10m Span ~ Log Normal

Normal Gumbel


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APPENDIXB

1200 ----------~r_-r_--__r--____--__

1150 - --1-+-+I---t-shys 1100 _-+ I-- ishyz ~ 1050 l = -t-l i e ~ OJ)

= --+1- ~ l -~ a = CQ

850 q - -I--middot-~ -1

800 I

750 +-----~----~----_----~----_r----~---~

-100 100 300 500 700 900 1100 1300

Reduced Variate

-ltgt- Plotted Points - 15m Span Log NonnaJ

-- Normal ---- Gumbel

Figure B103 15m span

1900

1800

S Z 1700 l = 1600 8 c ~ 1500 OJ)

= a = 1400

CQ

1300

1200

-100 100 300 500 7 00 9 00 1100 1300

Reduced Variate



Figure BI04 20m span

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APPENDIXB

3350 I

I

I

3250

1-~ --

- 3150S

z --1-shy ~c 3050 1

II I 2950e iQ

2850 011 s 27501l c

I = 2650

2550 -I middot I

2450

-100 100 300 500 700 900 1100 1300

Reduced Variate

-0- Plotted Points - 30m Span It- Log Normal

-- Normal Gumbel


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8 Axle Vehicles

210----------~------_----~----~----~

200~-----~-----4------~----~-----+--~~

190

~

~

1150 m(fF-~_+_------I----middotmiddotmiddot----middot--- middotmiddot --middot-middot middot -middot------------1

I~+_-----r----_------r-----~-----+----~

I f----- -I shy

180 +---------------

170 -t------------+-~

I I-shy ----------- 1 160 +-------1----4-----

-100 100 300 500 700 900 1100

Reduced Variate

- Ploned Points -- Sm Span Log Nonnal

-- Nonnal - Gumbel

Figure B106 5m span

290

280

270

260 ~ - ~ 250 Q 240 ~ 230 ~

rIl 220

210

200

190 -00 100 300

- Plotted Points - 10m Span ~ Log Normal

-- Normal -Gumbel


-1---1--shy-1----1-1--shy

-------shy - middoti-- -----shy-shy-shy- I

500 700 900 11 00

Reduced Variate

APPENDIXB

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APPENDTXB

370

350 Ij --shy - Ishy - - -shy

~ 330

01 310

- - --~---t-shy--

I+-shy- -i----+shy- - - shy--shy ~---_+_---I Q ~ 290os c ()

270

250

230

-100 100 300 500 700 900 1100

Reduced Variate


-- Normal Gwnbel


~o----~-----------~-----------------_

380

~ 360 01 Q 3~ ~ ~ c 320()

300

280

-100 100 300 500 700 900 1100

Reduced Variate

-0- Plotted Points - 20m Span -iti- Log Normal

-- Normal Gumbel


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APPENDIXB

500

480

460

~ 440 OIl

~ Q 420 ~ ltII OIl 400d

(I)

380

360

340

-100 100 300 500 700 900 1100

Reduced Variate

-ltgt- Plotted Points - 30m Span -ill- Log Normal

-- Normal Gwnbel


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APPENDIXB


8 Axle Vehicles

210~----~-------~----~--------------

205 ~---l-

200 -j---l-----

195 -+----l~oP ---1-shy +---1------1

190 -I----shy-shyr- - - - --t-shy- --r---+--shy- I

185 -t------t----i---i------r----

-100 100 300 500 700 900 1100 1300

Reduced Variate

- Ploued PoinlS - 5m Span 1- Log Nonnal

-- Normal Gumbel

Figure BIll 5m span

545

540

S Z 535 i 530 GI a 0 525 ~ ~ c a 520

C GI

IQ 515

510

505

-t-+---t-I-L I I

-100 100 300 500 700 900 1100 1300

Reduced Variate

-ltgt- Plotted PoinlS - 10m Span Log Normal

-- Normal Gumbel

Figure B I 12 10m span

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APPENDIX B

104)

1030

e 1020Z e l 1010c e 1000=gt OG

990c s c 980=I

970

960

-100 100 300 500 700 900 1100 13 00

Reduced Variate

-ltgt- Plotted Points - 20m Span -fI- Log NormaJ

-- Nonna --- Gumbel

Figure B1 13 15m span

1620-----~--~----~~--_----~----~--~

- e Z e l c e =gt OG

ac

c =I

1500+-----r---~----_T----_r----~----_--~

1600

1580

1560 l

i 154)

1520

-100 100 300 500 700 900 1100 1300

Reduced Variate

-ltgt- Plotted Points - 20m Span -fI- Log Normal

--Nonna --- Gumbel


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APPENDIX B

2970

~ 2950

S z 0 2930 (I)

is e 2910Q

~ 1gt11 Ca 2890 c

al

2870

2850+-----r-----~--~r_--~r_--~----_+----~

-100 100 300 500 700 900 IUlO 1300

Reduced Variate

--0- Plotted Points - 30m Span -I- Log Normal

--Normal -Gwnbel


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--

APPENDIXB


8 Axle Vehicles

200

195

Z ~ 190 ~ ~ 185 ~ -= (I)

180

i i I I ~ E bull

175

c_---+-__---_ ~--_f

~-+-----il-_+ _-+t_i ---t-I-I -100 100 300 500 700 900 1100 1300

Reduced Variate

-lt- Plotted Points - 5m Span -- Log Normal



~ ~

= ~ -= ~ (I)

275-----------~--------~----------~----_

270

265

260

- shy -- ----- shy ----1---shy

I 2S5 -t shy250

245

240

-100 100 3 00 500 700 900 1100 1300

Reduced Variate

-e- Plotted Points - 10m Span -iI- Log Normal

--Normal ---Gumbel


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APPENOIXB

325

320 I-- -I ~

315

310OJ ~ 305~ -= (I)

300

295

290

-100 100 300 500 700 900 1100 1300

Reduced Variate

-0- Plotted Points - 15m Span - Log Normal - Nannal Gumbel


Z e ~ Q

~

~ -= (I)

360~----------------~----~---------------

355

350

345

340

335

330

--+----~-- ~--- i shy - ---+-----1

i I I I -100 100 300 500 700 900 1100 1300

Reduced Variate


-Nannal Gwnbel


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APPENDIXB

QI ~ 415 +---f--shy

-~--t-I I

I -=r-i--- II

I 400+-----~----+_----+_----r_----+_----r_--~

430~----~----~----------~----~----~--~

425 --f ~ r - ~ 420 -I---~---li-- --- --t-shyZ I ==- i

~ o

lltU 410 +-- -r shy

~ ~-----------l405 -1--061+--1-----+ I

i i

-100 100 300 500 700 900 1100 1300

Reduced Variate

-0- Plotted Points - 30m Span - Log Normal -- Normal --- Gumbel


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nAppendix C

Liebenberg Combinations

II

II

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APPENDIX C

Page No

C1 LlEBENBERG amp HENDERSON VEHICLE COMBINATIONS 1

C2 ACTUAL PROBABILITY OF COMBINATION J1 - 2 AXLE VEHICLES 3

C3 ACTUAL PROBABILITY OF COMBINATIONS J2 - 3 AXLE VEHICLES 4

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C1 L1EBENBERG amp HENDERSON VEHICLE COMBINATIONS

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COMBlHATIO~ JI YECIES fYPE ~I~~~~ LwJl~I~I~~

C()to(91NAT1C)N J2 tEHClfS E J

CtJ4BN O J) ~ n 1Q n~ ~~ltS ~bullbull gt ~1~~~~~~_ 0

Jmj ~ xni Hpi ~~ m BrA ~zaJ V i~llw nJp DjIXP ~rmi lal

JAM PACKED NO IIotPampCf llOWtHCE HEEOED

COMBIPUTION Ht VEHICLES TYPE~-lli~ ~~~ ~ _ ~~41~d~~ l~ ) IlIO Wlg~~~

cOHa puTICN Hl YEHICIES lrPE4~N sesect ~lt4 ~ ~~~~N ~ ~hH __ ~ ~H laquo

~--__~I2t_l- ID 1Ogt-L~~-l~wJ

CQJIBINtJ1()j 3 owEHlCLlS TYPE bull TYIpound ~

nJ N ~ ~ (~=n ~~~~ =1S middot ~ ~~ ~ _I~_ ~~ ~ ~ --L~_~ Ig I Dt ~JIQ JPgti ~~~_uo~~ IZIP a~~~lILJ~~m ~xqi 1M lq e I)IIOQ XI

ICOMBINATIONS OF VEHICLES -BASED ON IIENDEflSO(S LONGITUOiNAl SPACII~G ARRANGEMENTS I

CCraquo-6INAT OH 51 ~ItN ~ ~1SO~ i5O~re~ [I1ICIE5 TrPpoundl ~~~l(]) ~~ ~~ j ~ A-yen

~~i--gt-=~~~iJ 1 iwi UP ji__

~IIIIHTIOH 52 ytHICpoundS TrPpound~S~N _ ~ 2~O~ ~B-~-sect ~Vi ~- ___~ ~ _ lyenl ~ __~lJ===t~ ~~--I

j UIQ )DlI lID ~lIQl l~l pAP l~i___HILJnt_ ~I middot 1m Lrl 1M iJllli 8 Lut

CClABIPTJC)N Sl V(HCL(S TYIE TYPE

~ ~ ~~ laquod~ ~~sect sr~~~ ~ ~ ~ ~ i-J_ M I I ~ 1c=1 him m ~~ ~i ~ i i 11M i IlZ 19 M I

OTHER NuN JAM PACKED COlltXllNATb I~PACl auQWuCf bullrCXD

FIGUREGROlJPS OF VEHICLE COMBINATIONS USED BY LIEBENBERG 3

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C2 ACTUAL PROBABILITY OF COMBINATION J1 - 2 AXLE VEHICLES

Sample Size 20689 vehicle month

CalculationProbabilityStatistical Event No Probability 2 axle vehicle is followed by another 2 Axle vehicle

I 022

2 23E-05 3

Probability 2 axle GVM gt 197 00002Probability 2 axle axle spacing is lt 2Am

4 46E-09 (2)(3) 5

Probability of (2) amp (3) Co-existing 876 years 11(4) Sample Size 12Recurrence period

Probability Critical Vehicle I is followed by a 2 axle vehicle

6 (I) (4)IOE-09

Probability Critical Vehicle I is followed by Critical Vehicle 2

7 47E-18 (6) (4)

8 1(7) Sample Size 1287E+II yearsRecurrence period

Probability Critical Vehicle 2 is followed by a 2 axle vehicle

9 10E-18 (1)(7)

Probability Critical Vehicle 2 is followed by Critical Vehicle 3

10 47E-27 (9)(4)

I I Recurrence period 85E+20 11(10) Sample Size 12

12 Probability Critical Vehicle 3 is followed by a 2 axle vehicle 10E-27 (1)(10)

13 Probability Critical Vehicle 3 is followed by Critical Vehicle 4 (12)(4)IOE-36

14 Recurrence period 38E+30 years 11(13) Sample Size 12

15 Probability Critical Vehicle 4 is followed by a 2 axle vehicle 23E-37 (I) (13)

16 Probability Critical Vehicle 4 is followed by Critical Vehicle 5 1lE-45 (15)(4)

17 11(16) Sample Size 12Recurrence period 38E+39 years

3

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C3 ACTUAL PROBABILITY OF COMBINATIONS J2 - 3 AXLE VEHICLES

4

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A-1

APPENDIX A

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nAppendix D

Impact Formula I

bull bull

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APPENDIX 0

Page No

01 MODEL FOR IMPACT EFFECTS ON BRIDGES FROM RR 9100401 amp 02 1

D11 CALCULATION MODEL 1

D 12 BRIDGE IMPACT FACTOR 1

D13 VEHICLE MASS REDUCTION FACTOR 2

D14 VEHICLE SPEED REDUCTION FACTOR 2

D1 5 COEFFICIENT OF VARIATION 2

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01 MODEL FOR IMPACT EFFECTS ON BRIDGES FROM RR 9100401 amp02

011 Calculation Model

Impact causes an increase in the loads which a vehicle applies to a bridge The impact factor applied to

the actual load effects was calculated using the following formula

Where

the final impact factor

the impact factor for the bridge



the coefficient of variation

012 Bridge Impact Factor

Based upon the currently available data the expression proposed by Honda et al (1986) for the

calculation of the bridge impact formula is used However the factor is halved to simulate the response

of concrete bridges under dynamic loads (RR 9100402 1995) At span lengths with natural

frequencies approaching 5Hz and less the reduction factor of 2 will be excluded to allow for dynamic

amplification due to the interaction between the vehicle and the structure

For a simply supported bridge with a span of L

3J =shy

b L

For a continuous bridge with n spans each L Long

J =~ b Lf

01 MODEL FOR IMPACT EFFECTS ON BRIDGES FROM RR 9100401 amp 02




Where













3 J =shy

b L


J =~ b Lf

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013 Vehicle Mass Reduction Factor

A heavier vehicle will have a smaller impact effect than a lighter vehicle A mass reduction factorfm is

therefore used

For a vehicle of mass T tons

1m =O819llOdeg436-00254T +OlSJ ifT gt=16t

lfthe vehicle weight is less than 16t 1m = 100

014 Vehicle speed reduction factor

The faster a vehicle is travelling the higher its impact The following expression was used to relate the

impact factor and the vehicle s speed V (in kmlh)

From this fonnula it can be seen that a speed of 80kmlh will yield a value for Is of 10

015 Coefficient of Variation

Significant scatter exists in the data from research into the response of bridges to impact loading The

coefficient of variation E accounts for this scatter and is approximately 12 of the total dynamic

response

2



therefore used


1m = 0819llOo436-oo254T + 015 J ifT gt= 16t




impact factor and the vehicles speed V (in kmIh)

From this formula it can be seen that a speed of 80kmh will yield a value for Is of 10




response

2

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nAppendix E

Equivalent Vehicle Study

bull

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APPENDIX E

Page No

E1 EQllIVALENT VEHICLE

E11 OCONNORS APPRAISAL OF ONTARIO BASE LENGTH 1

E12 DEVELOPMENT OF ALTERNATIVE DERIVATION OF EQUIVALENT BASE LENGTH 1

E13 SENSITIVITY ANALySiS 3

E14 SIMULATION STUDY 3

E1S ASSIGNMENT OF PARAMETERS TO SOUTH AFRICAN TRUCK SURVEY DATA 4

E2 COMPARISON OF VIRTUAL AND LEGAL TRUCK POPULATIONS 5

E3 ALTERNATIVE SELECTION OF EXTREME EVENTS 5

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E1 EQUIVALENT VEHICLE STUDY

The review of the WIM data recorded during a one month period involved the processing of 106917

vehicles It is expected that a greater nwnber of vehicles may be reviewed in future studies A method

of identifying the vehicles causing the most onerous force effects was therefore investigated From the

literature review the Ontario Equivalent Base Length concept and its further development by OConnor

(1981) was considered the most appropriate method

E11 OConnors Appraisal of Ontario Base Length

OConnor (1981) reviewed the validity of the Ontario Equivalent Base Length as described in Section

243 The review focused on the validity of replacing survey data with a histogram of points in (WBm)

space and the selection of a design vehicle on the basis that its equivalent base length follows the

Maximwn Observed Limit (MOL) curve

In review of the Ontario Equivalent Base Length it was recognised that a unifonnly distributed load

placed about the centre of a span will not necessarily simulate the maximwn force effects caused by a

heavy vehicle In many instances a group of axles at the rear of a vehicle will cause the maximwn load

effects An alternative method to calculating the equivalent base length was therefore reviewed A

third parameter the location parameter was developed to ensure that the load model was correctly

positioned on the span to produce the most onerous load effects

E12 Development of Alternative Derivation of Equivalent Base Length

In defIning the location parameter OConnor (1981) utilises the influence lines associated with simply

supported spans A load group was moved across the span as shown in Figure E1 The load causing

the maximum force effects when positioned at the maximwn ordinate of the influence lines was

identifIed This load was classified as the central load The load group was then divided into two subshy

groups a load group to left of the maximum ordinate and a load group to its right The central load was

then apportioned to the left and right so that both sub-groups swn to half of the total load group

III 2

I ~

Figure El - Simply Support Span Influence Lines and Central Load (Source OConnor C 1981)


The review of the WTh1 data recorded during a one month period involved the processing of 106917

vehicles It is expected that a greater number of vehicles may be reviewed in future studies A method








Maximum Observed Limit (MOL) curve


placed about the centre of a span will not necessarily simulate the maximum force effects caused by a

heavy vehicle In many instances a group of axles at the rear of a vehicle will cause the maximum load






supported spans A load group was moved across the span as shown in Figure El The load causing

the maximum force effects when positioned at the maximum ordinate of the influence lines was



then apportioned to the left and right so that both sub-groups sum to half of the total load group

W~ I i I

WI 2

I I ~

Figure El - Simply Support Span Influence Lines and Central Load (Source OConnor c 1981)

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A single concentrated load was then set to represent the subgroup as shown in Figure E2 This load

was positioned to generate the resultant moment of the individual loads within the sub group about the

maximum ordinate The distance from the load to the maximum ordinate is known as bR and bL

respectively The concentrated base length b is then equal to the sum of bR and bL

EDNCIr t pound~TI17m CJII sr K

Figure E2 -Equivalent Concentrated Load System (Source OConnor c 1981)

A location parameter x was derived to defme the central point of the equivalent system and was

calculated as the lessor of bpfb and bLIb

In the case of the simplified derivation of Bm the derivation of Bm is exactly twice the concentrated

base length However the application of a uniformly distributed load will not necessarily cause the

same force effects This outcome is because the concentrated loads are not located equi-distant from

the central load as quantified by the location parameter In using the concentrated base length the

central load may be located at the centre of the span and the concentrated loads will exactly generate the

moments caused by the axle loads to its left and right How~ver the centring of a uniformly distributed

load on the centre of the span will not necessarily produce the maximum force effects It is for this

reason that OConnor preferred the use of an equivalent concentrated load as shown in Figure E3

Figure E3 - Equivalent Concentrated Load (Source OConnor c 1981)

2

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E13 Sensitivity AnllnJltIlt

OConnor identified that trucks of varying axle combinations may have similar total loads and

concentrated base lengths A sensitivity analysis was therefore undertaken comparing the force effects

of five vehicles with THgt axle configurations but with the same Wand b values The calculated

maximum moments for simply supported spans in excess of 10m showed exact correlation

in the shorter spans the moments caused by the five trucks

In the case of continuous spans differences in the moments produced were present on the spans

It was found that the trucks with the closest location parameters produced the best correlation of

moments

The sensitivity dUV was then taken a further to compare a of three trucks axle

configuration but with identical b and x values Once more the central bending moments in a

simply mrrtpl1 span were consistent for in the case of short spans This result was to be

eXI)eclted because in the case of short spans it is a axle or group of axles that will produce the

greatest b(ndmg moment In the case of continuous spans the results showed convergence on

the longer spans However substantial differences in the shear force at the end of a continuous girder

were observed OConnor stated the following conclusions from the studies described herein

(i) No equivalent vehicle is for all cases

(ii) Vehicles with identical base length can different

(iii) It is difficult to judge if the differences shown to exist between hypothetical vehicles are

similar in magnitude to those that exist in practical vehicles and

(iv) There is some prospect -ampLlll5 a satisfactory equivalent vehicle

E14 Simulation Study

To follow on from the conclusions reached in his preliminary studies OConnor undertook a simulation

of the entire Ontario process In the place of survey data a population of vehicles was created with axle

weights and axle vcJ lying at the Australian legal limits

From the Wlb charts the critical Wand b parameters were extracted and three equivalent vehicles were

then gellerated In terms the shortest value of b with a Wequal to the maximum load was

chosen These vehicles were then used to generate a maximum emrel(me of the five load effect

functions These envelopes were then Vj~a~- those of the parent population

3

E13

OConnor identified that trucks of r - axle combinations may have similar total loads and

concentrated base A ~PTIV was therefore undertaken the force effects

uratlOllS but with the same Wand b values The calculated of five vehicles with ltHgt

maximum moments for -tmiddotrl spans in excess of showed exact correlation

in the shorter spans the moments caused the five trucks

In the case of continuous spans differences in the moments pn)OllCea were present on the spans

It was found that the trucks with the closest location the best correlation of

moments

The was then taken a further to compare a of three trucks axle

but with identical b and x values Once more the central moments in a

1m(rri1 span were consistent for in the case of short spans This result was to be

eXj)ecltea because in the case of short spans it is a axle or group of axles that will the

gn~atlaquo~st belld1ng moment In the case of continuous spans the results showed convergence on

the spans substantial differences in the shear force at the end of a continuous

were observed OConnor stated the conclusions from the studies described herein

No vehicle is for all cases

Vehicles with identical base can different

It is difficult to if the differences shown to exist between llYlJUWtll vehicles are

similar in magrultucie to those that exist in and

There is some prospect vehicle

E14 Simulation

To follow on from the conclusions reached in his nuu OConnor undertook a sinlUlation

of the entire Ontario process_ In the of vehicles was created with axle

and axle at the Australian limits

From the Wlb charts the critical Wand b parameters were extracted and three vehicles were

then In terms the shortest value of b with a W to the maximum load was

chosen These vehicles were then used to generate a maximum of the five load effect

functions_ These were then those of the parent

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The study concluded that the description of a vehicle by the proposed three parameters does not exactly

simulate its effects on single or continuous spans However in creating a design vehicle the aim is to

simulate the maximum force effects caused by a population of vehicles It was considered that the

method developed by OConnor provides a means of identifying trucks with characteristics likely to

produce the most onerous force effects Those parameters being

(i) Maximum W

(ii) Shortest b

(iii) Centred x =05

The outcome of the study was that it may be possible to use a single non-variable design vehicle with

sufficient accuracy this has subsequently happened in both the LFRD and the CSA-S06-00

E15 Assignment of Parameters to South African Truck Survey Data

In creating a credible population of possible axle configurations OConnor considered the subsets of

adjacent loads within the 191 trucks created from the specified set of axle configurations In all 4500

varying axle configurations were created The aim of this study was to review the parameters

associated with the axle configurations of the 106917 actual vehicles recorded in the WIM data Given

that there are no legal constraints on axle spacing in South Africa (other than the bridge formula) it is

considered that this is a valid population set when considering the derivation of an equivalent vehicle

The legal vehicle population set developed in Chapter 3 was used for the purpose of the study The

mass of the vehicles axle sets and individual axles was therefore compliant with the South African legal

limits

A virtual population of South African vehicles was also created following 0 Connors (1981)

guidelines using the possible permutations of axle configurations In assigning the axle masses the

South African maximum permissible axle masses were substituted The aim of this exercise was to

measure the variances associated with the use of a virtual population against a population of recorded

legal vehicles

The methodology developed by OConnor was replicated in assigning the parameters W b and x to each

vehicle In addition the bending moments and shears caused by the vehicle on a range of simply

supported spans were calculated The parameters associated with the most onerous bending moments

and shears were then reviewed for the purpose of deriving a South African Equivalent Vehicle

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E2 COMPARISON OF VIRTUAL AND LEGAL TRUCK POPULATIONS

In UlHlllJ the load effects the vehicles were grouped in tenns of their total number of axles This

grouping was done to compare the properties of the different vehicle classes

The maximum bending moments generated from the virtual and legal truck populations for spans from

Sm to 30m are shown in Table E 1 A close correlation between the bending moments derived from

both methods is observed Table E2 shows the same correlation in the calculated shear forces

5 197 189 4

10 547 562 3 15 1054 1054 0 20 1582 1626 3)

7

Table El Bending Moments Comparison 0 Connors Vehicle versus Vehicles

0 Connor Difference

5 184 173 -6

10 252 258 3 15 308 304 -1 20 347 346 0

Table E2 - Shear Force Comparison 0 Connors Vehicle versus Vehicles

The close omprulson was eXjlected as the axle weights of both populations were identicaL

the results indicate that the creation of a virtual population of vehicles adequately replicate the load

effects of actual vehicles These validate the use of virtual vehicles in Monte Carlo

simulations

E3 ALTERNATIVE SELECTION OF EXTREME EVENTS

An altemative method of selecting the extreme set of vehicles was investigated Using the 1IT1iPtprlt

developed OConnor the vehicles with the WIb ratios in each class were identified A

population set of 84 vehicles (28 from the 6 7 amp 8 vehicles the extreme events

over the period of the month was then created

The statistical nrrnprl1 of the extreme events were used to v~np a 1 in 120 year event the

Gumbel distribution A comparison of the load effects from the WIb population with those of the legal

population ~ecuon 3) is shown in Table E3 amp E4

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Bending Moments kNm

WIb Legal Difference SEan (m Extreme Vehicles Wlb Legal

5 293 301 -3 10 800 812 -1 15 1262 1364 -7 20 1903 2097 -9 30 3526 3631 -3

Table E3 Bending Moment Comparison Wlb Vehicles versus Legal Vehicles

Shear Forces kN) WIb Legal Difference

SEan m Extreme Vehicles WIb Legal 5 313 297 5 10 337 320 5 15 369 369 0 20 438 433 1 30 522 542 -4

Table E4 Shear Force Comparison Wlb Vehicles versus Legal Vehicles

The results for both bending moments and shear forces show good correlation this effectively validates

the use of W and b parameters to identify the critical vehicles The parameters therefore provide a

means of sorting Wllv[ data to reduce the number of results that require processing

6

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nAppendix F

Visual Basic Programs Appen

Visual Bas

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Typical VB Program written to calculate the maximum bending moments caused by survey vehicles on varying simply supported spans

Sub centralloadO

ApplicationCalculation = xlCalculationManual

Dim moment_array(2000 2000) As Double Dim shear_array(3000 3000) As Single Dim difCarray( 100) As Single Dim mom_array(35000 5) As Single Dim Rmax_array(35000) As Single Dim cum(II) As Single Dim span(5) As Integer

Start = Range(b2) Value Finish = Range(b3)Value

assigns variable inc= I span(l) = 5 span(2) = 10 span(3) = 15 span(4) = 20 span(5) 30

loop for spans For s = I To 5

For y = Start To Finish

axlel = Range(s amp y)Value axle2 = Range(t amp y) Value axle3 = Range(u amp y)Value axle4 = Range(v amp y)Value axle5 = Range(w amp y)Value axle6 = Range(x amp y)Value axle7 = Range(y amp y) Value axle8 = Range(z amp y)Value axle9 = Range(aa amp y) Value axleiO = Range(ab amp y)Value axiell = Range(ac amp y)Yalue

spac2 Range(af amp y)Value spac3 = Range(ag amp y)Value spac4 = Range(ah amp y)VaIue spac5 = Range(ai amp y)Value spac6 = Range(aj amp y)Value spac7 = Range(ak amp y)Value spac8 Range(al amp y)Value spac9 = Range(am amp y)Value spaciO = Range(an amp y)Value spac II Range(ao amp y)Value

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cum( I ) = spac2 cum(2) = cum I) + spac3 cum(3) cum(2) + cum(4) == cum(3) + cum(S) cum(4) + spac6 cum(6) == cum(S) + spac7 cum(7) == cum(6) + cum(S) = cum(7) + spac9 cum(9) = cum(S) + spac1 0 cum( I 0) cum(9) + spac 11

+ + + + spac6 + spac7 + + spac9 + spac I 0

n= Do While inc n lt span(s) + Length

pos = inc n

defines relative positions pos = pos If - cum(l) lt= 0 Or cum(l) 0 Then = 0 Else pos2 = posl cum(l)

lt= 0 Or cum(2) cum(1) Then = 0 Else posI - cum(2) Ifposl cum(3) lt= 0 Or cum(3) cum(2) Then pos4 0 Else == pos - cum(3) Ifposl - cum(4) lt= 0 Or cum(4) = cum(3) Then 0 Else =posl cum(4) Ifposl- lt=OOrcum(S) cum(4) Then pos6 =0 Else -cum(S) IfposI - cum(6) lt= 0 Or cum(6) = cum(S) Then pos7 0 Ese = posl - cum(6) If pos I cum(7) lt= 0 Or cum(7) cum(6) Then posS == 0 Else posS posl - cum(7) Ifposl - cum(S) lt= 0 Or cum(S) = cum(7) Then 0 Else pos9 = pos - cum(S) Ifpos cum(9) lt= 0 Or cum(9) cum(S) Then poslO 0 Else - cum(9) If pos I cum( I 0) lt= 0 Or cum(l 0) = cum(9) Then pos II = 0 Else pos II cum( 10)

assigns axle weight 0 ifnot on the beam Ifposl gt= span(s) Then axlel 0 Else axle Range(s amp y)Value

oOr gt= span(s) Then axle2 0 Else axle2 = Range(lft amp y)Value Ifpos3 = 0 Or pos3 gt= span(s) Then axle3 = 0 Else axle3 = amp y)Value If pos4 0 Or pos4 gt= span(s) Thenaxle4 =0 Else axle4 = Range(v amp y)Value If = 0 Or posS gt= span(s) Then axleS = 0 Else axleS = amp y)Value If pos6 = 0 Or pos6 gt= Then axle6 = 0 Else axle6 = Range(x amp y)Value Ifpos7 = 0 Or pos7 gt= span(s) Then axle7 = 0 Else axle7 = amp y)Value Ifpos8 = 0 Or posS gt= span(s) Then axleS = 0 Else axleS Range(z amp y)Value Ifpos9 0 Or pos9 gt= span(s) Then axle9 0 Else axle9 = Range(aa amp y)Value IfposlO 0 Or poslO gt= span(s) Then axlelO == 0 Else axlelO= Range(ab amp If I = 0 Or posll gt= span(s) Then axlell = 0 Else axlell amp y)Value

Wtotal axlel + axle2 + axle3 + axle4 + axleS + axle6 + axle7 + axle8 + axle9 + axlel 0 + axlell

calculate support reactions take moments about LHS MI == axlel posl M2 == axle2 M3 == axle3 M4 axle4 pos4 MS == axleS M6 axle6 M7 = axle7 pos7 MS axleS

+

n=l Do While inc n lt +

pos = inc n

defines relative VJH~ posl pos If 1) lt= 0 Or

lt=OOr lt=OOr lt=oOr lt=oOr lt=OOr lt=OOr lt=oOr lt=0 Or

10) lt= 0 Or

+ + +

o Then = 0 Else ) Then

Then Then Then

o ifnot on the beam Then axlel 0 Else axlel

Then axle2 0 Else axle2 = Then axle3 = 0 Else axle3 = Thenaxle4 0 Else axle4 = Then axle5 = 0 Else axle5 Then axle6 = 0 Else axle6 =

Then axle7 = 0 Else axle7 = Then axle8 0 Else axle8 Then axle9 0 Else axle9

Then axle 10 = 0 Else axle I 0 = Then axlell == 0 Else axlell

+ + spaclO

Wtotal axlel + axle2 + axle3 + axle4 + axle5 + axle6 + axle7 + axle8 + axle9 + axlel 0 + axlell

calculate support reactions take moments about LHS MI axlel posl M2 axle2 M3 = axle3 M4 axle4 M5 axle5 M6 axle6 M7 = axle7 M8 axle8

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M9 = axle9 pos9 MIO = axlelO poslO Mil = axlell posll

Mtotal = MI + M2 + M3 + M4 + M5 + M6 + M7 + M8 + M9 + MIO + Mil

R2 = Mtotal span(s) RI = Wtotal - R2

calculate moments along length of the beam x = I Do While x lt span(s) MRI = x RI Ifx gt posl Then MAl = (posl - x) axle I Else MAl = 0 Ifxgt pos2 Then MA2 = (pos2 - x) axle2 Else MA2 = 0 If x gt pos3 Then MA3 = (pos3 - x) axle3 Else MA3 = 0 Ifx gt pos4 Then MA4 = (pos4 - x) axle4 Else MA4 = 0 Ifx gt pos5 Then MA5 = (pos5 - x) axle5 Else MA5 = 0 If x gt pos6 Then MA6 = (pos6 - x) axle6 Else MA6 =0 If x gt pos7 Then MA 7 = (pos7 - x) axle7 Else MA 7 = 0 If x gt pos8 Then MA8 =(pos8 - x) axle8 Else MA8 =0 If x gt pos9 Then MA9 = (pos9 - x) axle9 Else MA9 = 0 Ifxgt poslO Then MAIO = (poslO - x) axlelO Else MAIO = 0 Ifx gt posll Then MAll = (posll - x) axlell Else MAl I = 0

m = MR I + MA I + MA2 + MA3 + MA4 + MA5 + MA6 + MA7 + MA8 + MA9 + MA10 + MA II moment_array(x n) = m IfR2 gt Rl Then R = R2 Else R= RI shear_array(x n) = R x=x+1 Loop

n=n+1 Loop

finds position of max moment maxrow = 0 maxcol = 0

For z = 0 To n For i = I To x If moment_array(i z) gt moment_array(maxrow maxcol) Then maxrow = i Ifmoment_array(i z) gt moment_array(maxrow maxcol) Then maxcol = z Next i

Next z

Range(aq amp y) Value = moment_array(maxrow maxcol) mom_array(y s) = moment_array(maxrow maxcol)

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finds position of max shear Rmaxrow= 0 Rmaxcol = 0

Forz = 0 To n For i = I To x Ifshear_array(i z) gt shear_array(Rmaxrow Rmaxcol) Then Rmaxrow= i If shear_array(i z) gt shear_array(Rmaxrow Rmaxcol) Then Rmaxcol = z Next i

Next z Range(OOar OO amp y)Value = shear_array(Rmaxrow Rmaxcol) Rmax _ array(y) = shear_array(Rmaxrow Rmaxcol)

Nexty

sort moment array max value to top max mom = Start For i = Start To Finish Ifmom_array(i s) gt mom_array(maxmom s) Then maxmom = i Next i Range(OOat OO amp s + Start - 1) = mom_array(maxmom s) Range(OOav OO amp s + Start - I) Value = maxmom

sorts vehicle moments For i = Start To Finish - I

Max=i For j = i + I To Finish

Ifmom_array(j s) gt mom_array(Max s) Then Max=j

End If Nextj temp = mom_array(i s) mom_array(i s) = mom_array(Max s) mom_array(Max s) = temp

Range(OObd OO amp i)Value = l1om_array(i I) Range(OObe amp i)Value = mom_array(i 2) Range(OObf amp i)Value = mom_array(i 3) Range(OObg amp i) Value = mom_array(i 4) Range(bh amp i)Value = mom_array(i 5) Next i

sort shear array max value to top maxshear = Start For i = Start To Finish If Rmax_array(i) gt Rmax_array(maxshear) Then maxshear = i Next i Range(au OO amp s + Start - I) = Rmax_array(maxshear)

Next s

ApplicationCalculation = xlCalculationAutomatic

End Sub


Forz = 0 To n For i = I To x If shear_array(i z) gt shear_array(Rmaxrow Rmaxcol) Then Rmaxrow = i If shear_array(i z) gt shear_array(Rmaxrow Rmaxcol) Then Rmaxcol = z Next i

Next z Range(ar amp y) Value = shear_array(Rmaxrow Rmaxcol) Rmax _ array(y) = shear _ array(Rmaxrow Rmaxcol)

Nexty

sort moment array max value to top max mom = Start For i = Start To Finish Ifmom_array(i s) gt mom_array(maxmom s) Then maxmom = i Next i Range(at amp s + Start - I) = mom_array(maxmom s) Range(av amp s + Start - I) Value = maxmom



If mom_array(j s) gt mom_array(Max s) Then Max =j


Range(bd amp i)Value = mom_array(i I) Range(be amp i)Value = mom_array(i 2) Range(bf amp i)Value = mom_array(i 3) Range(bg amp i) Value = mom_array(i 4) Range(bh amp i) Value = mom_array(i 5) Next i

sort shear array max value to top maxshear = Start For i = Start To Finish If Rmax_array(i) gt Rmax_array(maxshear) Then maxshear = i Next i Range(au amp s + Start - I) = Rmax_array(maxshear)

Next s


End Sub

The copyright of this thesis vests in the author No quotation from it or information derived from it is to be published without full acknowledgement of the source The thesis is to be used for private study or non-commercial research purposes only

Published by the University of Cape Town (UCT) in terms of the non-exclusive license granted to UCT by the author

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ABSTRACT





















(ii)

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DECLARATION




John R B Anderson

(iii)

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ACKNOWLEDGMENT





(iv)

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TABLE CONTENTS

No

1 INTRODUCTION

11 BACKGROUND 1-1

12 OF THE STUDy 1-2

1-3 13 SCOPE OF THE

14 METHODOLOGy 1-4






21 INTRODUCTION 2-1





25 CONCLUSIONS 2-15


31 INTRODUCTION 3-1







35 RESULTS 3-23

36 OVERLOADING 3-27

37 CONCLUSiONS 3-31

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41 TMH7 PART 2 4-1








45 CONCLUSIONS 4-23



52 RESULTS 5-3








(vi)


41 TMH7 PART 2 4-1








45 CONCLUSiONS 4-23



52 RESULTS 5-3








(vi)

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List of































(vii)

List of




24 - of H20 LRFD 1 2-7


26 CL-W Truck 2-10

2-10 27 - CL-W


31 -

32 -

33 -

34 -


of GVMs 3-8


Function of

Function of

Moments 30m span

Moments 5m span

3-9

3-9











41 -

42 -

44


Distributed Lane

Moments Due to

of Class 14 Vehicle


and 4-7

4-14


46 -

47 -

51 -

52 -

of Moments 4-19

gtr of Forces


4-20

5-2


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(viii)

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List of Tables































(ix)

List of Tables


























Table 41 - 4-6





(ix)

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(x)

Table 46

Table 47-






Table 411 -

Table 412 Shear

Table 51 -


Table 53-

Table 54-


WIM data v RR 4-22






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1 INTRODUCTION

11 BACKGROUND
















Regulations


June 1994














(1-1 )

1

11




with the aim of

the most onerous











the Road

commissioned the

to increase the

to consider the



(i)

The main

the


June 994



Vehicle Loads on

Vehicle Loads on












(1-1 )

Univers

ity of

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n






























(1-2)

12






vehicles






with

Ullman





and adds to the








WIM are






(1

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ity of

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RR 91100410 I amp 02




data
















considered

(1-3)



RR 9110040 I amp 02




data
















considered

(1-3)

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14 METHODOLOGY




identified were












approaches














(1-4)

14 METHODOLOGY


142



identified were

TMH7 Part 2 The




and



( I Code These



loads on

close






















(1

Univers

ity of

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(1-5)






Statistical

vehicles



vehicles on the N3





vehicle

load effects

and fits the

within a 120 year










both methods is



of an extreme











(1

Univers

ity of

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(c) Overloading















(1-6)

Critical Assessment




The extent of

vehicle set


vehicle set This

those

between the WIM

event of the actual














(1

Univers

ity of

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n

1~ REPORT STRUCTURE













reviewed in detail



















(1

1~ REPORT STRUCTURE




live

extent of

with the










reviewed in detail



In and the















in TMH7

the

load model are



of the WlM data

(1

Univers

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21 INTRODUCTION






these loads

















on bridges






and

21 INTRODUCTION








these loads


lIllUlLla on the









BS5400 1978

British Standards




Factor ( I

Code and


on






and

m


Univers

ity of

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the TMH7 Part 2


























(2-2)



to process and







live load models in

the TMH7 Part 2











- u- sensors









vehicles The


by the vehjcle axle

to the extreme

Allowances for









are shown in 21

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305 366 244 305 244 305 244 m


80 219 100 100 100 100 100 100 kN Axle loads (kN)

Ca)

7 x 305 IT = 213 m 0 ~----- -------__--- ___---

~[I ~[JJ 1 I 1 I 1 I] 70 B 96 896 896 896 8 96 896


(bJ























(2-3)

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241 BD 3788











24


























APPROACH




241 BD 3788









spans





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W= 260 kNfm


J

BS 5400 Part 2





















(2-5)

10 in the

for loaded







lt11 C l 0

150

E 100 lii CL

s



W= 260 kNfm

BS 153 Part SA

BS 5400 Part 2
















axle loads An


of 146 was

~nrn)~h used was


and lateral

factor of 18 was

to

were included





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(2-6)
















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242 AASHTO lRFD
























35 000 N 145 000 N 145000 N



Design Lane 3600 mm


(2-7)

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z [F(M)] (21)

Where

M Moment















from the

in 1975


data base For

calculated The



on normal






z

Where

M Moment

CDF of the moment M










Univers

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5~---------+--------~~~~----~ II NGntbs

I ~

j O~--------~~~-------------+------~

~------+ri~----------------+------~

~~--~~------~-------------+------~

Jr---~--------~-------------+------~

~~------------~------------~------~ o








243 CANADIAN CODE









(2-9)

Univers

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~ -i 1 3igtm

112ml


Imiddot 18 m

~ ~P) =~-----ffi--tB------ -~---- ----8t------shy

t J-----ffi-----ffi-ffi------ --ffi---- -----~------


ClaHance Errvelope

300 m





So6m 6ampm

180 m

66m






(2-10)

Univers

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IIgt

IIIQ

to

ro

to

IQ

~

0








bull bull ~ ~- _- _~ n N 0)





~~Jtli ~ -~ Rf



L~ M I ii 11011

H ~~ II 11

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t7 ~ zo ~ n ~i -ii41 1 II



I IJN ~ ~ 4 1 ) bull ~ 1 r-




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to measured












BD 3788

244 EUROPEAN CODE





bridge












2)








to measured









the Ontario

effects caused

Base





BD 3788


244 EUROPEAN CODE




is ENV 199





The

traffic












Univers

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Location

Axle loads Qik

(kN) qik

(kNm2 )



o

Q

~~H-050 200

-iti--Hl-fosomiddot


-iH----H1-gtI-O50

1m2


050 120

2 00

For IV 300 m








(2-13)

Univers

ity of

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of the total loads

(i) Free flowing

















(2-14 )






involved the of the

In the case of axle

double and

values were









of the total loads


(i) Free













methods in

relevance is

This

nnmrn of the ENV





Univers

ity of

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25 CONCLUSIONS





















TMH7 Part 2




load model









(2-15)

25







W1dertaken

live







methods that

models an












TMH7 Part 2




load model









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31 INTRODUCTION










9100401 amp 02



















(3-1 )

31 INTRODUCTION

32








vehicles on

deterministic

9100401 amp 02






WIM were set















Univers

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321 Actual Vehicles













Table 31


Vehicles Vehicles

No of Recorded

Vehicles 24901 34951 2587 62079


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F





In the


5 to 15 20 30 6 Axle Veh Mean 1040 2801 4734 7507 14319



Std Dev 345 915 1701 2794 5865


5 to 15 20 30 6 Axle Veh Mean 952 1224 1500 1782 2115



Std Dev 324 418 546 654 815


322 Legal Vehicles
















overestimated

it was

(3-3)

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standard deviation


5 10 15 20 30





5 10 15 20 30








regulations










(3-4)

Univers

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18000

(3-5)



Univers

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Accuracy of Data
























(COST 323 1997)



actual vehicle

(3-6)

33 APPROACH

of Data


















may be 25 more or


individual results






323 1



actual vehicle


the road vehicles



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940 1300 1500 1460 1180 1200 122 0 383Max 442 519 507 470 489 47 5 48 2 196Mean 100 207 208 216 207 213 207 870Std Dev


272 1267 1062 1535 1339 1190 831 8820 1476 2026 1734 1464 1522 1083 679 4725 1776 2242 1948 1260 1247 899 485 5430 2051 2146 1654 1128 1119 805 422 4835

40 3662 1796 1360 1119 1068 824 464 63 5976 1722 1342 1183 1061 943 535 4945 6436 1769 1304 1301 1233 1135 633 7350 4961 1775 1454 1476 1489 1375 864 7255 2460 2291 1850 1803 1788 1672 1195 6760 794 2747 2328 2117 2026 1805 1200 4565 144 3033 2590 2039 2046 1658 1080 3670 24 2694 2107 1528 1571 1218 705 1375

80 4 1976 1376 928 933 716 388 9 85 2 1019 719 394 423 275 151 4 90 0 487 __- 305 164 _ 170 __ 127- 51 _-- 1 ___ _ - _ _-_ _shy

95 I 213 112 58 47 47 18 0 100 0 80 43 31 23 19 6 0 105 0 43 14 8 5 5 3 0

0 17 8 4 2 2 2 0110 0 II 9 2 0 3 0 0115

120 0 3 3 0 2 2 0 0 125 0 6 1 I 0 0 I 0

More 0 2 1 I 0 0 0 0 30039 30039 24065 21383 20070 17360 10437 774Sum


(3-7)

Univers

ity of

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2500 12000

c 0c10000 ltI2000 C I ~

8000 c ~

1500 IltI

~H-I-t++-f-++-+ 000

-=e

~C qj 6000 iI a Q~ 1000

qj~ 4000 ~ ~ ~

500 20 00 I

U

o

Bin







(3-8)

Univers

ity of

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00030 -----------r-------------------r--------

o 00025 JI ~ 00020 i-----I~--_I_---t_-~--+---+-----f----I lIi i~ 00015 ~

] 00010 to

ampJ o ~ 00005 +----+----+----~-------_IIoc__

00000 +----+----+----j----i----+----+---

o 100 200 300 400 500 600 700

Weight(kN)


001200

sa 001000 v

~ 000800pound

000600 ~ 15 000400 ~ to ~ 0

000200 ~

000000

0 50 100 150 200 250



000080

000070

ll 0

000060 ~ 000050 ~

fshy 000040 S ~ l- 000030 g ampJ

000020

0

D

p 000010

000000

i-~-I- ---- __ ~

o 500 1000 1500 2000 2500 3000



(3-9)

Univers

ity of

Cap

e Tow

n


















events and







respectively




periods (Dawe 2003)

0)
















ENV 1991-3 et 200

The

the

(i)




events and

In the case of

of the extreme










Univers

ity of

Cap

e Tow

n






and for each class






lIN



(31)

2515517 + 080853w+ 0010328w2

z=w- 2 (32)1+ 1432788w+ 01 89269w + 0001

Where






=x+Krs (33)

Where

Xr Event at time T

x Mean of events

Kr rPllHPU factor

1)

Univers

ity of

Cap

e Tow

n









therefore similar


5 285 290 278 290 10 762 739 743 762 15 1266 1365 1372 1372 20 2069 2262 2242 2262 30 4740 4638 4740



5 263 261 258 263 10 323 343 339 343 15 417 439 436 439 20 495 522 537

653 675



6 Axle 533 281 91 -021 7 Axle 653 367 118 -073 8 584 122 -056










(3-12)

Univers

ity of

Cap

e Tow

n












m 04P(Xgtx ) =--- (34)

n+

Where











with B

Where


342 Extreme












Cunnanes formula

gt

Where











with B

Where

T Return where T 1

Univers

ity of

Cap

e Tow

n

--

- - -_--_- _ shy3000

2800+------I----+----+----~--~---~f- shy

S ~ 2600+----~---r_----~----~~~--4----~

ir j 2400+----+---1-------1~~---~---r---~ ~ ~~ ~b

~ 2200 +---~---~~~--1---~---+-------1

jJl

2000+---~~--1-----I---~---r---~

1800 -------1f----+-----t-- Plot Area Ir------+-----I


--6 Axle

----- - -------- - - ------- __- -----shy3200

3000

e ~ 2800 i S 2600 ~ ~I Vsect 2400 ai

jJl 2200

2000 o 2 4 6 8 10 12

Reduced V ruiate

-+-7 Axle

3000

I 2800

2600 ~

I~ 2400 I

I2200

Chart Area

2000

o 2 4 6 8

Reduced Vuiate

1-+-8 Axle I


(3-14 )

12

10

Univers

ity of

Cap

e Tow

n-- __ ___shy480

460

440

~ 420

400 ~

380ie (I)

u 360

340

320

300

380

360

340

~ 320 300 ~

280lt Vol

260

240

220

J -~

V ~

~ v

_ _

j~

~

- V

o 2 4 6 8 10

Reduced Variate

--6 Axle

o 2 4 6 8 10

Reduced Variate

--+-7 Axle

440

420

400

~ 380 i 360 ~

ie 340 -= ~ 320

300

280

V

1

Ir

~

V

o 2 4 6 8

Re(luced Variate

-+- 8 Axle


(3-15)

12

i

12

10

Univers

ity of

Cap

e Tow

n













No of Reduced Event

5m Spans

10m Spans

15m Spans

20m Spans

30m

22 28 42

22 28 42

22 28 42

22 28 42

22 28

2024 2000 1961

5448 5379 5254

8937 8835 8659

13728 13572 13313

25468

25224

99 99 98

267 271 285

376 387 405

583 597 611

969

979

31680 40320 60480

31680 40320 60480

31680 40320 60480

31680 40320 60480

31680

40320

751 727 687

751 727 687

751 727 687

751 727 687

751

727

763 782 813

763 782

813

763 782 813

763 782 813

763

782

278 277 276

749

750 757

1181 1186 1195

1818 1824 1828

3285

3288






(3-16)

Univers

ity of

Cap

e Tow

n

5 301 238 -21 10 812 631 -22 15 1364 1129 -17 20 2097 1756 -16 30 3631 3380 -7
















(3-17)

Univers

ity of

Cap

e Tow

n

1500 -------------------------------------------

1400 - S ~ 1300 -

~ 1200 S o ~ 1100 OJ)

=g 1000 ClJ

=l 900

800 +-----~----~----_r----~----~------~--~

-100 100 300 500 700 900 1100 1300

Reduced Variate


390

370

- 350 ~ - ClJ ~ 330 0 ~

~ 310 ClJ

c rJ)

290

270

250

Reduced Variate

-100 100 300 500 700 900 1100 1300




(3-18)

Univers

ity of

Cap

e Tow

n

1450 -----------~--------------------------_

1350

1250

1150

1050

950

-


Q rJ1

850 +-----~----~----~----~----~----~----~

-100 100 300 500 700 900 1100 1300

Reduced Variate


-Nonnal Gwnbel

360

350

340

330

320

310

300

290

280

270

260

-100 100 300 500 700 900

Reduced Variate

1100 1300


Nonnal Gwnbel


(3-19)

Univers

ity of

Cap

e Tow

n

1200

1150 --

3 1100

~ - 1050 ~

3 = 1000 0

~ 950 OJ)

0 = 900 ~ = ~ 850

800

750

-l00 l00 300 500 700 1100 l300

Reduced Variate

900


--Nonnal Gwnbel

370

350

-Z ~ - ~ (j 0 ~

11 ~ -= 00

330

310

290

270

250

230

-100 100 300 500

Reduced Variate

700 900 1100


-- Nonnal Gumbel


(3-20)

Univers

ity of

Cap

e Tow

n
































+





effective

years 40320











number of the

between the 28











the human and

the most




Univers

ity of

Cap

e Tow

n






a (37)





n

X Gumbel s = 1 1+11 + 11000Kn] 2 S (39)e

n







(3-22)

Univers

ity of

Cap

e Tow

n

---

4150

3950

3750

e 3550 ~ - 3350 = ~ e 3150 Q

~ 2950

2750

2550

2350

-100 100 300 500 700 900 1100 1300

Reduced Variate




35 RESULTS






91 00401 amp 02



5 276 301 231 301 10 757 812 624 812 15 1195 1364 1135 1364 20 1828 2097 1780 2097 30 3275 3631 3289 3631




5 297 233 201 297 10 320 314 279 320 15 369 350 349 369 20 431 433 392 433 30 489 542 481 542


(3-23)

Univers

ity of

Cap

e Tow

n




and







the vehicles axle


Mean 467 529 518 423 429 441 2806 6 Axle

Std Dev 68 196 199 199 188 189 913Vehicles 006 -014 -009 012 001 -021

Mean 488 557 555 529 545 501 490 3665 7 Axle

Std Dev 67 201 191 215 224 205 1176Vehicles 16 -059

Mean 470 504 526 455 456 446 391 384 3632 8 Axle







events


5 98 147 117 10 104 141 119 15 93 128 124 20 92 128 119 30 95


(3-24)

Univers

ity of

Cap

e Tow

n



5 151 130 104 10 120 1l0 127 15 103 88 133 20 103 95 116 30 103 113









NowakGumbel

5 290 301 -4 10 762 S12 -6 15 1372 1364 1 20 2262 2097 S 30 4740 3631


Shear Forces


NowakGumbel

5 263 297 -11 10 343 320 7 15 439 369 19 20 537 433 24

542







Univers

ity of

Cap

e Tow

n


5m 10m 15m 20m 30m


276 292 (+59)

301 (+89)

757 804 828

1195 1262 1297

(+56)

1829 1930 1982

3275 3436 3519

(+49)

(+74)


Univers

ity of

Cap

e Tow

n

36 OVERLOADING
















12

~ 08 D lte

D 0 shy 06p v ~

-a 04

8 02

o 100 200 300 400 500 600 700 800 900

Weight (lN)



(3-27)

Univers

ity of

Cap

e Tow

n











representative


6 Axle 00 19 20 21 12 25 7 Axle 03 77 69 09 09 56 37 8 Axle 83 280 310 13 09 44 67 70

444











was retained










(3-28)

Univers

ity of

Cap

e Tow

n













5 -2 -6 3 5 -1 7 10 6 -13 14 -9 -4 6 15 -11 -11 11 1 -6 5 20 -4 -7 6 5 -3 8

30 -4 -1 3 5 2 21













5 197 195 196 216 220 181 10 13 -8 10 510 547 520 582 600 486 14 10 -7

15 968 1054 986 946 1034 875 -2 -2 -11 20 1504 1582 1537 1452 1599 1388 -3 1 -10

30 2767 2917 2899 2676 2944 2697 -3 1 -7


(3-29)

Univers

ity of

Cap

e Tow

n



5 182 183 184 210 197 164 15 8 -11 10 246 251 252 249 250 220 1 0 -13 15 295 308 302 298 293 272 1 -5 -10 20 337 347 337 349 358 316 4 3 -6 30 411 440












Univers

ity of

Cap

e Tow

n

37 CONCLUSIONS










set of events

























(3-31)

37 CONCLUSIONS










set of events

























(3-31)

Univers

ity of

Cap

e Tow

n






June 1994









examined

41 TMH7 PART 2








to traffic










(4-1 )

2 amp i) UD i)J ol

The

Part 2





June 1994

Vehicle Loads on



Vehicle Loads on







examined

41 TMH7 PART 2

411 and OAfAIIID







to traffic






favoured this




Univers

ity of

Cap

e Tow

nL









fonnula (1970)


Where

Impact factor





















(4-2)









fonnula (1970)

cent = 5(100 + L) 10+L

Where

Impact factor






















(4-2)

Univers

ity of

Cap

e Tow

n












the WIM sensors

















group






(4-3)



The

412 NA

The




Curves

curve for

UH1lUH of the no-m






the WIM sensors

As

and








The



earlier work






20

group







Univers

ity of

Cap

e Tow

n


















40

-

sect ~ - C ~ 0

l C ~ I

Q

C 0is

5

0

10 100 1000

Loaded length (m)

~------------------------~~------------------------~

1-30

25

20 1-15

-- ------



(4-4)

Univers

ity of

Cap

e Tow

n

---

___bull___ __ _- --- ---___bull _bull40

35

---E 30 -+ --+-shy

Z ~ - 25 ~ CI 0

l 20 ~ ltII c = 15 i 10Q

+5

0

10 100 1000

Loaded length (m)
























(4-5)

Univers

ity of

Cap

e Tow

n















2-Axle 216 204 195 190 183 186 184 196

3-Axle 97 106 94 86 82 82 82 165


8-Axle 23 25 25 24 23 25 45 41 9-Axle 01 01 00 01 01 01 02 31

Total 100 100 100 100 100 100 100 100


















(4-6)

Univers

ity of

Cap

e Tow

n
















1600

1400

1200 middot 8 ~

1000 agt-= 8 0 800

~ = 600a =agt

co 400

200

0 4 6 8 10 12 14 16 18

Span m




5 35 10 28 15 23 20 20 30 16


(4-7)

Univers

ity of

Cap

e Tow

n





relevant















416 NB Loading









(4-8)


Given

Ipvntv of TMH7 Part


this

2 the

The

(1

of the

relevant


effects of vehicles



the



and research



415 Lateral






A lateral

at40m

factor of 14 was





416 NB

in the

The









Univers

ity of

Cap

e Tow

n








international and

























(4-9)








international and




the load effects of



of trnrP The in






422

The report

infrastructure

with a

the




with

(i)





Ease of enforcement


and







Univers

ity of

Cap

e Tow

n





applicable factor









Appendix D


Where

the final factor

















(4-10)





factor

ratios were

The statistical










D


Where

the final factor

the factor for the
















0)

Univers

ity of

Cap

e Tow

n



423 Review































(4-11 )





span

The

Review


Axle Loads The full





an

extent






In f1nntltvmo the


















then calculated by






1)

Univers

ity of

Cap

e Tow

n









(4-12)









Univers

ity of

Cap

e Tow

n





















431 Traffic loading



the



formula

( 4-13)














axle

This load




An

and





431 Traffic


technical rl(lgt(1

the




formula

Univers

ity of

Cap

e Tow

n








432 Impact Factor




ForT lt 16t

For T gt SOt



ImEact Allowance

RR91 0041 RR910041 SEan (m) TMH7 01 02

5 35 37 36 10 28 26 18 15 23 17 12 20 20 13 9 30 16 9 6


(4-14)

Univers

ity of

Cap

e Tow

n

433 Test loading
























ENV 1991-3

(4-15)

433 Test




of the



under PTVi






Assessment amp













ENV 1991-3

Univers

ity of

Cap

e Tow

n

I

1J- 8

_______- - 1 ~ ~-- ~

--tf-fBT-1--+Or

I

I IPi t I









240 140 0

NA

6 4 3 3









(4-16)

Univers

ity of

Cap

e Tow

n


5 415 293 42

10 949 810 17

15 1510 1553 -3

20 2442 2520 -3

30 5






most

5 378 10 413 15 506

20 576 30 739

234 324 414

504 684

62 27

22 14 8









436 Critical Review







surveys


in TMH7 Part 2

(4-1

Univers

ity of

Cap

e Tow

n














from the WIM data

(4-18)

In the














from the WIM data

Univers

ity of

Cap

e Tow

n











5 409 415 293 10 957 949 810 15 1527 1510 1553 20 2284 2442 2520 30 3847 5397 5130


6000 - shy

5000 - E

~ 4000-III= ~ 3000 ~ OJ)

= 2000a III= ~

1000

0

0


5 10 15 20 25 30 35 Span (m)

--- Study -0- RR91100402 ~ TMH7 I


(4-19)

Univers

ity of

Cap

e Tow

n

Shear Forces (kN)


5 297 378 234 10 320 413 324 15 369 506 414 20 433 576 504 30 542 739 684


800

700

600 -

~ 500 QJ ~ 0 400 ~ ~ QJ 300

c C-J

200

100

0

0 5 10 15 20 25 30 35

Span (m)












5 409 293 39 10 957 810 18 15 1527 1553 -2 20 2284 2520 -9 30 3847 5130 -25


(4-20)

Univers

ity of

Cap

e Tow

n

























(Section 413)

Shear Force (kN)


5 297 234 27 10 320 324 -1 15 369 414 -11 20 433 504 -14 30 542 684 -21







(4-21)

Univers

ity of

Cap

e Tow

n


Moment (kNm)


5 409 415 -2 10 957 949 1 15 1527 1510 1 20 2284 2442 -6 30 3847

Table 411 - Moment

5397









Shear Force (kN)


5 297 378 -21 10 320 413 -23 15 369 506 -27 20 433 576 -25 30 542 -27


(4-22)

Univers

ity of

Cap

e Tow

n

45 CONCLUSIONS













the roads















return period





(4-23)

45 CONCLUSIONS













the roads















return period





(4-23)

Univers

ity of

Cap

e Tow

n









data







these -0










(5-1 )

51

2

OF LOAD


Part 2 the

3 the




shown in

data











these prlmiddoto










Univers

ity of

Cap

e Tow

n

40 80 ~~~--------~~4~~------------~~

240

I

180


20 20 ~ II~ ~




13 ~ ~

240 240


12 ~ II

150 150

7 1991-3 design

12 ~

200 200


51 - Load Models

Univers

ity of

Cap

e Tow

n





y = -(1 + kV)

load factor r

bias factor


deviation


52 RESULTS




2300

2100 0-v 1900~ 0 1700~ 0

l 1500-=QI

E 1300 0

~ 1)1) ll00 = a 0900 = QI

tl

- - ~~- -- shy - shy - shy

I

I I--- L~- shy ~~t--==- -

r-shy

----r-=9 I

~ 0700

0500

- T - - shy -

o 5 10 15 20 25 30 35

Span (m)


(5-3)

Univers

ity of

Cap

e Tow

n








1800

0 1600 (I

laquoI

1l laquoI 1400 0

l ltII = 1200 8 0

~ ~ 1000 = 0 = ~ 0800

0600

o

~ ~--shy -

~~ n

5 10 15 20 25 30 35

Span (01)

-0-3 6 -4-7 8


1600

14000 (I laquoI

1l laquoI 1200 0

l

ltII (I

0 1000 laquoI ltII

-= ~ 0800

0600

0 5 10 15 20 25 30 35

Span (01)

6 -4-7


(5-4)

Univers

ity of

Cap

e Tow

n





1800

0 1600 v CltI ~ ~

CltI 1AOO 0

e ~ = 1200

0

~ ~ 1000 = a = ~ 0800 I=Q

0600

0 5 10 15 20 25 30 35

Span (m)

6 ~7


1600


v ~ 0 1000 ~

CltI ~ c 00 0800

0600

- - - shy - shy

~

0 5 10 15 20 25 30 35

Span (m)

-ltgt-3 6 ~7 -8


(5-5)

Univers

ity of

Cap

e Tow

n




Table 51 to 54










(5-6)




Table 51 to 54










(5-6)

Univers

ity of

Cap

e Tow

n

Bending Moments

Lane Load 9 kNm


1 124 012 010 154 162 155 145 125 2 133 029 022 240 225 179 166 141 3 091 018 020 171 123 ll1 ll4 114 4 1 56 017 011 223 193 177 180 173 5 172 037 022 339 247 219 219 208 6 084 002 003 091 087 085 090 091 7 123 004 003 139 132 127 131 8 097 002 002 105 101 098 103

Lane Load 18 kNm


1 105 015 014 153 151 138 126 106 2 112 029 026 228 202 158 144 119 3 080 019 023 166 ll7 103 104 099 4 126 023 018 223 183 160 157 141 5 138 039 028 318 224 190 184 164 6 074 004 006 091 084 080 081 079 7 103 010 010 143 130 ll9 119 ll1 8 084 006 007 106 099 092 093 089

Lane Load 27 kNm


I 091 017 018 150 141 125 ll3 093 2 097 029 029 216 182 141 127 103 3 072 019 027 160 ll2 096 095 088 4 107 025 024 216 170 144 138 120 5 ll6 038 033 294 203 167 158 136 6 067 007 010 093 083 077 077 072 7 090 0 14 015 144 126 lll 109 097 8 075 009 012 108 097 088 087 080

Best Fit


(5-7)

Univers

ity of

Cap

e Tow

n

Shear Forces

Lane Load 9 kNm

C

Model

1 2 3 4 5 6 7 8

Mean 102 114 081 144 1 53 075 11 1 088

SD 008 023 013 014 024 010 010 010

V

008 020 016 010 016 013 009 012

135 221 142 200 280 073 116 087


ll8 145 120 183 219 095 136 109

Lane Load 18 kNm


Lane Load 27 kNm


Best Fit


(5-8)

Univers

ity of

Cap

e Tow

n

Bending Moments

Lane Load 9 kNm

Model

I 2 3 4 5 6 7 8

Mean 134 1A2

099 169 186 092 135 107

SD 008 020 020 023 036 017 021 019

V

006 014 020 014 019 018 015 017

1A6

218 174 237 333 119 172 136


200 159 159 122 110 123 200 183 201 237 209 227 112 109 124 161 153 172 129 125 lAI

164 177 161 254 282 165 223 187

Lane Load 18 kNm

Model 1 2 3 4 5 6 7 8

Mean 113 119 087 136 lA8

081 112 092

SD 007

022 018 020 034

011 013 012

V

006 018 021 014 023 014 011 013

135 209 163 213 302 105 lA8

118


130 150 134 187 215 126 158 138

Lane Load 27 kNm

Model 1 2 3 4 5 6 7 8

Mean

098 103 078 115 124 072 097 081

SD

009 023 017 021 033 008 011 009

V

010 022 023 018 027 012 012 011

133 199 154 202 278 096 138 108

Load Factor y 122 108 105 164 127 123 105 090 096 156 132 136 187 154 157 085 077 084 117 104 109 095 086 092

114 131 117 155 177 103 128 111

Best Fit


(5-9)

Univers

ity of

Cap

e Tow

n

Shear Forces

Lane Load 9 kNm

Model

I 2 3 4 5 6 7 8

Mean

135 151 108 190 203 099 147 116

SD

007 026 0 15 017 027 015 017 016

V

005 017 014 009 014 015 012 014

202 250 179 285 325 118 138 105

Load Factor y 193 181 177 188 175 171 127 136 143 231 246 256 235 245 252 114 130 142 129 144 153 100 113 122

189 175 163 280 272 165 173 141

Lane Load 18 kNm

Model

1 2 3 4 5 6 7 8

Mean

115 128 095 154 163 087 123 101

SD 011 027 015 018 030 009 007 008

V

010 021 016 012 018 010 006 008

188 227 175 236 265 104 127 099

Load Factor y 170 157 150 164 150 144 122 126 130 182 185 185 184 183 181 097 107 113 113 121 124 090 099 103

154 142 141 190 184 125 131 112

Lane Load 27 kNm

Model 1 2 3 4 5 6 7 8

Mean 101 112 085 130 137 078 107 089

SD 014 028 015 021 031 005 007 005

V

013 025 018 016 023 006 006 005

178 216 172 206 236 097 118 094

Load Factor y 154 140 132 152 137 129 117 119 120 152 150 146 159 154 148 087 094 096 100 104 104 082 087 089

131 125 126 144 146 103 106 093

Best Fit


(5-10)

Univers

ity of

Cap

e Tow

n
























on bridges









(6-1 )
























on bridges









(6-1 )

Univers

ity of

Cap

e Tow

n










TMH7 Part 2









model



















research

and 1995 in South









TMH7 Part 2









model






the events








live load models




Univers

ity of

Cap

e Tow

n























Part 2










limited expenditure





(6-3)


















over return





Part 2










limited





Univers

ity of

Cap

e Tow

n




(6-4)




Univers

ity of

Cap

e Tow

n

BIBLIOGRAPHY







fedrale de Lausanne












452-461




July 1981

Univers

ity of

Cap

e Tow

n



























Unbaised OlOlttlIll






RR 911004101 The

RR 911004102 The

Assessment Code

an Increase in the

an Increase in the

R K and

Canadian Journal



code 1983 edition

D amp uaveIlDon

Canadian Journal

W British


AlVUUl T and


A S (

Research Record

National 1998


Final



( a

A statistical

6494-513

to the traffic on



of Girder




Crowthorne TRRL



Univers

ity of

Cap

e Tow

n



Engineers


Transport


TRB December 1987























Univers

ity of

Cap

e Tow

n


and Architects



Report)



Univers

ity of

Cap

e Tow

n

A-1

APPENDIX A

A-1

Univers

ity of

Cap

e Tow

nAppendix A


Appendix A


Univers

ity of

Cap

e Tow

n





bull bullbull


77 90 90 80 80 80

o 00 000 Max W = 497kN

Configuration 2

77 90 90 90 90 90

00 00 00 Max W = 527kN

Configuration 3

77 90 9090 90 90

o o 00 00 Max W =527kN

Configuration 4

77 90 90 80 80 80


Configuration 5

102 102

o 00 Max W =560kN


Univers

ity of

Cap

e Tow

n

bull bull bull

3

Configuration 7

80 80 80

000 MaxW = 560kN


Univers

ity of

Cap

e Tow

nbull bull bull

bull bull bull


Configuration 1

80 80 80

Max W = 560kN

Configuration 2

80 80 80

eee Max W = 560kN

Configuration 3

80 80 80

eee MaxW = 560kN

Configuration 4

90 90

MaxW= 560kN


Univers

ity of

Cap

e Tow

n


bull bull bull


5


77 60 60 60 60 60 60 60 60

o 0000 0000 MaxW = 557kN

Configuration 2

80 80 80

000 MaxW = 560kN

Configuration 3

80 80 80



Configuration 4

48 48 48 48 48

00000 MaxW = 557kN


Univers

ity of

Cap

e Tow

n

bullbull bull

bull bull bull

bull bull bull

APPENDlXC

s Ii

~ [I $

~ 1- fl~


Configuration 1

90 90

Max W =560kN

Configuration 2

80 80 80

MaxW = 560kN

Configuration 3

90 90

00 0 MaxW = 560kN

Configuration 4

80 80 80

000 MaxW = 560kN

Configuration 5

80 80 80

Univers

ity of

Cap

e Tow

nAppendix B


bull

Appendix B


bull

Univers

ity of

Cap

e Tow

n

APPENDIXB


6 Axle Vehicles

2~ ------------------------------------

220+------+------+_----_+------+_--~~~--~

e ~200+------+------+------+----~~-----+----~

5 ~ 180 +_----_+------r---~~~----+-----_+----~ s =i 160 +_-----r----~~----_+------+_----_+----~ = I~+-----~------+------+------+------+----~

120 r------+------r-----+-----+------+--~ o 2 4 6 8 10 12

Reduced Variate

---6 Axle

Figure B I Sm span

o 2 4 6 8 0 12

Reduced Variate

-6 Axle

Figure B2 10m span

650

600

~ 550 o ~ 500 8 Q

~ 450 CgtII S 0 ~400 =

350

300

I

~

~

~

Univers

ity of

Cap

e Tow

n

APPENDIX B

1050

1000

9508 ~ 900

-= 850e Q

~ 800 c ~

a 750 ~ ~ 700

650

600

o 2 4 6 8 10 12

~

p y

r

V

Reduced Variate

--6 Axle

Figure B3 15m span

1600

1500 middotLL7 8 ~ 1400 r ~ ~ 1300 e Q

Ishy ~ 1200 ~ c V] 1100 ~ V ~ 1000

900

o 2 4 6 8 10 12

Reduced Variate

--6 Axle

Figure B4 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

3000

2800

8 ~ 2600 sect ~ 2400

E OIlca 2200 ==GI

=I

2000

1800

V

_V

Ijj


10 12

--6 Axle

Figure B5 30m span

Univers

ity of

Cap

e Tow

n

APPENDIXB


6 Axle Vehicles

24)

220

~ 200 180~ ca

c IIl 160

14)

120

0 2 4 6

Reduced Variate

8 10 12

---- 6 Axle

Figure B6 5m span

290

270

__ 250 Z ~ 2l 230 ~ 1 210

c IIl 190

170

150

~ b V

~

~ I

I o 2 4 6 8 10 12

Reduced Variate

--6 Axle

Figure B7 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

330

310

~ 290 Z ~ 270 Q

r 250 ~

c (IJ

230

210

190

o 2 4 6 8 10 12

V

J1V

I ~ I l

Reduced Variate

Figure B8 15m span


6 Axle

Figure B9 20m span

380

360

340

Z ~ 320 300 ~

01 280

c (IJ

260

240

220

--

V ~

~

)1

~

Univers

ity of

Cap

e Tow

n

APPENDIXB

430

410

390 Z 370 ltJ ~ =gt 350 ~ ~ 330c

00

310

290

270 o 2 4 6 12

r V

V ~

~V 1

8 10

I I

I I

1

I I I

i

I I i I

Reduced Variate

--6 Axle


Univers

ity of

Cap

e Tow

n

APPENDIXB


6 Axle Vehicles

200

195

e Z ~

190

-= S 185 ~

~ 011 9 180 0

= Ql

175

170

0 2 4 6

Reduced Variate

8 10 12

--6 Axle I

Figure B 11 5m span

530

520

e ~51O -= ~ 500 ~ 011

=a 490 =

Ql

480

470

V ~

~V ~

o

r

2 4 6 8 10 12

Reduced Variate

I --6 Axle I


Univers

ity of

Cap

e Tow

n

APPENDIXB

1000

950 5 ~ c 900 OJ e Q

~ C)I) 8509 -g c OJ = 800

750


o 2 4 6 8 10 12

Reduced Variate

--6 Axle I


0 122 4 6 8 10

Reduced Variate

--6 Axle

1550

1500

5 ~ 1450 a OJ

C 1400Q

~ C)I)

a a 1350 OJ =

1300

1250

~7

shy

~ V

-~

~

Univers

ity of

Cap

e Tow

n

APPENDIX B

- ~

V d ~

AV V

I

-i

V

2 4 6 8 10 12

Reduced Variate

--6 Axle

2850

2800

e 2750 Z 0 2700 Se2650 Q

~ 2600 ~

5 2550-g ga 2500

2450

2400

o


Univers

ity of

Cap

e Tow

n

APPENDIXB


6 Axle Vehicles

185

180

~ 175 cJ ~

170~ -= en

165

160 0 2 4 6

Reduced Variate

I --6 Axle

8 IO 12

Figure B 16 5m span

250

245

240

235

~ 230

~ 225 ~ ~ 220 -= en

215

210

205

200 -

f

- I

~ ~

7 V


I --6 Axle I

12 o 8 IO


Univers

ity of

Cap

e Tow

n

APPENDIXB

305

300

295

290 ~ 285 0 ~ 280 ~

275 270

265

260 o

2

~

~ r It

V


--+-- 6 Axle I

FigureBl8 15m span


--+-- 6 Axle I


340

335

~ 330

u 3250 ~ 01

320

315

310

~ V V

J ~

~

L V

Univers

ity of

Cap

e Tow

n

APPENDIXB

405

400

395 -

~ 390

QI OJ

Q 385 ~

eo QI 380

c en 375

370

365 o 2 4 6 8 10 12

--~

V

~ V

~

-~

i I

I i i

l Reduced Variate

-+- 6 Axle I

Figure B20 30m span

Univers

ity of

Cap

e Tow

n

APPENDIXB


7 Axle Vehicles

240

220 a ~ 200


CQ

140

120 0 2 4 6

Reduced Variate

--+---7 Axle

Figure B21 Sm span

700

650

~ 600

- 550 ~

~ 500 ~ 450a = ~400

350

300 12o 2 4 6 8 10

4~

h 1

~

I t

I

I

~ -I I

I I I I

Reduced Variate

--+---7 Axle

Figure B22 10m span

8 10 12

Univers

ity of

Cap

e Tow

n

APPENDIXB

1200

1100 e z 0 1000 C a Q 900 1gt11 CIa 800 CI

cQ

700

600


-+--7 Axle

Figure B23 15m span

1800

1700

Le 1600

~ C 1500 sect 1400 ~ ~ 1300a ~ 1200cQ

1100

1000

o 2 4 6 8 10 12

~

d ~

~

7 bull

Reduced Variate

-+--7 Axle

Figure B24 20m span

8 10 12

Univers

ity of

Cap

e Tow

n

APPENDIXB

3200

3000 e 2 2800 CI OJ

e 2600Q


2200

2000


8 IO 12

--7 Axle

Figure B25 30m span

Univers

ity of

Cap

e Tow

n

APPENDIXB


7 Axle Vehicles

240 ----------- ----- ---------------------

220 +---~r_--_+----r----+_---r_--~

~200 +-----4------+----~------+-----~~~~ ~ ~ ~ 160+----~r_---_+-----_b~--+_-----r_--~

140 +----~r_-~~~---r------+-----r_--~

180 +---~r_--_+-----r----~~---r_--~

120+-----r_--_+---~---+------r_---_4

o 2 4 6

Reduced Variate

-+--7 Axle

8 10 12

Figure B26 5m span

270----~------_-------_----~

250+----~----+---~---~--~~--~

Z 230 +---middot~~---+---~----~~--~----~ C ~ 8 210 +-----4-----~---~~~-+---~---~ r ~ ~ 190 +------I-------t~---_t__----+_---__t---_i

170+---~~--~---_t__---+-----__t---_i

150+----~------_+------~------+-----_4-----~

o 2 4 6

Reduced Variate

-+--7 Axle

8 10 12

Figure B27 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

320

300

~ 280 - 41 OJ ~ 260 41

~ 240

220

200

V

V

V

~~

~ f7

I i I I I i

I i 1

o 2 4 6

Reduced Variate

--+-7 Axle

8 0 12

Figure B28 15m span

390

370

~ 350 Z 0 41 330OJ C ~

30 41

c (J 290

270

250

o

h pound

7 6A V I

~

V

4V 2 4 6 8

I r

I I I

I i I

i I


--+-7 Axle

Figure B29 20m span

Univers

ity of

Cap

e Tow

n

APPENDrxB

480

460

44)

Z 420 ~ ~ 400 0

380 os

CI 360(I)

340

320

300

~

)~

d ~ ~

~

k

o 2 4 6

Reduced Variate

-+-7 Axle

8 10 12

Figure B30 30m span

Univers

ity of

Cap

e Tow

n

APPENDIX B


7 Axle Vehicles

200

~ 195

e Z 190 e Jif75 185

8 Q 180 CD

a fS 175 =I 170

~ 165


I ---7 Axle

Figure B31 5m span

o 2 4 6 12

Reduced Variate

580

560

e 54)

~ 520

il 500 01

sect 480 ~ 460

]44) 01

=I 420

400

380

-

I

j ~

--~ ~ ~

I

L

4

8 10

I

I

I

i

---7 Axle

Figure B32 10m span

Univers

ity of

Cap

e Tow

n

APPENDIX 8

1100

1050

e ~ 1000

C 01 e 950 Q

011

= 900a I 01 ~

850

800 0 2 4 6 8 10 12

Reduced Variate

--7 Axle

Figure 833 15m span

1700

1650

e 1600

L ~ 1550 01= e f1500Q

011

= 1450 rIIa 01= ~ ~ 1400

~

1350 ~~

1300 o 2 4 6 8 10 12

Reduced Variate

--7 Axle

Figure 834 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

3000

2950

ez 2900 ~ 2850 e ~

~ 2800 = a ~ 2750 =

2700

2650


-+-7 Axle

4

v

- V

Figure B35 30m span

Univers

ity of

Cap

e Tow

n

APPENDIXB


7 Axle Vehicles

~ ltI ~ 1 -= C-I

190

185

180

175

170

165

160

155

150

145

140

--shy

J r

) -

i-~

~ J1V


I ---7 Axle I

Figure B36 5m span

260

~V250

Y240 ~ ~ 230 -~ 5 ~ -= C-I 220

~

210 ~

200 o 2 4 6 8 10 12

Reduced Variate

I ---7 Axle I

Figure B37 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

320

~ 310

~ 300 r ~ 290 1

~

280 ~

~ ~ CI 270 (I) 260 -

250

240


--+-7 Axle

Figure B38 15m span

355

350

345

340

~ 335 330 ~ 325 ~

CI 320 (I)

315

310

305

300


--+-7 Axle

~

( L

l

~ ~

gt

~ ~

L

~

Figure B39 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

420

415

410

~ 4tl5

tJ

or 400

z (Il

395

390

385


I --7 Axle

Figure B40 30m span

t ~ i-

~~

1pound J

Univers

ity of

Cap

e Tow

n

APPENDIX B


8 Axle Vehicles

o 2 3 4 5 6 7 8 9

Reduced Variate

--+- 8 Axle

Figure B41 Sm span

o 2 3 4 5 6 7 8 9

Reduced Variate

1 --+-8 Axle I

Figure B42 10m span

e 3

550

500

- 450 c e c ~400 OIlca ~

CQ 350

300

V V ~

~--shy V

~ V~

8 ~

550

500

- 450 c a V

V r shy --

V -c ~400 ~

-V a c=350

300

~ V

Univers

ity of

Cap

e Tow

n

1050

1000

8 950

Z 900~

C 850a 0

~ 800 Oilc

750ac =I 700

650

600

o 2 3 4 5

Reduced Variate

1 --+-8 Axle

Figure B43 15m span

1600

1500

e Z 1400 ~ C a 1300 0

~ Oilc 1200ac

=I 1100

1000

o 2 3 4 5

Reduced Variate

--+- 8 Axle

Figure B44 20m span

I

-~ ~

shy

~ ~

~ ~ shy

V

I

~ ~~

- ~

~ ~

~ ~

V III

~

6 7 8

APPENDIXB

9

6 7 8 9

Univers

ity of

Cap

e Tow

n

APPENDIXB

I 17 I

7 ~ ~ I-

I

1

-e ~ i i

~ shy I- I

~ ~ 1

f

~ ~

i

I 2 3 4 5 6 7 8 9

Reduced Variate

1 -+--8 Axle I

3000

2900

2800 8 2700 ~

2600 -= 8 ~

2500 = ~ 2400 0laquo1 = a 2300 = ~

~ 2200

2100

2000 o

Figure B45 30m span

Univers

ity of

Cap

e Tow

n

APPENDIXB


8 Axle Vehicles

260

240

~ 220

~

~V ~ 200 ~ c

IIl 180

160

140

~

~

V ~V

V-

~

o 2 3 4 5

Reduced Variate

I --8 Axle I

6 7 8 9

Figure B46 5m span

250 I

240

~ ~~

~

~

~ ~ I

~

~ I

I I

230

220

~ 210 ~ ~200

I 190 ~ IIl 180

I 1170

J160

150

o 2 3 4 5 6 7 8 9

Reduced Variate

I --8 Axle I

Figure B47 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

310

290

~ 270

0 250

gj I 230rJl

210

190 o 2 3 4 5 9

Reduced Variate

-+-- 8 Axle I

Figure B48 15m span

r-- i I

L i v

v ~

I

~ ~ I

-11 I

~ i j

6 7 8

V

I

360

340

320 Z o 300 ~ ~ 280

c rJl 260

240

220

10-shy

-~

-V

- ~

o 2 3 4 5

Reduced Variate

-+-- 8 Axle I

6 7 8 9

Figure B49 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

440

420

400

~ 380 Q 360 ~ ~ 340 c CIl

320

300

280 o 2 3 4 5 6 7 8 9

~ ~

---~VIII

~

I

L Y I

~ ~ I

~ ~- I

i I I I

1

I I i

Reduced Variate

-+- 8 Axle I

Figure B50 30m span

Univers

ity of

Cap

e Tow

n

APPENDIX B


8 Axle Vehicles

I

I

570

550

a ~ 530

-= ~ ~ 510 ~ 01)

9 ~ 490 OJ

I=Q

470

450

L

I

I i

~- ~

~

-~ shy i

~

I

I j i


--8 Axle I

6 7 8 9

Figure BS I Sm span

570

550

e ~ 530 -

~ -= E lt) 510 ~ 01)c 490ac ~

I=Q

470

~V

-~ ~ ~

~ shy-shy

~

450


I -shy 8 Axle I

6 7 8 9

Figure B52 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

1030 1 i1010

I990e IZ e 970 c ~ 95013 Q

~ 930 OIl

Is= 910 = I= ~

890 1

870 i

850

V ~

[i i

~ V I

~~ I I

~ ~ I I

I

I I

V

I

o 2 3 4 5 6 7 8 9

Reduced Variate

1 -+-8 Axle

Figure B53 15m span

1600 I

~ 15508 ~ z e ~ -c 1500 shy8 ~

~ Q OIl 1450 s= ~ =

V = 1400

1350 o 2 3 4 5 6 7 8 9

Reduced Variate

-+-8 Axle I

Figure B54 20m span

Univers

ity of

Cap

e Tow

n

APPENDIX 8

3000-----r-------------~----~----r---~----~----~

e ~ - 2900 E 8 Q

~ ~

aI 2800 I =

2700+---~~--~----~----~---+----~----~---+--~

o 2 3 4 5

Reduced Variate

-+-8 Axle

Figure 855 30m span

6 7 8 9

Univers

ity of

Cap

e Tow

n

APPENDIX B


8 Axle Vehicles

260

255

250

Z 245

~ ~

240 235= ~ 230~

c CIl 225

220

V

215

210

~ I

~~

~r V

~

~ ~r

I i I

l i

I

o

Figure 856 5m span

2 3 4 5

Reduced Variate

-+- 8 Axle

6 7 8 9

3000

~ --~ ~ 2900 V ~ V

~ V 01 41 ~c

CIl 2800

V ~

2700

o 2 3 4 5 6 7 8 9

Reduced Variate

1 -+-8 Axle I

Figure 857 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

-

o 2 3 4 5 6 7 8 9

Reduced Variate

-+- 8 Axle

Figure B58 15m span

305

300

295

~ 290 III ltJ 285Q ~ ~ 280 c rI)

275

270 I 265

L ~

~ ~

tr V

~

I-shyi-shy

I

I i I

I I I i i I

I

345

340

335

Z 330 ~ III 325 Qr 320 =OJ c 315IJ)

V

~

-U i-

~

310

305 V-300

shy

i I

I I I

I i i

i I


1 -+-8 Axle

6 7 8 9

Figure B59 20m span

Univers

ity of

Cap

e Tow

n

I

APPENDIXB

415

40

405 Z ~ 400 0 ~ 395 gJ

c (I)

390

385

380

o 2 3 6 7 8 9

I

~ V

~

~ ~

~ ~

~

4 5 Reduced Variate

I --8 Axle

k I L

-I

i

I i

i

i

i I

Figure B60 30m span

Univers

ity of

Cap

e Tow

n

APPENDIX B


6 Axle Vehicles

295---------~----------~----------~--_

275

e 255

~ lt11

C 235 e ~ Q

~ 215

195

--t-- i

i-----i---

175 +-----r-----r-------------------r----~

-100 100 300 500 700 900 1100 1300

Reduced Variate

Figure B61 5m span



bull

Univers

ity of

Cap

e Tow

n

APPENDIX 8

1500~----~----------~----r---~~--------~

I I I1400 -1 shy --+-__--_1shy

~ 1300 --~-~---j---+I -

i 1200 -1-shy - -+-shy - -+-shy8 Q


~ ~~~-- I I I 900 r-- ---t---T 800+-----+-----~----r_----r_----r-----~--~

-100 100 300 500 700 900 11 00 1300

Reduced Variate


Figure 863 15m span

2200

2100

~2000 a ~ 1900

i 1800 g1700

~1600 = i 1500

11 1400

1300

1200

I 1

-1 I I

I I I

L---shyI

___shy---- shy

-100 100 300 500 700 900 1100 1300

Reduced Variate


Figure 864 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

3800

3600

e 3400Z e I 3200 QI e

3000Q

~

2800a QI 2600=

2400

2200

-100 100 300 500 700 900 1100 1300

Reduced Variate


Figure B65 30m span

Univers

ity of

Cap

e Tow

n

APPENDIXB


6 Axle Vehicles

300

280

Z 260

0 240 ~ 220i ~ fIJ

200

180

160

I--I-shy

I --shy

i

I

-100 100 300 500 700 900 1100 1300

Reduced Variate


--Nonnal Gumbel

Figure B66 5m span

340

~ - Q CIS ~ fIJ

200

Reduced Variate

320 ~-l--middot- 1 --300

280

260

240 i

220 I T

I

-100 100 300 500 700 900

-I 1100 1300


--Nonnal Gumbel

Figure B67 10m span

Univers

ity of

Cap

e Tow

n

390

370

350

~ 330 r 0

310 ~

CI rJl

290

270

250

i -i----~--~middot~--- -+ -- ---~-- ----~--shy




-100 100 300 500 700 900 1100 1300

Reduced Variate


-- Normal Gwnbel

Figure B68 15m span

440

420

400

~ 380 0 r 01 360

CI rJl

340

320

300

-100 100 300 500 700 900 1100 [300

Reduced Variate


--Normal Gwnbel

Figure B69 20m span

APPENDIXB

Univers

ity of

Cap

e Tow

n

APPENDIXB

510

490

470

~ 450 Ol _ e

430~ 01 41 410

CIl

390

370

350

-100 100 300 500 700 900 1100 1300

Reduced Variate


-- Normal - Gumbel

1 _ - --1-

j ---+--~~I i

-1----1-----

-+-------tli

- -+---~ I - i - --L-- -l- - -l

-I -+---1-- 1


Univers

ity of

Cap

e Tow

n

APPENDIXB


6 Axle Vehicles

220

215


ltgt 200 I~ ~


I 185 19----1----1- -------------r

180

-100 100 300 500 700 900 1100

Reduced Variate


Normal -It- Gwnbel

Figure B71 Sm span

670

650

e 630 Z e 610 7 ltI 590S ltgt ~ 570

cI ~

550 I ltI

cQ 530

510

490

I +---+--+---shy- T - shy -

1 ------

-100 100 300 500 700 900 1100

Reduced Variate



Figure B72 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

1450 -r------------------------

e z 13502 1250

ltII

C e 0 1150 5 ~

1050 c CQ

950

I

~-+_____ I

850+----r---r----~--~---+----~

-100 100 300 500 700 900 1100

Reduced Variate



Figure B73 15m span

1910

1860

e 1810 Z 2 1760l c

1710e 0

1660

5 ~

1610 c CQ 1560

1510

1460

-100 100 1100

--------1 ---

~-r---~-- ----shy- 1- --1-- - -I-

I i

300 500 700 900

Reduced Variate



Figure B74 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

3150 ----------------------------

3100

3050

3000

2950

2900

2850

2800



i I I i -

- i

i

I--I - - -1-shy

I -LOO 100 300 500 700 900 1100

Reduced Variate


-- Normal --Gumbel

Figure B75 30m span

Univers

ity of

Cap

e Tow

n

190

APPENDIXB


6 Axle Vehicles

Z 186 Cshy Ol

184 01 Olc 182

CIl

180

178

-100

I 188 +---1-shy

t-+----shy

100 300 500 700 900 1100 1300

Reduced Variate


-- Normal ~Gumbel

Figure B76 5m span

290

280

270Z e ~ 260 lt=

250 ~ c

rJ)

240

230

220

-100 100 300 500 700 900 1100 1300

Reduced Variate


--Normal ~Gumbel

Figure B77 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

325 i

--------------t------~t__-__I320

315

Z 310cshy 305 Q

300 = c (JJ 295

290

285

280

-100 100 300 500 700 1100 13 00

+--------+--- +-----i---Le----+- -I

=---=------- ------I

j-__+--_ - i___ __ I

900

+-_-I- shyI

Reduced Variate


-- Normal --Gumbel

Figure B78 15m span

355~----~----~----~--~~--------------~

350 +shy

345

340 -Jshy

335

- -I I II

--J---- t---j---- k-- ------------I_____I

---l-

330~~--T----r-----~--~~--~----_----__t

-100 100 300 500 7 00 900 1100 13_00 Reduced Variate


-- Normal Gumbel

Figure B79 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

420

415

410

~ 405 ~ 400 ~ c CIl 395

390

385

-100 100

---1shy--T

I 3_00 500 700 900 11 00 1300

Redoced Variate


Figure B8D 30m span

Univers

ity of

Cap

e Tow

n

APPENDIXB


7 Axle Vehicles

310

--L290

e 270Z ~ l 250c a 230Qa 01)


170 I I i

150

-100 100 300 500 700 900 1100 1300

Reduced Variate


--Normal Gwnbel

Figure B81 5m span

i

600 +----

850~----~--~----~----------------T_--~

800

750 ----1 -1-1-1 -+1-----gt+-1 700 --------I----b---i------ -t-- i_ _ 650 -I- ----+---- +- - -- - --=L--+---tI

~ ac ~ 550

500

450+-----r---~----_+----_r----~----~--~

-100 100 300 500 700 900 1100 1300

Reduced Variate


-- Nonnal Gwnbel

Figure B82 10m span

Univers

ity of

Cap

e Tow

n

1350 ~-+ ~ -1250 - i - ishy1150

I 1050 I 950 I

APPENDIX B

1450 ~--~------------------r----------

850+----r---~----_r---4_----r_-~---~

-100 100 300 500 700 900 1100 1300

Reduced Variate


Normal --Gwnbel

Figure B83 ISm span

2150

2050

E 1950 z ~ 1850 l I 1750S ~

~ 1650 toll

aI 1550 I = 1450

1350

1250

-100 100 300 500

Reduced Variate

__1__ _

i ~~----- --~I -----

700 900 1100 1300


Normal --Gwnbel

Figure B84 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB


2650 f----i~-_+---r---i---+---ir-----l

-100 100 300 500 700 900 lUXgt 13 00

Reduced Variate



Figure B85 30m span

3850 ------1----------------------

3650

3450

3250

3050

2850

Univers

ity of

Cap

e Tow

n

APPENDIXB


7 Axle Vehicles

~ Qj e r ltII Qj

-= CIl

280

260

24)

220

I I +---+-----l-- -+_-+--~I- --


200

180 -l--~_-__+- ------L--__+------ shyt----shy160+-----r---------+-----r-----r----~--~

-100 100 300 500 700 900 1100 1300

Reduced Variate


Normal -+-Gumbel

Figure B86 5m span

320 I

300 1___

I I ~ 280 I Qj

--t-~-- - e 260r g

-= 24) -CIl

220

200

-100 100 300 500 700 900 1100 1300

Redoced Variate



Figure B87 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

360

350

340

~ 330 - 320~ ltJ ~ 310 01 300 -= rIl

290


280

270

260

-100 100 300 500 700 900 1100 1300

Reduced Variate


Normal Gwnbe1

Figure B88 15m span

450r-----~----r_----~----~----~--~----_

430 ~---+_---+_--_+_--_+_--_+--_=_+--_l

Z 410

0 ~ 390ltJ ~ 37001 ~

-= rIl 350

330


310

-100 100 300 500 700 900 1100 1300

Reduced Variate


Normal Gwnbel

Figure B89 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

~ y Q ~ CII d rJJ

560

540

520

500

480

460

440

420

400

380

360

I I



+----+ishy - ---- -+------L shy-shy-----~--___l I I -

-100 100 300 500 700 900 1100 1300

Reduced Variate


Normal --- Gwnbel

Figure B90 30m span

Univers

ity of

Cap

e Tow

n

APPENDIXB


7 Axle Vehicles

210

205 5 z e 200 ~ c e ~ 195

E till ca 190 c

=

185

180

-100 100 300 500 700 900 11 00 1300

Reduced Variate

I r----+-I-- ---~-------+---t---I I


Normal Gumbel

Figure B9 I Sm span

5 Z e l c e ~

E

aC till

c =

535

530

525

520

515

510

505

500


Normal Gumbel


-100 100 300 500 700 900 1100 1300

Reduced Variate

Figure B92 10m span

Univers

ity of

Cap

e Tow

n

1150

1100 - middot 1050

1000 r --

950

900


i I

- 1i

APPENDIX B

1200 -------~----____--____----_

850+---r-----r--~--~---~--_T----~

-100 100 300 500 700 900 1100 1300

Reduced Variate



Figure 893 15m span

e

1650

1630

1610

~ 1590 ~ c 1570 e Q 1550 ~ ell 1530= a c 1510 = 1490

1470

1450

I I -~-t-shyI

i il )

l--shy

-100 100 300 500 700 900 1100 1300

Reduced Variate



Figure 894 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

I i I

-~-+--1-1 ~ I-1--

2820+-----r---~~--~----~----_+----_+----~

-100 100 300 500 700 900 1100 1300

Reduced Variate


-- Normal Gumbel

Figure B95 30m span

2940

2920 e Z 2900ltII

I -OJ

8 ltgt 2880 ~ OG Ia 2860 I OJ

CQ

2840

Univers

ity of

Cap

e Tow

n

APPENDIXB


7 Axle Vehicles

210

205 +---f---l----I I---r----f-----

----- -JbI~__+ - I

--~-l ---- - ---+----+-- i

200 -J-- -+- - - j--shy

~ 195 -- ---1- -+----

ltj 41 190

ri I II i __ J ---r--shy 185

41 -= I ~ I - I ~+---r---rIl 180

175 +-ltSgt---- - +-i--i---T --+--shy i

170

-100 100 300 500 700 900 1100 1300

Reduced Variate


-- Normal --Gumbel

Reduced Variate


--Normal --Gumbel

Figure B97 10m span

Univers

ity of

Cap

e Tow

n

360

+ JiUO--t---

-j---t----+--- -~-- - T -3S0

-340 r- -r- I ~- -1- -shy~ 330 ltJ ~ Q 320 +---h-=-~~--1 ~~-Ib~01

310c ~ -- I-- r-----1-shyen


280

-100 100 300 Soo 700 900 1100 1300

Reduced Variate


-- Normal Gumbel

Figure B98 ISm span

390r---~----~----~-----1

~ 370

~

----------~--~

380 +--------- I - ---r ---+- - - - ------- ---+-- - - - - --1

I - +1--- -+-

3S0 +----+

330+-----r---~----_+---_r----~----~-~

~ 360 +--shygj t3

340



Figure B99 20m span

APPENDIXB

Univers

ity of

Cap

e Tow

n

APPENDIX B

423

421

419

417Z 415 Q

413 ltlI c 411 (IJ

409

407

405

-100 100 300 500 700 900 1100 1300

Reduced Variate



Univers

ity of

Cap

e Tow

n

APPENDIXB


8 Axle Vehicles

240

230

e 220

~ - 210 -= 200e 0

E 190 011c a 180 c = 170

160

150

-100

-I----tl ---+shy

I

-r I i-----1L-~II --_t_

_ -+shy _ _ i

100 300 500 700 900 1100 1300

Reduced Variate


Normal Gumbel

Figure BIOI Sm span

650

8 600 z -I - I c 550 e 0

E 011 500ca I = 450

4OO+-----r---------+-----r-----r----~--~

-II

-100 100 300 500 700 900 1100 1300

Reduced Variate


Normal Gumbel


Univers

ity of

Cap

e Tow

n

APPENDIXB

1200 ----------~r_-r_--__r--____--__


= --+1- ~ l -~ a = CQ

850 q - -I--middot-~ -1

800 I

750 +-----~----~----_----~----_r----~---~

-100 100 300 500 700 900 1100 1300

Reduced Variate




1900

1800

S Z 1700 l = 1600 8 c ~ 1500 OJ)

= a = 1400

CQ

1300

1200

-100 100 300 500 7 00 9 00 1100 1300

Reduced Variate




Univers

ity of

Cap

e Tow

n

APPENDIXB

3350 I

I

I

3250

1-~ --

- 3150S

z --1-shy ~c 3050 1

II I 2950e iQ

2850 011 s 27501l c

I = 2650

2550 -I middot I

2450

-100 100 300 500 700 900 1100 1300

Reduced Variate


-- Normal Gumbel


Univers

ity of

Cap

e Tow

n


8 Axle Vehicles

210----------~------_----~----~----~

200~-----~-----4------~----~-----+--~~

190

~

~


I~+_-----r----_------r-----~-----+----~

I f----- -I shy

180 +---------------

170 -t------------+-~

I I-shy ----------- 1 160 +-------1----4-----

-100 100 300 500 700 900 1100

Reduced Variate


-- Nonnal - Gumbel

Figure B106 5m span

290

280

270

260 ~ - ~ 250 Q 240 ~ 230 ~

rIl 220

210

200

190 -00 100 300


-- Normal -Gumbel


-1---1--shy-1----1-1--shy


500 700 900 11 00

Reduced Variate

APPENDIXB

Univers

ity of

Cap

e Tow

n

APPENDTXB

370


~ 330

01 310

- - --~---t-shy--


270

250

230

-100 100 300 500 700 900 1100

Reduced Variate


-- Normal Gwnbel


~o----~-----------~-----------------_

380

~ 360 01 Q 3~ ~ ~ c 320()

300

280

-100 100 300 500 700 900 1100

Reduced Variate


-- Normal Gumbel


Univers

ity of

Cap

e Tow

n

APPENDIXB

500

480

460

~ 440 OIl

~ Q 420 ~ ltII OIl 400d

(I)

380

360

340

-100 100 300 500 700 900 1100

Reduced Variate


-- Normal Gwnbel


Univers

ity of

Cap

e Tow

n

APPENDIXB


8 Axle Vehicles

210~----~-------~----~--------------

205 ~---l-

200 -j---l-----

195 -+----l~oP ---1-shy +---1------1


185 -t------t----i---i------r----

-100 100 300 500 700 900 1100 1300

Reduced Variate


-- Normal Gumbel

Figure BIll 5m span

545

540

S Z 535 i 530 GI a 0 525 ~ ~ c a 520

C GI

IQ 515

510

505

-t-+---t-I-L I I

-100 100 300 500 700 900 1100 1300

Reduced Variate


-- Normal Gumbel


Univers

ity of

Cap

e Tow

n

APPENDIX B

104)

1030

e 1020Z e l 1010c e 1000=gt OG

990c s c 980=I

970

960

-100 100 300 500 700 900 1100 13 00

Reduced Variate


-- Nonna --- Gumbel


1620-----~--~----~~--_----~----~--~


ac

c =I

1500+-----r---~----_T----_r----~----_--~

1600

1580

1560 l

i 154)

1520

-100 100 300 500 700 900 1100 1300

Reduced Variate


--Nonna --- Gumbel


Univers

ity of

Cap

e Tow

n

APPENDIX B

2970

~ 2950

S z 0 2930 (I)

is e 2910Q

~ 1gt11 Ca 2890 c

al

2870

2850+-----r-----~--~r_--~r_--~----_+----~

-100 100 300 500 700 900 IUlO 1300

Reduced Variate


--Normal -Gwnbel


Univers

ity of

Cap

e Tow

n

--

APPENDIXB


8 Axle Vehicles

200

195

Z ~ 190 ~ ~ 185 ~ -= (I)

180

i i I I ~ E bull

175

c_---+-__---_ ~--_f

~-+-----il-_+ _-+t_i ---t-I-I -100 100 300 500 700 900 1100 1300

Reduced Variate




~ ~

= ~ -= ~ (I)

275-----------~--------~----------~----_

270

265

260

- shy -- ----- shy ----1---shy

I 2S5 -t shy250

245

240

-100 100 3 00 500 700 900 1100 1300

Reduced Variate


--Normal ---Gumbel


Univers

ity of

Cap

e Tow

n

APPENOIXB

325

320 I-- -I ~

315

310OJ ~ 305~ -= (I)

300

295

290

-100 100 300 500 700 900 1100 1300

Reduced Variate



Z e ~ Q

~

~ -= (I)

360~----------------~----~---------------

355

350

345

340

335

330

--+----~-- ~--- i shy - ---+-----1

i I I I -100 100 300 500 700 900 1100 1300

Reduced Variate


-Nannal Gwnbel


Univers

ity of

Cap

e Tow

n

APPENDIXB

QI ~ 415 +---f--shy

-~--t-I I

I -=r-i--- II

I 400+-----~----+_----+_----r_----+_----r_--~

430~----~----~----------~----~----~--~

425 --f ~ r - ~ 420 -I---~---li-- --- --t-shyZ I ==- i

~ o

lltU 410 +-- -r shy

~ ~-----------l405 -1--061+--1-----+ I

i i

-100 100 300 500 700 900 1100 1300

Reduced Variate



Univers

ity of

Cap

e Tow

nAppendix C


II

II

Univers

ity of

Cap

e Tow

n

APPENDIX C

Page No




Univers

ity of

Cap

e Tow

n


Univers

ity of

Cap

e Tow

n




















Univers

ity of

Cap

e Tow

n




I 022

2 23E-05 3


4 46E-09 (2)(3) 5



6 (I) (4)IOE-09


7 47E-18 (6) (4)



9 10E-18 (1)(7)


10 47E-27 (9)(4)








3

Univers

ity of

Cap

e Tow

n


4

Univers

ity of

Cap

e Tow

n

A-1

APPENDIX A

Univers

ity of

Cap

e Tow

nAppendix D

Impact Formula I

bull bull

Univers

ity of

Cap

e Tow

n

APPENDIX 0

Page No







Univers

ity of

Cap

e Tow

n





Where













3J =shy

b L


J =~ b Lf





Where













3 J =shy

b L


J =~ b Lf

Univers

ity of

Cap

e Tow

n



therefore used











response

2



therefore used











response

2

Univers

ity of

Cap

e Tow

nAppendix E


bull

Univers

ity of

Cap

e Tow

n

1

APPENDIX E

Page No









Univers

ity of

Cap

e Tow

n

























III 2

I ~


























W~ I i I

WI 2

I I ~


Univers

ity of

Cap

e Tow

n


















2

Univers

ity of

Cap

e Tow

n









moments





















3

E13








moments













E14 Simulation








3

Univers

ity of

Cap

e Tow

n






(i) Maximum W

(ii) Shortest b

(iii) Centred x =05












limits





legal vehicles





4

Univers

ity of

Cap

e Tow

n







5 197 189 4

10 547 562 3 15 1054 1054 0 20 1582 1626 3)

7


0 Connor Difference

5 184 173 -6

10 252 258 3 15 308 304 -1 20 347 346 0





simulations









5

Univers

ity of

Cap

e Tow

n

Bending Moments kNm


5 293 301 -3 10 800 812 -1 15 1262 1364 -7 20 1903 2097 -9 30 3526 3631 -3








6

Univers

ity of

Cap

e Tow

nAppendix F


Visual Bas

Univers

ity of

Cap

e Tow

n


Sub centralloadO









Univers

ity of

Cap

e Tow

n




pos = inc n







+


pos = inc n



10) lt= 0 Or

+ + +


Then Then Then





+ + spaclO



Univers

ity of

Cap

e Tow

n






n=n+1 Loop



Next z


Univers

ity of

Cap

e Tow

n




Nexty








Next s


End Sub




Nexty








Next s


End Sub

Univers

ity of

Cap

e Tow

n

ABSTRACT





















(ii)

Univers

ity of

Cap

e Tow

n

DECLARATION




John R B Anderson

(iii)

Univers

ity of

Cap

e Tow

n

ACKNOWLEDGMENT





(iv)

Univers

ity of

Cap

e Tow

n

TABLE CONTENTS

No

1 INTRODUCTION

11 BACKGROUND 1-1

12 OF THE STUDy 1-2

1-3 13 SCOPE OF THE

14 METHODOLOGy 1-4






21 INTRODUCTION 2-1





25 CONCLUSIONS 2-15


31 INTRODUCTION 3-1







35 RESULTS 3-23

36 OVERLOADING 3-27

37 CONCLUSiONS 3-31

Univers

ity of

Cap

e Tow

n


41 TMH7 PART 2 4-1








45 CONCLUSIONS 4-23



52 RESULTS 5-3








(vi)


41 TMH7 PART 2 4-1








45 CONCLUSiONS 4-23



52 RESULTS 5-3








(vi)

Univers

ity of

Cap

e Tow

n

List of































(vii)

List of




24 - of H20 LRFD 1 2-7


26 CL-W Truck 2-10

2-10 27 - CL-W


31 -

32 -

33 -

34 -


of GVMs 3-8


Function of

Function of

Moments 30m span

Moments 5m span

3-9

3-9











41 -

42 -

44


Distributed Lane

Moments Due to

of Class 14 Vehicle


and 4-7

4-14


46 -

47 -

51 -

52 -

of Moments 4-19

gtr of Forces


4-20

5-2


Univers

ity of

Cap

e Tow

n





(viii)

Univers

ity of

Cap

e Tow

n

List of Tables































(ix)

List of Tables


























Table 41 - 4-6





(ix)

Univers

ity of

Cap

e Tow

n












(x)

Table 46

Table 47-






Table 411 -

Table 412 Shear

Table 51 -


Table 53-

Table 54-


WIM data v RR 4-22






Univers

ity of

Cap

e Tow

n

1 INTRODUCTION

11 BACKGROUND
















Regulations


June 1994














(1-1 )

1

11




with the aim of

the most onerous











the Road

commissioned the

to increase the

to consider the



(i)

The main

the


June 994



Vehicle Loads on

Vehicle Loads on












(1-1 )

Univers

ity of

Cap

e Tow

n






























(1-2)

12






vehicles






with

Ullman





and adds to the








WIM are






(1

Univers

ity of

Cap

e Tow

n



RR 91100410 I amp 02




data
















considered

(1-3)



RR 9110040 I amp 02




data
















considered

(1-3)

Univers

ity of

Cap

e Tow

n

14 METHODOLOGY




identified were












approaches














(1-4)

14 METHODOLOGY


142



identified were

TMH7 Part 2 The




and



( I Code These



loads on

close






















(1

Univers

ity of

Cap

e Tow

n


































(1-5)






Statistical

vehicles



vehicles on the N3





vehicle

load effects

and fits the

within a 120 year










both methods is



of an extreme











(1

Univers

ity of

Cap

e Tow

n





(c) Overloading















(1-6)

Critical Assessment




The extent of

vehicle set


vehicle set This

those

between the WIM

event of the actual














(1

Univers

ity of

Cap

e Tow

n

1~ REPORT STRUCTURE













reviewed in detail



















(1

1~ REPORT STRUCTURE




live

extent of

with the










reviewed in detail



In and the















in TMH7

the

load model are



of the WlM data

(1

Univers

ity of

Cap

e Tow

n


21 INTRODUCTION






these loads

















on bridges






and

21 INTRODUCTION








these loads


lIllUlLla on the









BS5400 1978

British Standards




Factor ( I

Code and


on






and

m


Univers

ity of

Cap

e Tow

n










the TMH7 Part 2


























(2-2)



to process and







live load models in

the TMH7 Part 2











- u- sensors









vehicles The


by the vehjcle axle

to the extreme

Allowances for









are shown in 21

Univers

ity of

Cap

e Tow

n

305 366 244 305 244 305 244 m


80 219 100 100 100 100 100 100 kN Axle loads (kN)

Ca)

7 x 305 IT = 213 m 0 ~----- -------__--- ___---

~[I ~[JJ 1 I 1 I 1 I] 70 B 96 896 896 896 8 96 896


(bJ























(2-3)

Univers

ity of

Cap

e Tow

n



























241 BD 3788











24


























APPROACH




241 BD 3788









spans





Univers

ity of

Cap

e Tow

n








W= 260 kNfm


J

BS 5400 Part 2





















(2-5)

10 in the

for loaded







lt11 C l 0

150

E 100 lii CL

s



W= 260 kNfm

BS 153 Part SA

BS 5400 Part 2
















axle loads An


of 146 was

~nrn)~h used was


and lateral

factor of 18 was

to

were included





Univers

ity of

Cap

e Tow

n
















(2-6)
















Univers

ity of

Cap

e Tow

n

242 AASHTO lRFD
























35 000 N 145 000 N 145000 N



Design Lane 3600 mm


(2-7)

Univers

ity of

Cap

e Tow

n








z [F(M)] (21)

Where

M Moment















from the

in 1975


data base For

calculated The



on normal






z

Where

M Moment

CDF of the moment M










Univers

ity of

Cap

e Tow

n

5~---------+--------~~~~----~ II NGntbs

I ~

j O~--------~~~-------------+------~

~------+ri~----------------+------~

~~--~~------~-------------+------~

Jr---~--------~-------------+------~

~~------------~------------~------~ o








243 CANADIAN CODE









(2-9)

Univers

ity of

Cap

e Tow

n



~ -i 1 3igtm

112ml


Imiddot 18 m

~ ~P) =~-----ffi--tB------ -~---- ----8t------shy

t J-----ffi-----ffi-ffi------ --ffi---- -----~------


ClaHance Errvelope

300 m





So6m 6ampm

180 m

66m






(2-10)

Univers

ity of

Cap

e Tow

n























IIgt

IIIQ

to

ro

to

IQ

~

0








bull bull ~ ~- _- _~ n N 0)





~~Jtli ~ -~ Rf



L~ M I ii 11011

H ~~ II 11

_ r _ t

t7 ~ zo ~ n ~i -ii41 1 II



I IJN ~ ~ 4 1 ) bull ~ 1 r-




(2-11 )

Univers

ity of

Cap

e Tow

n








to measured












BD 3788

244 EUROPEAN CODE





bridge












2)








to measured









the Ontario

effects caused

Base





BD 3788


244 EUROPEAN CODE




is ENV 199





The

traffic












Univers

ity of

Cap

e Tow

n








Location

Axle loads Qik

(kN) qik

(kNm2 )



o

Q

~~H-050 200

-iti--Hl-fosomiddot


-iH----H1-gtI-O50

1m2


050 120

2 00

For IV 300 m








(2-13)

Univers

ity of

Cap

e Tow

n














of the total loads

(i) Free flowing

















(2-14 )






involved the of the

In the case of axle

double and

values were









of the total loads


(i) Free













methods in

relevance is

This

nnmrn of the ENV





Univers

ity of

Cap

e Tow

n

25 CONCLUSIONS





















TMH7 Part 2




load model









(2-15)

25







W1dertaken

live







methods that

models an












TMH7 Part 2




load model









Univers

ity of

Cap

e Tow

n


31 INTRODUCTION










9100401 amp 02



















(3-1 )

31 INTRODUCTION

32








vehicles on

deterministic

9100401 amp 02






WIM were set















Univers

ity of

Cap

e Tow

n

















321 Actual Vehicles













Table 31


Vehicles Vehicles

No of Recorded

Vehicles 24901 34951 2587 62079


Univers

ity of

Cap

e Tow

n

F





In the


5 to 15 20 30 6 Axle Veh Mean 1040 2801 4734 7507 14319



Std Dev 345 915 1701 2794 5865


5 to 15 20 30 6 Axle Veh Mean 952 1224 1500 1782 2115



Std Dev 324 418 546 654 815


322 Legal Vehicles
















overestimated

it was

(3-3)

Univers

ity of

Cap

e Tow

n







standard deviation


5 10 15 20 30





5 10 15 20 30








regulations










(3-4)

Univers

ity of

Cap

e Tow

n



18000

(3-5)



Univers

ity of

Cap

e Tow

n


Accuracy of Data
























(COST 323 1997)



actual vehicle

(3-6)

33 APPROACH

of Data


















may be 25 more or


individual results






323 1



actual vehicle


the road vehicles



Univers

ity of

Cap

e Tow

n











940 1300 1500 1460 1180 1200 122 0 383Max 442 519 507 470 489 47 5 48 2 196Mean 100 207 208 216 207 213 207 870Std Dev


272 1267 1062 1535 1339 1190 831 8820 1476 2026 1734 1464 1522 1083 679 4725 1776 2242 1948 1260 1247 899 485 5430 2051 2146 1654 1128 1119 805 422 4835

40 3662 1796 1360 1119 1068 824 464 63 5976 1722 1342 1183 1061 943 535 4945 6436 1769 1304 1301 1233 1135 633 7350 4961 1775 1454 1476 1489 1375 864 7255 2460 2291 1850 1803 1788 1672 1195 6760 794 2747 2328 2117 2026 1805 1200 4565 144 3033 2590 2039 2046 1658 1080 3670 24 2694 2107 1528 1571 1218 705 1375

80 4 1976 1376 928 933 716 388 9 85 2 1019 719 394 423 275 151 4 90 0 487 __- 305 164 _ 170 __ 127- 51 _-- 1 ___ _ - _ _-_ _shy

95 I 213 112 58 47 47 18 0 100 0 80 43 31 23 19 6 0 105 0 43 14 8 5 5 3 0

0 17 8 4 2 2 2 0110 0 II 9 2 0 3 0 0115

120 0 3 3 0 2 2 0 0 125 0 6 1 I 0 0 I 0

More 0 2 1 I 0 0 0 0 30039 30039 24065 21383 20070 17360 10437 774Sum


(3-7)

Univers

ity of

Cap

e Tow

n







2500 12000

c 0c10000 ltI2000 C I ~

8000 c ~

1500 IltI

~H-I-t++-f-++-+ 000

-=e

~C qj 6000 iI a Q~ 1000

qj~ 4000 ~ ~ ~

500 20 00 I

U

o

Bin







(3-8)

Univers

ity of

Cap

e Tow

n

00030 -----------r-------------------r--------

o 00025 JI ~ 00020 i-----I~--_I_---t_-~--+---+-----f----I lIi i~ 00015 ~

] 00010 to

ampJ o ~ 00005 +----+----+----~-------_IIoc__

00000 +----+----+----j----i----+----+---

o 100 200 300 400 500 600 700

Weight(kN)


001200

sa 001000 v

~ 000800pound

000600 ~ 15 000400 ~ to ~ 0

000200 ~

000000

0 50 100 150 200 250



000080

000070

ll 0

000060 ~ 000050 ~

fshy 000040 S ~ l- 000030 g ampJ

000020

0

D

p 000010

000000

i-~-I- ---- __ ~

o 500 1000 1500 2000 2500 3000



(3-9)

Univers

ity of

Cap

e Tow

n


















events and







respectively




periods (Dawe 2003)

0)
















ENV 1991-3 et 200

The

the

(i)




events and

In the case of

of the extreme










Univers

ity of

Cap

e Tow

n






and for each class






lIN



(31)

2515517 + 080853w+ 0010328w2

z=w- 2 (32)1+ 1432788w+ 01 89269w + 0001

Where






=x+Krs (33)

Where

Xr Event at time T

x Mean of events

Kr rPllHPU factor

1)

Univers

ity of

Cap

e Tow

n









therefore similar


5 285 290 278 290 10 762 739 743 762 15 1266 1365 1372 1372 20 2069 2262 2242 2262 30 4740 4638 4740



5 263 261 258 263 10 323 343 339 343 15 417 439 436 439 20 495 522 537

653 675



6 Axle 533 281 91 -021 7 Axle 653 367 118 -073 8 584 122 -056










(3-12)

Univers

ity of

Cap

e Tow

n












m 04P(Xgtx ) =--- (34)

n+

Where











with B

Where


342 Extreme












Cunnanes formula

gt

Where











with B

Where

T Return where T 1

Univers

ity of

Cap

e Tow

n

--

- - -_--_- _ shy3000

2800+------I----+----+----~--~---~f- shy

S ~ 2600+----~---r_----~----~~~--4----~

ir j 2400+----+---1-------1~~---~---r---~ ~ ~~ ~b

~ 2200 +---~---~~~--1---~---+-------1

jJl

2000+---~~--1-----I---~---r---~

1800 -------1f----+-----t-- Plot Area Ir------+-----I


--6 Axle

----- - -------- - - ------- __- -----shy3200

3000

e ~ 2800 i S 2600 ~ ~I Vsect 2400 ai

jJl 2200

2000 o 2 4 6 8 10 12

Reduced V ruiate

-+-7 Axle

3000

I 2800

2600 ~

I~ 2400 I

I2200

Chart Area

2000

o 2 4 6 8

Reduced Vuiate

1-+-8 Axle I


(3-14 )

12

10

Univers

ity of

Cap

e Tow

n-- __ ___shy480

460

440

~ 420

400 ~

380ie (I)

u 360

340

320

300

380

360

340

~ 320 300 ~

280lt Vol

260

240

220

J -~

V ~

~ v

_ _

j~

~

- V

o 2 4 6 8 10

Reduced Variate

--6 Axle

o 2 4 6 8 10

Reduced Variate

--+-7 Axle

440

420

400

~ 380 i 360 ~

ie 340 -= ~ 320

300

280

V

1

Ir

~

V

o 2 4 6 8

Re(luced Variate

-+- 8 Axle


(3-15)

12

i

12

10

Univers

ity of

Cap

e Tow

n













No of Reduced Event

5m Spans

10m Spans

15m Spans

20m Spans

30m

22 28 42

22 28 42

22 28 42

22 28 42

22 28

2024 2000 1961

5448 5379 5254

8937 8835 8659

13728 13572 13313

25468

25224

99 99 98

267 271 285

376 387 405

583 597 611

969

979

31680 40320 60480

31680 40320 60480

31680 40320 60480

31680 40320 60480

31680

40320

751 727 687

751 727 687

751 727 687

751 727 687

751

727

763 782 813

763 782

813

763 782 813

763 782 813

763

782

278 277 276

749

750 757

1181 1186 1195

1818 1824 1828

3285

3288






(3-16)

Univers

ity of

Cap

e Tow

n

5 301 238 -21 10 812 631 -22 15 1364 1129 -17 20 2097 1756 -16 30 3631 3380 -7
















(3-17)

Univers

ity of

Cap

e Tow

n

1500 -------------------------------------------

1400 - S ~ 1300 -

~ 1200 S o ~ 1100 OJ)

=g 1000 ClJ

=l 900

800 +-----~----~----_r----~----~------~--~

-100 100 300 500 700 900 1100 1300

Reduced Variate


390

370

- 350 ~ - ClJ ~ 330 0 ~

~ 310 ClJ

c rJ)

290

270

250

Reduced Variate

-100 100 300 500 700 900 1100 1300




(3-18)

Univers

ity of

Cap

e Tow

n

1450 -----------~--------------------------_

1350

1250

1150

1050

950

-


Q rJ1

850 +-----~----~----~----~----~----~----~

-100 100 300 500 700 900 1100 1300

Reduced Variate


-Nonnal Gwnbel

360

350

340

330

320

310

300

290

280

270

260

-100 100 300 500 700 900

Reduced Variate

1100 1300


Nonnal Gwnbel


(3-19)

Univers

ity of

Cap

e Tow

n

1200

1150 --

3 1100

~ - 1050 ~

3 = 1000 0

~ 950 OJ)

0 = 900 ~ = ~ 850

800

750

-l00 l00 300 500 700 1100 l300

Reduced Variate

900


--Nonnal Gwnbel

370

350

-Z ~ - ~ (j 0 ~

11 ~ -= 00

330

310

290

270

250

230

-100 100 300 500

Reduced Variate

700 900 1100


-- Nonnal Gumbel


(3-20)

Univers

ity of

Cap

e Tow

n
































+





effective

years 40320











number of the

between the 28











the human and

the most




Univers

ity of

Cap

e Tow

n






a (37)





n

X Gumbel s = 1 1+11 + 11000Kn] 2 S (39)e

n







(3-22)

Univers

ity of

Cap

e Tow

n

---

4150

3950

3750

e 3550 ~ - 3350 = ~ e 3150 Q

~ 2950

2750

2550

2350

-100 100 300 500 700 900 1100 1300

Reduced Variate




35 RESULTS






91 00401 amp 02



5 276 301 231 301 10 757 812 624 812 15 1195 1364 1135 1364 20 1828 2097 1780 2097 30 3275 3631 3289 3631




5 297 233 201 297 10 320 314 279 320 15 369 350 349 369 20 431 433 392 433 30 489 542 481 542


(3-23)

Univers

ity of

Cap

e Tow

n




and







the vehicles axle


Mean 467 529 518 423 429 441 2806 6 Axle

Std Dev 68 196 199 199 188 189 913Vehicles 006 -014 -009 012 001 -021

Mean 488 557 555 529 545 501 490 3665 7 Axle

Std Dev 67 201 191 215 224 205 1176Vehicles 16 -059

Mean 470 504 526 455 456 446 391 384 3632 8 Axle







events


5 98 147 117 10 104 141 119 15 93 128 124 20 92 128 119 30 95


(3-24)

Univers

ity of

Cap

e Tow

n



5 151 130 104 10 120 1l0 127 15 103 88 133 20 103 95 116 30 103 113









NowakGumbel

5 290 301 -4 10 762 S12 -6 15 1372 1364 1 20 2262 2097 S 30 4740 3631


Shear Forces


NowakGumbel

5 263 297 -11 10 343 320 7 15 439 369 19 20 537 433 24

542







Univers

ity of

Cap

e Tow

n


5m 10m 15m 20m 30m


276 292 (+59)

301 (+89)

757 804 828

1195 1262 1297

(+56)

1829 1930 1982

3275 3436 3519

(+49)

(+74)


Univers

ity of

Cap

e Tow

n

36 OVERLOADING
















12

~ 08 D lte

D 0 shy 06p v ~

-a 04

8 02

o 100 200 300 400 500 600 700 800 900

Weight (lN)



(3-27)

Univers

ity of

Cap

e Tow

n











representative


6 Axle 00 19 20 21 12 25 7 Axle 03 77 69 09 09 56 37 8 Axle 83 280 310 13 09 44 67 70

444











was retained










(3-28)

Univers

ity of

Cap

e Tow

n













5 -2 -6 3 5 -1 7 10 6 -13 14 -9 -4 6 15 -11 -11 11 1 -6 5 20 -4 -7 6 5 -3 8

30 -4 -1 3 5 2 21













5 197 195 196 216 220 181 10 13 -8 10 510 547 520 582 600 486 14 10 -7

15 968 1054 986 946 1034 875 -2 -2 -11 20 1504 1582 1537 1452 1599 1388 -3 1 -10

30 2767 2917 2899 2676 2944 2697 -3 1 -7


(3-29)

Univers

ity of

Cap

e Tow

n



5 182 183 184 210 197 164 15 8 -11 10 246 251 252 249 250 220 1 0 -13 15 295 308 302 298 293 272 1 -5 -10 20 337 347 337 349 358 316 4 3 -6 30 411 440












Univers

ity of

Cap

e Tow

n

37 CONCLUSIONS










set of events

























(3-31)

37 CONCLUSIONS










set of events

























(3-31)

Univers

ity of

Cap

e Tow

n






June 1994









examined

41 TMH7 PART 2








to traffic










(4-1 )

2 amp i) UD i)J ol

The

Part 2





June 1994

Vehicle Loads on



Vehicle Loads on







examined

41 TMH7 PART 2

411 and OAfAIIID







to traffic






favoured this




Univers

ity of

Cap

e Tow

nL









fonnula (1970)


Where

Impact factor





















(4-2)









fonnula (1970)

cent = 5(100 + L) 10+L

Where

Impact factor






















(4-2)

Univers

ity of

Cap

e Tow

n












the WIM sensors

















group






(4-3)



The

412 NA

The




Curves

curve for

UH1lUH of the no-m






the WIM sensors

As

and








The



earlier work






20

group







Univers

ity of

Cap

e Tow

n


















40

-

sect ~ - C ~ 0

l C ~ I

Q

C 0is

5

0

10 100 1000

Loaded length (m)

~------------------------~~------------------------~

1-30

25

20 1-15

-- ------



(4-4)

Univers

ity of

Cap

e Tow

n

---

___bull___ __ _- --- ---___bull _bull40

35

---E 30 -+ --+-shy

Z ~ - 25 ~ CI 0

l 20 ~ ltII c = 15 i 10Q

+5

0

10 100 1000

Loaded length (m)
























(4-5)

Univers

ity of

Cap

e Tow

n















2-Axle 216 204 195 190 183 186 184 196

3-Axle 97 106 94 86 82 82 82 165


8-Axle 23 25 25 24 23 25 45 41 9-Axle 01 01 00 01 01 01 02 31

Total 100 100 100 100 100 100 100 100


















(4-6)

Univers

ity of

Cap

e Tow

n
















1600

1400

1200 middot 8 ~

1000 agt-= 8 0 800

~ = 600a =agt

co 400

200

0 4 6 8 10 12 14 16 18

Span m




5 35 10 28 15 23 20 20 30 16


(4-7)

Univers

ity of

Cap

e Tow

n





relevant















416 NB Loading









(4-8)


Given

Ipvntv of TMH7 Part


this

2 the

The

(1

of the

relevant


effects of vehicles



the



and research



415 Lateral






A lateral

at40m

factor of 14 was





416 NB

in the

The









Univers

ity of

Cap

e Tow

n








international and

























(4-9)








international and




the load effects of



of trnrP The in






422

The report

infrastructure

with a

the




with

(i)





Ease of enforcement


and







Univers

ity of

Cap

e Tow

n





applicable factor









Appendix D


Where

the final factor

















(4-10)





factor

ratios were

The statistical










D


Where

the final factor

the factor for the
















0)

Univers

ity of

Cap

e Tow

n



423 Review































(4-11 )





span

The

Review


Axle Loads The full





an

extent






In f1nntltvmo the


















then calculated by






1)

Univers

ity of

Cap

e Tow

n









(4-12)









Univers

ity of

Cap

e Tow

n





















431 Traffic loading



the



formula

( 4-13)














axle

This load




An

and





431 Traffic


technical rl(lgt(1

the




formula

Univers

ity of

Cap

e Tow

n








432 Impact Factor




ForT lt 16t

For T gt SOt



ImEact Allowance

RR91 0041 RR910041 SEan (m) TMH7 01 02

5 35 37 36 10 28 26 18 15 23 17 12 20 20 13 9 30 16 9 6


(4-14)

Univers

ity of

Cap

e Tow

n

433 Test loading
























ENV 1991-3

(4-15)

433 Test




of the



under PTVi






Assessment amp













ENV 1991-3

Univers

ity of

Cap

e Tow

n

I

1J- 8

_______- - 1 ~ ~-- ~

--tf-fBT-1--+Or

I

I IPi t I









240 140 0

NA

6 4 3 3









(4-16)

Univers

ity of

Cap

e Tow

n


5 415 293 42

10 949 810 17

15 1510 1553 -3

20 2442 2520 -3

30 5






most

5 378 10 413 15 506

20 576 30 739

234 324 414

504 684

62 27

22 14 8









436 Critical Review







surveys


in TMH7 Part 2

(4-1

Univers

ity of

Cap

e Tow

n














from the WIM data

(4-18)

In the














from the WIM data

Univers

ity of

Cap

e Tow

n











5 409 415 293 10 957 949 810 15 1527 1510 1553 20 2284 2442 2520 30 3847 5397 5130


6000 - shy

5000 - E

~ 4000-III= ~ 3000 ~ OJ)

= 2000a III= ~

1000

0

0


5 10 15 20 25 30 35 Span (m)

--- Study -0- RR91100402 ~ TMH7 I


(4-19)

Univers

ity of

Cap

e Tow

n

Shear Forces (kN)


5 297 378 234 10 320 413 324 15 369 506 414 20 433 576 504 30 542 739 684


800

700

600 -

~ 500 QJ ~ 0 400 ~ ~ QJ 300

c C-J

200

100

0

0 5 10 15 20 25 30 35

Span (m)












5 409 293 39 10 957 810 18 15 1527 1553 -2 20 2284 2520 -9 30 3847 5130 -25


(4-20)

Univers

ity of

Cap

e Tow

n

























(Section 413)

Shear Force (kN)


5 297 234 27 10 320 324 -1 15 369 414 -11 20 433 504 -14 30 542 684 -21







(4-21)

Univers

ity of

Cap

e Tow

n


Moment (kNm)


5 409 415 -2 10 957 949 1 15 1527 1510 1 20 2284 2442 -6 30 3847

Table 411 - Moment

5397









Shear Force (kN)


5 297 378 -21 10 320 413 -23 15 369 506 -27 20 433 576 -25 30 542 -27


(4-22)

Univers

ity of

Cap

e Tow

n

45 CONCLUSIONS













the roads















return period





(4-23)

45 CONCLUSIONS













the roads















return period





(4-23)

Univers

ity of

Cap

e Tow

n









data







these -0










(5-1 )

51

2

OF LOAD


Part 2 the

3 the




shown in

data











these prlmiddoto










Univers

ity of

Cap

e Tow

n

40 80 ~~~--------~~4~~------------~~

240

I

180


20 20 ~ II~ ~




13 ~ ~

240 240


12 ~ II

150 150

7 1991-3 design

12 ~

200 200


51 - Load Models

Univers

ity of

Cap

e Tow

n





y = -(1 + kV)

load factor r

bias factor


deviation


52 RESULTS




2300

2100 0-v 1900~ 0 1700~ 0

l 1500-=QI

E 1300 0

~ 1)1) ll00 = a 0900 = QI

tl

- - ~~- -- shy - shy - shy

I

I I--- L~- shy ~~t--==- -

r-shy

----r-=9 I

~ 0700

0500

- T - - shy -

o 5 10 15 20 25 30 35

Span (m)


(5-3)

Univers

ity of

Cap

e Tow

n








1800

0 1600 (I

laquoI

1l laquoI 1400 0

l ltII = 1200 8 0

~ ~ 1000 = 0 = ~ 0800

0600

o

~ ~--shy -

~~ n

5 10 15 20 25 30 35

Span (01)

-0-3 6 -4-7 8


1600

14000 (I laquoI

1l laquoI 1200 0

l

ltII (I

0 1000 laquoI ltII

-= ~ 0800

0600

0 5 10 15 20 25 30 35

Span (01)

6 -4-7


(5-4)

Univers

ity of

Cap

e Tow

n





1800

0 1600 v CltI ~ ~

CltI 1AOO 0

e ~ = 1200

0

~ ~ 1000 = a = ~ 0800 I=Q

0600

0 5 10 15 20 25 30 35

Span (m)

6 ~7


1600


v ~ 0 1000 ~

CltI ~ c 00 0800

0600

- - - shy - shy

~

0 5 10 15 20 25 30 35

Span (m)

-ltgt-3 6 ~7 -8


(5-5)

Univers

ity of

Cap

e Tow

n




Table 51 to 54










(5-6)




Table 51 to 54










(5-6)

Univers

ity of

Cap

e Tow

n

Bending Moments

Lane Load 9 kNm


1 124 012 010 154 162 155 145 125 2 133 029 022 240 225 179 166 141 3 091 018 020 171 123 ll1 ll4 114 4 1 56 017 011 223 193 177 180 173 5 172 037 022 339 247 219 219 208 6 084 002 003 091 087 085 090 091 7 123 004 003 139 132 127 131 8 097 002 002 105 101 098 103

Lane Load 18 kNm


1 105 015 014 153 151 138 126 106 2 112 029 026 228 202 158 144 119 3 080 019 023 166 ll7 103 104 099 4 126 023 018 223 183 160 157 141 5 138 039 028 318 224 190 184 164 6 074 004 006 091 084 080 081 079 7 103 010 010 143 130 ll9 119 ll1 8 084 006 007 106 099 092 093 089

Lane Load 27 kNm


I 091 017 018 150 141 125 ll3 093 2 097 029 029 216 182 141 127 103 3 072 019 027 160 ll2 096 095 088 4 107 025 024 216 170 144 138 120 5 ll6 038 033 294 203 167 158 136 6 067 007 010 093 083 077 077 072 7 090 0 14 015 144 126 lll 109 097 8 075 009 012 108 097 088 087 080

Best Fit


(5-7)

Univers

ity of

Cap

e Tow

n

Shear Forces

Lane Load 9 kNm

C

Model

1 2 3 4 5 6 7 8

Mean 102 114 081 144 1 53 075 11 1 088

SD 008 023 013 014 024 010 010 010

V

008 020 016 010 016 013 009 012

135 221 142 200 280 073 116 087


ll8 145 120 183 219 095 136 109

Lane Load 18 kNm


Lane Load 27 kNm


Best Fit


(5-8)

Univers

ity of

Cap

e Tow

n

Bending Moments

Lane Load 9 kNm

Model

I 2 3 4 5 6 7 8

Mean 134 1A2

099 169 186 092 135 107

SD 008 020 020 023 036 017 021 019

V

006 014 020 014 019 018 015 017

1A6

218 174 237 333 119 172 136


200 159 159 122 110 123 200 183 201 237 209 227 112 109 124 161 153 172 129 125 lAI

164 177 161 254 282 165 223 187

Lane Load 18 kNm

Model 1 2 3 4 5 6 7 8

Mean 113 119 087 136 lA8

081 112 092

SD 007

022 018 020 034

011 013 012

V

006 018 021 014 023 014 011 013

135 209 163 213 302 105 lA8

118


130 150 134 187 215 126 158 138

Lane Load 27 kNm

Model 1 2 3 4 5 6 7 8

Mean

098 103 078 115 124 072 097 081

SD

009 023 017 021 033 008 011 009

V

010 022 023 018 027 012 012 011

133 199 154 202 278 096 138 108

Load Factor y 122 108 105 164 127 123 105 090 096 156 132 136 187 154 157 085 077 084 117 104 109 095 086 092

114 131 117 155 177 103 128 111

Best Fit


(5-9)

Univers

ity of

Cap

e Tow

n

Shear Forces

Lane Load 9 kNm

Model

I 2 3 4 5 6 7 8

Mean

135 151 108 190 203 099 147 116

SD

007 026 0 15 017 027 015 017 016

V

005 017 014 009 014 015 012 014

202 250 179 285 325 118 138 105

Load Factor y 193 181 177 188 175 171 127 136 143 231 246 256 235 245 252 114 130 142 129 144 153 100 113 122

189 175 163 280 272 165 173 141

Lane Load 18 kNm

Model

1 2 3 4 5 6 7 8

Mean

115 128 095 154 163 087 123 101

SD 011 027 015 018 030 009 007 008

V

010 021 016 012 018 010 006 008

188 227 175 236 265 104 127 099

Load Factor y 170 157 150 164 150 144 122 126 130 182 185 185 184 183 181 097 107 113 113 121 124 090 099 103

154 142 141 190 184 125 131 112

Lane Load 27 kNm

Model 1 2 3 4 5 6 7 8

Mean 101 112 085 130 137 078 107 089

SD 014 028 015 021 031 005 007 005

V

013 025 018 016 023 006 006 005

178 216 172 206 236 097 118 094

Load Factor y 154 140 132 152 137 129 117 119 120 152 150 146 159 154 148 087 094 096 100 104 104 082 087 089

131 125 126 144 146 103 106 093

Best Fit


(5-10)

Univers

ity of

Cap

e Tow

n
























on bridges









(6-1 )
























on bridges









(6-1 )

Univers

ity of

Cap

e Tow

n










TMH7 Part 2









model



















research

and 1995 in South









TMH7 Part 2









model






the events








live load models




Univers

ity of

Cap

e Tow

n























Part 2










limited expenditure





(6-3)


















over return





Part 2










limited





Univers

ity of

Cap

e Tow

n




(6-4)




Univers

ity of

Cap

e Tow

n

BIBLIOGRAPHY







fedrale de Lausanne












452-461




July 1981

Univers

ity of

Cap

e Tow

n



























Unbaised OlOlttlIll






RR 911004101 The

RR 911004102 The

Assessment Code

an Increase in the

an Increase in the

R K and

Canadian Journal



code 1983 edition

D amp uaveIlDon

Canadian Journal

W British


AlVUUl T and


A S (

Research Record

National 1998


Final



( a

A statistical

6494-513

to the traffic on



of Girder




Crowthorne TRRL



Univers

ity of

Cap

e Tow

n



Engineers


Transport


TRB December 1987























Univers

ity of

Cap

e Tow

n


and Architects



Report)



Univers

ity of

Cap

e Tow

n

A-1

APPENDIX A

A-1

Univers

ity of

Cap

e Tow

nAppendix A


Appendix A


Univers

ity of

Cap

e Tow

n





bull bullbull


77 90 90 80 80 80

o 00 000 Max W = 497kN

Configuration 2

77 90 90 90 90 90

00 00 00 Max W = 527kN

Configuration 3

77 90 9090 90 90

o o 00 00 Max W =527kN

Configuration 4

77 90 90 80 80 80


Configuration 5

102 102

o 00 Max W =560kN


Univers

ity of

Cap

e Tow

n

bull bull bull

3

Configuration 7

80 80 80

000 MaxW = 560kN


Univers

ity of

Cap

e Tow

nbull bull bull

bull bull bull


Configuration 1

80 80 80

Max W = 560kN

Configuration 2

80 80 80

eee Max W = 560kN

Configuration 3

80 80 80

eee MaxW = 560kN

Configuration 4

90 90

MaxW= 560kN


Univers

ity of

Cap

e Tow

n


bull bull bull


5


77 60 60 60 60 60 60 60 60

o 0000 0000 MaxW = 557kN

Configuration 2

80 80 80

000 MaxW = 560kN

Configuration 3

80 80 80



Configuration 4

48 48 48 48 48

00000 MaxW = 557kN


Univers

ity of

Cap

e Tow

n

bullbull bull

bull bull bull

bull bull bull

APPENDlXC

s Ii

~ [I $

~ 1- fl~


Configuration 1

90 90

Max W =560kN

Configuration 2

80 80 80

MaxW = 560kN

Configuration 3

90 90

00 0 MaxW = 560kN

Configuration 4

80 80 80

000 MaxW = 560kN

Configuration 5

80 80 80

Univers

ity of

Cap

e Tow

nAppendix B


bull

Appendix B


bull

Univers

ity of

Cap

e Tow

n

APPENDIXB


6 Axle Vehicles

2~ ------------------------------------

220+------+------+_----_+------+_--~~~--~

e ~200+------+------+------+----~~-----+----~

5 ~ 180 +_----_+------r---~~~----+-----_+----~ s =i 160 +_-----r----~~----_+------+_----_+----~ = I~+-----~------+------+------+------+----~

120 r------+------r-----+-----+------+--~ o 2 4 6 8 10 12

Reduced Variate

---6 Axle

Figure B I Sm span

o 2 4 6 8 0 12

Reduced Variate

-6 Axle

Figure B2 10m span

650

600

~ 550 o ~ 500 8 Q

~ 450 CgtII S 0 ~400 =

350

300

I

~

~

~

Univers

ity of

Cap

e Tow

n

APPENDIX B

1050

1000

9508 ~ 900

-= 850e Q

~ 800 c ~

a 750 ~ ~ 700

650

600

o 2 4 6 8 10 12

~

p y

r

V

Reduced Variate

--6 Axle

Figure B3 15m span

1600

1500 middotLL7 8 ~ 1400 r ~ ~ 1300 e Q

Ishy ~ 1200 ~ c V] 1100 ~ V ~ 1000

900

o 2 4 6 8 10 12

Reduced Variate

--6 Axle

Figure B4 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

3000

2800

8 ~ 2600 sect ~ 2400

E OIlca 2200 ==GI

=I

2000

1800

V

_V

Ijj


10 12

--6 Axle

Figure B5 30m span

Univers

ity of

Cap

e Tow

n

APPENDIXB


6 Axle Vehicles

24)

220

~ 200 180~ ca

c IIl 160

14)

120

0 2 4 6

Reduced Variate

8 10 12

---- 6 Axle

Figure B6 5m span

290

270

__ 250 Z ~ 2l 230 ~ 1 210

c IIl 190

170

150

~ b V

~

~ I

I o 2 4 6 8 10 12

Reduced Variate

--6 Axle

Figure B7 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

330

310

~ 290 Z ~ 270 Q

r 250 ~

c (IJ

230

210

190

o 2 4 6 8 10 12

V

J1V

I ~ I l

Reduced Variate

Figure B8 15m span


6 Axle

Figure B9 20m span

380

360

340

Z ~ 320 300 ~

01 280

c (IJ

260

240

220

--

V ~

~

)1

~

Univers

ity of

Cap

e Tow

n

APPENDIXB

430

410

390 Z 370 ltJ ~ =gt 350 ~ ~ 330c

00

310

290

270 o 2 4 6 12

r V

V ~

~V 1

8 10

I I

I I

1

I I I

i

I I i I

Reduced Variate

--6 Axle


Univers

ity of

Cap

e Tow

n

APPENDIXB


6 Axle Vehicles

200

195

e Z ~

190

-= S 185 ~

~ 011 9 180 0

= Ql

175

170

0 2 4 6

Reduced Variate

8 10 12

--6 Axle I

Figure B 11 5m span

530

520

e ~51O -= ~ 500 ~ 011

=a 490 =

Ql

480

470

V ~

~V ~

o

r

2 4 6 8 10 12

Reduced Variate

I --6 Axle I


Univers

ity of

Cap

e Tow

n

APPENDIXB

1000

950 5 ~ c 900 OJ e Q

~ C)I) 8509 -g c OJ = 800

750


o 2 4 6 8 10 12

Reduced Variate

--6 Axle I


0 122 4 6 8 10

Reduced Variate

--6 Axle

1550

1500

5 ~ 1450 a OJ

C 1400Q

~ C)I)

a a 1350 OJ =

1300

1250

~7

shy

~ V

-~

~

Univers

ity of

Cap

e Tow

n

APPENDIX B

- ~

V d ~

AV V

I

-i

V

2 4 6 8 10 12

Reduced Variate

--6 Axle

2850

2800

e 2750 Z 0 2700 Se2650 Q

~ 2600 ~

5 2550-g ga 2500

2450

2400

o


Univers

ity of

Cap

e Tow

n

APPENDIXB


6 Axle Vehicles

185

180

~ 175 cJ ~

170~ -= en

165

160 0 2 4 6

Reduced Variate

I --6 Axle

8 IO 12

Figure B 16 5m span

250

245

240

235

~ 230

~ 225 ~ ~ 220 -= en

215

210

205

200 -

f

- I

~ ~

7 V


I --6 Axle I

12 o 8 IO


Univers

ity of

Cap

e Tow

n

APPENDIXB

305

300

295

290 ~ 285 0 ~ 280 ~

275 270

265

260 o

2

~

~ r It

V


--+-- 6 Axle I

FigureBl8 15m span


--+-- 6 Axle I


340

335

~ 330

u 3250 ~ 01

320

315

310

~ V V

J ~

~

L V

Univers

ity of

Cap

e Tow

n

APPENDIXB

405

400

395 -

~ 390

QI OJ

Q 385 ~

eo QI 380

c en 375

370

365 o 2 4 6 8 10 12

--~

V

~ V

~

-~

i I

I i i

l Reduced Variate

-+- 6 Axle I

Figure B20 30m span

Univers

ity of

Cap

e Tow

n

APPENDIXB


7 Axle Vehicles

240

220 a ~ 200


CQ

140

120 0 2 4 6

Reduced Variate

--+---7 Axle

Figure B21 Sm span

700

650

~ 600

- 550 ~

~ 500 ~ 450a = ~400

350

300 12o 2 4 6 8 10

4~

h 1

~

I t

I

I

~ -I I

I I I I

Reduced Variate

--+---7 Axle

Figure B22 10m span

8 10 12

Univers

ity of

Cap

e Tow

n

APPENDIXB

1200

1100 e z 0 1000 C a Q 900 1gt11 CIa 800 CI

cQ

700

600


-+--7 Axle

Figure B23 15m span

1800

1700

Le 1600

~ C 1500 sect 1400 ~ ~ 1300a ~ 1200cQ

1100

1000

o 2 4 6 8 10 12

~

d ~

~

7 bull

Reduced Variate

-+--7 Axle

Figure B24 20m span

8 10 12

Univers

ity of

Cap

e Tow

n

APPENDIXB

3200

3000 e 2 2800 CI OJ

e 2600Q


2200

2000


8 IO 12

--7 Axle

Figure B25 30m span

Univers

ity of

Cap

e Tow

n

APPENDIXB


7 Axle Vehicles

240 ----------- ----- ---------------------

220 +---~r_--_+----r----+_---r_--~

~200 +-----4------+----~------+-----~~~~ ~ ~ ~ 160+----~r_---_+-----_b~--+_-----r_--~

140 +----~r_-~~~---r------+-----r_--~

180 +---~r_--_+-----r----~~---r_--~

120+-----r_--_+---~---+------r_---_4

o 2 4 6

Reduced Variate

-+--7 Axle

8 10 12

Figure B26 5m span

270----~------_-------_----~

250+----~----+---~---~--~~--~

Z 230 +---middot~~---+---~----~~--~----~ C ~ 8 210 +-----4-----~---~~~-+---~---~ r ~ ~ 190 +------I-------t~---_t__----+_---__t---_i

170+---~~--~---_t__---+-----__t---_i

150+----~------_+------~------+-----_4-----~

o 2 4 6

Reduced Variate

-+--7 Axle

8 10 12

Figure B27 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

320

300

~ 280 - 41 OJ ~ 260 41

~ 240

220

200

V

V

V

~~

~ f7

I i I I I i

I i 1

o 2 4 6

Reduced Variate

--+-7 Axle

8 0 12

Figure B28 15m span

390

370

~ 350 Z 0 41 330OJ C ~

30 41

c (J 290

270

250

o

h pound

7 6A V I

~

V

4V 2 4 6 8

I r

I I I

I i I

i I


--+-7 Axle

Figure B29 20m span

Univers

ity of

Cap

e Tow

n

APPENDrxB

480

460

44)

Z 420 ~ ~ 400 0

380 os

CI 360(I)

340

320

300

~

)~

d ~ ~

~

k

o 2 4 6

Reduced Variate

-+-7 Axle

8 10 12

Figure B30 30m span

Univers

ity of

Cap

e Tow

n

APPENDIX B


7 Axle Vehicles

200

~ 195

e Z 190 e Jif75 185

8 Q 180 CD

a fS 175 =I 170

~ 165


I ---7 Axle

Figure B31 5m span

o 2 4 6 12

Reduced Variate

580

560

e 54)

~ 520

il 500 01

sect 480 ~ 460

]44) 01

=I 420

400

380

-

I

j ~

--~ ~ ~

I

L

4

8 10

I

I

I

i

---7 Axle

Figure B32 10m span

Univers

ity of

Cap

e Tow

n

APPENDIX 8

1100

1050

e ~ 1000

C 01 e 950 Q

011

= 900a I 01 ~

850

800 0 2 4 6 8 10 12

Reduced Variate

--7 Axle

Figure 833 15m span

1700

1650

e 1600

L ~ 1550 01= e f1500Q

011

= 1450 rIIa 01= ~ ~ 1400

~

1350 ~~

1300 o 2 4 6 8 10 12

Reduced Variate

--7 Axle

Figure 834 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

3000

2950

ez 2900 ~ 2850 e ~

~ 2800 = a ~ 2750 =

2700

2650


-+-7 Axle

4

v

- V

Figure B35 30m span

Univers

ity of

Cap

e Tow

n

APPENDIXB


7 Axle Vehicles

~ ltI ~ 1 -= C-I

190

185

180

175

170

165

160

155

150

145

140

--shy

J r

) -

i-~

~ J1V


I ---7 Axle I

Figure B36 5m span

260

~V250

Y240 ~ ~ 230 -~ 5 ~ -= C-I 220

~

210 ~

200 o 2 4 6 8 10 12

Reduced Variate

I ---7 Axle I

Figure B37 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

320

~ 310

~ 300 r ~ 290 1

~

280 ~

~ ~ CI 270 (I) 260 -

250

240


--+-7 Axle

Figure B38 15m span

355

350

345

340

~ 335 330 ~ 325 ~

CI 320 (I)

315

310

305

300


--+-7 Axle

~

( L

l

~ ~

gt

~ ~

L

~

Figure B39 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

420

415

410

~ 4tl5

tJ

or 400

z (Il

395

390

385


I --7 Axle

Figure B40 30m span

t ~ i-

~~

1pound J

Univers

ity of

Cap

e Tow

n

APPENDIX B


8 Axle Vehicles

o 2 3 4 5 6 7 8 9

Reduced Variate

--+- 8 Axle

Figure B41 Sm span

o 2 3 4 5 6 7 8 9

Reduced Variate

1 --+-8 Axle I

Figure B42 10m span

e 3

550

500

- 450 c e c ~400 OIlca ~

CQ 350

300

V V ~

~--shy V

~ V~

8 ~

550

500

- 450 c a V

V r shy --

V -c ~400 ~

-V a c=350

300

~ V

Univers

ity of

Cap

e Tow

n

1050

1000

8 950

Z 900~

C 850a 0

~ 800 Oilc

750ac =I 700

650

600

o 2 3 4 5

Reduced Variate

1 --+-8 Axle

Figure B43 15m span

1600

1500

e Z 1400 ~ C a 1300 0

~ Oilc 1200ac

=I 1100

1000

o 2 3 4 5

Reduced Variate

--+- 8 Axle

Figure B44 20m span

I

-~ ~

shy

~ ~

~ ~ shy

V

I

~ ~~

- ~

~ ~

~ ~

V III

~

6 7 8

APPENDIXB

9

6 7 8 9

Univers

ity of

Cap

e Tow

n

APPENDIXB

I 17 I

7 ~ ~ I-

I

1

-e ~ i i

~ shy I- I

~ ~ 1

f

~ ~

i

I 2 3 4 5 6 7 8 9

Reduced Variate

1 -+--8 Axle I

3000

2900

2800 8 2700 ~

2600 -= 8 ~

2500 = ~ 2400 0laquo1 = a 2300 = ~

~ 2200

2100

2000 o

Figure B45 30m span

Univers

ity of

Cap

e Tow

n

APPENDIXB


8 Axle Vehicles

260

240

~ 220

~

~V ~ 200 ~ c

IIl 180

160

140

~

~

V ~V

V-

~

o 2 3 4 5

Reduced Variate

I --8 Axle I

6 7 8 9

Figure B46 5m span

250 I

240

~ ~~

~

~

~ ~ I

~

~ I

I I

230

220

~ 210 ~ ~200

I 190 ~ IIl 180

I 1170

J160

150

o 2 3 4 5 6 7 8 9

Reduced Variate

I --8 Axle I

Figure B47 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

310

290

~ 270

0 250

gj I 230rJl

210

190 o 2 3 4 5 9

Reduced Variate

-+-- 8 Axle I

Figure B48 15m span

r-- i I

L i v

v ~

I

~ ~ I

-11 I

~ i j

6 7 8

V

I

360

340

320 Z o 300 ~ ~ 280

c rJl 260

240

220

10-shy

-~

-V

- ~

o 2 3 4 5

Reduced Variate

-+-- 8 Axle I

6 7 8 9

Figure B49 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

440

420

400

~ 380 Q 360 ~ ~ 340 c CIl

320

300

280 o 2 3 4 5 6 7 8 9

~ ~

---~VIII

~

I

L Y I

~ ~ I

~ ~- I

i I I I

1

I I i

Reduced Variate

-+- 8 Axle I

Figure B50 30m span

Univers

ity of

Cap

e Tow

n

APPENDIX B


8 Axle Vehicles

I

I

570

550

a ~ 530

-= ~ ~ 510 ~ 01)

9 ~ 490 OJ

I=Q

470

450

L

I

I i

~- ~

~

-~ shy i

~

I

I j i


--8 Axle I

6 7 8 9

Figure BS I Sm span

570

550

e ~ 530 -

~ -= E lt) 510 ~ 01)c 490ac ~

I=Q

470

~V

-~ ~ ~

~ shy-shy

~

450


I -shy 8 Axle I

6 7 8 9

Figure B52 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

1030 1 i1010

I990e IZ e 970 c ~ 95013 Q

~ 930 OIl

Is= 910 = I= ~

890 1

870 i

850

V ~

[i i

~ V I

~~ I I

~ ~ I I

I

I I

V

I

o 2 3 4 5 6 7 8 9

Reduced Variate

1 -+-8 Axle

Figure B53 15m span

1600 I

~ 15508 ~ z e ~ -c 1500 shy8 ~

~ Q OIl 1450 s= ~ =

V = 1400

1350 o 2 3 4 5 6 7 8 9

Reduced Variate

-+-8 Axle I

Figure B54 20m span

Univers

ity of

Cap

e Tow

n

APPENDIX 8

3000-----r-------------~----~----r---~----~----~

e ~ - 2900 E 8 Q

~ ~

aI 2800 I =

2700+---~~--~----~----~---+----~----~---+--~

o 2 3 4 5

Reduced Variate

-+-8 Axle

Figure 855 30m span

6 7 8 9

Univers

ity of

Cap

e Tow

n

APPENDIX B


8 Axle Vehicles

260

255

250

Z 245

~ ~

240 235= ~ 230~

c CIl 225

220

V

215

210

~ I

~~

~r V

~

~ ~r

I i I

l i

I

o

Figure 856 5m span

2 3 4 5

Reduced Variate

-+- 8 Axle

6 7 8 9

3000

~ --~ ~ 2900 V ~ V

~ V 01 41 ~c

CIl 2800

V ~

2700

o 2 3 4 5 6 7 8 9

Reduced Variate

1 -+-8 Axle I

Figure 857 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

-

o 2 3 4 5 6 7 8 9

Reduced Variate

-+- 8 Axle

Figure B58 15m span

305

300

295

~ 290 III ltJ 285Q ~ ~ 280 c rI)

275

270 I 265

L ~

~ ~

tr V

~

I-shyi-shy

I

I i I

I I I i i I

I

345

340

335

Z 330 ~ III 325 Qr 320 =OJ c 315IJ)

V

~

-U i-

~

310

305 V-300

shy

i I

I I I

I i i

i I


1 -+-8 Axle

6 7 8 9

Figure B59 20m span

Univers

ity of

Cap

e Tow

n

I

APPENDIXB

415

40

405 Z ~ 400 0 ~ 395 gJ

c (I)

390

385

380

o 2 3 6 7 8 9

I

~ V

~

~ ~

~ ~

~

4 5 Reduced Variate

I --8 Axle

k I L

-I

i

I i

i

i

i I

Figure B60 30m span

Univers

ity of

Cap

e Tow

n

APPENDIX B


6 Axle Vehicles

295---------~----------~----------~--_

275

e 255

~ lt11

C 235 e ~ Q

~ 215

195

--t-- i

i-----i---

175 +-----r-----r-------------------r----~

-100 100 300 500 700 900 1100 1300

Reduced Variate

Figure B61 5m span



bull

Univers

ity of

Cap

e Tow

n

APPENDIX 8

1500~----~----------~----r---~~--------~

I I I1400 -1 shy --+-__--_1shy

~ 1300 --~-~---j---+I -

i 1200 -1-shy - -+-shy - -+-shy8 Q


~ ~~~-- I I I 900 r-- ---t---T 800+-----+-----~----r_----r_----r-----~--~

-100 100 300 500 700 900 11 00 1300

Reduced Variate


Figure 863 15m span

2200

2100

~2000 a ~ 1900

i 1800 g1700

~1600 = i 1500

11 1400

1300

1200

I 1

-1 I I

I I I

L---shyI

___shy---- shy

-100 100 300 500 700 900 1100 1300

Reduced Variate


Figure 864 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

3800

3600

e 3400Z e I 3200 QI e

3000Q

~

2800a QI 2600=

2400

2200

-100 100 300 500 700 900 1100 1300

Reduced Variate


Figure B65 30m span

Univers

ity of

Cap

e Tow

n

APPENDIXB


6 Axle Vehicles

300

280

Z 260

0 240 ~ 220i ~ fIJ

200

180

160

I--I-shy

I --shy

i

I

-100 100 300 500 700 900 1100 1300

Reduced Variate


--Nonnal Gumbel

Figure B66 5m span

340

~ - Q CIS ~ fIJ

200

Reduced Variate

320 ~-l--middot- 1 --300

280

260

240 i

220 I T

I

-100 100 300 500 700 900

-I 1100 1300


--Nonnal Gumbel

Figure B67 10m span

Univers

ity of

Cap

e Tow

n

390

370

350

~ 330 r 0

310 ~

CI rJl

290

270

250

i -i----~--~middot~--- -+ -- ---~-- ----~--shy




-100 100 300 500 700 900 1100 1300

Reduced Variate


-- Normal Gwnbel

Figure B68 15m span

440

420

400

~ 380 0 r 01 360

CI rJl

340

320

300

-100 100 300 500 700 900 1100 [300

Reduced Variate


--Normal Gwnbel

Figure B69 20m span

APPENDIXB

Univers

ity of

Cap

e Tow

n

APPENDIXB

510

490

470

~ 450 Ol _ e

430~ 01 41 410

CIl

390

370

350

-100 100 300 500 700 900 1100 1300

Reduced Variate


-- Normal - Gumbel

1 _ - --1-

j ---+--~~I i

-1----1-----

-+-------tli

- -+---~ I - i - --L-- -l- - -l

-I -+---1-- 1


Univers

ity of

Cap

e Tow

n

APPENDIXB


6 Axle Vehicles

220

215


ltgt 200 I~ ~


I 185 19----1----1- -------------r

180

-100 100 300 500 700 900 1100

Reduced Variate


Normal -It- Gwnbel

Figure B71 Sm span

670

650

e 630 Z e 610 7 ltI 590S ltgt ~ 570

cI ~

550 I ltI

cQ 530

510

490

I +---+--+---shy- T - shy -

1 ------

-100 100 300 500 700 900 1100

Reduced Variate



Figure B72 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

1450 -r------------------------

e z 13502 1250

ltII

C e 0 1150 5 ~

1050 c CQ

950

I

~-+_____ I

850+----r---r----~--~---+----~

-100 100 300 500 700 900 1100

Reduced Variate



Figure B73 15m span

1910

1860

e 1810 Z 2 1760l c

1710e 0

1660

5 ~

1610 c CQ 1560

1510

1460

-100 100 1100

--------1 ---

~-r---~-- ----shy- 1- --1-- - -I-

I i

300 500 700 900

Reduced Variate



Figure B74 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

3150 ----------------------------

3100

3050

3000

2950

2900

2850

2800



i I I i -

- i

i

I--I - - -1-shy

I -LOO 100 300 500 700 900 1100

Reduced Variate


-- Normal --Gumbel

Figure B75 30m span

Univers

ity of

Cap

e Tow

n

190

APPENDIXB


6 Axle Vehicles

Z 186 Cshy Ol

184 01 Olc 182

CIl

180

178

-100

I 188 +---1-shy

t-+----shy

100 300 500 700 900 1100 1300

Reduced Variate


-- Normal ~Gumbel

Figure B76 5m span

290

280

270Z e ~ 260 lt=

250 ~ c

rJ)

240

230

220

-100 100 300 500 700 900 1100 1300

Reduced Variate


--Normal ~Gumbel

Figure B77 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

325 i

--------------t------~t__-__I320

315

Z 310cshy 305 Q

300 = c (JJ 295

290

285

280

-100 100 300 500 700 1100 13 00

+--------+--- +-----i---Le----+- -I

=---=------- ------I

j-__+--_ - i___ __ I

900

+-_-I- shyI

Reduced Variate


-- Normal --Gumbel

Figure B78 15m span

355~----~----~----~--~~--------------~

350 +shy

345

340 -Jshy

335

- -I I II

--J---- t---j---- k-- ------------I_____I

---l-

330~~--T----r-----~--~~--~----_----__t

-100 100 300 500 7 00 900 1100 13_00 Reduced Variate


-- Normal Gumbel

Figure B79 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

420

415

410

~ 405 ~ 400 ~ c CIl 395

390

385

-100 100

---1shy--T

I 3_00 500 700 900 11 00 1300

Redoced Variate


Figure B8D 30m span

Univers

ity of

Cap

e Tow

n

APPENDIXB


7 Axle Vehicles

310

--L290

e 270Z ~ l 250c a 230Qa 01)


170 I I i

150

-100 100 300 500 700 900 1100 1300

Reduced Variate


--Normal Gwnbel

Figure B81 5m span

i

600 +----

850~----~--~----~----------------T_--~

800

750 ----1 -1-1-1 -+1-----gt+-1 700 --------I----b---i------ -t-- i_ _ 650 -I- ----+---- +- - -- - --=L--+---tI

~ ac ~ 550

500

450+-----r---~----_+----_r----~----~--~

-100 100 300 500 700 900 1100 1300

Reduced Variate


-- Nonnal Gwnbel

Figure B82 10m span

Univers

ity of

Cap

e Tow

n

1350 ~-+ ~ -1250 - i - ishy1150

I 1050 I 950 I

APPENDIX B

1450 ~--~------------------r----------

850+----r---~----_r---4_----r_-~---~

-100 100 300 500 700 900 1100 1300

Reduced Variate


Normal --Gwnbel

Figure B83 ISm span

2150

2050

E 1950 z ~ 1850 l I 1750S ~

~ 1650 toll

aI 1550 I = 1450

1350

1250

-100 100 300 500

Reduced Variate

__1__ _

i ~~----- --~I -----

700 900 1100 1300


Normal --Gwnbel

Figure B84 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB


2650 f----i~-_+---r---i---+---ir-----l

-100 100 300 500 700 900 lUXgt 13 00

Reduced Variate



Figure B85 30m span

3850 ------1----------------------

3650

3450

3250

3050

2850

Univers

ity of

Cap

e Tow

n

APPENDIXB


7 Axle Vehicles

~ Qj e r ltII Qj

-= CIl

280

260

24)

220

I I +---+-----l-- -+_-+--~I- --


200

180 -l--~_-__+- ------L--__+------ shyt----shy160+-----r---------+-----r-----r----~--~

-100 100 300 500 700 900 1100 1300

Reduced Variate


Normal -+-Gumbel

Figure B86 5m span

320 I

300 1___

I I ~ 280 I Qj

--t-~-- - e 260r g

-= 24) -CIl

220

200

-100 100 300 500 700 900 1100 1300

Redoced Variate



Figure B87 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

360

350

340

~ 330 - 320~ ltJ ~ 310 01 300 -= rIl

290


280

270

260

-100 100 300 500 700 900 1100 1300

Reduced Variate


Normal Gwnbe1

Figure B88 15m span

450r-----~----r_----~----~----~--~----_

430 ~---+_---+_--_+_--_+_--_+--_=_+--_l

Z 410

0 ~ 390ltJ ~ 37001 ~

-= rIl 350

330


310

-100 100 300 500 700 900 1100 1300

Reduced Variate


Normal Gwnbel

Figure B89 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

~ y Q ~ CII d rJJ

560

540

520

500

480

460

440

420

400

380

360

I I



+----+ishy - ---- -+------L shy-shy-----~--___l I I -

-100 100 300 500 700 900 1100 1300

Reduced Variate


Normal --- Gwnbel

Figure B90 30m span

Univers

ity of

Cap

e Tow

n

APPENDIXB


7 Axle Vehicles

210

205 5 z e 200 ~ c e ~ 195

E till ca 190 c

=

185

180

-100 100 300 500 700 900 11 00 1300

Reduced Variate

I r----+-I-- ---~-------+---t---I I


Normal Gumbel

Figure B9 I Sm span

5 Z e l c e ~

E

aC till

c =

535

530

525

520

515

510

505

500


Normal Gumbel


-100 100 300 500 700 900 1100 1300

Reduced Variate

Figure B92 10m span

Univers

ity of

Cap

e Tow

n

1150

1100 - middot 1050

1000 r --

950

900


i I

- 1i

APPENDIX B

1200 -------~----____--____----_

850+---r-----r--~--~---~--_T----~

-100 100 300 500 700 900 1100 1300

Reduced Variate



Figure 893 15m span

e

1650

1630

1610

~ 1590 ~ c 1570 e Q 1550 ~ ell 1530= a c 1510 = 1490

1470

1450

I I -~-t-shyI

i il )

l--shy

-100 100 300 500 700 900 1100 1300

Reduced Variate



Figure 894 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

I i I

-~-+--1-1 ~ I-1--

2820+-----r---~~--~----~----_+----_+----~

-100 100 300 500 700 900 1100 1300

Reduced Variate


-- Normal Gumbel

Figure B95 30m span

2940

2920 e Z 2900ltII

I -OJ

8 ltgt 2880 ~ OG Ia 2860 I OJ

CQ

2840

Univers

ity of

Cap

e Tow

n

APPENDIXB


7 Axle Vehicles

210

205 +---f---l----I I---r----f-----

----- -JbI~__+ - I

--~-l ---- - ---+----+-- i

200 -J-- -+- - - j--shy

~ 195 -- ---1- -+----

ltj 41 190

ri I II i __ J ---r--shy 185

41 -= I ~ I - I ~+---r---rIl 180

175 +-ltSgt---- - +-i--i---T --+--shy i

170

-100 100 300 500 700 900 1100 1300

Reduced Variate


-- Normal --Gumbel

Reduced Variate


--Normal --Gumbel

Figure B97 10m span

Univers

ity of

Cap

e Tow

n

360

+ JiUO--t---

-j---t----+--- -~-- - T -3S0

-340 r- -r- I ~- -1- -shy~ 330 ltJ ~ Q 320 +---h-=-~~--1 ~~-Ib~01

310c ~ -- I-- r-----1-shyen


280

-100 100 300 Soo 700 900 1100 1300

Reduced Variate


-- Normal Gumbel

Figure B98 ISm span

390r---~----~----~-----1

~ 370

~

----------~--~

380 +--------- I - ---r ---+- - - - ------- ---+-- - - - - --1

I - +1--- -+-

3S0 +----+

330+-----r---~----_+---_r----~----~-~

~ 360 +--shygj t3

340



Figure B99 20m span

APPENDIXB

Univers

ity of

Cap

e Tow

n

APPENDIX B

423

421

419

417Z 415 Q

413 ltlI c 411 (IJ

409

407

405

-100 100 300 500 700 900 1100 1300

Reduced Variate



Univers

ity of

Cap

e Tow

n

APPENDIXB


8 Axle Vehicles

240

230

e 220

~ - 210 -= 200e 0

E 190 011c a 180 c = 170

160

150

-100

-I----tl ---+shy

I

-r I i-----1L-~II --_t_

_ -+shy _ _ i

100 300 500 700 900 1100 1300

Reduced Variate


Normal Gumbel

Figure BIOI Sm span

650

8 600 z -I - I c 550 e 0

E 011 500ca I = 450

4OO+-----r---------+-----r-----r----~--~

-II

-100 100 300 500 700 900 1100 1300

Reduced Variate


Normal Gumbel


Univers

ity of

Cap

e Tow

n

APPENDIXB

1200 ----------~r_-r_--__r--____--__


= --+1- ~ l -~ a = CQ

850 q - -I--middot-~ -1

800 I

750 +-----~----~----_----~----_r----~---~

-100 100 300 500 700 900 1100 1300

Reduced Variate




1900

1800

S Z 1700 l = 1600 8 c ~ 1500 OJ)

= a = 1400

CQ

1300

1200

-100 100 300 500 7 00 9 00 1100 1300

Reduced Variate




Univers

ity of

Cap

e Tow

n

APPENDIXB

3350 I

I

I

3250

1-~ --

- 3150S

z --1-shy ~c 3050 1

II I 2950e iQ

2850 011 s 27501l c

I = 2650

2550 -I middot I

2450

-100 100 300 500 700 900 1100 1300

Reduced Variate


-- Normal Gumbel


Univers

ity of

Cap

e Tow

n


8 Axle Vehicles

210----------~------_----~----~----~

200~-----~-----4------~----~-----+--~~

190

~

~


I~+_-----r----_------r-----~-----+----~

I f----- -I shy

180 +---------------

170 -t------------+-~

I I-shy ----------- 1 160 +-------1----4-----

-100 100 300 500 700 900 1100

Reduced Variate


-- Nonnal - Gumbel

Figure B106 5m span

290

280

270

260 ~ - ~ 250 Q 240 ~ 230 ~

rIl 220

210

200

190 -00 100 300


-- Normal -Gumbel


-1---1--shy-1----1-1--shy


500 700 900 11 00

Reduced Variate

APPENDIXB

Univers

ity of

Cap

e Tow

n

APPENDTXB

370


~ 330

01 310

- - --~---t-shy--


270

250

230

-100 100 300 500 700 900 1100

Reduced Variate


-- Normal Gwnbel


~o----~-----------~-----------------_

380

~ 360 01 Q 3~ ~ ~ c 320()

300

280

-100 100 300 500 700 900 1100

Reduced Variate


-- Normal Gumbel


Univers

ity of

Cap

e Tow

n

APPENDIXB

500

480

460

~ 440 OIl

~ Q 420 ~ ltII OIl 400d

(I)

380

360

340

-100 100 300 500 700 900 1100

Reduced Variate


-- Normal Gwnbel


Univers

ity of

Cap

e Tow

n

APPENDIXB


8 Axle Vehicles

210~----~-------~----~--------------

205 ~---l-

200 -j---l-----

195 -+----l~oP ---1-shy +---1------1


185 -t------t----i---i------r----

-100 100 300 500 700 900 1100 1300

Reduced Variate


-- Normal Gumbel

Figure BIll 5m span

545

540

S Z 535 i 530 GI a 0 525 ~ ~ c a 520

C GI

IQ 515

510

505

-t-+---t-I-L I I

-100 100 300 500 700 900 1100 1300

Reduced Variate


-- Normal Gumbel


Univers

ity of

Cap

e Tow

n

APPENDIX B

104)

1030

e 1020Z e l 1010c e 1000=gt OG

990c s c 980=I

970

960

-100 100 300 500 700 900 1100 13 00

Reduced Variate


-- Nonna --- Gumbel


1620-----~--~----~~--_----~----~--~


ac

c =I

1500+-----r---~----_T----_r----~----_--~

1600

1580

1560 l

i 154)

1520

-100 100 300 500 700 900 1100 1300

Reduced Variate


--Nonna --- Gumbel


Univers

ity of

Cap

e Tow

n

APPENDIX B

2970

~ 2950

S z 0 2930 (I)

is e 2910Q

~ 1gt11 Ca 2890 c

al

2870

2850+-----r-----~--~r_--~r_--~----_+----~

-100 100 300 500 700 900 IUlO 1300

Reduced Variate


--Normal -Gwnbel


Univers

ity of

Cap

e Tow

n

--

APPENDIXB


8 Axle Vehicles

200

195

Z ~ 190 ~ ~ 185 ~ -= (I)

180

i i I I ~ E bull

175

c_---+-__---_ ~--_f

~-+-----il-_+ _-+t_i ---t-I-I -100 100 300 500 700 900 1100 1300

Reduced Variate




~ ~

= ~ -= ~ (I)

275-----------~--------~----------~----_

270

265

260

- shy -- ----- shy ----1---shy

I 2S5 -t shy250

245

240

-100 100 3 00 500 700 900 1100 1300

Reduced Variate


--Normal ---Gumbel


Univers

ity of

Cap

e Tow

n

APPENOIXB

325

320 I-- -I ~

315

310OJ ~ 305~ -= (I)

300

295

290

-100 100 300 500 700 900 1100 1300

Reduced Variate



Z e ~ Q

~

~ -= (I)

360~----------------~----~---------------

355

350

345

340

335

330

--+----~-- ~--- i shy - ---+-----1

i I I I -100 100 300 500 700 900 1100 1300

Reduced Variate


-Nannal Gwnbel


Univers

ity of

Cap

e Tow

n

APPENDIXB

QI ~ 415 +---f--shy

-~--t-I I

I -=r-i--- II

I 400+-----~----+_----+_----r_----+_----r_--~

430~----~----~----------~----~----~--~

425 --f ~ r - ~ 420 -I---~---li-- --- --t-shyZ I ==- i

~ o

lltU 410 +-- -r shy

~ ~-----------l405 -1--061+--1-----+ I

i i

-100 100 300 500 700 900 1100 1300

Reduced Variate



Univers

ity of

Cap

e Tow

nAppendix C


II

II

Univers

ity of

Cap

e Tow

n

APPENDIX C

Page No




Univers

ity of

Cap

e Tow

n


Univers

ity of

Cap

e Tow

n




















Univers

ity of

Cap

e Tow

n




I 022

2 23E-05 3


4 46E-09 (2)(3) 5



6 (I) (4)IOE-09


7 47E-18 (6) (4)



9 10E-18 (1)(7)


10 47E-27 (9)(4)








3

Univers

ity of

Cap

e Tow

n


4

Univers

ity of

Cap

e Tow

n

A-1

APPENDIX A

Univers

ity of

Cap

e Tow

nAppendix D

Impact Formula I

bull bull

Univers

ity of

Cap

e Tow

n

APPENDIX 0

Page No







Univers

ity of

Cap

e Tow

n





Where













3J =shy

b L


J =~ b Lf





Where













3 J =shy

b L


J =~ b Lf

Univers

ity of

Cap

e Tow

n



therefore used











response

2



therefore used











response

2

Univers

ity of

Cap

e Tow

nAppendix E


bull

Univers

ity of

Cap

e Tow

n

1

APPENDIX E

Page No









Univers

ity of

Cap

e Tow

n

























III 2

I ~


























W~ I i I

WI 2

I I ~


Univers

ity of

Cap

e Tow

n


















2

Univers

ity of

Cap

e Tow

n









moments





















3

E13








moments













E14 Simulation








3

Univers

ity of

Cap

e Tow

n






(i) Maximum W

(ii) Shortest b

(iii) Centred x =05












limits





legal vehicles





4

Univers

ity of

Cap

e Tow

n







5 197 189 4

10 547 562 3 15 1054 1054 0 20 1582 1626 3)

7


0 Connor Difference

5 184 173 -6

10 252 258 3 15 308 304 -1 20 347 346 0





simulations









5

Univers

ity of

Cap

e Tow

n

Bending Moments kNm


5 293 301 -3 10 800 812 -1 15 1262 1364 -7 20 1903 2097 -9 30 3526 3631 -3








6

Univers

ity of

Cap

e Tow

nAppendix F


Visual Bas

Univers

ity of

Cap

e Tow

n


Sub centralloadO









Univers

ity of

Cap

e Tow

n




pos = inc n







+


pos = inc n



10) lt= 0 Or

+ + +


Then Then Then





+ + spaclO



Univers

ity of

Cap

e Tow

n






n=n+1 Loop



Next z


Univers

ity of

Cap

e Tow

n




Nexty








Next s


End Sub




Nexty








Next s


End Sub

Univers

ity of

Cap

e Tow

n

DECLARATION




John R B Anderson

(iii)

Univers

ity of

Cap

e Tow

n

ACKNOWLEDGMENT





(iv)

Univers

ity of

Cap

e Tow

n

TABLE CONTENTS

No

1 INTRODUCTION

11 BACKGROUND 1-1

12 OF THE STUDy 1-2

1-3 13 SCOPE OF THE

14 METHODOLOGy 1-4






21 INTRODUCTION 2-1





25 CONCLUSIONS 2-15


31 INTRODUCTION 3-1







35 RESULTS 3-23

36 OVERLOADING 3-27

37 CONCLUSiONS 3-31

Univers

ity of

Cap

e Tow

n


41 TMH7 PART 2 4-1








45 CONCLUSIONS 4-23



52 RESULTS 5-3








(vi)


41 TMH7 PART 2 4-1








45 CONCLUSiONS 4-23



52 RESULTS 5-3








(vi)

Univers

ity of

Cap

e Tow

n

List of































(vii)

List of




24 - of H20 LRFD 1 2-7


26 CL-W Truck 2-10

2-10 27 - CL-W


31 -

32 -

33 -

34 -


of GVMs 3-8


Function of

Function of

Moments 30m span

Moments 5m span

3-9

3-9











41 -

42 -

44


Distributed Lane

Moments Due to

of Class 14 Vehicle


and 4-7

4-14


46 -

47 -

51 -

52 -

of Moments 4-19

gtr of Forces


4-20

5-2


Univers

ity of

Cap

e Tow

n





(viii)

Univers

ity of

Cap

e Tow

n

List of Tables































(ix)

List of Tables


























Table 41 - 4-6





(ix)

Univers

ity of

Cap

e Tow

n












(x)

Table 46

Table 47-






Table 411 -

Table 412 Shear

Table 51 -


Table 53-

Table 54-


WIM data v RR 4-22






Univers

ity of

Cap

e Tow

n

1 INTRODUCTION

11 BACKGROUND
















Regulations


June 1994














(1-1 )

1

11




with the aim of

the most onerous











the Road

commissioned the

to increase the

to consider the



(i)

The main

the


June 994



Vehicle Loads on

Vehicle Loads on












(1-1 )

Univers

ity of

Cap

e Tow

n






























(1-2)

12






vehicles






with

Ullman





and adds to the








WIM are






(1

Univers

ity of

Cap

e Tow

n



RR 91100410 I amp 02




data
















considered

(1-3)



RR 9110040 I amp 02




data
















considered

(1-3)

Univers

ity of

Cap

e Tow

n

14 METHODOLOGY




identified were












approaches














(1-4)

14 METHODOLOGY


142



identified were

TMH7 Part 2 The




and



( I Code These



loads on

close






















(1

Univers

ity of

Cap

e Tow

n


































(1-5)






Statistical

vehicles



vehicles on the N3





vehicle

load effects

and fits the

within a 120 year










both methods is



of an extreme











(1

Univers

ity of

Cap

e Tow

n





(c) Overloading















(1-6)

Critical Assessment




The extent of

vehicle set


vehicle set This

those

between the WIM

event of the actual














(1

Univers

ity of

Cap

e Tow

n

1~ REPORT STRUCTURE













reviewed in detail



















(1

1~ REPORT STRUCTURE




live

extent of

with the










reviewed in detail



In and the















in TMH7

the

load model are



of the WlM data

(1

Univers

ity of

Cap

e Tow

n


21 INTRODUCTION






these loads

















on bridges






and

21 INTRODUCTION








these loads


lIllUlLla on the









BS5400 1978

British Standards




Factor ( I

Code and


on






and

m


Univers

ity of

Cap

e Tow

n










the TMH7 Part 2


























(2-2)



to process and







live load models in

the TMH7 Part 2











- u- sensors









vehicles The


by the vehjcle axle

to the extreme

Allowances for









are shown in 21

Univers

ity of

Cap

e Tow

n

305 366 244 305 244 305 244 m


80 219 100 100 100 100 100 100 kN Axle loads (kN)

Ca)

7 x 305 IT = 213 m 0 ~----- -------__--- ___---

~[I ~[JJ 1 I 1 I 1 I] 70 B 96 896 896 896 8 96 896


(bJ























(2-3)

Univers

ity of

Cap

e Tow

n



























241 BD 3788











24


























APPROACH




241 BD 3788









spans





Univers

ity of

Cap

e Tow

n








W= 260 kNfm


J

BS 5400 Part 2





















(2-5)

10 in the

for loaded







lt11 C l 0

150

E 100 lii CL

s



W= 260 kNfm

BS 153 Part SA

BS 5400 Part 2
















axle loads An


of 146 was

~nrn)~h used was


and lateral

factor of 18 was

to

were included





Univers

ity of

Cap

e Tow

n
















(2-6)
















Univers

ity of

Cap

e Tow

n

242 AASHTO lRFD
























35 000 N 145 000 N 145000 N



Design Lane 3600 mm


(2-7)

Univers

ity of

Cap

e Tow

n








z [F(M)] (21)

Where

M Moment















from the

in 1975


data base For

calculated The



on normal






z

Where

M Moment

CDF of the moment M










Univers

ity of

Cap

e Tow

n

5~---------+--------~~~~----~ II NGntbs

I ~

j O~--------~~~-------------+------~

~------+ri~----------------+------~

~~--~~------~-------------+------~

Jr---~--------~-------------+------~

~~------------~------------~------~ o








243 CANADIAN CODE









(2-9)

Univers

ity of

Cap

e Tow

n



~ -i 1 3igtm

112ml


Imiddot 18 m

~ ~P) =~-----ffi--tB------ -~---- ----8t------shy

t J-----ffi-----ffi-ffi------ --ffi---- -----~------


ClaHance Errvelope

300 m





So6m 6ampm

180 m

66m






(2-10)

Univers

ity of

Cap

e Tow

n























IIgt

IIIQ

to

ro

to

IQ

~

0








bull bull ~ ~- _- _~ n N 0)





~~Jtli ~ -~ Rf



L~ M I ii 11011

H ~~ II 11

_ r _ t

t7 ~ zo ~ n ~i -ii41 1 II



I IJN ~ ~ 4 1 ) bull ~ 1 r-




(2-11 )

Univers

ity of

Cap

e Tow

n








to measured












BD 3788

244 EUROPEAN CODE





bridge












2)








to measured









the Ontario

effects caused

Base





BD 3788


244 EUROPEAN CODE




is ENV 199





The

traffic












Univers

ity of

Cap

e Tow

n








Location

Axle loads Qik

(kN) qik

(kNm2 )



o

Q

~~H-050 200

-iti--Hl-fosomiddot


-iH----H1-gtI-O50

1m2


050 120

2 00

For IV 300 m








(2-13)

Univers

ity of

Cap

e Tow

n














of the total loads

(i) Free flowing

















(2-14 )






involved the of the

In the case of axle

double and

values were









of the total loads


(i) Free













methods in

relevance is

This

nnmrn of the ENV





Univers

ity of

Cap

e Tow

n

25 CONCLUSIONS





















TMH7 Part 2




load model









(2-15)

25







W1dertaken

live







methods that

models an












TMH7 Part 2




load model









Univers

ity of

Cap

e Tow

n


31 INTRODUCTION










9100401 amp 02



















(3-1 )

31 INTRODUCTION

32








vehicles on

deterministic

9100401 amp 02






WIM were set















Univers

ity of

Cap

e Tow

n

















321 Actual Vehicles













Table 31


Vehicles Vehicles

No of Recorded

Vehicles 24901 34951 2587 62079


Univers

ity of

Cap

e Tow

n

F





In the


5 to 15 20 30 6 Axle Veh Mean 1040 2801 4734 7507 14319



Std Dev 345 915 1701 2794 5865


5 to 15 20 30 6 Axle Veh Mean 952 1224 1500 1782 2115



Std Dev 324 418 546 654 815


322 Legal Vehicles
















overestimated

it was

(3-3)

Univers

ity of

Cap

e Tow

n







standard deviation


5 10 15 20 30





5 10 15 20 30








regulations










(3-4)

Univers

ity of

Cap

e Tow

n



18000

(3-5)



Univers

ity of

Cap

e Tow

n


Accuracy of Data
























(COST 323 1997)



actual vehicle

(3-6)

33 APPROACH

of Data


















may be 25 more or


individual results






323 1



actual vehicle


the road vehicles



Univers

ity of

Cap

e Tow

n











940 1300 1500 1460 1180 1200 122 0 383Max 442 519 507 470 489 47 5 48 2 196Mean 100 207 208 216 207 213 207 870Std Dev


272 1267 1062 1535 1339 1190 831 8820 1476 2026 1734 1464 1522 1083 679 4725 1776 2242 1948 1260 1247 899 485 5430 2051 2146 1654 1128 1119 805 422 4835

40 3662 1796 1360 1119 1068 824 464 63 5976 1722 1342 1183 1061 943 535 4945 6436 1769 1304 1301 1233 1135 633 7350 4961 1775 1454 1476 1489 1375 864 7255 2460 2291 1850 1803 1788 1672 1195 6760 794 2747 2328 2117 2026 1805 1200 4565 144 3033 2590 2039 2046 1658 1080 3670 24 2694 2107 1528 1571 1218 705 1375

80 4 1976 1376 928 933 716 388 9 85 2 1019 719 394 423 275 151 4 90 0 487 __- 305 164 _ 170 __ 127- 51 _-- 1 ___ _ - _ _-_ _shy

95 I 213 112 58 47 47 18 0 100 0 80 43 31 23 19 6 0 105 0 43 14 8 5 5 3 0

0 17 8 4 2 2 2 0110 0 II 9 2 0 3 0 0115

120 0 3 3 0 2 2 0 0 125 0 6 1 I 0 0 I 0

More 0 2 1 I 0 0 0 0 30039 30039 24065 21383 20070 17360 10437 774Sum


(3-7)

Univers

ity of

Cap

e Tow

n







2500 12000

c 0c10000 ltI2000 C I ~

8000 c ~

1500 IltI

~H-I-t++-f-++-+ 000

-=e

~C qj 6000 iI a Q~ 1000

qj~ 4000 ~ ~ ~

500 20 00 I

U

o

Bin







(3-8)

Univers

ity of

Cap

e Tow

n

00030 -----------r-------------------r--------

o 00025 JI ~ 00020 i-----I~--_I_---t_-~--+---+-----f----I lIi i~ 00015 ~

] 00010 to

ampJ o ~ 00005 +----+----+----~-------_IIoc__

00000 +----+----+----j----i----+----+---

o 100 200 300 400 500 600 700

Weight(kN)


001200

sa 001000 v

~ 000800pound

000600 ~ 15 000400 ~ to ~ 0

000200 ~

000000

0 50 100 150 200 250



000080

000070

ll 0

000060 ~ 000050 ~

fshy 000040 S ~ l- 000030 g ampJ

000020

0

D

p 000010

000000

i-~-I- ---- __ ~

o 500 1000 1500 2000 2500 3000



(3-9)

Univers

ity of

Cap

e Tow

n


















events and







respectively




periods (Dawe 2003)

0)
















ENV 1991-3 et 200

The

the

(i)




events and

In the case of

of the extreme










Univers

ity of

Cap

e Tow

n






and for each class






lIN



(31)

2515517 + 080853w+ 0010328w2

z=w- 2 (32)1+ 1432788w+ 01 89269w + 0001

Where






=x+Krs (33)

Where

Xr Event at time T

x Mean of events

Kr rPllHPU factor

1)

Univers

ity of

Cap

e Tow

n









therefore similar


5 285 290 278 290 10 762 739 743 762 15 1266 1365 1372 1372 20 2069 2262 2242 2262 30 4740 4638 4740



5 263 261 258 263 10 323 343 339 343 15 417 439 436 439 20 495 522 537

653 675



6 Axle 533 281 91 -021 7 Axle 653 367 118 -073 8 584 122 -056










(3-12)

Univers

ity of

Cap

e Tow

n












m 04P(Xgtx ) =--- (34)

n+

Where











with B

Where


342 Extreme












Cunnanes formula

gt

Where











with B

Where

T Return where T 1

Univers

ity of

Cap

e Tow

n

--

- - -_--_- _ shy3000

2800+------I----+----+----~--~---~f- shy

S ~ 2600+----~---r_----~----~~~--4----~

ir j 2400+----+---1-------1~~---~---r---~ ~ ~~ ~b

~ 2200 +---~---~~~--1---~---+-------1

jJl

2000+---~~--1-----I---~---r---~

1800 -------1f----+-----t-- Plot Area Ir------+-----I


--6 Axle

----- - -------- - - ------- __- -----shy3200

3000

e ~ 2800 i S 2600 ~ ~I Vsect 2400 ai

jJl 2200

2000 o 2 4 6 8 10 12

Reduced V ruiate

-+-7 Axle

3000

I 2800

2600 ~

I~ 2400 I

I2200

Chart Area

2000

o 2 4 6 8

Reduced Vuiate

1-+-8 Axle I


(3-14 )

12

10

Univers

ity of

Cap

e Tow

n-- __ ___shy480

460

440

~ 420

400 ~

380ie (I)

u 360

340

320

300

380

360

340

~ 320 300 ~

280lt Vol

260

240

220

J -~

V ~

~ v

_ _

j~

~

- V

o 2 4 6 8 10

Reduced Variate

--6 Axle

o 2 4 6 8 10

Reduced Variate

--+-7 Axle

440

420

400

~ 380 i 360 ~

ie 340 -= ~ 320

300

280

V

1

Ir

~

V

o 2 4 6 8

Re(luced Variate

-+- 8 Axle


(3-15)

12

i

12

10

Univers

ity of

Cap

e Tow

n













No of Reduced Event

5m Spans

10m Spans

15m Spans

20m Spans

30m

22 28 42

22 28 42

22 28 42

22 28 42

22 28

2024 2000 1961

5448 5379 5254

8937 8835 8659

13728 13572 13313

25468

25224

99 99 98

267 271 285

376 387 405

583 597 611

969

979

31680 40320 60480

31680 40320 60480

31680 40320 60480

31680 40320 60480

31680

40320

751 727 687

751 727 687

751 727 687

751 727 687

751

727

763 782 813

763 782

813

763 782 813

763 782 813

763

782

278 277 276

749

750 757

1181 1186 1195

1818 1824 1828

3285

3288






(3-16)

Univers

ity of

Cap

e Tow

n

5 301 238 -21 10 812 631 -22 15 1364 1129 -17 20 2097 1756 -16 30 3631 3380 -7
















(3-17)

Univers

ity of

Cap

e Tow

n

1500 -------------------------------------------

1400 - S ~ 1300 -

~ 1200 S o ~ 1100 OJ)

=g 1000 ClJ

=l 900

800 +-----~----~----_r----~----~------~--~

-100 100 300 500 700 900 1100 1300

Reduced Variate


390

370

- 350 ~ - ClJ ~ 330 0 ~

~ 310 ClJ

c rJ)

290

270

250

Reduced Variate

-100 100 300 500 700 900 1100 1300




(3-18)

Univers

ity of

Cap

e Tow

n

1450 -----------~--------------------------_

1350

1250

1150

1050

950

-


Q rJ1

850 +-----~----~----~----~----~----~----~

-100 100 300 500 700 900 1100 1300

Reduced Variate


-Nonnal Gwnbel

360

350

340

330

320

310

300

290

280

270

260

-100 100 300 500 700 900

Reduced Variate

1100 1300


Nonnal Gwnbel


(3-19)

Univers

ity of

Cap

e Tow

n

1200

1150 --

3 1100

~ - 1050 ~

3 = 1000 0

~ 950 OJ)

0 = 900 ~ = ~ 850

800

750

-l00 l00 300 500 700 1100 l300

Reduced Variate

900


--Nonnal Gwnbel

370

350

-Z ~ - ~ (j 0 ~

11 ~ -= 00

330

310

290

270

250

230

-100 100 300 500

Reduced Variate

700 900 1100


-- Nonnal Gumbel


(3-20)

Univers

ity of

Cap

e Tow

n
































+





effective

years 40320











number of the

between the 28











the human and

the most




Univers

ity of

Cap

e Tow

n






a (37)





n

X Gumbel s = 1 1+11 + 11000Kn] 2 S (39)e

n







(3-22)

Univers

ity of

Cap

e Tow

n

---

4150

3950

3750

e 3550 ~ - 3350 = ~ e 3150 Q

~ 2950

2750

2550

2350

-100 100 300 500 700 900 1100 1300

Reduced Variate




35 RESULTS






91 00401 amp 02



5 276 301 231 301 10 757 812 624 812 15 1195 1364 1135 1364 20 1828 2097 1780 2097 30 3275 3631 3289 3631




5 297 233 201 297 10 320 314 279 320 15 369 350 349 369 20 431 433 392 433 30 489 542 481 542


(3-23)

Univers

ity of

Cap

e Tow

n




and







the vehicles axle


Mean 467 529 518 423 429 441 2806 6 Axle

Std Dev 68 196 199 199 188 189 913Vehicles 006 -014 -009 012 001 -021

Mean 488 557 555 529 545 501 490 3665 7 Axle

Std Dev 67 201 191 215 224 205 1176Vehicles 16 -059

Mean 470 504 526 455 456 446 391 384 3632 8 Axle







events


5 98 147 117 10 104 141 119 15 93 128 124 20 92 128 119 30 95


(3-24)

Univers

ity of

Cap

e Tow

n



5 151 130 104 10 120 1l0 127 15 103 88 133 20 103 95 116 30 103 113









NowakGumbel

5 290 301 -4 10 762 S12 -6 15 1372 1364 1 20 2262 2097 S 30 4740 3631


Shear Forces


NowakGumbel

5 263 297 -11 10 343 320 7 15 439 369 19 20 537 433 24

542







Univers

ity of

Cap

e Tow

n


5m 10m 15m 20m 30m


276 292 (+59)

301 (+89)

757 804 828

1195 1262 1297

(+56)

1829 1930 1982

3275 3436 3519

(+49)

(+74)


Univers

ity of

Cap

e Tow

n

36 OVERLOADING
















12

~ 08 D lte

D 0 shy 06p v ~

-a 04

8 02

o 100 200 300 400 500 600 700 800 900

Weight (lN)



(3-27)

Univers

ity of

Cap

e Tow

n











representative


6 Axle 00 19 20 21 12 25 7 Axle 03 77 69 09 09 56 37 8 Axle 83 280 310 13 09 44 67 70

444











was retained










(3-28)

Univers

ity of

Cap

e Tow

n













5 -2 -6 3 5 -1 7 10 6 -13 14 -9 -4 6 15 -11 -11 11 1 -6 5 20 -4 -7 6 5 -3 8

30 -4 -1 3 5 2 21













5 197 195 196 216 220 181 10 13 -8 10 510 547 520 582 600 486 14 10 -7

15 968 1054 986 946 1034 875 -2 -2 -11 20 1504 1582 1537 1452 1599 1388 -3 1 -10

30 2767 2917 2899 2676 2944 2697 -3 1 -7


(3-29)

Univers

ity of

Cap

e Tow

n



5 182 183 184 210 197 164 15 8 -11 10 246 251 252 249 250 220 1 0 -13 15 295 308 302 298 293 272 1 -5 -10 20 337 347 337 349 358 316 4 3 -6 30 411 440












Univers

ity of

Cap

e Tow

n

37 CONCLUSIONS










set of events

























(3-31)

37 CONCLUSIONS










set of events

























(3-31)

Univers

ity of

Cap

e Tow

n






June 1994









examined

41 TMH7 PART 2








to traffic










(4-1 )

2 amp i) UD i)J ol

The

Part 2





June 1994

Vehicle Loads on



Vehicle Loads on







examined

41 TMH7 PART 2

411 and OAfAIIID







to traffic






favoured this




Univers

ity of

Cap

e Tow

nL









fonnula (1970)


Where

Impact factor





















(4-2)









fonnula (1970)

cent = 5(100 + L) 10+L

Where

Impact factor






















(4-2)

Univers

ity of

Cap

e Tow

n












the WIM sensors

















group






(4-3)



The

412 NA

The




Curves

curve for

UH1lUH of the no-m






the WIM sensors

As

and








The



earlier work






20

group







Univers

ity of

Cap

e Tow

n


















40

-

sect ~ - C ~ 0

l C ~ I

Q

C 0is

5

0

10 100 1000

Loaded length (m)

~------------------------~~------------------------~

1-30

25

20 1-15

-- ------



(4-4)

Univers

ity of

Cap

e Tow

n

---

___bull___ __ _- --- ---___bull _bull40

35

---E 30 -+ --+-shy

Z ~ - 25 ~ CI 0

l 20 ~ ltII c = 15 i 10Q

+5

0

10 100 1000

Loaded length (m)
























(4-5)

Univers

ity of

Cap

e Tow

n















2-Axle 216 204 195 190 183 186 184 196

3-Axle 97 106 94 86 82 82 82 165


8-Axle 23 25 25 24 23 25 45 41 9-Axle 01 01 00 01 01 01 02 31

Total 100 100 100 100 100 100 100 100


















(4-6)

Univers

ity of

Cap

e Tow

n
















1600

1400

1200 middot 8 ~

1000 agt-= 8 0 800

~ = 600a =agt

co 400

200

0 4 6 8 10 12 14 16 18

Span m




5 35 10 28 15 23 20 20 30 16


(4-7)

Univers

ity of

Cap

e Tow

n





relevant















416 NB Loading









(4-8)


Given

Ipvntv of TMH7 Part


this

2 the

The

(1

of the

relevant


effects of vehicles



the



and research



415 Lateral






A lateral

at40m

factor of 14 was





416 NB

in the

The









Univers

ity of

Cap

e Tow

n








international and

























(4-9)








international and




the load effects of



of trnrP The in






422

The report

infrastructure

with a

the




with

(i)





Ease of enforcement


and







Univers

ity of

Cap

e Tow

n





applicable factor









Appendix D


Where

the final factor

















(4-10)





factor

ratios were

The statistical










D


Where

the final factor

the factor for the
















0)

Univers

ity of

Cap

e Tow

n



423 Review































(4-11 )





span

The

Review


Axle Loads The full





an

extent






In f1nntltvmo the


















then calculated by






1)

Univers

ity of

Cap

e Tow

n









(4-12)









Univers

ity of

Cap

e Tow

n





















431 Traffic loading



the



formula

( 4-13)














axle

This load




An

and





431 Traffic


technical rl(lgt(1

the




formula

Univers

ity of

Cap

e Tow

n








432 Impact Factor




ForT lt 16t

For T gt SOt



ImEact Allowance

RR91 0041 RR910041 SEan (m) TMH7 01 02

5 35 37 36 10 28 26 18 15 23 17 12 20 20 13 9 30 16 9 6


(4-14)

Univers

ity of

Cap

e Tow

n

433 Test loading
























ENV 1991-3

(4-15)

433 Test




of the



under PTVi






Assessment amp













ENV 1991-3

Univers

ity of

Cap

e Tow

n

I

1J- 8

_______- - 1 ~ ~-- ~

--tf-fBT-1--+Or

I

I IPi t I









240 140 0

NA

6 4 3 3









(4-16)

Univers

ity of

Cap

e Tow

n


5 415 293 42

10 949 810 17

15 1510 1553 -3

20 2442 2520 -3

30 5






most

5 378 10 413 15 506

20 576 30 739

234 324 414

504 684

62 27

22 14 8









436 Critical Review







surveys


in TMH7 Part 2

(4-1

Univers

ity of

Cap

e Tow

n














from the WIM data

(4-18)

In the














from the WIM data

Univers

ity of

Cap

e Tow

n











5 409 415 293 10 957 949 810 15 1527 1510 1553 20 2284 2442 2520 30 3847 5397 5130


6000 - shy

5000 - E

~ 4000-III= ~ 3000 ~ OJ)

= 2000a III= ~

1000

0

0


5 10 15 20 25 30 35 Span (m)

--- Study -0- RR91100402 ~ TMH7 I


(4-19)

Univers

ity of

Cap

e Tow

n

Shear Forces (kN)


5 297 378 234 10 320 413 324 15 369 506 414 20 433 576 504 30 542 739 684


800

700

600 -

~ 500 QJ ~ 0 400 ~ ~ QJ 300

c C-J

200

100

0

0 5 10 15 20 25 30 35

Span (m)












5 409 293 39 10 957 810 18 15 1527 1553 -2 20 2284 2520 -9 30 3847 5130 -25


(4-20)

Univers

ity of

Cap

e Tow

n

























(Section 413)

Shear Force (kN)


5 297 234 27 10 320 324 -1 15 369 414 -11 20 433 504 -14 30 542 684 -21







(4-21)

Univers

ity of

Cap

e Tow

n


Moment (kNm)


5 409 415 -2 10 957 949 1 15 1527 1510 1 20 2284 2442 -6 30 3847

Table 411 - Moment

5397









Shear Force (kN)


5 297 378 -21 10 320 413 -23 15 369 506 -27 20 433 576 -25 30 542 -27


(4-22)

Univers

ity of

Cap

e Tow

n

45 CONCLUSIONS













the roads















return period





(4-23)

45 CONCLUSIONS













the roads















return period





(4-23)

Univers

ity of

Cap

e Tow

n









data







these -0










(5-1 )

51

2

OF LOAD


Part 2 the

3 the




shown in

data











these prlmiddoto










Univers

ity of

Cap

e Tow

n

40 80 ~~~--------~~4~~------------~~

240

I

180


20 20 ~ II~ ~




13 ~ ~

240 240


12 ~ II

150 150

7 1991-3 design

12 ~

200 200


51 - Load Models

Univers

ity of

Cap

e Tow

n





y = -(1 + kV)

load factor r

bias factor


deviation


52 RESULTS




2300

2100 0-v 1900~ 0 1700~ 0

l 1500-=QI

E 1300 0

~ 1)1) ll00 = a 0900 = QI

tl

- - ~~- -- shy - shy - shy

I

I I--- L~- shy ~~t--==- -

r-shy

----r-=9 I

~ 0700

0500

- T - - shy -

o 5 10 15 20 25 30 35

Span (m)


(5-3)

Univers

ity of

Cap

e Tow

n








1800

0 1600 (I

laquoI

1l laquoI 1400 0

l ltII = 1200 8 0

~ ~ 1000 = 0 = ~ 0800

0600

o

~ ~--shy -

~~ n

5 10 15 20 25 30 35

Span (01)

-0-3 6 -4-7 8


1600

14000 (I laquoI

1l laquoI 1200 0

l

ltII (I

0 1000 laquoI ltII

-= ~ 0800

0600

0 5 10 15 20 25 30 35

Span (01)

6 -4-7


(5-4)

Univers

ity of

Cap

e Tow

n





1800

0 1600 v CltI ~ ~

CltI 1AOO 0

e ~ = 1200

0

~ ~ 1000 = a = ~ 0800 I=Q

0600

0 5 10 15 20 25 30 35

Span (m)

6 ~7


1600


v ~ 0 1000 ~

CltI ~ c 00 0800

0600

- - - shy - shy

~

0 5 10 15 20 25 30 35

Span (m)

-ltgt-3 6 ~7 -8


(5-5)

Univers

ity of

Cap

e Tow

n




Table 51 to 54










(5-6)




Table 51 to 54










(5-6)

Univers

ity of

Cap

e Tow

n

Bending Moments

Lane Load 9 kNm


1 124 012 010 154 162 155 145 125 2 133 029 022 240 225 179 166 141 3 091 018 020 171 123 ll1 ll4 114 4 1 56 017 011 223 193 177 180 173 5 172 037 022 339 247 219 219 208 6 084 002 003 091 087 085 090 091 7 123 004 003 139 132 127 131 8 097 002 002 105 101 098 103

Lane Load 18 kNm


1 105 015 014 153 151 138 126 106 2 112 029 026 228 202 158 144 119 3 080 019 023 166 ll7 103 104 099 4 126 023 018 223 183 160 157 141 5 138 039 028 318 224 190 184 164 6 074 004 006 091 084 080 081 079 7 103 010 010 143 130 ll9 119 ll1 8 084 006 007 106 099 092 093 089

Lane Load 27 kNm


I 091 017 018 150 141 125 ll3 093 2 097 029 029 216 182 141 127 103 3 072 019 027 160 ll2 096 095 088 4 107 025 024 216 170 144 138 120 5 ll6 038 033 294 203 167 158 136 6 067 007 010 093 083 077 077 072 7 090 0 14 015 144 126 lll 109 097 8 075 009 012 108 097 088 087 080

Best Fit


(5-7)

Univers

ity of

Cap

e Tow

n

Shear Forces

Lane Load 9 kNm

C

Model

1 2 3 4 5 6 7 8

Mean 102 114 081 144 1 53 075 11 1 088

SD 008 023 013 014 024 010 010 010

V

008 020 016 010 016 013 009 012

135 221 142 200 280 073 116 087


ll8 145 120 183 219 095 136 109

Lane Load 18 kNm


Lane Load 27 kNm


Best Fit


(5-8)

Univers

ity of

Cap

e Tow

n

Bending Moments

Lane Load 9 kNm

Model

I 2 3 4 5 6 7 8

Mean 134 1A2

099 169 186 092 135 107

SD 008 020 020 023 036 017 021 019

V

006 014 020 014 019 018 015 017

1A6

218 174 237 333 119 172 136


200 159 159 122 110 123 200 183 201 237 209 227 112 109 124 161 153 172 129 125 lAI

164 177 161 254 282 165 223 187

Lane Load 18 kNm

Model 1 2 3 4 5 6 7 8

Mean 113 119 087 136 lA8

081 112 092

SD 007

022 018 020 034

011 013 012

V

006 018 021 014 023 014 011 013

135 209 163 213 302 105 lA8

118


130 150 134 187 215 126 158 138

Lane Load 27 kNm

Model 1 2 3 4 5 6 7 8

Mean

098 103 078 115 124 072 097 081

SD

009 023 017 021 033 008 011 009

V

010 022 023 018 027 012 012 011

133 199 154 202 278 096 138 108

Load Factor y 122 108 105 164 127 123 105 090 096 156 132 136 187 154 157 085 077 084 117 104 109 095 086 092

114 131 117 155 177 103 128 111

Best Fit


(5-9)

Univers

ity of

Cap

e Tow

n

Shear Forces

Lane Load 9 kNm

Model

I 2 3 4 5 6 7 8

Mean

135 151 108 190 203 099 147 116

SD

007 026 0 15 017 027 015 017 016

V

005 017 014 009 014 015 012 014

202 250 179 285 325 118 138 105

Load Factor y 193 181 177 188 175 171 127 136 143 231 246 256 235 245 252 114 130 142 129 144 153 100 113 122

189 175 163 280 272 165 173 141

Lane Load 18 kNm

Model

1 2 3 4 5 6 7 8

Mean

115 128 095 154 163 087 123 101

SD 011 027 015 018 030 009 007 008

V

010 021 016 012 018 010 006 008

188 227 175 236 265 104 127 099

Load Factor y 170 157 150 164 150 144 122 126 130 182 185 185 184 183 181 097 107 113 113 121 124 090 099 103

154 142 141 190 184 125 131 112

Lane Load 27 kNm

Model 1 2 3 4 5 6 7 8

Mean 101 112 085 130 137 078 107 089

SD 014 028 015 021 031 005 007 005

V

013 025 018 016 023 006 006 005

178 216 172 206 236 097 118 094

Load Factor y 154 140 132 152 137 129 117 119 120 152 150 146 159 154 148 087 094 096 100 104 104 082 087 089

131 125 126 144 146 103 106 093

Best Fit


(5-10)

Univers

ity of

Cap

e Tow

n
























on bridges









(6-1 )
























on bridges









(6-1 )

Univers

ity of

Cap

e Tow

n










TMH7 Part 2









model



















research

and 1995 in South









TMH7 Part 2









model






the events








live load models




Univers

ity of

Cap

e Tow

n























Part 2










limited expenditure





(6-3)


















over return





Part 2










limited





Univers

ity of

Cap

e Tow

n




(6-4)




Univers

ity of

Cap

e Tow

n

BIBLIOGRAPHY







fedrale de Lausanne












452-461




July 1981

Univers

ity of

Cap

e Tow

n



























Unbaised OlOlttlIll






RR 911004101 The

RR 911004102 The

Assessment Code

an Increase in the

an Increase in the

R K and

Canadian Journal



code 1983 edition

D amp uaveIlDon

Canadian Journal

W British


AlVUUl T and


A S (

Research Record

National 1998


Final



( a

A statistical

6494-513

to the traffic on



of Girder




Crowthorne TRRL



Univers

ity of

Cap

e Tow

n



Engineers


Transport


TRB December 1987























Univers

ity of

Cap

e Tow

n


and Architects



Report)



Univers

ity of

Cap

e Tow

n

A-1

APPENDIX A

A-1

Univers

ity of

Cap

e Tow

nAppendix A


Appendix A


Univers

ity of

Cap

e Tow

n





bull bullbull


77 90 90 80 80 80

o 00 000 Max W = 497kN

Configuration 2

77 90 90 90 90 90

00 00 00 Max W = 527kN

Configuration 3

77 90 9090 90 90

o o 00 00 Max W =527kN

Configuration 4

77 90 90 80 80 80


Configuration 5

102 102

o 00 Max W =560kN


Univers

ity of

Cap

e Tow

n

bull bull bull

3

Configuration 7

80 80 80

000 MaxW = 560kN


Univers

ity of

Cap

e Tow

nbull bull bull

bull bull bull


Configuration 1

80 80 80

Max W = 560kN

Configuration 2

80 80 80

eee Max W = 560kN

Configuration 3

80 80 80

eee MaxW = 560kN

Configuration 4

90 90

MaxW= 560kN


Univers

ity of

Cap

e Tow

n


bull bull bull


5


77 60 60 60 60 60 60 60 60

o 0000 0000 MaxW = 557kN

Configuration 2

80 80 80

000 MaxW = 560kN

Configuration 3

80 80 80



Configuration 4

48 48 48 48 48

00000 MaxW = 557kN


Univers

ity of

Cap

e Tow

n

bullbull bull

bull bull bull

bull bull bull

APPENDlXC

s Ii

~ [I $

~ 1- fl~


Configuration 1

90 90

Max W =560kN

Configuration 2

80 80 80

MaxW = 560kN

Configuration 3

90 90

00 0 MaxW = 560kN

Configuration 4

80 80 80

000 MaxW = 560kN

Configuration 5

80 80 80

Univers

ity of

Cap

e Tow

nAppendix B


bull

Appendix B


bull

Univers

ity of

Cap

e Tow

n

APPENDIXB


6 Axle Vehicles

2~ ------------------------------------

220+------+------+_----_+------+_--~~~--~

e ~200+------+------+------+----~~-----+----~

5 ~ 180 +_----_+------r---~~~----+-----_+----~ s =i 160 +_-----r----~~----_+------+_----_+----~ = I~+-----~------+------+------+------+----~

120 r------+------r-----+-----+------+--~ o 2 4 6 8 10 12

Reduced Variate

---6 Axle

Figure B I Sm span

o 2 4 6 8 0 12

Reduced Variate

-6 Axle

Figure B2 10m span

650

600

~ 550 o ~ 500 8 Q

~ 450 CgtII S 0 ~400 =

350

300

I

~

~

~

Univers

ity of

Cap

e Tow

n

APPENDIX B

1050

1000

9508 ~ 900

-= 850e Q

~ 800 c ~

a 750 ~ ~ 700

650

600

o 2 4 6 8 10 12

~

p y

r

V

Reduced Variate

--6 Axle

Figure B3 15m span

1600

1500 middotLL7 8 ~ 1400 r ~ ~ 1300 e Q

Ishy ~ 1200 ~ c V] 1100 ~ V ~ 1000

900

o 2 4 6 8 10 12

Reduced Variate

--6 Axle

Figure B4 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

3000

2800

8 ~ 2600 sect ~ 2400

E OIlca 2200 ==GI

=I

2000

1800

V

_V

Ijj


10 12

--6 Axle

Figure B5 30m span

Univers

ity of

Cap

e Tow

n

APPENDIXB


6 Axle Vehicles

24)

220

~ 200 180~ ca

c IIl 160

14)

120

0 2 4 6

Reduced Variate

8 10 12

---- 6 Axle

Figure B6 5m span

290

270

__ 250 Z ~ 2l 230 ~ 1 210

c IIl 190

170

150

~ b V

~

~ I

I o 2 4 6 8 10 12

Reduced Variate

--6 Axle

Figure B7 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

330

310

~ 290 Z ~ 270 Q

r 250 ~

c (IJ

230

210

190

o 2 4 6 8 10 12

V

J1V

I ~ I l

Reduced Variate

Figure B8 15m span


6 Axle

Figure B9 20m span

380

360

340

Z ~ 320 300 ~

01 280

c (IJ

260

240

220

--

V ~

~

)1

~

Univers

ity of

Cap

e Tow

n

APPENDIXB

430

410

390 Z 370 ltJ ~ =gt 350 ~ ~ 330c

00

310

290

270 o 2 4 6 12

r V

V ~

~V 1

8 10

I I

I I

1

I I I

i

I I i I

Reduced Variate

--6 Axle


Univers

ity of

Cap

e Tow

n

APPENDIXB


6 Axle Vehicles

200

195

e Z ~

190

-= S 185 ~

~ 011 9 180 0

= Ql

175

170

0 2 4 6

Reduced Variate

8 10 12

--6 Axle I

Figure B 11 5m span

530

520

e ~51O -= ~ 500 ~ 011

=a 490 =

Ql

480

470

V ~

~V ~

o

r

2 4 6 8 10 12

Reduced Variate

I --6 Axle I


Univers

ity of

Cap

e Tow

n

APPENDIXB

1000

950 5 ~ c 900 OJ e Q

~ C)I) 8509 -g c OJ = 800

750


o 2 4 6 8 10 12

Reduced Variate

--6 Axle I


0 122 4 6 8 10

Reduced Variate

--6 Axle

1550

1500

5 ~ 1450 a OJ

C 1400Q

~ C)I)

a a 1350 OJ =

1300

1250

~7

shy

~ V

-~

~

Univers

ity of

Cap

e Tow

n

APPENDIX B

- ~

V d ~

AV V

I

-i

V

2 4 6 8 10 12

Reduced Variate

--6 Axle

2850

2800

e 2750 Z 0 2700 Se2650 Q

~ 2600 ~

5 2550-g ga 2500

2450

2400

o


Univers

ity of

Cap

e Tow

n

APPENDIXB


6 Axle Vehicles

185

180

~ 175 cJ ~

170~ -= en

165

160 0 2 4 6

Reduced Variate

I --6 Axle

8 IO 12

Figure B 16 5m span

250

245

240

235

~ 230

~ 225 ~ ~ 220 -= en

215

210

205

200 -

f

- I

~ ~

7 V


I --6 Axle I

12 o 8 IO


Univers

ity of

Cap

e Tow

n

APPENDIXB

305

300

295

290 ~ 285 0 ~ 280 ~

275 270

265

260 o

2

~

~ r It

V


--+-- 6 Axle I

FigureBl8 15m span


--+-- 6 Axle I


340

335

~ 330

u 3250 ~ 01

320

315

310

~ V V

J ~

~

L V

Univers

ity of

Cap

e Tow

n

APPENDIXB

405

400

395 -

~ 390

QI OJ

Q 385 ~

eo QI 380

c en 375

370

365 o 2 4 6 8 10 12

--~

V

~ V

~

-~

i I

I i i

l Reduced Variate

-+- 6 Axle I

Figure B20 30m span

Univers

ity of

Cap

e Tow

n

APPENDIXB


7 Axle Vehicles

240

220 a ~ 200


CQ

140

120 0 2 4 6

Reduced Variate

--+---7 Axle

Figure B21 Sm span

700

650

~ 600

- 550 ~

~ 500 ~ 450a = ~400

350

300 12o 2 4 6 8 10

4~

h 1

~

I t

I

I

~ -I I

I I I I

Reduced Variate

--+---7 Axle

Figure B22 10m span

8 10 12

Univers

ity of

Cap

e Tow

n

APPENDIXB

1200

1100 e z 0 1000 C a Q 900 1gt11 CIa 800 CI

cQ

700

600


-+--7 Axle

Figure B23 15m span

1800

1700

Le 1600

~ C 1500 sect 1400 ~ ~ 1300a ~ 1200cQ

1100

1000

o 2 4 6 8 10 12

~

d ~

~

7 bull

Reduced Variate

-+--7 Axle

Figure B24 20m span

8 10 12

Univers

ity of

Cap

e Tow

n

APPENDIXB

3200

3000 e 2 2800 CI OJ

e 2600Q


2200

2000


8 IO 12

--7 Axle

Figure B25 30m span

Univers

ity of

Cap

e Tow

n

APPENDIXB


7 Axle Vehicles

240 ----------- ----- ---------------------

220 +---~r_--_+----r----+_---r_--~

~200 +-----4------+----~------+-----~~~~ ~ ~ ~ 160+----~r_---_+-----_b~--+_-----r_--~

140 +----~r_-~~~---r------+-----r_--~

180 +---~r_--_+-----r----~~---r_--~

120+-----r_--_+---~---+------r_---_4

o 2 4 6

Reduced Variate

-+--7 Axle

8 10 12

Figure B26 5m span

270----~------_-------_----~

250+----~----+---~---~--~~--~

Z 230 +---middot~~---+---~----~~--~----~ C ~ 8 210 +-----4-----~---~~~-+---~---~ r ~ ~ 190 +------I-------t~---_t__----+_---__t---_i

170+---~~--~---_t__---+-----__t---_i

150+----~------_+------~------+-----_4-----~

o 2 4 6

Reduced Variate

-+--7 Axle

8 10 12

Figure B27 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

320

300

~ 280 - 41 OJ ~ 260 41

~ 240

220

200

V

V

V

~~

~ f7

I i I I I i

I i 1

o 2 4 6

Reduced Variate

--+-7 Axle

8 0 12

Figure B28 15m span

390

370

~ 350 Z 0 41 330OJ C ~

30 41

c (J 290

270

250

o

h pound

7 6A V I

~

V

4V 2 4 6 8

I r

I I I

I i I

i I


--+-7 Axle

Figure B29 20m span

Univers

ity of

Cap

e Tow

n

APPENDrxB

480

460

44)

Z 420 ~ ~ 400 0

380 os

CI 360(I)

340

320

300

~

)~

d ~ ~

~

k

o 2 4 6

Reduced Variate

-+-7 Axle

8 10 12

Figure B30 30m span

Univers

ity of

Cap

e Tow

n

APPENDIX B


7 Axle Vehicles

200

~ 195

e Z 190 e Jif75 185

8 Q 180 CD

a fS 175 =I 170

~ 165


I ---7 Axle

Figure B31 5m span

o 2 4 6 12

Reduced Variate

580

560

e 54)

~ 520

il 500 01

sect 480 ~ 460

]44) 01

=I 420

400

380

-

I

j ~

--~ ~ ~

I

L

4

8 10

I

I

I

i

---7 Axle

Figure B32 10m span

Univers

ity of

Cap

e Tow

n

APPENDIX 8

1100

1050

e ~ 1000

C 01 e 950 Q

011

= 900a I 01 ~

850

800 0 2 4 6 8 10 12

Reduced Variate

--7 Axle

Figure 833 15m span

1700

1650

e 1600

L ~ 1550 01= e f1500Q

011

= 1450 rIIa 01= ~ ~ 1400

~

1350 ~~

1300 o 2 4 6 8 10 12

Reduced Variate

--7 Axle

Figure 834 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

3000

2950

ez 2900 ~ 2850 e ~

~ 2800 = a ~ 2750 =

2700

2650


-+-7 Axle

4

v

- V

Figure B35 30m span

Univers

ity of

Cap

e Tow

n

APPENDIXB


7 Axle Vehicles

~ ltI ~ 1 -= C-I

190

185

180

175

170

165

160

155

150

145

140

--shy

J r

) -

i-~

~ J1V


I ---7 Axle I

Figure B36 5m span

260

~V250

Y240 ~ ~ 230 -~ 5 ~ -= C-I 220

~

210 ~

200 o 2 4 6 8 10 12

Reduced Variate

I ---7 Axle I

Figure B37 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

320

~ 310

~ 300 r ~ 290 1

~

280 ~

~ ~ CI 270 (I) 260 -

250

240


--+-7 Axle

Figure B38 15m span

355

350

345

340

~ 335 330 ~ 325 ~

CI 320 (I)

315

310

305

300


--+-7 Axle

~

( L

l

~ ~

gt

~ ~

L

~

Figure B39 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

420

415

410

~ 4tl5

tJ

or 400

z (Il

395

390

385


I --7 Axle

Figure B40 30m span

t ~ i-

~~

1pound J

Univers

ity of

Cap

e Tow

n

APPENDIX B


8 Axle Vehicles

o 2 3 4 5 6 7 8 9

Reduced Variate

--+- 8 Axle

Figure B41 Sm span

o 2 3 4 5 6 7 8 9

Reduced Variate

1 --+-8 Axle I

Figure B42 10m span

e 3

550

500

- 450 c e c ~400 OIlca ~

CQ 350

300

V V ~

~--shy V

~ V~

8 ~

550

500

- 450 c a V

V r shy --

V -c ~400 ~

-V a c=350

300

~ V

Univers

ity of

Cap

e Tow

n

1050

1000

8 950

Z 900~

C 850a 0

~ 800 Oilc

750ac =I 700

650

600

o 2 3 4 5

Reduced Variate

1 --+-8 Axle

Figure B43 15m span

1600

1500

e Z 1400 ~ C a 1300 0

~ Oilc 1200ac

=I 1100

1000

o 2 3 4 5

Reduced Variate

--+- 8 Axle

Figure B44 20m span

I

-~ ~

shy

~ ~

~ ~ shy

V

I

~ ~~

- ~

~ ~

~ ~

V III

~

6 7 8

APPENDIXB

9

6 7 8 9

Univers

ity of

Cap

e Tow

n

APPENDIXB

I 17 I

7 ~ ~ I-

I

1

-e ~ i i

~ shy I- I

~ ~ 1

f

~ ~

i

I 2 3 4 5 6 7 8 9

Reduced Variate

1 -+--8 Axle I

3000

2900

2800 8 2700 ~

2600 -= 8 ~

2500 = ~ 2400 0laquo1 = a 2300 = ~

~ 2200

2100

2000 o

Figure B45 30m span

Univers

ity of

Cap

e Tow

n

APPENDIXB


8 Axle Vehicles

260

240

~ 220

~

~V ~ 200 ~ c

IIl 180

160

140

~

~

V ~V

V-

~

o 2 3 4 5

Reduced Variate

I --8 Axle I

6 7 8 9

Figure B46 5m span

250 I

240

~ ~~

~

~

~ ~ I

~

~ I

I I

230

220

~ 210 ~ ~200

I 190 ~ IIl 180

I 1170

J160

150

o 2 3 4 5 6 7 8 9

Reduced Variate

I --8 Axle I

Figure B47 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

310

290

~ 270

0 250

gj I 230rJl

210

190 o 2 3 4 5 9

Reduced Variate

-+-- 8 Axle I

Figure B48 15m span

r-- i I

L i v

v ~

I

~ ~ I

-11 I

~ i j

6 7 8

V

I

360

340

320 Z o 300 ~ ~ 280

c rJl 260

240

220

10-shy

-~

-V

- ~

o 2 3 4 5

Reduced Variate

-+-- 8 Axle I

6 7 8 9

Figure B49 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

440

420

400

~ 380 Q 360 ~ ~ 340 c CIl

320

300

280 o 2 3 4 5 6 7 8 9

~ ~

---~VIII

~

I

L Y I

~ ~ I

~ ~- I

i I I I

1

I I i

Reduced Variate

-+- 8 Axle I

Figure B50 30m span

Univers

ity of

Cap

e Tow

n

APPENDIX B


8 Axle Vehicles

I

I

570

550

a ~ 530

-= ~ ~ 510 ~ 01)

9 ~ 490 OJ

I=Q

470

450

L

I

I i

~- ~

~

-~ shy i

~

I

I j i


--8 Axle I

6 7 8 9

Figure BS I Sm span

570

550

e ~ 530 -

~ -= E lt) 510 ~ 01)c 490ac ~

I=Q

470

~V

-~ ~ ~

~ shy-shy

~

450


I -shy 8 Axle I

6 7 8 9

Figure B52 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

1030 1 i1010

I990e IZ e 970 c ~ 95013 Q

~ 930 OIl

Is= 910 = I= ~

890 1

870 i

850

V ~

[i i

~ V I

~~ I I

~ ~ I I

I

I I

V

I

o 2 3 4 5 6 7 8 9

Reduced Variate

1 -+-8 Axle

Figure B53 15m span

1600 I

~ 15508 ~ z e ~ -c 1500 shy8 ~

~ Q OIl 1450 s= ~ =

V = 1400

1350 o 2 3 4 5 6 7 8 9

Reduced Variate

-+-8 Axle I

Figure B54 20m span

Univers

ity of

Cap

e Tow

n

APPENDIX 8

3000-----r-------------~----~----r---~----~----~

e ~ - 2900 E 8 Q

~ ~

aI 2800 I =

2700+---~~--~----~----~---+----~----~---+--~

o 2 3 4 5

Reduced Variate

-+-8 Axle

Figure 855 30m span

6 7 8 9

Univers

ity of

Cap

e Tow

n

APPENDIX B


8 Axle Vehicles

260

255

250

Z 245

~ ~

240 235= ~ 230~

c CIl 225

220

V

215

210

~ I

~~

~r V

~

~ ~r

I i I

l i

I

o

Figure 856 5m span

2 3 4 5

Reduced Variate

-+- 8 Axle

6 7 8 9

3000

~ --~ ~ 2900 V ~ V

~ V 01 41 ~c

CIl 2800

V ~

2700

o 2 3 4 5 6 7 8 9

Reduced Variate

1 -+-8 Axle I

Figure 857 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

-

o 2 3 4 5 6 7 8 9

Reduced Variate

-+- 8 Axle

Figure B58 15m span

305

300

295

~ 290 III ltJ 285Q ~ ~ 280 c rI)

275

270 I 265

L ~

~ ~

tr V

~

I-shyi-shy

I

I i I

I I I i i I

I

345

340

335

Z 330 ~ III 325 Qr 320 =OJ c 315IJ)

V

~

-U i-

~

310

305 V-300

shy

i I

I I I

I i i

i I


1 -+-8 Axle

6 7 8 9

Figure B59 20m span

Univers

ity of

Cap

e Tow

n

I

APPENDIXB

415

40

405 Z ~ 400 0 ~ 395 gJ

c (I)

390

385

380

o 2 3 6 7 8 9

I

~ V

~

~ ~

~ ~

~

4 5 Reduced Variate

I --8 Axle

k I L

-I

i

I i

i

i

i I

Figure B60 30m span

Univers

ity of

Cap

e Tow

n

APPENDIX B


6 Axle Vehicles

295---------~----------~----------~--_

275

e 255

~ lt11

C 235 e ~ Q

~ 215

195

--t-- i

i-----i---

175 +-----r-----r-------------------r----~

-100 100 300 500 700 900 1100 1300

Reduced Variate

Figure B61 5m span



bull

Univers

ity of

Cap

e Tow

n

APPENDIX 8

1500~----~----------~----r---~~--------~

I I I1400 -1 shy --+-__--_1shy

~ 1300 --~-~---j---+I -

i 1200 -1-shy - -+-shy - -+-shy8 Q


~ ~~~-- I I I 900 r-- ---t---T 800+-----+-----~----r_----r_----r-----~--~

-100 100 300 500 700 900 11 00 1300

Reduced Variate


Figure 863 15m span

2200

2100

~2000 a ~ 1900

i 1800 g1700

~1600 = i 1500

11 1400

1300

1200

I 1

-1 I I

I I I

L---shyI

___shy---- shy

-100 100 300 500 700 900 1100 1300

Reduced Variate


Figure 864 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

3800

3600

e 3400Z e I 3200 QI e

3000Q

~

2800a QI 2600=

2400

2200

-100 100 300 500 700 900 1100 1300

Reduced Variate


Figure B65 30m span

Univers

ity of

Cap

e Tow

n

APPENDIXB


6 Axle Vehicles

300

280

Z 260

0 240 ~ 220i ~ fIJ

200

180

160

I--I-shy

I --shy

i

I

-100 100 300 500 700 900 1100 1300

Reduced Variate


--Nonnal Gumbel

Figure B66 5m span

340

~ - Q CIS ~ fIJ

200

Reduced Variate

320 ~-l--middot- 1 --300

280

260

240 i

220 I T

I

-100 100 300 500 700 900

-I 1100 1300


--Nonnal Gumbel

Figure B67 10m span

Univers

ity of

Cap

e Tow

n

390

370

350

~ 330 r 0

310 ~

CI rJl

290

270

250

i -i----~--~middot~--- -+ -- ---~-- ----~--shy




-100 100 300 500 700 900 1100 1300

Reduced Variate


-- Normal Gwnbel

Figure B68 15m span

440

420

400

~ 380 0 r 01 360

CI rJl

340

320

300

-100 100 300 500 700 900 1100 [300

Reduced Variate


--Normal Gwnbel

Figure B69 20m span

APPENDIXB

Univers

ity of

Cap

e Tow

n

APPENDIXB

510

490

470

~ 450 Ol _ e

430~ 01 41 410

CIl

390

370

350

-100 100 300 500 700 900 1100 1300

Reduced Variate


-- Normal - Gumbel

1 _ - --1-

j ---+--~~I i

-1----1-----

-+-------tli

- -+---~ I - i - --L-- -l- - -l

-I -+---1-- 1


Univers

ity of

Cap

e Tow

n

APPENDIXB


6 Axle Vehicles

220

215


ltgt 200 I~ ~


I 185 19----1----1- -------------r

180

-100 100 300 500 700 900 1100

Reduced Variate


Normal -It- Gwnbel

Figure B71 Sm span

670

650

e 630 Z e 610 7 ltI 590S ltgt ~ 570

cI ~

550 I ltI

cQ 530

510

490

I +---+--+---shy- T - shy -

1 ------

-100 100 300 500 700 900 1100

Reduced Variate



Figure B72 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

1450 -r------------------------

e z 13502 1250

ltII

C e 0 1150 5 ~

1050 c CQ

950

I

~-+_____ I

850+----r---r----~--~---+----~

-100 100 300 500 700 900 1100

Reduced Variate



Figure B73 15m span

1910

1860

e 1810 Z 2 1760l c

1710e 0

1660

5 ~

1610 c CQ 1560

1510

1460

-100 100 1100

--------1 ---

~-r---~-- ----shy- 1- --1-- - -I-

I i

300 500 700 900

Reduced Variate



Figure B74 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

3150 ----------------------------

3100

3050

3000

2950

2900

2850

2800



i I I i -

- i

i

I--I - - -1-shy

I -LOO 100 300 500 700 900 1100

Reduced Variate


-- Normal --Gumbel

Figure B75 30m span

Univers

ity of

Cap

e Tow

n

190

APPENDIXB


6 Axle Vehicles

Z 186 Cshy Ol

184 01 Olc 182

CIl

180

178

-100

I 188 +---1-shy

t-+----shy

100 300 500 700 900 1100 1300

Reduced Variate


-- Normal ~Gumbel

Figure B76 5m span

290

280

270Z e ~ 260 lt=

250 ~ c

rJ)

240

230

220

-100 100 300 500 700 900 1100 1300

Reduced Variate


--Normal ~Gumbel

Figure B77 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

325 i

--------------t------~t__-__I320

315

Z 310cshy 305 Q

300 = c (JJ 295

290

285

280

-100 100 300 500 700 1100 13 00

+--------+--- +-----i---Le----+- -I

=---=------- ------I

j-__+--_ - i___ __ I

900

+-_-I- shyI

Reduced Variate


-- Normal --Gumbel

Figure B78 15m span

355~----~----~----~--~~--------------~

350 +shy

345

340 -Jshy

335

- -I I II

--J---- t---j---- k-- ------------I_____I

---l-

330~~--T----r-----~--~~--~----_----__t

-100 100 300 500 7 00 900 1100 13_00 Reduced Variate


-- Normal Gumbel

Figure B79 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

420

415

410

~ 405 ~ 400 ~ c CIl 395

390

385

-100 100

---1shy--T

I 3_00 500 700 900 11 00 1300

Redoced Variate


Figure B8D 30m span

Univers

ity of

Cap

e Tow

n

APPENDIXB


7 Axle Vehicles

310

--L290

e 270Z ~ l 250c a 230Qa 01)


170 I I i

150

-100 100 300 500 700 900 1100 1300

Reduced Variate


--Normal Gwnbel

Figure B81 5m span

i

600 +----

850~----~--~----~----------------T_--~

800

750 ----1 -1-1-1 -+1-----gt+-1 700 --------I----b---i------ -t-- i_ _ 650 -I- ----+---- +- - -- - --=L--+---tI

~ ac ~ 550

500

450+-----r---~----_+----_r----~----~--~

-100 100 300 500 700 900 1100 1300

Reduced Variate


-- Nonnal Gwnbel

Figure B82 10m span

Univers

ity of

Cap

e Tow

n

1350 ~-+ ~ -1250 - i - ishy1150

I 1050 I 950 I

APPENDIX B

1450 ~--~------------------r----------

850+----r---~----_r---4_----r_-~---~

-100 100 300 500 700 900 1100 1300

Reduced Variate


Normal --Gwnbel

Figure B83 ISm span

2150

2050

E 1950 z ~ 1850 l I 1750S ~

~ 1650 toll

aI 1550 I = 1450

1350

1250

-100 100 300 500

Reduced Variate

__1__ _

i ~~----- --~I -----

700 900 1100 1300


Normal --Gwnbel

Figure B84 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB


2650 f----i~-_+---r---i---+---ir-----l

-100 100 300 500 700 900 lUXgt 13 00

Reduced Variate



Figure B85 30m span

3850 ------1----------------------

3650

3450

3250

3050

2850

Univers

ity of

Cap

e Tow

n

APPENDIXB


7 Axle Vehicles

~ Qj e r ltII Qj

-= CIl

280

260

24)

220

I I +---+-----l-- -+_-+--~I- --


200

180 -l--~_-__+- ------L--__+------ shyt----shy160+-----r---------+-----r-----r----~--~

-100 100 300 500 700 900 1100 1300

Reduced Variate


Normal -+-Gumbel

Figure B86 5m span

320 I

300 1___

I I ~ 280 I Qj

--t-~-- - e 260r g

-= 24) -CIl

220

200

-100 100 300 500 700 900 1100 1300

Redoced Variate



Figure B87 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

360

350

340

~ 330 - 320~ ltJ ~ 310 01 300 -= rIl

290


280

270

260

-100 100 300 500 700 900 1100 1300

Reduced Variate


Normal Gwnbe1

Figure B88 15m span

450r-----~----r_----~----~----~--~----_

430 ~---+_---+_--_+_--_+_--_+--_=_+--_l

Z 410

0 ~ 390ltJ ~ 37001 ~

-= rIl 350

330


310

-100 100 300 500 700 900 1100 1300

Reduced Variate


Normal Gwnbel

Figure B89 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

~ y Q ~ CII d rJJ

560

540

520

500

480

460

440

420

400

380

360

I I



+----+ishy - ---- -+------L shy-shy-----~--___l I I -

-100 100 300 500 700 900 1100 1300

Reduced Variate


Normal --- Gwnbel

Figure B90 30m span

Univers

ity of

Cap

e Tow

n

APPENDIXB


7 Axle Vehicles

210

205 5 z e 200 ~ c e ~ 195

E till ca 190 c

=

185

180

-100 100 300 500 700 900 11 00 1300

Reduced Variate

I r----+-I-- ---~-------+---t---I I


Normal Gumbel

Figure B9 I Sm span

5 Z e l c e ~

E

aC till

c =

535

530

525

520

515

510

505

500


Normal Gumbel


-100 100 300 500 700 900 1100 1300

Reduced Variate

Figure B92 10m span

Univers

ity of

Cap

e Tow

n

1150

1100 - middot 1050

1000 r --

950

900


i I

- 1i

APPENDIX B

1200 -------~----____--____----_

850+---r-----r--~--~---~--_T----~

-100 100 300 500 700 900 1100 1300

Reduced Variate



Figure 893 15m span

e

1650

1630

1610

~ 1590 ~ c 1570 e Q 1550 ~ ell 1530= a c 1510 = 1490

1470

1450

I I -~-t-shyI

i il )

l--shy

-100 100 300 500 700 900 1100 1300

Reduced Variate



Figure 894 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

I i I

-~-+--1-1 ~ I-1--

2820+-----r---~~--~----~----_+----_+----~

-100 100 300 500 700 900 1100 1300

Reduced Variate


-- Normal Gumbel

Figure B95 30m span

2940

2920 e Z 2900ltII

I -OJ

8 ltgt 2880 ~ OG Ia 2860 I OJ

CQ

2840

Univers

ity of

Cap

e Tow

n

APPENDIXB


7 Axle Vehicles

210

205 +---f---l----I I---r----f-----

----- -JbI~__+ - I

--~-l ---- - ---+----+-- i

200 -J-- -+- - - j--shy

~ 195 -- ---1- -+----

ltj 41 190

ri I II i __ J ---r--shy 185

41 -= I ~ I - I ~+---r---rIl 180

175 +-ltSgt---- - +-i--i---T --+--shy i

170

-100 100 300 500 700 900 1100 1300

Reduced Variate


-- Normal --Gumbel

Reduced Variate


--Normal --Gumbel

Figure B97 10m span

Univers

ity of

Cap

e Tow

n

360

+ JiUO--t---

-j---t----+--- -~-- - T -3S0

-340 r- -r- I ~- -1- -shy~ 330 ltJ ~ Q 320 +---h-=-~~--1 ~~-Ib~01

310c ~ -- I-- r-----1-shyen


280

-100 100 300 Soo 700 900 1100 1300

Reduced Variate


-- Normal Gumbel

Figure B98 ISm span

390r---~----~----~-----1

~ 370

~

----------~--~

380 +--------- I - ---r ---+- - - - ------- ---+-- - - - - --1

I - +1--- -+-

3S0 +----+

330+-----r---~----_+---_r----~----~-~

~ 360 +--shygj t3

340



Figure B99 20m span

APPENDIXB

Univers

ity of

Cap

e Tow

n

APPENDIX B

423

421

419

417Z 415 Q

413 ltlI c 411 (IJ

409

407

405

-100 100 300 500 700 900 1100 1300

Reduced Variate



Univers

ity of

Cap

e Tow

n

APPENDIXB


8 Axle Vehicles

240

230

e 220

~ - 210 -= 200e 0

E 190 011c a 180 c = 170

160

150

-100

-I----tl ---+shy

I

-r I i-----1L-~II --_t_

_ -+shy _ _ i

100 300 500 700 900 1100 1300

Reduced Variate


Normal Gumbel

Figure BIOI Sm span

650

8 600 z -I - I c 550 e 0

E 011 500ca I = 450

4OO+-----r---------+-----r-----r----~--~

-II

-100 100 300 500 700 900 1100 1300

Reduced Variate


Normal Gumbel


Univers

ity of

Cap

e Tow

n

APPENDIXB

1200 ----------~r_-r_--__r--____--__


= --+1- ~ l -~ a = CQ

850 q - -I--middot-~ -1

800 I

750 +-----~----~----_----~----_r----~---~

-100 100 300 500 700 900 1100 1300

Reduced Variate




1900

1800

S Z 1700 l = 1600 8 c ~ 1500 OJ)

= a = 1400

CQ

1300

1200

-100 100 300 500 7 00 9 00 1100 1300

Reduced Variate




Univers

ity of

Cap

e Tow

n

APPENDIXB

3350 I

I

I

3250

1-~ --

- 3150S

z --1-shy ~c 3050 1

II I 2950e iQ

2850 011 s 27501l c

I = 2650

2550 -I middot I

2450

-100 100 300 500 700 900 1100 1300

Reduced Variate


-- Normal Gumbel


Univers

ity of

Cap

e Tow

n


8 Axle Vehicles

210----------~------_----~----~----~

200~-----~-----4------~----~-----+--~~

190

~

~


I~+_-----r----_------r-----~-----+----~

I f----- -I shy

180 +---------------

170 -t------------+-~

I I-shy ----------- 1 160 +-------1----4-----

-100 100 300 500 700 900 1100

Reduced Variate


-- Nonnal - Gumbel

Figure B106 5m span

290

280

270

260 ~ - ~ 250 Q 240 ~ 230 ~

rIl 220

210

200

190 -00 100 300


-- Normal -Gumbel


-1---1--shy-1----1-1--shy


500 700 900 11 00

Reduced Variate

APPENDIXB

Univers

ity of

Cap

e Tow

n

APPENDTXB

370


~ 330

01 310

- - --~---t-shy--


270

250

230

-100 100 300 500 700 900 1100

Reduced Variate


-- Normal Gwnbel


~o----~-----------~-----------------_

380

~ 360 01 Q 3~ ~ ~ c 320()

300

280

-100 100 300 500 700 900 1100

Reduced Variate


-- Normal Gumbel


Univers

ity of

Cap

e Tow

n

APPENDIXB

500

480

460

~ 440 OIl

~ Q 420 ~ ltII OIl 400d

(I)

380

360

340

-100 100 300 500 700 900 1100

Reduced Variate


-- Normal Gwnbel


Univers

ity of

Cap

e Tow

n

APPENDIXB


8 Axle Vehicles

210~----~-------~----~--------------

205 ~---l-

200 -j---l-----

195 -+----l~oP ---1-shy +---1------1


185 -t------t----i---i------r----

-100 100 300 500 700 900 1100 1300

Reduced Variate


-- Normal Gumbel

Figure BIll 5m span

545

540

S Z 535 i 530 GI a 0 525 ~ ~ c a 520

C GI

IQ 515

510

505

-t-+---t-I-L I I

-100 100 300 500 700 900 1100 1300

Reduced Variate


-- Normal Gumbel


Univers

ity of

Cap

e Tow

n

APPENDIX B

104)

1030

e 1020Z e l 1010c e 1000=gt OG

990c s c 980=I

970

960

-100 100 300 500 700 900 1100 13 00

Reduced Variate


-- Nonna --- Gumbel


1620-----~--~----~~--_----~----~--~


ac

c =I

1500+-----r---~----_T----_r----~----_--~

1600

1580

1560 l

i 154)

1520

-100 100 300 500 700 900 1100 1300

Reduced Variate


--Nonna --- Gumbel


Univers

ity of

Cap

e Tow

n

APPENDIX B

2970

~ 2950

S z 0 2930 (I)

is e 2910Q

~ 1gt11 Ca 2890 c

al

2870

2850+-----r-----~--~r_--~r_--~----_+----~

-100 100 300 500 700 900 IUlO 1300

Reduced Variate


--Normal -Gwnbel


Univers

ity of

Cap

e Tow

n

--

APPENDIXB


8 Axle Vehicles

200

195

Z ~ 190 ~ ~ 185 ~ -= (I)

180

i i I I ~ E bull

175

c_---+-__---_ ~--_f

~-+-----il-_+ _-+t_i ---t-I-I -100 100 300 500 700 900 1100 1300

Reduced Variate




~ ~

= ~ -= ~ (I)

275-----------~--------~----------~----_

270

265

260

- shy -- ----- shy ----1---shy

I 2S5 -t shy250

245

240

-100 100 3 00 500 700 900 1100 1300

Reduced Variate


--Normal ---Gumbel


Univers

ity of

Cap

e Tow

n

APPENOIXB

325

320 I-- -I ~

315

310OJ ~ 305~ -= (I)

300

295

290

-100 100 300 500 700 900 1100 1300

Reduced Variate



Z e ~ Q

~

~ -= (I)

360~----------------~----~---------------

355

350

345

340

335

330

--+----~-- ~--- i shy - ---+-----1

i I I I -100 100 300 500 700 900 1100 1300

Reduced Variate


-Nannal Gwnbel


Univers

ity of

Cap

e Tow

n

APPENDIXB

QI ~ 415 +---f--shy

-~--t-I I

I -=r-i--- II

I 400+-----~----+_----+_----r_----+_----r_--~

430~----~----~----------~----~----~--~

425 --f ~ r - ~ 420 -I---~---li-- --- --t-shyZ I ==- i

~ o

lltU 410 +-- -r shy

~ ~-----------l405 -1--061+--1-----+ I

i i

-100 100 300 500 700 900 1100 1300

Reduced Variate



Univers

ity of

Cap

e Tow

nAppendix C


II

II

Univers

ity of

Cap

e Tow

n

APPENDIX C

Page No




Univers

ity of

Cap

e Tow

n


Univers

ity of

Cap

e Tow

n




















Univers

ity of

Cap

e Tow

n




I 022

2 23E-05 3


4 46E-09 (2)(3) 5



6 (I) (4)IOE-09


7 47E-18 (6) (4)



9 10E-18 (1)(7)


10 47E-27 (9)(4)








3

Univers

ity of

Cap

e Tow

n


4

Univers

ity of

Cap

e Tow

n

A-1

APPENDIX A

Univers

ity of

Cap

e Tow

nAppendix D

Impact Formula I

bull bull

Univers

ity of

Cap

e Tow

n

APPENDIX 0

Page No







Univers

ity of

Cap

e Tow

n





Where













3J =shy

b L


J =~ b Lf





Where













3 J =shy

b L


J =~ b Lf

Univers

ity of

Cap

e Tow

n



therefore used











response

2



therefore used











response

2

Univers

ity of

Cap

e Tow

nAppendix E


bull

Univers

ity of

Cap

e Tow

n

1

APPENDIX E

Page No









Univers

ity of

Cap

e Tow

n

























III 2

I ~


























W~ I i I

WI 2

I I ~


Univers

ity of

Cap

e Tow

n


















2

Univers

ity of

Cap

e Tow

n









moments





















3

E13








moments













E14 Simulation








3

Univers

ity of

Cap

e Tow

n






(i) Maximum W

(ii) Shortest b

(iii) Centred x =05












limits





legal vehicles





4

Univers

ity of

Cap

e Tow

n







5 197 189 4

10 547 562 3 15 1054 1054 0 20 1582 1626 3)

7


0 Connor Difference

5 184 173 -6

10 252 258 3 15 308 304 -1 20 347 346 0





simulations









5

Univers

ity of

Cap

e Tow

n

Bending Moments kNm


5 293 301 -3 10 800 812 -1 15 1262 1364 -7 20 1903 2097 -9 30 3526 3631 -3








6

Univers

ity of

Cap

e Tow

nAppendix F


Visual Bas

Univers

ity of

Cap

e Tow

n


Sub centralloadO









Univers

ity of

Cap

e Tow

n




pos = inc n







+


pos = inc n



10) lt= 0 Or

+ + +


Then Then Then





+ + spaclO



Univers

ity of

Cap

e Tow

n






n=n+1 Loop



Next z


Univers

ity of

Cap

e Tow

n




Nexty








Next s


End Sub




Nexty








Next s


End Sub

Univers

ity of

Cap

e Tow

n

ACKNOWLEDGMENT





(iv)

Univers

ity of

Cap

e Tow

n

TABLE CONTENTS

No

1 INTRODUCTION

11 BACKGROUND 1-1

12 OF THE STUDy 1-2

1-3 13 SCOPE OF THE

14 METHODOLOGy 1-4






21 INTRODUCTION 2-1





25 CONCLUSIONS 2-15


31 INTRODUCTION 3-1







35 RESULTS 3-23

36 OVERLOADING 3-27

37 CONCLUSiONS 3-31

Univers

ity of

Cap

e Tow

n


41 TMH7 PART 2 4-1








45 CONCLUSIONS 4-23



52 RESULTS 5-3








(vi)


41 TMH7 PART 2 4-1








45 CONCLUSiONS 4-23



52 RESULTS 5-3








(vi)

Univers

ity of

Cap

e Tow

n

List of































(vii)

List of




24 - of H20 LRFD 1 2-7


26 CL-W Truck 2-10

2-10 27 - CL-W


31 -

32 -

33 -

34 -


of GVMs 3-8


Function of

Function of

Moments 30m span

Moments 5m span

3-9

3-9











41 -

42 -

44


Distributed Lane

Moments Due to

of Class 14 Vehicle


and 4-7

4-14


46 -

47 -

51 -

52 -

of Moments 4-19

gtr of Forces


4-20

5-2


Univers

ity of

Cap

e Tow

n





(viii)

Univers

ity of

Cap

e Tow

n

List of Tables































(ix)

List of Tables


























Table 41 - 4-6





(ix)

Univers

ity of

Cap

e Tow

n












(x)

Table 46

Table 47-






Table 411 -

Table 412 Shear

Table 51 -


Table 53-

Table 54-


WIM data v RR 4-22






Univers

ity of

Cap

e Tow

n

1 INTRODUCTION

11 BACKGROUND
















Regulations


June 1994














(1-1 )

1

11




with the aim of

the most onerous











the Road

commissioned the

to increase the

to consider the



(i)

The main

the


June 994



Vehicle Loads on

Vehicle Loads on












(1-1 )

Univers

ity of

Cap

e Tow

n






























(1-2)

12






vehicles






with

Ullman





and adds to the








WIM are






(1

Univers

ity of

Cap

e Tow

n



RR 91100410 I amp 02




data
















considered

(1-3)



RR 9110040 I amp 02




data
















considered

(1-3)

Univers

ity of

Cap

e Tow

n

14 METHODOLOGY




identified were












approaches














(1-4)

14 METHODOLOGY


142



identified were

TMH7 Part 2 The




and



( I Code These



loads on

close






















(1

Univers

ity of

Cap

e Tow

n


































(1-5)






Statistical

vehicles



vehicles on the N3





vehicle

load effects

and fits the

within a 120 year










both methods is



of an extreme











(1

Univers

ity of

Cap

e Tow

n





(c) Overloading















(1-6)

Critical Assessment




The extent of

vehicle set


vehicle set This

those

between the WIM

event of the actual














(1

Univers

ity of

Cap

e Tow

n

1~ REPORT STRUCTURE













reviewed in detail



















(1

1~ REPORT STRUCTURE




live

extent of

with the










reviewed in detail



In and the















in TMH7

the

load model are



of the WlM data

(1

Univers

ity of

Cap

e Tow

n


21 INTRODUCTION






these loads

















on bridges






and

21 INTRODUCTION








these loads


lIllUlLla on the









BS5400 1978

British Standards




Factor ( I

Code and


on






and

m


Univers

ity of

Cap

e Tow

n










the TMH7 Part 2


























(2-2)



to process and







live load models in

the TMH7 Part 2











- u- sensors









vehicles The


by the vehjcle axle

to the extreme

Allowances for









are shown in 21

Univers

ity of

Cap

e Tow

n

305 366 244 305 244 305 244 m


80 219 100 100 100 100 100 100 kN Axle loads (kN)

Ca)

7 x 305 IT = 213 m 0 ~----- -------__--- ___---

~[I ~[JJ 1 I 1 I 1 I] 70 B 96 896 896 896 8 96 896


(bJ























(2-3)

Univers

ity of

Cap

e Tow

n



























241 BD 3788











24


























APPROACH




241 BD 3788









spans





Univers

ity of

Cap

e Tow

n








W= 260 kNfm


J

BS 5400 Part 2





















(2-5)

10 in the

for loaded







lt11 C l 0

150

E 100 lii CL

s



W= 260 kNfm

BS 153 Part SA

BS 5400 Part 2
















axle loads An


of 146 was

~nrn)~h used was


and lateral

factor of 18 was

to

were included





Univers

ity of

Cap

e Tow

n
















(2-6)
















Univers

ity of

Cap

e Tow

n

242 AASHTO lRFD
























35 000 N 145 000 N 145000 N



Design Lane 3600 mm


(2-7)

Univers

ity of

Cap

e Tow

n








z [F(M)] (21)

Where

M Moment















from the

in 1975


data base For

calculated The



on normal






z

Where

M Moment

CDF of the moment M










Univers

ity of

Cap

e Tow

n

5~---------+--------~~~~----~ II NGntbs

I ~

j O~--------~~~-------------+------~

~------+ri~----------------+------~

~~--~~------~-------------+------~

Jr---~--------~-------------+------~

~~------------~------------~------~ o








243 CANADIAN CODE









(2-9)

Univers

ity of

Cap

e Tow

n



~ -i 1 3igtm

112ml


Imiddot 18 m

~ ~P) =~-----ffi--tB------ -~---- ----8t------shy

t J-----ffi-----ffi-ffi------ --ffi---- -----~------


ClaHance Errvelope

300 m





So6m 6ampm

180 m

66m






(2-10)

Univers

ity of

Cap

e Tow

n























IIgt

IIIQ

to

ro

to

IQ

~

0








bull bull ~ ~- _- _~ n N 0)





~~Jtli ~ -~ Rf



L~ M I ii 11011

H ~~ II 11

_ r _ t

t7 ~ zo ~ n ~i -ii41 1 II



I IJN ~ ~ 4 1 ) bull ~ 1 r-




(2-11 )

Univers

ity of

Cap

e Tow

n








to measured












BD 3788

244 EUROPEAN CODE





bridge












2)








to measured









the Ontario

effects caused

Base





BD 3788


244 EUROPEAN CODE




is ENV 199





The

traffic












Univers

ity of

Cap

e Tow

n








Location

Axle loads Qik

(kN) qik

(kNm2 )



o

Q

~~H-050 200

-iti--Hl-fosomiddot


-iH----H1-gtI-O50

1m2


050 120

2 00

For IV 300 m








(2-13)

Univers

ity of

Cap

e Tow

n














of the total loads

(i) Free flowing

















(2-14 )






involved the of the

In the case of axle

double and

values were









of the total loads


(i) Free













methods in

relevance is

This

nnmrn of the ENV





Univers

ity of

Cap

e Tow

n

25 CONCLUSIONS





















TMH7 Part 2




load model









(2-15)

25







W1dertaken

live







methods that

models an












TMH7 Part 2




load model









Univers

ity of

Cap

e Tow

n


31 INTRODUCTION










9100401 amp 02



















(3-1 )

31 INTRODUCTION

32








vehicles on

deterministic

9100401 amp 02






WIM were set















Univers

ity of

Cap

e Tow

n

















321 Actual Vehicles













Table 31


Vehicles Vehicles

No of Recorded

Vehicles 24901 34951 2587 62079


Univers

ity of

Cap

e Tow

n

F





In the


5 to 15 20 30 6 Axle Veh Mean 1040 2801 4734 7507 14319



Std Dev 345 915 1701 2794 5865


5 to 15 20 30 6 Axle Veh Mean 952 1224 1500 1782 2115



Std Dev 324 418 546 654 815


322 Legal Vehicles
















overestimated

it was

(3-3)

Univers

ity of

Cap

e Tow

n







standard deviation


5 10 15 20 30





5 10 15 20 30








regulations










(3-4)

Univers

ity of

Cap

e Tow

n



18000

(3-5)



Univers

ity of

Cap

e Tow

n


Accuracy of Data
























(COST 323 1997)



actual vehicle

(3-6)

33 APPROACH

of Data


















may be 25 more or


individual results






323 1



actual vehicle


the road vehicles



Univers

ity of

Cap

e Tow

n











940 1300 1500 1460 1180 1200 122 0 383Max 442 519 507 470 489 47 5 48 2 196Mean 100 207 208 216 207 213 207 870Std Dev


272 1267 1062 1535 1339 1190 831 8820 1476 2026 1734 1464 1522 1083 679 4725 1776 2242 1948 1260 1247 899 485 5430 2051 2146 1654 1128 1119 805 422 4835

40 3662 1796 1360 1119 1068 824 464 63 5976 1722 1342 1183 1061 943 535 4945 6436 1769 1304 1301 1233 1135 633 7350 4961 1775 1454 1476 1489 1375 864 7255 2460 2291 1850 1803 1788 1672 1195 6760 794 2747 2328 2117 2026 1805 1200 4565 144 3033 2590 2039 2046 1658 1080 3670 24 2694 2107 1528 1571 1218 705 1375

80 4 1976 1376 928 933 716 388 9 85 2 1019 719 394 423 275 151 4 90 0 487 __- 305 164 _ 170 __ 127- 51 _-- 1 ___ _ - _ _-_ _shy

95 I 213 112 58 47 47 18 0 100 0 80 43 31 23 19 6 0 105 0 43 14 8 5 5 3 0

0 17 8 4 2 2 2 0110 0 II 9 2 0 3 0 0115

120 0 3 3 0 2 2 0 0 125 0 6 1 I 0 0 I 0

More 0 2 1 I 0 0 0 0 30039 30039 24065 21383 20070 17360 10437 774Sum


(3-7)

Univers

ity of

Cap

e Tow

n







2500 12000

c 0c10000 ltI2000 C I ~

8000 c ~

1500 IltI

~H-I-t++-f-++-+ 000

-=e

~C qj 6000 iI a Q~ 1000

qj~ 4000 ~ ~ ~

500 20 00 I

U

o

Bin







(3-8)

Univers

ity of

Cap

e Tow

n

00030 -----------r-------------------r--------

o 00025 JI ~ 00020 i-----I~--_I_---t_-~--+---+-----f----I lIi i~ 00015 ~

] 00010 to

ampJ o ~ 00005 +----+----+----~-------_IIoc__

00000 +----+----+----j----i----+----+---

o 100 200 300 400 500 600 700

Weight(kN)


001200

sa 001000 v

~ 000800pound

000600 ~ 15 000400 ~ to ~ 0

000200 ~

000000

0 50 100 150 200 250



000080

000070

ll 0

000060 ~ 000050 ~

fshy 000040 S ~ l- 000030 g ampJ

000020

0

D

p 000010

000000

i-~-I- ---- __ ~

o 500 1000 1500 2000 2500 3000



(3-9)

Univers

ity of

Cap

e Tow

n


















events and







respectively




periods (Dawe 2003)

0)
















ENV 1991-3 et 200

The

the

(i)




events and

In the case of

of the extreme










Univers

ity of

Cap

e Tow

n






and for each class






lIN



(31)

2515517 + 080853w+ 0010328w2

z=w- 2 (32)1+ 1432788w+ 01 89269w + 0001

Where






=x+Krs (33)

Where

Xr Event at time T

x Mean of events

Kr rPllHPU factor

1)

Univers

ity of

Cap

e Tow

n









therefore similar


5 285 290 278 290 10 762 739 743 762 15 1266 1365 1372 1372 20 2069 2262 2242 2262 30 4740 4638 4740



5 263 261 258 263 10 323 343 339 343 15 417 439 436 439 20 495 522 537

653 675



6 Axle 533 281 91 -021 7 Axle 653 367 118 -073 8 584 122 -056










(3-12)

Univers

ity of

Cap

e Tow

n












m 04P(Xgtx ) =--- (34)

n+

Where











with B

Where


342 Extreme












Cunnanes formula

gt

Where











with B

Where

T Return where T 1

Univers

ity of

Cap

e Tow

n

--

- - -_--_- _ shy3000

2800+------I----+----+----~--~---~f- shy

S ~ 2600+----~---r_----~----~~~--4----~

ir j 2400+----+---1-------1~~---~---r---~ ~ ~~ ~b

~ 2200 +---~---~~~--1---~---+-------1

jJl

2000+---~~--1-----I---~---r---~

1800 -------1f----+-----t-- Plot Area Ir------+-----I


--6 Axle

----- - -------- - - ------- __- -----shy3200

3000

e ~ 2800 i S 2600 ~ ~I Vsect 2400 ai

jJl 2200

2000 o 2 4 6 8 10 12

Reduced V ruiate

-+-7 Axle

3000

I 2800

2600 ~

I~ 2400 I

I2200

Chart Area

2000

o 2 4 6 8

Reduced Vuiate

1-+-8 Axle I


(3-14 )

12

10

Univers

ity of

Cap

e Tow

n-- __ ___shy480

460

440

~ 420

400 ~

380ie (I)

u 360

340

320

300

380

360

340

~ 320 300 ~

280lt Vol

260

240

220

J -~

V ~

~ v

_ _

j~

~

- V

o 2 4 6 8 10

Reduced Variate

--6 Axle

o 2 4 6 8 10

Reduced Variate

--+-7 Axle

440

420

400

~ 380 i 360 ~

ie 340 -= ~ 320

300

280

V

1

Ir

~

V

o 2 4 6 8

Re(luced Variate

-+- 8 Axle


(3-15)

12

i

12

10

Univers

ity of

Cap

e Tow

n













No of Reduced Event

5m Spans

10m Spans

15m Spans

20m Spans

30m

22 28 42

22 28 42

22 28 42

22 28 42

22 28

2024 2000 1961

5448 5379 5254

8937 8835 8659

13728 13572 13313

25468

25224

99 99 98

267 271 285

376 387 405

583 597 611

969

979

31680 40320 60480

31680 40320 60480

31680 40320 60480

31680 40320 60480

31680

40320

751 727 687

751 727 687

751 727 687

751 727 687

751

727

763 782 813

763 782

813

763 782 813

763 782 813

763

782

278 277 276

749

750 757

1181 1186 1195

1818 1824 1828

3285

3288






(3-16)

Univers

ity of

Cap

e Tow

n

5 301 238 -21 10 812 631 -22 15 1364 1129 -17 20 2097 1756 -16 30 3631 3380 -7
















(3-17)

Univers

ity of

Cap

e Tow

n

1500 -------------------------------------------

1400 - S ~ 1300 -

~ 1200 S o ~ 1100 OJ)

=g 1000 ClJ

=l 900

800 +-----~----~----_r----~----~------~--~

-100 100 300 500 700 900 1100 1300

Reduced Variate


390

370

- 350 ~ - ClJ ~ 330 0 ~

~ 310 ClJ

c rJ)

290

270

250

Reduced Variate

-100 100 300 500 700 900 1100 1300




(3-18)

Univers

ity of

Cap

e Tow

n

1450 -----------~--------------------------_

1350

1250

1150

1050

950

-


Q rJ1

850 +-----~----~----~----~----~----~----~

-100 100 300 500 700 900 1100 1300

Reduced Variate


-Nonnal Gwnbel

360

350

340

330

320

310

300

290

280

270

260

-100 100 300 500 700 900

Reduced Variate

1100 1300


Nonnal Gwnbel


(3-19)

Univers

ity of

Cap

e Tow

n

1200

1150 --

3 1100

~ - 1050 ~

3 = 1000 0

~ 950 OJ)

0 = 900 ~ = ~ 850

800

750

-l00 l00 300 500 700 1100 l300

Reduced Variate

900


--Nonnal Gwnbel

370

350

-Z ~ - ~ (j 0 ~

11 ~ -= 00

330

310

290

270

250

230

-100 100 300 500

Reduced Variate

700 900 1100


-- Nonnal Gumbel


(3-20)

Univers

ity of

Cap

e Tow

n
































+





effective

years 40320











number of the

between the 28











the human and

the most




Univers

ity of

Cap

e Tow

n






a (37)





n

X Gumbel s = 1 1+11 + 11000Kn] 2 S (39)e

n







(3-22)

Univers

ity of

Cap

e Tow

n

---

4150

3950

3750

e 3550 ~ - 3350 = ~ e 3150 Q

~ 2950

2750

2550

2350

-100 100 300 500 700 900 1100 1300

Reduced Variate




35 RESULTS






91 00401 amp 02



5 276 301 231 301 10 757 812 624 812 15 1195 1364 1135 1364 20 1828 2097 1780 2097 30 3275 3631 3289 3631




5 297 233 201 297 10 320 314 279 320 15 369 350 349 369 20 431 433 392 433 30 489 542 481 542


(3-23)

Univers

ity of

Cap

e Tow

n




and







the vehicles axle


Mean 467 529 518 423 429 441 2806 6 Axle

Std Dev 68 196 199 199 188 189 913Vehicles 006 -014 -009 012 001 -021

Mean 488 557 555 529 545 501 490 3665 7 Axle

Std Dev 67 201 191 215 224 205 1176Vehicles 16 -059

Mean 470 504 526 455 456 446 391 384 3632 8 Axle







events


5 98 147 117 10 104 141 119 15 93 128 124 20 92 128 119 30 95


(3-24)

Univers

ity of

Cap

e Tow

n



5 151 130 104 10 120 1l0 127 15 103 88 133 20 103 95 116 30 103 113









NowakGumbel

5 290 301 -4 10 762 S12 -6 15 1372 1364 1 20 2262 2097 S 30 4740 3631


Shear Forces


NowakGumbel

5 263 297 -11 10 343 320 7 15 439 369 19 20 537 433 24

542







Univers

ity of

Cap

e Tow

n


5m 10m 15m 20m 30m


276 292 (+59)

301 (+89)

757 804 828

1195 1262 1297

(+56)

1829 1930 1982

3275 3436 3519

(+49)

(+74)


Univers

ity of

Cap

e Tow

n

36 OVERLOADING
















12

~ 08 D lte

D 0 shy 06p v ~

-a 04

8 02

o 100 200 300 400 500 600 700 800 900

Weight (lN)



(3-27)

Univers

ity of

Cap

e Tow

n











representative


6 Axle 00 19 20 21 12 25 7 Axle 03 77 69 09 09 56 37 8 Axle 83 280 310 13 09 44 67 70

444











was retained










(3-28)

Univers

ity of

Cap

e Tow

n













5 -2 -6 3 5 -1 7 10 6 -13 14 -9 -4 6 15 -11 -11 11 1 -6 5 20 -4 -7 6 5 -3 8

30 -4 -1 3 5 2 21













5 197 195 196 216 220 181 10 13 -8 10 510 547 520 582 600 486 14 10 -7

15 968 1054 986 946 1034 875 -2 -2 -11 20 1504 1582 1537 1452 1599 1388 -3 1 -10

30 2767 2917 2899 2676 2944 2697 -3 1 -7


(3-29)

Univers

ity of

Cap

e Tow

n



5 182 183 184 210 197 164 15 8 -11 10 246 251 252 249 250 220 1 0 -13 15 295 308 302 298 293 272 1 -5 -10 20 337 347 337 349 358 316 4 3 -6 30 411 440












Univers

ity of

Cap

e Tow

n

37 CONCLUSIONS










set of events

























(3-31)

37 CONCLUSIONS










set of events

























(3-31)

Univers

ity of

Cap

e Tow

n






June 1994









examined

41 TMH7 PART 2








to traffic










(4-1 )

2 amp i) UD i)J ol

The

Part 2





June 1994

Vehicle Loads on



Vehicle Loads on







examined

41 TMH7 PART 2

411 and OAfAIIID







to traffic






favoured this




Univers

ity of

Cap

e Tow

nL









fonnula (1970)


Where

Impact factor





















(4-2)









fonnula (1970)

cent = 5(100 + L) 10+L

Where

Impact factor






















(4-2)

Univers

ity of

Cap

e Tow

n












the WIM sensors

















group






(4-3)



The

412 NA

The




Curves

curve for

UH1lUH of the no-m






the WIM sensors

As

and








The



earlier work






20

group







Univers

ity of

Cap

e Tow

n


















40

-

sect ~ - C ~ 0

l C ~ I

Q

C 0is

5

0

10 100 1000

Loaded length (m)

~------------------------~~------------------------~

1-30

25

20 1-15

-- ------



(4-4)

Univers

ity of

Cap

e Tow

n

---

___bull___ __ _- --- ---___bull _bull40

35

---E 30 -+ --+-shy

Z ~ - 25 ~ CI 0

l 20 ~ ltII c = 15 i 10Q

+5

0

10 100 1000

Loaded length (m)
























(4-5)

Univers

ity of

Cap

e Tow

n















2-Axle 216 204 195 190 183 186 184 196

3-Axle 97 106 94 86 82 82 82 165


8-Axle 23 25 25 24 23 25 45 41 9-Axle 01 01 00 01 01 01 02 31

Total 100 100 100 100 100 100 100 100


















(4-6)

Univers

ity of

Cap

e Tow

n
















1600

1400

1200 middot 8 ~

1000 agt-= 8 0 800

~ = 600a =agt

co 400

200

0 4 6 8 10 12 14 16 18

Span m




5 35 10 28 15 23 20 20 30 16


(4-7)

Univers

ity of

Cap

e Tow

n





relevant















416 NB Loading









(4-8)


Given

Ipvntv of TMH7 Part


this

2 the

The

(1

of the

relevant


effects of vehicles



the



and research



415 Lateral






A lateral

at40m

factor of 14 was





416 NB

in the

The









Univers

ity of

Cap

e Tow

n








international and

























(4-9)








international and




the load effects of



of trnrP The in






422

The report

infrastructure

with a

the




with

(i)





Ease of enforcement


and







Univers

ity of

Cap

e Tow

n





applicable factor









Appendix D


Where

the final factor

















(4-10)





factor

ratios were

The statistical










D


Where

the final factor

the factor for the
















0)

Univers

ity of

Cap

e Tow

n



423 Review































(4-11 )





span

The

Review


Axle Loads The full





an

extent






In f1nntltvmo the


















then calculated by






1)

Univers

ity of

Cap

e Tow

n









(4-12)









Univers

ity of

Cap

e Tow

n





















431 Traffic loading



the



formula

( 4-13)














axle

This load




An

and





431 Traffic


technical rl(lgt(1

the




formula

Univers

ity of

Cap

e Tow

n








432 Impact Factor




ForT lt 16t

For T gt SOt



ImEact Allowance

RR91 0041 RR910041 SEan (m) TMH7 01 02

5 35 37 36 10 28 26 18 15 23 17 12 20 20 13 9 30 16 9 6


(4-14)

Univers

ity of

Cap

e Tow

n

433 Test loading
























ENV 1991-3

(4-15)

433 Test




of the



under PTVi






Assessment amp













ENV 1991-3

Univers

ity of

Cap

e Tow

n

I

1J- 8

_______- - 1 ~ ~-- ~

--tf-fBT-1--+Or

I

I IPi t I









240 140 0

NA

6 4 3 3









(4-16)

Univers

ity of

Cap

e Tow

n


5 415 293 42

10 949 810 17

15 1510 1553 -3

20 2442 2520 -3

30 5






most

5 378 10 413 15 506

20 576 30 739

234 324 414

504 684

62 27

22 14 8









436 Critical Review







surveys


in TMH7 Part 2

(4-1

Univers

ity of

Cap

e Tow

n














from the WIM data

(4-18)

In the














from the WIM data

Univers

ity of

Cap

e Tow

n











5 409 415 293 10 957 949 810 15 1527 1510 1553 20 2284 2442 2520 30 3847 5397 5130


6000 - shy

5000 - E

~ 4000-III= ~ 3000 ~ OJ)

= 2000a III= ~

1000

0

0


5 10 15 20 25 30 35 Span (m)

--- Study -0- RR91100402 ~ TMH7 I


(4-19)

Univers

ity of

Cap

e Tow

n

Shear Forces (kN)


5 297 378 234 10 320 413 324 15 369 506 414 20 433 576 504 30 542 739 684


800

700

600 -

~ 500 QJ ~ 0 400 ~ ~ QJ 300

c C-J

200

100

0

0 5 10 15 20 25 30 35

Span (m)












5 409 293 39 10 957 810 18 15 1527 1553 -2 20 2284 2520 -9 30 3847 5130 -25


(4-20)

Univers

ity of

Cap

e Tow

n

























(Section 413)

Shear Force (kN)


5 297 234 27 10 320 324 -1 15 369 414 -11 20 433 504 -14 30 542 684 -21







(4-21)

Univers

ity of

Cap

e Tow

n


Moment (kNm)


5 409 415 -2 10 957 949 1 15 1527 1510 1 20 2284 2442 -6 30 3847

Table 411 - Moment

5397









Shear Force (kN)


5 297 378 -21 10 320 413 -23 15 369 506 -27 20 433 576 -25 30 542 -27


(4-22)

Univers

ity of

Cap

e Tow

n

45 CONCLUSIONS













the roads















return period





(4-23)

45 CONCLUSIONS













the roads















return period





(4-23)

Univers

ity of

Cap

e Tow

n









data







these -0










(5-1 )

51

2

OF LOAD


Part 2 the

3 the




shown in

data











these prlmiddoto










Univers

ity of

Cap

e Tow

n

40 80 ~~~--------~~4~~------------~~

240

I

180


20 20 ~ II~ ~




13 ~ ~

240 240


12 ~ II

150 150

7 1991-3 design

12 ~

200 200


51 - Load Models

Univers

ity of

Cap

e Tow

n





y = -(1 + kV)

load factor r

bias factor


deviation


52 RESULTS




2300

2100 0-v 1900~ 0 1700~ 0

l 1500-=QI

E 1300 0

~ 1)1) ll00 = a 0900 = QI

tl

- - ~~- -- shy - shy - shy

I

I I--- L~- shy ~~t--==- -

r-shy

----r-=9 I

~ 0700

0500

- T - - shy -

o 5 10 15 20 25 30 35

Span (m)


(5-3)

Univers

ity of

Cap

e Tow

n








1800

0 1600 (I

laquoI

1l laquoI 1400 0

l ltII = 1200 8 0

~ ~ 1000 = 0 = ~ 0800

0600

o

~ ~--shy -

~~ n

5 10 15 20 25 30 35

Span (01)

-0-3 6 -4-7 8


1600

14000 (I laquoI

1l laquoI 1200 0

l

ltII (I

0 1000 laquoI ltII

-= ~ 0800

0600

0 5 10 15 20 25 30 35

Span (01)

6 -4-7


(5-4)

Univers

ity of

Cap

e Tow

n





1800

0 1600 v CltI ~ ~

CltI 1AOO 0

e ~ = 1200

0

~ ~ 1000 = a = ~ 0800 I=Q

0600

0 5 10 15 20 25 30 35

Span (m)

6 ~7


1600


v ~ 0 1000 ~

CltI ~ c 00 0800

0600

- - - shy - shy

~

0 5 10 15 20 25 30 35

Span (m)

-ltgt-3 6 ~7 -8


(5-5)

Univers

ity of

Cap

e Tow

n




Table 51 to 54










(5-6)




Table 51 to 54










(5-6)

Univers

ity of

Cap

e Tow

n

Bending Moments

Lane Load 9 kNm


1 124 012 010 154 162 155 145 125 2 133 029 022 240 225 179 166 141 3 091 018 020 171 123 ll1 ll4 114 4 1 56 017 011 223 193 177 180 173 5 172 037 022 339 247 219 219 208 6 084 002 003 091 087 085 090 091 7 123 004 003 139 132 127 131 8 097 002 002 105 101 098 103

Lane Load 18 kNm


1 105 015 014 153 151 138 126 106 2 112 029 026 228 202 158 144 119 3 080 019 023 166 ll7 103 104 099 4 126 023 018 223 183 160 157 141 5 138 039 028 318 224 190 184 164 6 074 004 006 091 084 080 081 079 7 103 010 010 143 130 ll9 119 ll1 8 084 006 007 106 099 092 093 089

Lane Load 27 kNm


I 091 017 018 150 141 125 ll3 093 2 097 029 029 216 182 141 127 103 3 072 019 027 160 ll2 096 095 088 4 107 025 024 216 170 144 138 120 5 ll6 038 033 294 203 167 158 136 6 067 007 010 093 083 077 077 072 7 090 0 14 015 144 126 lll 109 097 8 075 009 012 108 097 088 087 080

Best Fit


(5-7)

Univers

ity of

Cap

e Tow

n

Shear Forces

Lane Load 9 kNm

C

Model

1 2 3 4 5 6 7 8

Mean 102 114 081 144 1 53 075 11 1 088

SD 008 023 013 014 024 010 010 010

V

008 020 016 010 016 013 009 012

135 221 142 200 280 073 116 087


ll8 145 120 183 219 095 136 109

Lane Load 18 kNm


Lane Load 27 kNm


Best Fit


(5-8)

Univers

ity of

Cap

e Tow

n

Bending Moments

Lane Load 9 kNm

Model

I 2 3 4 5 6 7 8

Mean 134 1A2

099 169 186 092 135 107

SD 008 020 020 023 036 017 021 019

V

006 014 020 014 019 018 015 017

1A6

218 174 237 333 119 172 136


200 159 159 122 110 123 200 183 201 237 209 227 112 109 124 161 153 172 129 125 lAI

164 177 161 254 282 165 223 187

Lane Load 18 kNm

Model 1 2 3 4 5 6 7 8

Mean 113 119 087 136 lA8

081 112 092

SD 007

022 018 020 034

011 013 012

V

006 018 021 014 023 014 011 013

135 209 163 213 302 105 lA8

118


130 150 134 187 215 126 158 138

Lane Load 27 kNm

Model 1 2 3 4 5 6 7 8

Mean

098 103 078 115 124 072 097 081

SD

009 023 017 021 033 008 011 009

V

010 022 023 018 027 012 012 011

133 199 154 202 278 096 138 108

Load Factor y 122 108 105 164 127 123 105 090 096 156 132 136 187 154 157 085 077 084 117 104 109 095 086 092

114 131 117 155 177 103 128 111

Best Fit


(5-9)

Univers

ity of

Cap

e Tow

n

Shear Forces

Lane Load 9 kNm

Model

I 2 3 4 5 6 7 8

Mean

135 151 108 190 203 099 147 116

SD

007 026 0 15 017 027 015 017 016

V

005 017 014 009 014 015 012 014

202 250 179 285 325 118 138 105

Load Factor y 193 181 177 188 175 171 127 136 143 231 246 256 235 245 252 114 130 142 129 144 153 100 113 122

189 175 163 280 272 165 173 141

Lane Load 18 kNm

Model

1 2 3 4 5 6 7 8

Mean

115 128 095 154 163 087 123 101

SD 011 027 015 018 030 009 007 008

V

010 021 016 012 018 010 006 008

188 227 175 236 265 104 127 099

Load Factor y 170 157 150 164 150 144 122 126 130 182 185 185 184 183 181 097 107 113 113 121 124 090 099 103

154 142 141 190 184 125 131 112

Lane Load 27 kNm

Model 1 2 3 4 5 6 7 8

Mean 101 112 085 130 137 078 107 089

SD 014 028 015 021 031 005 007 005

V

013 025 018 016 023 006 006 005

178 216 172 206 236 097 118 094

Load Factor y 154 140 132 152 137 129 117 119 120 152 150 146 159 154 148 087 094 096 100 104 104 082 087 089

131 125 126 144 146 103 106 093

Best Fit


(5-10)

Univers

ity of

Cap

e Tow

n
























on bridges









(6-1 )
























on bridges









(6-1 )

Univers

ity of

Cap

e Tow

n










TMH7 Part 2









model



















research

and 1995 in South









TMH7 Part 2









model






the events








live load models




Univers

ity of

Cap

e Tow

n























Part 2










limited expenditure





(6-3)


















over return





Part 2










limited





Univers

ity of

Cap

e Tow

n




(6-4)




Univers

ity of

Cap

e Tow

n

BIBLIOGRAPHY







fedrale de Lausanne












452-461




July 1981

Univers

ity of

Cap

e Tow

n



























Unbaised OlOlttlIll






RR 911004101 The

RR 911004102 The

Assessment Code

an Increase in the

an Increase in the

R K and

Canadian Journal



code 1983 edition

D amp uaveIlDon

Canadian Journal

W British


AlVUUl T and


A S (

Research Record

National 1998


Final



( a

A statistical

6494-513

to the traffic on



of Girder




Crowthorne TRRL



Univers

ity of

Cap

e Tow

n



Engineers


Transport


TRB December 1987























Univers

ity of

Cap

e Tow

n


and Architects



Report)



Univers

ity of

Cap

e Tow

n

A-1

APPENDIX A

A-1

Univers

ity of

Cap

e Tow

nAppendix A


Appendix A


Univers

ity of

Cap

e Tow

n





bull bullbull


77 90 90 80 80 80

o 00 000 Max W = 497kN

Configuration 2

77 90 90 90 90 90

00 00 00 Max W = 527kN

Configuration 3

77 90 9090 90 90

o o 00 00 Max W =527kN

Configuration 4

77 90 90 80 80 80


Configuration 5

102 102

o 00 Max W =560kN


Univers

ity of

Cap

e Tow

n

bull bull bull

3

Configuration 7

80 80 80

000 MaxW = 560kN


Univers

ity of

Cap

e Tow

nbull bull bull

bull bull bull


Configuration 1

80 80 80

Max W = 560kN

Configuration 2

80 80 80

eee Max W = 560kN

Configuration 3

80 80 80

eee MaxW = 560kN

Configuration 4

90 90

MaxW= 560kN


Univers

ity of

Cap

e Tow

n


bull bull bull


5


77 60 60 60 60 60 60 60 60

o 0000 0000 MaxW = 557kN

Configuration 2

80 80 80

000 MaxW = 560kN

Configuration 3

80 80 80



Configuration 4

48 48 48 48 48

00000 MaxW = 557kN


Univers

ity of

Cap

e Tow

n

bullbull bull

bull bull bull

bull bull bull

APPENDlXC

s Ii

~ [I $

~ 1- fl~


Configuration 1

90 90

Max W =560kN

Configuration 2

80 80 80

MaxW = 560kN

Configuration 3

90 90

00 0 MaxW = 560kN

Configuration 4

80 80 80

000 MaxW = 560kN

Configuration 5

80 80 80

Univers

ity of

Cap

e Tow

nAppendix B


bull

Appendix B


bull

Univers

ity of

Cap

e Tow

n

APPENDIXB


6 Axle Vehicles

2~ ------------------------------------

220+------+------+_----_+------+_--~~~--~

e ~200+------+------+------+----~~-----+----~

5 ~ 180 +_----_+------r---~~~----+-----_+----~ s =i 160 +_-----r----~~----_+------+_----_+----~ = I~+-----~------+------+------+------+----~

120 r------+------r-----+-----+------+--~ o 2 4 6 8 10 12

Reduced Variate

---6 Axle

Figure B I Sm span

o 2 4 6 8 0 12

Reduced Variate

-6 Axle

Figure B2 10m span

650

600

~ 550 o ~ 500 8 Q

~ 450 CgtII S 0 ~400 =

350

300

I

~

~

~

Univers

ity of

Cap

e Tow

n

APPENDIX B

1050

1000

9508 ~ 900

-= 850e Q

~ 800 c ~

a 750 ~ ~ 700

650

600

o 2 4 6 8 10 12

~

p y

r

V

Reduced Variate

--6 Axle

Figure B3 15m span

1600

1500 middotLL7 8 ~ 1400 r ~ ~ 1300 e Q

Ishy ~ 1200 ~ c V] 1100 ~ V ~ 1000

900

o 2 4 6 8 10 12

Reduced Variate

--6 Axle

Figure B4 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

3000

2800

8 ~ 2600 sect ~ 2400

E OIlca 2200 ==GI

=I

2000

1800

V

_V

Ijj


10 12

--6 Axle

Figure B5 30m span

Univers

ity of

Cap

e Tow

n

APPENDIXB


6 Axle Vehicles

24)

220

~ 200 180~ ca

c IIl 160

14)

120

0 2 4 6

Reduced Variate

8 10 12

---- 6 Axle

Figure B6 5m span

290

270

__ 250 Z ~ 2l 230 ~ 1 210

c IIl 190

170

150

~ b V

~

~ I

I o 2 4 6 8 10 12

Reduced Variate

--6 Axle

Figure B7 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

330

310

~ 290 Z ~ 270 Q

r 250 ~

c (IJ

230

210

190

o 2 4 6 8 10 12

V

J1V

I ~ I l

Reduced Variate

Figure B8 15m span


6 Axle

Figure B9 20m span

380

360

340

Z ~ 320 300 ~

01 280

c (IJ

260

240

220

--

V ~

~

)1

~

Univers

ity of

Cap

e Tow

n

APPENDIXB

430

410

390 Z 370 ltJ ~ =gt 350 ~ ~ 330c

00

310

290

270 o 2 4 6 12

r V

V ~

~V 1

8 10

I I

I I

1

I I I

i

I I i I

Reduced Variate

--6 Axle


Univers

ity of

Cap

e Tow

n

APPENDIXB


6 Axle Vehicles

200

195

e Z ~

190

-= S 185 ~

~ 011 9 180 0

= Ql

175

170

0 2 4 6

Reduced Variate

8 10 12

--6 Axle I

Figure B 11 5m span

530

520

e ~51O -= ~ 500 ~ 011

=a 490 =

Ql

480

470

V ~

~V ~

o

r

2 4 6 8 10 12

Reduced Variate

I --6 Axle I


Univers

ity of

Cap

e Tow

n

APPENDIXB

1000

950 5 ~ c 900 OJ e Q

~ C)I) 8509 -g c OJ = 800

750


o 2 4 6 8 10 12

Reduced Variate

--6 Axle I


0 122 4 6 8 10

Reduced Variate

--6 Axle

1550

1500

5 ~ 1450 a OJ

C 1400Q

~ C)I)

a a 1350 OJ =

1300

1250

~7

shy

~ V

-~

~

Univers

ity of

Cap

e Tow

n

APPENDIX B

- ~

V d ~

AV V

I

-i

V

2 4 6 8 10 12

Reduced Variate

--6 Axle

2850

2800

e 2750 Z 0 2700 Se2650 Q

~ 2600 ~

5 2550-g ga 2500

2450

2400

o


Univers

ity of

Cap

e Tow

n

APPENDIXB


6 Axle Vehicles

185

180

~ 175 cJ ~

170~ -= en

165

160 0 2 4 6

Reduced Variate

I --6 Axle

8 IO 12

Figure B 16 5m span

250

245

240

235

~ 230

~ 225 ~ ~ 220 -= en

215

210

205

200 -

f

- I

~ ~

7 V


I --6 Axle I

12 o 8 IO


Univers

ity of

Cap

e Tow

n

APPENDIXB

305

300

295

290 ~ 285 0 ~ 280 ~

275 270

265

260 o

2

~

~ r It

V


--+-- 6 Axle I

FigureBl8 15m span


--+-- 6 Axle I


340

335

~ 330

u 3250 ~ 01

320

315

310

~ V V

J ~

~

L V

Univers

ity of

Cap

e Tow

n

APPENDIXB

405

400

395 -

~ 390

QI OJ

Q 385 ~

eo QI 380

c en 375

370

365 o 2 4 6 8 10 12

--~

V

~ V

~

-~

i I

I i i

l Reduced Variate

-+- 6 Axle I

Figure B20 30m span

Univers

ity of

Cap

e Tow

n

APPENDIXB


7 Axle Vehicles

240

220 a ~ 200


CQ

140

120 0 2 4 6

Reduced Variate

--+---7 Axle

Figure B21 Sm span

700

650

~ 600

- 550 ~

~ 500 ~ 450a = ~400

350

300 12o 2 4 6 8 10

4~

h 1

~

I t

I

I

~ -I I

I I I I

Reduced Variate

--+---7 Axle

Figure B22 10m span

8 10 12

Univers

ity of

Cap

e Tow

n

APPENDIXB

1200

1100 e z 0 1000 C a Q 900 1gt11 CIa 800 CI

cQ

700

600


-+--7 Axle

Figure B23 15m span

1800

1700

Le 1600

~ C 1500 sect 1400 ~ ~ 1300a ~ 1200cQ

1100

1000

o 2 4 6 8 10 12

~

d ~

~

7 bull

Reduced Variate

-+--7 Axle

Figure B24 20m span

8 10 12

Univers

ity of

Cap

e Tow

n

APPENDIXB

3200

3000 e 2 2800 CI OJ

e 2600Q


2200

2000


8 IO 12

--7 Axle

Figure B25 30m span

Univers

ity of

Cap

e Tow

n

APPENDIXB


7 Axle Vehicles

240 ----------- ----- ---------------------

220 +---~r_--_+----r----+_---r_--~

~200 +-----4------+----~------+-----~~~~ ~ ~ ~ 160+----~r_---_+-----_b~--+_-----r_--~

140 +----~r_-~~~---r------+-----r_--~

180 +---~r_--_+-----r----~~---r_--~

120+-----r_--_+---~---+------r_---_4

o 2 4 6

Reduced Variate

-+--7 Axle

8 10 12

Figure B26 5m span

270----~------_-------_----~

250+----~----+---~---~--~~--~

Z 230 +---middot~~---+---~----~~--~----~ C ~ 8 210 +-----4-----~---~~~-+---~---~ r ~ ~ 190 +------I-------t~---_t__----+_---__t---_i

170+---~~--~---_t__---+-----__t---_i

150+----~------_+------~------+-----_4-----~

o 2 4 6

Reduced Variate

-+--7 Axle

8 10 12

Figure B27 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

320

300

~ 280 - 41 OJ ~ 260 41

~ 240

220

200

V

V

V

~~

~ f7

I i I I I i

I i 1

o 2 4 6

Reduced Variate

--+-7 Axle

8 0 12

Figure B28 15m span

390

370

~ 350 Z 0 41 330OJ C ~

30 41

c (J 290

270

250

o

h pound

7 6A V I

~

V

4V 2 4 6 8

I r

I I I

I i I

i I


--+-7 Axle

Figure B29 20m span

Univers

ity of

Cap

e Tow

n

APPENDrxB

480

460

44)

Z 420 ~ ~ 400 0

380 os

CI 360(I)

340

320

300

~

)~

d ~ ~

~

k

o 2 4 6

Reduced Variate

-+-7 Axle

8 10 12

Figure B30 30m span

Univers

ity of

Cap

e Tow

n

APPENDIX B


7 Axle Vehicles

200

~ 195

e Z 190 e Jif75 185

8 Q 180 CD

a fS 175 =I 170

~ 165


I ---7 Axle

Figure B31 5m span

o 2 4 6 12

Reduced Variate

580

560

e 54)

~ 520

il 500 01

sect 480 ~ 460

]44) 01

=I 420

400

380

-

I

j ~

--~ ~ ~

I

L

4

8 10

I

I

I

i

---7 Axle

Figure B32 10m span

Univers

ity of

Cap

e Tow

n

APPENDIX 8

1100

1050

e ~ 1000

C 01 e 950 Q

011

= 900a I 01 ~

850

800 0 2 4 6 8 10 12

Reduced Variate

--7 Axle

Figure 833 15m span

1700

1650

e 1600

L ~ 1550 01= e f1500Q

011

= 1450 rIIa 01= ~ ~ 1400

~

1350 ~~

1300 o 2 4 6 8 10 12

Reduced Variate

--7 Axle

Figure 834 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

3000

2950

ez 2900 ~ 2850 e ~

~ 2800 = a ~ 2750 =

2700

2650


-+-7 Axle

4

v

- V

Figure B35 30m span

Univers

ity of

Cap

e Tow

n

APPENDIXB


7 Axle Vehicles

~ ltI ~ 1 -= C-I

190

185

180

175

170

165

160

155

150

145

140

--shy

J r

) -

i-~

~ J1V


I ---7 Axle I

Figure B36 5m span

260

~V250

Y240 ~ ~ 230 -~ 5 ~ -= C-I 220

~

210 ~

200 o 2 4 6 8 10 12

Reduced Variate

I ---7 Axle I

Figure B37 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

320

~ 310

~ 300 r ~ 290 1

~

280 ~

~ ~ CI 270 (I) 260 -

250

240


--+-7 Axle

Figure B38 15m span

355

350

345

340

~ 335 330 ~ 325 ~

CI 320 (I)

315

310

305

300


--+-7 Axle

~

( L

l

~ ~

gt

~ ~

L

~

Figure B39 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

420

415

410

~ 4tl5

tJ

or 400

z (Il

395

390

385


I --7 Axle

Figure B40 30m span

t ~ i-

~~

1pound J

Univers

ity of

Cap

e Tow

n

APPENDIX B


8 Axle Vehicles

o 2 3 4 5 6 7 8 9

Reduced Variate

--+- 8 Axle

Figure B41 Sm span

o 2 3 4 5 6 7 8 9

Reduced Variate

1 --+-8 Axle I

Figure B42 10m span

e 3

550

500

- 450 c e c ~400 OIlca ~

CQ 350

300

V V ~

~--shy V

~ V~

8 ~

550

500

- 450 c a V

V r shy --

V -c ~400 ~

-V a c=350

300

~ V

Univers

ity of

Cap

e Tow

n

1050

1000

8 950

Z 900~

C 850a 0

~ 800 Oilc

750ac =I 700

650

600

o 2 3 4 5

Reduced Variate

1 --+-8 Axle

Figure B43 15m span

1600

1500

e Z 1400 ~ C a 1300 0

~ Oilc 1200ac

=I 1100

1000

o 2 3 4 5

Reduced Variate

--+- 8 Axle

Figure B44 20m span

I

-~ ~

shy

~ ~

~ ~ shy

V

I

~ ~~

- ~

~ ~

~ ~

V III

~

6 7 8

APPENDIXB

9

6 7 8 9

Univers

ity of

Cap

e Tow

n

APPENDIXB

I 17 I

7 ~ ~ I-

I

1

-e ~ i i

~ shy I- I

~ ~ 1

f

~ ~

i

I 2 3 4 5 6 7 8 9

Reduced Variate

1 -+--8 Axle I

3000

2900

2800 8 2700 ~

2600 -= 8 ~

2500 = ~ 2400 0laquo1 = a 2300 = ~

~ 2200

2100

2000 o

Figure B45 30m span

Univers

ity of

Cap

e Tow

n

APPENDIXB


8 Axle Vehicles

260

240

~ 220

~

~V ~ 200 ~ c

IIl 180

160

140

~

~

V ~V

V-

~

o 2 3 4 5

Reduced Variate

I --8 Axle I

6 7 8 9

Figure B46 5m span

250 I

240

~ ~~

~

~

~ ~ I

~

~ I

I I

230

220

~ 210 ~ ~200

I 190 ~ IIl 180

I 1170

J160

150

o 2 3 4 5 6 7 8 9

Reduced Variate

I --8 Axle I

Figure B47 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

310

290

~ 270

0 250

gj I 230rJl

210

190 o 2 3 4 5 9

Reduced Variate

-+-- 8 Axle I

Figure B48 15m span

r-- i I

L i v

v ~

I

~ ~ I

-11 I

~ i j

6 7 8

V

I

360

340

320 Z o 300 ~ ~ 280

c rJl 260

240

220

10-shy

-~

-V

- ~

o 2 3 4 5

Reduced Variate

-+-- 8 Axle I

6 7 8 9

Figure B49 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

440

420

400

~ 380 Q 360 ~ ~ 340 c CIl

320

300

280 o 2 3 4 5 6 7 8 9

~ ~

---~VIII

~

I

L Y I

~ ~ I

~ ~- I

i I I I

1

I I i

Reduced Variate

-+- 8 Axle I

Figure B50 30m span

Univers

ity of

Cap

e Tow

n

APPENDIX B


8 Axle Vehicles

I

I

570

550

a ~ 530

-= ~ ~ 510 ~ 01)

9 ~ 490 OJ

I=Q

470

450

L

I

I i

~- ~

~

-~ shy i

~

I

I j i


--8 Axle I

6 7 8 9

Figure BS I Sm span

570

550

e ~ 530 -

~ -= E lt) 510 ~ 01)c 490ac ~

I=Q

470

~V

-~ ~ ~

~ shy-shy

~

450


I -shy 8 Axle I

6 7 8 9

Figure B52 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

1030 1 i1010

I990e IZ e 970 c ~ 95013 Q

~ 930 OIl

Is= 910 = I= ~

890 1

870 i

850

V ~

[i i

~ V I

~~ I I

~ ~ I I

I

I I

V

I

o 2 3 4 5 6 7 8 9

Reduced Variate

1 -+-8 Axle

Figure B53 15m span

1600 I

~ 15508 ~ z e ~ -c 1500 shy8 ~

~ Q OIl 1450 s= ~ =

V = 1400

1350 o 2 3 4 5 6 7 8 9

Reduced Variate

-+-8 Axle I

Figure B54 20m span

Univers

ity of

Cap

e Tow

n

APPENDIX 8

3000-----r-------------~----~----r---~----~----~

e ~ - 2900 E 8 Q

~ ~

aI 2800 I =

2700+---~~--~----~----~---+----~----~---+--~

o 2 3 4 5

Reduced Variate

-+-8 Axle

Figure 855 30m span

6 7 8 9

Univers

ity of

Cap

e Tow

n

APPENDIX B


8 Axle Vehicles

260

255

250

Z 245

~ ~

240 235= ~ 230~

c CIl 225

220

V

215

210

~ I

~~

~r V

~

~ ~r

I i I

l i

I

o

Figure 856 5m span

2 3 4 5

Reduced Variate

-+- 8 Axle

6 7 8 9

3000

~ --~ ~ 2900 V ~ V

~ V 01 41 ~c

CIl 2800

V ~

2700

o 2 3 4 5 6 7 8 9

Reduced Variate

1 -+-8 Axle I

Figure 857 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

-

o 2 3 4 5 6 7 8 9

Reduced Variate

-+- 8 Axle

Figure B58 15m span

305

300

295

~ 290 III ltJ 285Q ~ ~ 280 c rI)

275

270 I 265

L ~

~ ~

tr V

~

I-shyi-shy

I

I i I

I I I i i I

I

345

340

335

Z 330 ~ III 325 Qr 320 =OJ c 315IJ)

V

~

-U i-

~

310

305 V-300

shy

i I

I I I

I i i

i I


1 -+-8 Axle

6 7 8 9

Figure B59 20m span

Univers

ity of

Cap

e Tow

n

I

APPENDIXB

415

40

405 Z ~ 400 0 ~ 395 gJ

c (I)

390

385

380

o 2 3 6 7 8 9

I

~ V

~

~ ~

~ ~

~

4 5 Reduced Variate

I --8 Axle

k I L

-I

i

I i

i

i

i I

Figure B60 30m span

Univers

ity of

Cap

e Tow

n

APPENDIX B


6 Axle Vehicles

295---------~----------~----------~--_

275

e 255

~ lt11

C 235 e ~ Q

~ 215

195

--t-- i

i-----i---

175 +-----r-----r-------------------r----~

-100 100 300 500 700 900 1100 1300

Reduced Variate

Figure B61 5m span



bull

Univers

ity of

Cap

e Tow

n

APPENDIX 8

1500~----~----------~----r---~~--------~

I I I1400 -1 shy --+-__--_1shy

~ 1300 --~-~---j---+I -

i 1200 -1-shy - -+-shy - -+-shy8 Q


~ ~~~-- I I I 900 r-- ---t---T 800+-----+-----~----r_----r_----r-----~--~

-100 100 300 500 700 900 11 00 1300

Reduced Variate


Figure 863 15m span

2200

2100

~2000 a ~ 1900

i 1800 g1700

~1600 = i 1500

11 1400

1300

1200

I 1

-1 I I

I I I

L---shyI

___shy---- shy

-100 100 300 500 700 900 1100 1300

Reduced Variate


Figure 864 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

3800

3600

e 3400Z e I 3200 QI e

3000Q

~

2800a QI 2600=

2400

2200

-100 100 300 500 700 900 1100 1300

Reduced Variate


Figure B65 30m span

Univers

ity of

Cap

e Tow

n

APPENDIXB


6 Axle Vehicles

300

280

Z 260

0 240 ~ 220i ~ fIJ

200

180

160

I--I-shy

I --shy

i

I

-100 100 300 500 700 900 1100 1300

Reduced Variate


--Nonnal Gumbel

Figure B66 5m span

340

~ - Q CIS ~ fIJ

200

Reduced Variate

320 ~-l--middot- 1 --300

280

260

240 i

220 I T

I

-100 100 300 500 700 900

-I 1100 1300


--Nonnal Gumbel

Figure B67 10m span

Univers

ity of

Cap

e Tow

n

390

370

350

~ 330 r 0

310 ~

CI rJl

290

270

250

i -i----~--~middot~--- -+ -- ---~-- ----~--shy




-100 100 300 500 700 900 1100 1300

Reduced Variate


-- Normal Gwnbel

Figure B68 15m span

440

420

400

~ 380 0 r 01 360

CI rJl

340

320

300

-100 100 300 500 700 900 1100 [300

Reduced Variate


--Normal Gwnbel

Figure B69 20m span

APPENDIXB

Univers

ity of

Cap

e Tow

n

APPENDIXB

510

490

470

~ 450 Ol _ e

430~ 01 41 410

CIl

390

370

350

-100 100 300 500 700 900 1100 1300

Reduced Variate


-- Normal - Gumbel

1 _ - --1-

j ---+--~~I i

-1----1-----

-+-------tli

- -+---~ I - i - --L-- -l- - -l

-I -+---1-- 1


Univers

ity of

Cap

e Tow

n

APPENDIXB


6 Axle Vehicles

220

215


ltgt 200 I~ ~


I 185 19----1----1- -------------r

180

-100 100 300 500 700 900 1100

Reduced Variate


Normal -It- Gwnbel

Figure B71 Sm span

670

650

e 630 Z e 610 7 ltI 590S ltgt ~ 570

cI ~

550 I ltI

cQ 530

510

490

I +---+--+---shy- T - shy -

1 ------

-100 100 300 500 700 900 1100

Reduced Variate



Figure B72 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

1450 -r------------------------

e z 13502 1250

ltII

C e 0 1150 5 ~

1050 c CQ

950

I

~-+_____ I

850+----r---r----~--~---+----~

-100 100 300 500 700 900 1100

Reduced Variate



Figure B73 15m span

1910

1860

e 1810 Z 2 1760l c

1710e 0

1660

5 ~

1610 c CQ 1560

1510

1460

-100 100 1100

--------1 ---

~-r---~-- ----shy- 1- --1-- - -I-

I i

300 500 700 900

Reduced Variate



Figure B74 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

3150 ----------------------------

3100

3050

3000

2950

2900

2850

2800



i I I i -

- i

i

I--I - - -1-shy

I -LOO 100 300 500 700 900 1100

Reduced Variate


-- Normal --Gumbel

Figure B75 30m span

Univers

ity of

Cap

e Tow

n

190

APPENDIXB


6 Axle Vehicles

Z 186 Cshy Ol

184 01 Olc 182

CIl

180

178

-100

I 188 +---1-shy

t-+----shy

100 300 500 700 900 1100 1300

Reduced Variate


-- Normal ~Gumbel

Figure B76 5m span

290

280

270Z e ~ 260 lt=

250 ~ c

rJ)

240

230

220

-100 100 300 500 700 900 1100 1300

Reduced Variate


--Normal ~Gumbel

Figure B77 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

325 i

--------------t------~t__-__I320

315

Z 310cshy 305 Q

300 = c (JJ 295

290

285

280

-100 100 300 500 700 1100 13 00

+--------+--- +-----i---Le----+- -I

=---=------- ------I

j-__+--_ - i___ __ I

900

+-_-I- shyI

Reduced Variate


-- Normal --Gumbel

Figure B78 15m span

355~----~----~----~--~~--------------~

350 +shy

345

340 -Jshy

335

- -I I II

--J---- t---j---- k-- ------------I_____I

---l-

330~~--T----r-----~--~~--~----_----__t

-100 100 300 500 7 00 900 1100 13_00 Reduced Variate


-- Normal Gumbel

Figure B79 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

420

415

410

~ 405 ~ 400 ~ c CIl 395

390

385

-100 100

---1shy--T

I 3_00 500 700 900 11 00 1300

Redoced Variate


Figure B8D 30m span

Univers

ity of

Cap

e Tow

n

APPENDIXB


7 Axle Vehicles

310

--L290

e 270Z ~ l 250c a 230Qa 01)


170 I I i

150

-100 100 300 500 700 900 1100 1300

Reduced Variate


--Normal Gwnbel

Figure B81 5m span

i

600 +----

850~----~--~----~----------------T_--~

800

750 ----1 -1-1-1 -+1-----gt+-1 700 --------I----b---i------ -t-- i_ _ 650 -I- ----+---- +- - -- - --=L--+---tI

~ ac ~ 550

500

450+-----r---~----_+----_r----~----~--~

-100 100 300 500 700 900 1100 1300

Reduced Variate


-- Nonnal Gwnbel

Figure B82 10m span

Univers

ity of

Cap

e Tow

n

1350 ~-+ ~ -1250 - i - ishy1150

I 1050 I 950 I

APPENDIX B

1450 ~--~------------------r----------

850+----r---~----_r---4_----r_-~---~

-100 100 300 500 700 900 1100 1300

Reduced Variate


Normal --Gwnbel

Figure B83 ISm span

2150

2050

E 1950 z ~ 1850 l I 1750S ~

~ 1650 toll

aI 1550 I = 1450

1350

1250

-100 100 300 500

Reduced Variate

__1__ _

i ~~----- --~I -----

700 900 1100 1300


Normal --Gwnbel

Figure B84 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB


2650 f----i~-_+---r---i---+---ir-----l

-100 100 300 500 700 900 lUXgt 13 00

Reduced Variate



Figure B85 30m span

3850 ------1----------------------

3650

3450

3250

3050

2850

Univers

ity of

Cap

e Tow

n

APPENDIXB


7 Axle Vehicles

~ Qj e r ltII Qj

-= CIl

280

260

24)

220

I I +---+-----l-- -+_-+--~I- --


200

180 -l--~_-__+- ------L--__+------ shyt----shy160+-----r---------+-----r-----r----~--~

-100 100 300 500 700 900 1100 1300

Reduced Variate


Normal -+-Gumbel

Figure B86 5m span

320 I

300 1___

I I ~ 280 I Qj

--t-~-- - e 260r g

-= 24) -CIl

220

200

-100 100 300 500 700 900 1100 1300

Redoced Variate



Figure B87 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

360

350

340

~ 330 - 320~ ltJ ~ 310 01 300 -= rIl

290


280

270

260

-100 100 300 500 700 900 1100 1300

Reduced Variate


Normal Gwnbe1

Figure B88 15m span

450r-----~----r_----~----~----~--~----_

430 ~---+_---+_--_+_--_+_--_+--_=_+--_l

Z 410

0 ~ 390ltJ ~ 37001 ~

-= rIl 350

330


310

-100 100 300 500 700 900 1100 1300

Reduced Variate


Normal Gwnbel

Figure B89 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

~ y Q ~ CII d rJJ

560

540

520

500

480

460

440

420

400

380

360

I I



+----+ishy - ---- -+------L shy-shy-----~--___l I I -

-100 100 300 500 700 900 1100 1300

Reduced Variate


Normal --- Gwnbel

Figure B90 30m span

Univers

ity of

Cap

e Tow

n

APPENDIXB


7 Axle Vehicles

210

205 5 z e 200 ~ c e ~ 195

E till ca 190 c

=

185

180

-100 100 300 500 700 900 11 00 1300

Reduced Variate

I r----+-I-- ---~-------+---t---I I


Normal Gumbel

Figure B9 I Sm span

5 Z e l c e ~

E

aC till

c =

535

530

525

520

515

510

505

500


Normal Gumbel


-100 100 300 500 700 900 1100 1300

Reduced Variate

Figure B92 10m span

Univers

ity of

Cap

e Tow

n

1150

1100 - middot 1050

1000 r --

950

900


i I

- 1i

APPENDIX B

1200 -------~----____--____----_

850+---r-----r--~--~---~--_T----~

-100 100 300 500 700 900 1100 1300

Reduced Variate



Figure 893 15m span

e

1650

1630

1610

~ 1590 ~ c 1570 e Q 1550 ~ ell 1530= a c 1510 = 1490

1470

1450

I I -~-t-shyI

i il )

l--shy

-100 100 300 500 700 900 1100 1300

Reduced Variate



Figure 894 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

I i I

-~-+--1-1 ~ I-1--

2820+-----r---~~--~----~----_+----_+----~

-100 100 300 500 700 900 1100 1300

Reduced Variate


-- Normal Gumbel

Figure B95 30m span

2940

2920 e Z 2900ltII

I -OJ

8 ltgt 2880 ~ OG Ia 2860 I OJ

CQ

2840

Univers

ity of

Cap

e Tow

n

APPENDIXB


7 Axle Vehicles

210

205 +---f---l----I I---r----f-----

----- -JbI~__+ - I

--~-l ---- - ---+----+-- i

200 -J-- -+- - - j--shy

~ 195 -- ---1- -+----

ltj 41 190

ri I II i __ J ---r--shy 185

41 -= I ~ I - I ~+---r---rIl 180

175 +-ltSgt---- - +-i--i---T --+--shy i

170

-100 100 300 500 700 900 1100 1300

Reduced Variate


-- Normal --Gumbel

Reduced Variate


--Normal --Gumbel

Figure B97 10m span

Univers

ity of

Cap

e Tow

n

360

+ JiUO--t---

-j---t----+--- -~-- - T -3S0

-340 r- -r- I ~- -1- -shy~ 330 ltJ ~ Q 320 +---h-=-~~--1 ~~-Ib~01

310c ~ -- I-- r-----1-shyen


280

-100 100 300 Soo 700 900 1100 1300

Reduced Variate


-- Normal Gumbel

Figure B98 ISm span

390r---~----~----~-----1

~ 370

~

----------~--~

380 +--------- I - ---r ---+- - - - ------- ---+-- - - - - --1

I - +1--- -+-

3S0 +----+

330+-----r---~----_+---_r----~----~-~

~ 360 +--shygj t3

340



Figure B99 20m span

APPENDIXB

Univers

ity of

Cap

e Tow

n

APPENDIX B

423

421

419

417Z 415 Q

413 ltlI c 411 (IJ

409

407

405

-100 100 300 500 700 900 1100 1300

Reduced Variate



Univers

ity of

Cap

e Tow

n

APPENDIXB


8 Axle Vehicles

240

230

e 220

~ - 210 -= 200e 0

E 190 011c a 180 c = 170

160

150

-100

-I----tl ---+shy

I

-r I i-----1L-~II --_t_

_ -+shy _ _ i

100 300 500 700 900 1100 1300

Reduced Variate


Normal Gumbel

Figure BIOI Sm span

650

8 600 z -I - I c 550 e 0

E 011 500ca I = 450

4OO+-----r---------+-----r-----r----~--~

-II

-100 100 300 500 700 900 1100 1300

Reduced Variate


Normal Gumbel


Univers

ity of

Cap

e Tow

n

APPENDIXB

1200 ----------~r_-r_--__r--____--__


= --+1- ~ l -~ a = CQ

850 q - -I--middot-~ -1

800 I

750 +-----~----~----_----~----_r----~---~

-100 100 300 500 700 900 1100 1300

Reduced Variate




1900

1800

S Z 1700 l = 1600 8 c ~ 1500 OJ)

= a = 1400

CQ

1300

1200

-100 100 300 500 7 00 9 00 1100 1300

Reduced Variate




Univers

ity of

Cap

e Tow

n

APPENDIXB

3350 I

I

I

3250

1-~ --

- 3150S

z --1-shy ~c 3050 1

II I 2950e iQ

2850 011 s 27501l c

I = 2650

2550 -I middot I

2450

-100 100 300 500 700 900 1100 1300

Reduced Variate


-- Normal Gumbel


Univers

ity of

Cap

e Tow

n


8 Axle Vehicles

210----------~------_----~----~----~

200~-----~-----4------~----~-----+--~~

190

~

~


I~+_-----r----_------r-----~-----+----~

I f----- -I shy

180 +---------------

170 -t------------+-~

I I-shy ----------- 1 160 +-------1----4-----

-100 100 300 500 700 900 1100

Reduced Variate


-- Nonnal - Gumbel

Figure B106 5m span

290

280

270

260 ~ - ~ 250 Q 240 ~ 230 ~

rIl 220

210

200

190 -00 100 300


-- Normal -Gumbel


-1---1--shy-1----1-1--shy


500 700 900 11 00

Reduced Variate

APPENDIXB

Univers

ity of

Cap

e Tow

n

APPENDTXB

370


~ 330

01 310

- - --~---t-shy--


270

250

230

-100 100 300 500 700 900 1100

Reduced Variate


-- Normal Gwnbel


~o----~-----------~-----------------_

380

~ 360 01 Q 3~ ~ ~ c 320()

300

280

-100 100 300 500 700 900 1100

Reduced Variate


-- Normal Gumbel


Univers

ity of

Cap

e Tow

n

APPENDIXB

500

480

460

~ 440 OIl

~ Q 420 ~ ltII OIl 400d

(I)

380

360

340

-100 100 300 500 700 900 1100

Reduced Variate


-- Normal Gwnbel


Univers

ity of

Cap

e Tow

n

APPENDIXB


8 Axle Vehicles

210~----~-------~----~--------------

205 ~---l-

200 -j---l-----

195 -+----l~oP ---1-shy +---1------1


185 -t------t----i---i------r----

-100 100 300 500 700 900 1100 1300

Reduced Variate


-- Normal Gumbel

Figure BIll 5m span

545

540

S Z 535 i 530 GI a 0 525 ~ ~ c a 520

C GI

IQ 515

510

505

-t-+---t-I-L I I

-100 100 300 500 700 900 1100 1300

Reduced Variate


-- Normal Gumbel


Univers

ity of

Cap

e Tow

n

APPENDIX B

104)

1030

e 1020Z e l 1010c e 1000=gt OG

990c s c 980=I

970

960

-100 100 300 500 700 900 1100 13 00

Reduced Variate


-- Nonna --- Gumbel


1620-----~--~----~~--_----~----~--~


ac

c =I

1500+-----r---~----_T----_r----~----_--~

1600

1580

1560 l

i 154)

1520

-100 100 300 500 700 900 1100 1300

Reduced Variate


--Nonna --- Gumbel


Univers

ity of

Cap

e Tow

n

APPENDIX B

2970

~ 2950

S z 0 2930 (I)

is e 2910Q

~ 1gt11 Ca 2890 c

al

2870

2850+-----r-----~--~r_--~r_--~----_+----~

-100 100 300 500 700 900 IUlO 1300

Reduced Variate


--Normal -Gwnbel


Univers

ity of

Cap

e Tow

n

--

APPENDIXB


8 Axle Vehicles

200

195

Z ~ 190 ~ ~ 185 ~ -= (I)

180

i i I I ~ E bull

175

c_---+-__---_ ~--_f

~-+-----il-_+ _-+t_i ---t-I-I -100 100 300 500 700 900 1100 1300

Reduced Variate




~ ~

= ~ -= ~ (I)

275-----------~--------~----------~----_

270

265

260

- shy -- ----- shy ----1---shy

I 2S5 -t shy250

245

240

-100 100 3 00 500 700 900 1100 1300

Reduced Variate


--Normal ---Gumbel


Univers

ity of

Cap

e Tow

n

APPENOIXB

325

320 I-- -I ~

315

310OJ ~ 305~ -= (I)

300

295

290

-100 100 300 500 700 900 1100 1300

Reduced Variate



Z e ~ Q

~

~ -= (I)

360~----------------~----~---------------

355

350

345

340

335

330

--+----~-- ~--- i shy - ---+-----1

i I I I -100 100 300 500 700 900 1100 1300

Reduced Variate


-Nannal Gwnbel


Univers

ity of

Cap

e Tow

n

APPENDIXB

QI ~ 415 +---f--shy

-~--t-I I

I -=r-i--- II

I 400+-----~----+_----+_----r_----+_----r_--~

430~----~----~----------~----~----~--~

425 --f ~ r - ~ 420 -I---~---li-- --- --t-shyZ I ==- i

~ o

lltU 410 +-- -r shy

~ ~-----------l405 -1--061+--1-----+ I

i i

-100 100 300 500 700 900 1100 1300

Reduced Variate



Univers

ity of

Cap

e Tow

nAppendix C


II

II

Univers

ity of

Cap

e Tow

n

APPENDIX C

Page No




Univers

ity of

Cap

e Tow

n


Univers

ity of

Cap

e Tow

n




















Univers

ity of

Cap

e Tow

n




I 022

2 23E-05 3


4 46E-09 (2)(3) 5



6 (I) (4)IOE-09


7 47E-18 (6) (4)



9 10E-18 (1)(7)


10 47E-27 (9)(4)








3

Univers

ity of

Cap

e Tow

n


4

Univers

ity of

Cap

e Tow

n

A-1

APPENDIX A

Univers

ity of

Cap

e Tow

nAppendix D

Impact Formula I

bull bull

Univers

ity of

Cap

e Tow

n

APPENDIX 0

Page No







Univers

ity of

Cap

e Tow

n





Where













3J =shy

b L


J =~ b Lf





Where













3 J =shy

b L


J =~ b Lf

Univers

ity of

Cap

e Tow

n



therefore used











response

2



therefore used











response

2

Univers

ity of

Cap

e Tow

nAppendix E


bull

Univers

ity of

Cap

e Tow

n

1

APPENDIX E

Page No









Univers

ity of

Cap

e Tow

n

























III 2

I ~


























W~ I i I

WI 2

I I ~


Univers

ity of

Cap

e Tow

n


















2

Univers

ity of

Cap

e Tow

n









moments





















3

E13








moments













E14 Simulation








3

Univers

ity of

Cap

e Tow

n






(i) Maximum W

(ii) Shortest b

(iii) Centred x =05












limits





legal vehicles





4

Univers

ity of

Cap

e Tow

n







5 197 189 4

10 547 562 3 15 1054 1054 0 20 1582 1626 3)

7


0 Connor Difference

5 184 173 -6

10 252 258 3 15 308 304 -1 20 347 346 0





simulations









5

Univers

ity of

Cap

e Tow

n

Bending Moments kNm


5 293 301 -3 10 800 812 -1 15 1262 1364 -7 20 1903 2097 -9 30 3526 3631 -3








6

Univers

ity of

Cap

e Tow

nAppendix F


Visual Bas

Univers

ity of

Cap

e Tow

n


Sub centralloadO









Univers

ity of

Cap

e Tow

n




pos = inc n







+


pos = inc n



10) lt= 0 Or

+ + +


Then Then Then





+ + spaclO



Univers

ity of

Cap

e Tow

n






n=n+1 Loop



Next z


Univers

ity of

Cap

e Tow

n




Nexty








Next s


End Sub




Nexty








Next s


End Sub

Univers

ity of

Cap

e Tow

n

TABLE CONTENTS

No

1 INTRODUCTION

11 BACKGROUND 1-1

12 OF THE STUDy 1-2

1-3 13 SCOPE OF THE

14 METHODOLOGy 1-4






21 INTRODUCTION 2-1





25 CONCLUSIONS 2-15


31 INTRODUCTION 3-1







35 RESULTS 3-23

36 OVERLOADING 3-27

37 CONCLUSiONS 3-31

Univers

ity of

Cap

e Tow

n


41 TMH7 PART 2 4-1








45 CONCLUSIONS 4-23



52 RESULTS 5-3








(vi)


41 TMH7 PART 2 4-1








45 CONCLUSiONS 4-23



52 RESULTS 5-3








(vi)

Univers

ity of

Cap

e Tow

n

List of































(vii)

List of




24 - of H20 LRFD 1 2-7


26 CL-W Truck 2-10

2-10 27 - CL-W


31 -

32 -

33 -

34 -


of GVMs 3-8


Function of

Function of

Moments 30m span

Moments 5m span

3-9

3-9











41 -

42 -

44


Distributed Lane

Moments Due to

of Class 14 Vehicle


and 4-7

4-14


46 -

47 -

51 -

52 -

of Moments 4-19

gtr of Forces


4-20

5-2


Univers

ity of

Cap

e Tow

n





(viii)

Univers

ity of

Cap

e Tow

n

List of Tables































(ix)

List of Tables


























Table 41 - 4-6





(ix)

Univers

ity of

Cap

e Tow

n












(x)

Table 46

Table 47-






Table 411 -

Table 412 Shear

Table 51 -


Table 53-

Table 54-


WIM data v RR 4-22






Univers

ity of

Cap

e Tow

n

1 INTRODUCTION

11 BACKGROUND
















Regulations


June 1994














(1-1 )

1

11




with the aim of

the most onerous











the Road

commissioned the

to increase the

to consider the



(i)

The main

the


June 994



Vehicle Loads on

Vehicle Loads on












(1-1 )

Univers

ity of

Cap

e Tow

n






























(1-2)

12






vehicles






with

Ullman





and adds to the








WIM are






(1

Univers

ity of

Cap

e Tow

n



RR 91100410 I amp 02




data
















considered

(1-3)



RR 9110040 I amp 02




data
















considered

(1-3)

Univers

ity of

Cap

e Tow

n

14 METHODOLOGY




identified were












approaches














(1-4)

14 METHODOLOGY


142



identified were

TMH7 Part 2 The




and



( I Code These



loads on

close






















(1

Univers

ity of

Cap

e Tow

n


































(1-5)






Statistical

vehicles



vehicles on the N3





vehicle

load effects

and fits the

within a 120 year










both methods is



of an extreme











(1

Univers

ity of

Cap

e Tow

n





(c) Overloading















(1-6)

Critical Assessment




The extent of

vehicle set


vehicle set This

those

between the WIM

event of the actual














(1

Univers

ity of

Cap

e Tow

n

1~ REPORT STRUCTURE













reviewed in detail



















(1

1~ REPORT STRUCTURE




live

extent of

with the










reviewed in detail



In and the















in TMH7

the

load model are



of the WlM data

(1

Univers

ity of

Cap

e Tow

n


21 INTRODUCTION






these loads

















on bridges






and

21 INTRODUCTION








these loads


lIllUlLla on the









BS5400 1978

British Standards




Factor ( I

Code and


on






and

m


Univers

ity of

Cap

e Tow

n










the TMH7 Part 2


























(2-2)



to process and







live load models in

the TMH7 Part 2











- u- sensors









vehicles The


by the vehjcle axle

to the extreme

Allowances for









are shown in 21

Univers

ity of

Cap

e Tow

n

305 366 244 305 244 305 244 m


80 219 100 100 100 100 100 100 kN Axle loads (kN)

Ca)

7 x 305 IT = 213 m 0 ~----- -------__--- ___---

~[I ~[JJ 1 I 1 I 1 I] 70 B 96 896 896 896 8 96 896


(bJ























(2-3)

Univers

ity of

Cap

e Tow

n



























241 BD 3788











24


























APPROACH




241 BD 3788









spans





Univers

ity of

Cap

e Tow

n








W= 260 kNfm


J

BS 5400 Part 2





















(2-5)

10 in the

for loaded







lt11 C l 0

150

E 100 lii CL

s



W= 260 kNfm

BS 153 Part SA

BS 5400 Part 2
















axle loads An


of 146 was

~nrn)~h used was


and lateral

factor of 18 was

to

were included





Univers

ity of

Cap

e Tow

n
















(2-6)
















Univers

ity of

Cap

e Tow

n

242 AASHTO lRFD
























35 000 N 145 000 N 145000 N



Design Lane 3600 mm


(2-7)

Univers

ity of

Cap

e Tow

n








z [F(M)] (21)

Where

M Moment















from the

in 1975


data base For

calculated The



on normal






z

Where

M Moment

CDF of the moment M










Univers

ity of

Cap

e Tow

n

5~---------+--------~~~~----~ II NGntbs

I ~

j O~--------~~~-------------+------~

~------+ri~----------------+------~

~~--~~------~-------------+------~

Jr---~--------~-------------+------~

~~------------~------------~------~ o








243 CANADIAN CODE









(2-9)

Univers

ity of

Cap

e Tow

n



~ -i 1 3igtm

112ml


Imiddot 18 m

~ ~P) =~-----ffi--tB------ -~---- ----8t------shy

t J-----ffi-----ffi-ffi------ --ffi---- -----~------


ClaHance Errvelope

300 m





So6m 6ampm

180 m

66m






(2-10)

Univers

ity of

Cap

e Tow

n























IIgt

IIIQ

to

ro

to

IQ

~

0








bull bull ~ ~- _- _~ n N 0)





~~Jtli ~ -~ Rf



L~ M I ii 11011

H ~~ II 11

_ r _ t

t7 ~ zo ~ n ~i -ii41 1 II



I IJN ~ ~ 4 1 ) bull ~ 1 r-




(2-11 )

Univers

ity of

Cap

e Tow

n








to measured












BD 3788

244 EUROPEAN CODE





bridge












2)








to measured









the Ontario

effects caused

Base





BD 3788


244 EUROPEAN CODE




is ENV 199





The

traffic












Univers

ity of

Cap

e Tow

n








Location

Axle loads Qik

(kN) qik

(kNm2 )



o

Q

~~H-050 200

-iti--Hl-fosomiddot


-iH----H1-gtI-O50

1m2


050 120

2 00

For IV 300 m








(2-13)

Univers

ity of

Cap

e Tow

n














of the total loads

(i) Free flowing

















(2-14 )






involved the of the

In the case of axle

double and

values were









of the total loads


(i) Free













methods in

relevance is

This

nnmrn of the ENV





Univers

ity of

Cap

e Tow

n

25 CONCLUSIONS





















TMH7 Part 2




load model









(2-15)

25







W1dertaken

live







methods that

models an












TMH7 Part 2




load model









Univers

ity of

Cap

e Tow

n


31 INTRODUCTION










9100401 amp 02



















(3-1 )

31 INTRODUCTION

32








vehicles on

deterministic

9100401 amp 02






WIM were set















Univers

ity of

Cap

e Tow

n

















321 Actual Vehicles













Table 31


Vehicles Vehicles

No of Recorded

Vehicles 24901 34951 2587 62079


Univers

ity of

Cap

e Tow

n

F





In the


5 to 15 20 30 6 Axle Veh Mean 1040 2801 4734 7507 14319



Std Dev 345 915 1701 2794 5865


5 to 15 20 30 6 Axle Veh Mean 952 1224 1500 1782 2115



Std Dev 324 418 546 654 815


322 Legal Vehicles
















overestimated

it was

(3-3)

Univers

ity of

Cap

e Tow

n







standard deviation


5 10 15 20 30





5 10 15 20 30








regulations










(3-4)

Univers

ity of

Cap

e Tow

n



18000

(3-5)



Univers

ity of

Cap

e Tow

n


Accuracy of Data
























(COST 323 1997)



actual vehicle

(3-6)

33 APPROACH

of Data


















may be 25 more or


individual results






323 1



actual vehicle


the road vehicles



Univers

ity of

Cap

e Tow

n











940 1300 1500 1460 1180 1200 122 0 383Max 442 519 507 470 489 47 5 48 2 196Mean 100 207 208 216 207 213 207 870Std Dev


272 1267 1062 1535 1339 1190 831 8820 1476 2026 1734 1464 1522 1083 679 4725 1776 2242 1948 1260 1247 899 485 5430 2051 2146 1654 1128 1119 805 422 4835

40 3662 1796 1360 1119 1068 824 464 63 5976 1722 1342 1183 1061 943 535 4945 6436 1769 1304 1301 1233 1135 633 7350 4961 1775 1454 1476 1489 1375 864 7255 2460 2291 1850 1803 1788 1672 1195 6760 794 2747 2328 2117 2026 1805 1200 4565 144 3033 2590 2039 2046 1658 1080 3670 24 2694 2107 1528 1571 1218 705 1375

80 4 1976 1376 928 933 716 388 9 85 2 1019 719 394 423 275 151 4 90 0 487 __- 305 164 _ 170 __ 127- 51 _-- 1 ___ _ - _ _-_ _shy

95 I 213 112 58 47 47 18 0 100 0 80 43 31 23 19 6 0 105 0 43 14 8 5 5 3 0

0 17 8 4 2 2 2 0110 0 II 9 2 0 3 0 0115

120 0 3 3 0 2 2 0 0 125 0 6 1 I 0 0 I 0

More 0 2 1 I 0 0 0 0 30039 30039 24065 21383 20070 17360 10437 774Sum


(3-7)

Univers

ity of

Cap

e Tow

n







2500 12000

c 0c10000 ltI2000 C I ~

8000 c ~

1500 IltI

~H-I-t++-f-++-+ 000

-=e

~C qj 6000 iI a Q~ 1000

qj~ 4000 ~ ~ ~

500 20 00 I

U

o

Bin







(3-8)

Univers

ity of

Cap

e Tow

n

00030 -----------r-------------------r--------

o 00025 JI ~ 00020 i-----I~--_I_---t_-~--+---+-----f----I lIi i~ 00015 ~

] 00010 to

ampJ o ~ 00005 +----+----+----~-------_IIoc__

00000 +----+----+----j----i----+----+---

o 100 200 300 400 500 600 700

Weight(kN)


001200

sa 001000 v

~ 000800pound

000600 ~ 15 000400 ~ to ~ 0

000200 ~

000000

0 50 100 150 200 250



000080

000070

ll 0

000060 ~ 000050 ~

fshy 000040 S ~ l- 000030 g ampJ

000020

0

D

p 000010

000000

i-~-I- ---- __ ~

o 500 1000 1500 2000 2500 3000



(3-9)

Univers

ity of

Cap

e Tow

n


















events and







respectively




periods (Dawe 2003)

0)
















ENV 1991-3 et 200

The

the

(i)




events and

In the case of

of the extreme










Univers

ity of

Cap

e Tow

n






and for each class






lIN



(31)

2515517 + 080853w+ 0010328w2

z=w- 2 (32)1+ 1432788w+ 01 89269w + 0001

Where






=x+Krs (33)

Where

Xr Event at time T

x Mean of events

Kr rPllHPU factor

1)

Univers

ity of

Cap

e Tow

n









therefore similar


5 285 290 278 290 10 762 739 743 762 15 1266 1365 1372 1372 20 2069 2262 2242 2262 30 4740 4638 4740



5 263 261 258 263 10 323 343 339 343 15 417 439 436 439 20 495 522 537

653 675



6 Axle 533 281 91 -021 7 Axle 653 367 118 -073 8 584 122 -056










(3-12)

Univers

ity of

Cap

e Tow

n












m 04P(Xgtx ) =--- (34)

n+

Where











with B

Where


342 Extreme












Cunnanes formula

gt

Where











with B

Where

T Return where T 1

Univers

ity of

Cap

e Tow

n

--

- - -_--_- _ shy3000

2800+------I----+----+----~--~---~f- shy

S ~ 2600+----~---r_----~----~~~--4----~

ir j 2400+----+---1-------1~~---~---r---~ ~ ~~ ~b

~ 2200 +---~---~~~--1---~---+-------1

jJl

2000+---~~--1-----I---~---r---~

1800 -------1f----+-----t-- Plot Area Ir------+-----I


--6 Axle

----- - -------- - - ------- __- -----shy3200

3000

e ~ 2800 i S 2600 ~ ~I Vsect 2400 ai

jJl 2200

2000 o 2 4 6 8 10 12

Reduced V ruiate

-+-7 Axle

3000

I 2800

2600 ~

I~ 2400 I

I2200

Chart Area

2000

o 2 4 6 8

Reduced Vuiate

1-+-8 Axle I


(3-14 )

12

10

Univers

ity of

Cap

e Tow

n-- __ ___shy480

460

440

~ 420

400 ~

380ie (I)

u 360

340

320

300

380

360

340

~ 320 300 ~

280lt Vol

260

240

220

J -~

V ~

~ v

_ _

j~

~

- V

o 2 4 6 8 10

Reduced Variate

--6 Axle

o 2 4 6 8 10

Reduced Variate

--+-7 Axle

440

420

400

~ 380 i 360 ~

ie 340 -= ~ 320

300

280

V

1

Ir

~

V

o 2 4 6 8

Re(luced Variate

-+- 8 Axle


(3-15)

12

i

12

10

Univers

ity of

Cap

e Tow

n













No of Reduced Event

5m Spans

10m Spans

15m Spans

20m Spans

30m

22 28 42

22 28 42

22 28 42

22 28 42

22 28

2024 2000 1961

5448 5379 5254

8937 8835 8659

13728 13572 13313

25468

25224

99 99 98

267 271 285

376 387 405

583 597 611

969

979

31680 40320 60480

31680 40320 60480

31680 40320 60480

31680 40320 60480

31680

40320

751 727 687

751 727 687

751 727 687

751 727 687

751

727

763 782 813

763 782

813

763 782 813

763 782 813

763

782

278 277 276

749

750 757

1181 1186 1195

1818 1824 1828

3285

3288






(3-16)

Univers

ity of

Cap

e Tow

n

5 301 238 -21 10 812 631 -22 15 1364 1129 -17 20 2097 1756 -16 30 3631 3380 -7
















(3-17)

Univers

ity of

Cap

e Tow

n

1500 -------------------------------------------

1400 - S ~ 1300 -

~ 1200 S o ~ 1100 OJ)

=g 1000 ClJ

=l 900

800 +-----~----~----_r----~----~------~--~

-100 100 300 500 700 900 1100 1300

Reduced Variate


390

370

- 350 ~ - ClJ ~ 330 0 ~

~ 310 ClJ

c rJ)

290

270

250

Reduced Variate

-100 100 300 500 700 900 1100 1300




(3-18)

Univers

ity of

Cap

e Tow

n

1450 -----------~--------------------------_

1350

1250

1150

1050

950

-


Q rJ1

850 +-----~----~----~----~----~----~----~

-100 100 300 500 700 900 1100 1300

Reduced Variate


-Nonnal Gwnbel

360

350

340

330

320

310

300

290

280

270

260

-100 100 300 500 700 900

Reduced Variate

1100 1300


Nonnal Gwnbel


(3-19)

Univers

ity of

Cap

e Tow

n

1200

1150 --

3 1100

~ - 1050 ~

3 = 1000 0

~ 950 OJ)

0 = 900 ~ = ~ 850

800

750

-l00 l00 300 500 700 1100 l300

Reduced Variate

900


--Nonnal Gwnbel

370

350

-Z ~ - ~ (j 0 ~

11 ~ -= 00

330

310

290

270

250

230

-100 100 300 500

Reduced Variate

700 900 1100


-- Nonnal Gumbel


(3-20)

Univers

ity of

Cap

e Tow

n
































+





effective

years 40320











number of the

between the 28











the human and

the most




Univers

ity of

Cap

e Tow

n






a (37)





n

X Gumbel s = 1 1+11 + 11000Kn] 2 S (39)e

n







(3-22)

Univers

ity of

Cap

e Tow

n

---

4150

3950

3750

e 3550 ~ - 3350 = ~ e 3150 Q

~ 2950

2750

2550

2350

-100 100 300 500 700 900 1100 1300

Reduced Variate




35 RESULTS






91 00401 amp 02



5 276 301 231 301 10 757 812 624 812 15 1195 1364 1135 1364 20 1828 2097 1780 2097 30 3275 3631 3289 3631




5 297 233 201 297 10 320 314 279 320 15 369 350 349 369 20 431 433 392 433 30 489 542 481 542


(3-23)

Univers

ity of

Cap

e Tow

n




and







the vehicles axle


Mean 467 529 518 423 429 441 2806 6 Axle

Std Dev 68 196 199 199 188 189 913Vehicles 006 -014 -009 012 001 -021

Mean 488 557 555 529 545 501 490 3665 7 Axle

Std Dev 67 201 191 215 224 205 1176Vehicles 16 -059

Mean 470 504 526 455 456 446 391 384 3632 8 Axle







events


5 98 147 117 10 104 141 119 15 93 128 124 20 92 128 119 30 95


(3-24)

Univers

ity of

Cap

e Tow

n



5 151 130 104 10 120 1l0 127 15 103 88 133 20 103 95 116 30 103 113









NowakGumbel

5 290 301 -4 10 762 S12 -6 15 1372 1364 1 20 2262 2097 S 30 4740 3631


Shear Forces


NowakGumbel

5 263 297 -11 10 343 320 7 15 439 369 19 20 537 433 24

542







Univers

ity of

Cap

e Tow

n


5m 10m 15m 20m 30m


276 292 (+59)

301 (+89)

757 804 828

1195 1262 1297

(+56)

1829 1930 1982

3275 3436 3519

(+49)

(+74)


Univers

ity of

Cap

e Tow

n

36 OVERLOADING
















12

~ 08 D lte

D 0 shy 06p v ~

-a 04

8 02

o 100 200 300 400 500 600 700 800 900

Weight (lN)



(3-27)

Univers

ity of

Cap

e Tow

n











representative


6 Axle 00 19 20 21 12 25 7 Axle 03 77 69 09 09 56 37 8 Axle 83 280 310 13 09 44 67 70

444











was retained










(3-28)

Univers

ity of

Cap

e Tow

n













5 -2 -6 3 5 -1 7 10 6 -13 14 -9 -4 6 15 -11 -11 11 1 -6 5 20 -4 -7 6 5 -3 8

30 -4 -1 3 5 2 21













5 197 195 196 216 220 181 10 13 -8 10 510 547 520 582 600 486 14 10 -7

15 968 1054 986 946 1034 875 -2 -2 -11 20 1504 1582 1537 1452 1599 1388 -3 1 -10

30 2767 2917 2899 2676 2944 2697 -3 1 -7


(3-29)

Univers

ity of

Cap

e Tow

n



5 182 183 184 210 197 164 15 8 -11 10 246 251 252 249 250 220 1 0 -13 15 295 308 302 298 293 272 1 -5 -10 20 337 347 337 349 358 316 4 3 -6 30 411 440












Univers

ity of

Cap

e Tow

n

37 CONCLUSIONS










set of events

























(3-31)

37 CONCLUSIONS










set of events

























(3-31)

Univers

ity of

Cap

e Tow

n






June 1994









examined

41 TMH7 PART 2








to traffic










(4-1 )

2 amp i) UD i)J ol

The

Part 2





June 1994

Vehicle Loads on



Vehicle Loads on







examined

41 TMH7 PART 2

411 and OAfAIIID







to traffic






favoured this




Univers

ity of

Cap

e Tow

nL









fonnula (1970)


Where

Impact factor





















(4-2)









fonnula (1970)

cent = 5(100 + L) 10+L

Where

Impact factor






















(4-2)

Univers

ity of

Cap

e Tow

n












the WIM sensors

















group






(4-3)



The

412 NA

The




Curves

curve for

UH1lUH of the no-m






the WIM sensors

As

and








The



earlier work






20

group







Univers

ity of

Cap

e Tow

n


















40

-

sect ~ - C ~ 0

l C ~ I

Q

C 0is

5

0

10 100 1000

Loaded length (m)

~------------------------~~------------------------~

1-30

25

20 1-15

-- ------



(4-4)

Univers

ity of

Cap

e Tow

n

---

___bull___ __ _- --- ---___bull _bull40

35

---E 30 -+ --+-shy

Z ~ - 25 ~ CI 0

l 20 ~ ltII c = 15 i 10Q

+5

0

10 100 1000

Loaded length (m)
























(4-5)

Univers

ity of

Cap

e Tow

n















2-Axle 216 204 195 190 183 186 184 196

3-Axle 97 106 94 86 82 82 82 165


8-Axle 23 25 25 24 23 25 45 41 9-Axle 01 01 00 01 01 01 02 31

Total 100 100 100 100 100 100 100 100


















(4-6)

Univers

ity of

Cap

e Tow

n
















1600

1400

1200 middot 8 ~

1000 agt-= 8 0 800

~ = 600a =agt

co 400

200

0 4 6 8 10 12 14 16 18

Span m




5 35 10 28 15 23 20 20 30 16


(4-7)

Univers

ity of

Cap

e Tow

n





relevant















416 NB Loading









(4-8)


Given

Ipvntv of TMH7 Part


this

2 the

The

(1

of the

relevant


effects of vehicles



the



and research



415 Lateral






A lateral

at40m

factor of 14 was





416 NB

in the

The









Univers

ity of

Cap

e Tow

n








international and

























(4-9)








international and




the load effects of



of trnrP The in






422

The report

infrastructure

with a

the




with

(i)





Ease of enforcement


and







Univers

ity of

Cap

e Tow

n





applicable factor









Appendix D


Where

the final factor

















(4-10)





factor

ratios were

The statistical










D


Where

the final factor

the factor for the
















0)

Univers

ity of

Cap

e Tow

n



423 Review































(4-11 )





span

The

Review


Axle Loads The full





an

extent






In f1nntltvmo the


















then calculated by






1)

Univers

ity of

Cap

e Tow

n









(4-12)









Univers

ity of

Cap

e Tow

n





















431 Traffic loading



the



formula

( 4-13)














axle

This load




An

and





431 Traffic


technical rl(lgt(1

the




formula

Univers

ity of

Cap

e Tow

n








432 Impact Factor




ForT lt 16t

For T gt SOt



ImEact Allowance

RR91 0041 RR910041 SEan (m) TMH7 01 02

5 35 37 36 10 28 26 18 15 23 17 12 20 20 13 9 30 16 9 6


(4-14)

Univers

ity of

Cap

e Tow

n

433 Test loading
























ENV 1991-3

(4-15)

433 Test




of the



under PTVi






Assessment amp













ENV 1991-3

Univers

ity of

Cap

e Tow

n

I

1J- 8

_______- - 1 ~ ~-- ~

--tf-fBT-1--+Or

I

I IPi t I









240 140 0

NA

6 4 3 3









(4-16)

Univers

ity of

Cap

e Tow

n


5 415 293 42

10 949 810 17

15 1510 1553 -3

20 2442 2520 -3

30 5






most

5 378 10 413 15 506

20 576 30 739

234 324 414

504 684

62 27

22 14 8









436 Critical Review







surveys


in TMH7 Part 2

(4-1

Univers

ity of

Cap

e Tow

n














from the WIM data

(4-18)

In the














from the WIM data

Univers

ity of

Cap

e Tow

n











5 409 415 293 10 957 949 810 15 1527 1510 1553 20 2284 2442 2520 30 3847 5397 5130


6000 - shy

5000 - E

~ 4000-III= ~ 3000 ~ OJ)

= 2000a III= ~

1000

0

0


5 10 15 20 25 30 35 Span (m)

--- Study -0- RR91100402 ~ TMH7 I


(4-19)

Univers

ity of

Cap

e Tow

n

Shear Forces (kN)


5 297 378 234 10 320 413 324 15 369 506 414 20 433 576 504 30 542 739 684


800

700

600 -

~ 500 QJ ~ 0 400 ~ ~ QJ 300

c C-J

200

100

0

0 5 10 15 20 25 30 35

Span (m)












5 409 293 39 10 957 810 18 15 1527 1553 -2 20 2284 2520 -9 30 3847 5130 -25


(4-20)

Univers

ity of

Cap

e Tow

n

























(Section 413)

Shear Force (kN)


5 297 234 27 10 320 324 -1 15 369 414 -11 20 433 504 -14 30 542 684 -21







(4-21)

Univers

ity of

Cap

e Tow

n


Moment (kNm)


5 409 415 -2 10 957 949 1 15 1527 1510 1 20 2284 2442 -6 30 3847

Table 411 - Moment

5397









Shear Force (kN)


5 297 378 -21 10 320 413 -23 15 369 506 -27 20 433 576 -25 30 542 -27


(4-22)

Univers

ity of

Cap

e Tow

n

45 CONCLUSIONS













the roads















return period





(4-23)

45 CONCLUSIONS













the roads















return period





(4-23)

Univers

ity of

Cap

e Tow

n









data







these -0










(5-1 )

51

2

OF LOAD


Part 2 the

3 the




shown in

data











these prlmiddoto










Univers

ity of

Cap

e Tow

n

40 80 ~~~--------~~4~~------------~~

240

I

180


20 20 ~ II~ ~




13 ~ ~

240 240


12 ~ II

150 150

7 1991-3 design

12 ~

200 200


51 - Load Models

Univers

ity of

Cap

e Tow

n





y = -(1 + kV)

load factor r

bias factor


deviation


52 RESULTS




2300

2100 0-v 1900~ 0 1700~ 0

l 1500-=QI

E 1300 0

~ 1)1) ll00 = a 0900 = QI

tl

- - ~~- -- shy - shy - shy

I

I I--- L~- shy ~~t--==- -

r-shy

----r-=9 I

~ 0700

0500

- T - - shy -

o 5 10 15 20 25 30 35

Span (m)


(5-3)

Univers

ity of

Cap

e Tow

n








1800

0 1600 (I

laquoI

1l laquoI 1400 0

l ltII = 1200 8 0

~ ~ 1000 = 0 = ~ 0800

0600

o

~ ~--shy -

~~ n

5 10 15 20 25 30 35

Span (01)

-0-3 6 -4-7 8


1600

14000 (I laquoI

1l laquoI 1200 0

l

ltII (I

0 1000 laquoI ltII

-= ~ 0800

0600

0 5 10 15 20 25 30 35

Span (01)

6 -4-7


(5-4)

Univers

ity of

Cap

e Tow

n





1800

0 1600 v CltI ~ ~

CltI 1AOO 0

e ~ = 1200

0

~ ~ 1000 = a = ~ 0800 I=Q

0600

0 5 10 15 20 25 30 35

Span (m)

6 ~7


1600


v ~ 0 1000 ~

CltI ~ c 00 0800

0600

- - - shy - shy

~

0 5 10 15 20 25 30 35

Span (m)

-ltgt-3 6 ~7 -8


(5-5)

Univers

ity of

Cap

e Tow

n




Table 51 to 54










(5-6)




Table 51 to 54










(5-6)

Univers

ity of

Cap

e Tow

n

Bending Moments

Lane Load 9 kNm


1 124 012 010 154 162 155 145 125 2 133 029 022 240 225 179 166 141 3 091 018 020 171 123 ll1 ll4 114 4 1 56 017 011 223 193 177 180 173 5 172 037 022 339 247 219 219 208 6 084 002 003 091 087 085 090 091 7 123 004 003 139 132 127 131 8 097 002 002 105 101 098 103

Lane Load 18 kNm


1 105 015 014 153 151 138 126 106 2 112 029 026 228 202 158 144 119 3 080 019 023 166 ll7 103 104 099 4 126 023 018 223 183 160 157 141 5 138 039 028 318 224 190 184 164 6 074 004 006 091 084 080 081 079 7 103 010 010 143 130 ll9 119 ll1 8 084 006 007 106 099 092 093 089

Lane Load 27 kNm


I 091 017 018 150 141 125 ll3 093 2 097 029 029 216 182 141 127 103 3 072 019 027 160 ll2 096 095 088 4 107 025 024 216 170 144 138 120 5 ll6 038 033 294 203 167 158 136 6 067 007 010 093 083 077 077 072 7 090 0 14 015 144 126 lll 109 097 8 075 009 012 108 097 088 087 080

Best Fit


(5-7)

Univers

ity of

Cap

e Tow

n

Shear Forces

Lane Load 9 kNm

C

Model

1 2 3 4 5 6 7 8

Mean 102 114 081 144 1 53 075 11 1 088

SD 008 023 013 014 024 010 010 010

V

008 020 016 010 016 013 009 012

135 221 142 200 280 073 116 087


ll8 145 120 183 219 095 136 109

Lane Load 18 kNm


Lane Load 27 kNm


Best Fit


(5-8)

Univers

ity of

Cap

e Tow

n

Bending Moments

Lane Load 9 kNm

Model

I 2 3 4 5 6 7 8

Mean 134 1A2

099 169 186 092 135 107

SD 008 020 020 023 036 017 021 019

V

006 014 020 014 019 018 015 017

1A6

218 174 237 333 119 172 136


200 159 159 122 110 123 200 183 201 237 209 227 112 109 124 161 153 172 129 125 lAI

164 177 161 254 282 165 223 187

Lane Load 18 kNm

Model 1 2 3 4 5 6 7 8

Mean 113 119 087 136 lA8

081 112 092

SD 007

022 018 020 034

011 013 012

V

006 018 021 014 023 014 011 013

135 209 163 213 302 105 lA8

118


130 150 134 187 215 126 158 138

Lane Load 27 kNm

Model 1 2 3 4 5 6 7 8

Mean

098 103 078 115 124 072 097 081

SD

009 023 017 021 033 008 011 009

V

010 022 023 018 027 012 012 011

133 199 154 202 278 096 138 108

Load Factor y 122 108 105 164 127 123 105 090 096 156 132 136 187 154 157 085 077 084 117 104 109 095 086 092

114 131 117 155 177 103 128 111

Best Fit


(5-9)

Univers

ity of

Cap

e Tow

n

Shear Forces

Lane Load 9 kNm

Model

I 2 3 4 5 6 7 8

Mean

135 151 108 190 203 099 147 116

SD

007 026 0 15 017 027 015 017 016

V

005 017 014 009 014 015 012 014

202 250 179 285 325 118 138 105

Load Factor y 193 181 177 188 175 171 127 136 143 231 246 256 235 245 252 114 130 142 129 144 153 100 113 122

189 175 163 280 272 165 173 141

Lane Load 18 kNm

Model

1 2 3 4 5 6 7 8

Mean

115 128 095 154 163 087 123 101

SD 011 027 015 018 030 009 007 008

V

010 021 016 012 018 010 006 008

188 227 175 236 265 104 127 099

Load Factor y 170 157 150 164 150 144 122 126 130 182 185 185 184 183 181 097 107 113 113 121 124 090 099 103

154 142 141 190 184 125 131 112

Lane Load 27 kNm

Model 1 2 3 4 5 6 7 8

Mean 101 112 085 130 137 078 107 089

SD 014 028 015 021 031 005 007 005

V

013 025 018 016 023 006 006 005

178 216 172 206 236 097 118 094

Load Factor y 154 140 132 152 137 129 117 119 120 152 150 146 159 154 148 087 094 096 100 104 104 082 087 089

131 125 126 144 146 103 106 093

Best Fit


(5-10)

Univers

ity of

Cap

e Tow

n
























on bridges









(6-1 )
























on bridges









(6-1 )

Univers

ity of

Cap

e Tow

n










TMH7 Part 2









model



















research

and 1995 in South









TMH7 Part 2









model






the events








live load models




Univers

ity of

Cap

e Tow

n























Part 2










limited expenditure





(6-3)


















over return





Part 2










limited





Univers

ity of

Cap

e Tow

n




(6-4)




Univers

ity of

Cap

e Tow

n

BIBLIOGRAPHY







fedrale de Lausanne












452-461




July 1981

Univers

ity of

Cap

e Tow

n



























Unbaised OlOlttlIll






RR 911004101 The

RR 911004102 The

Assessment Code

an Increase in the

an Increase in the

R K and

Canadian Journal



code 1983 edition

D amp uaveIlDon

Canadian Journal

W British


AlVUUl T and


A S (

Research Record

National 1998


Final



( a

A statistical

6494-513

to the traffic on



of Girder




Crowthorne TRRL



Univers

ity of

Cap

e Tow

n



Engineers


Transport


TRB December 1987























Univers

ity of

Cap

e Tow

n


and Architects



Report)



Univers

ity of

Cap

e Tow

n

A-1

APPENDIX A

A-1

Univers

ity of

Cap

e Tow

nAppendix A


Appendix A


Univers

ity of

Cap

e Tow

n





bull bullbull


77 90 90 80 80 80

o 00 000 Max W = 497kN

Configuration 2

77 90 90 90 90 90

00 00 00 Max W = 527kN

Configuration 3

77 90 9090 90 90

o o 00 00 Max W =527kN

Configuration 4

77 90 90 80 80 80


Configuration 5

102 102

o 00 Max W =560kN


Univers

ity of

Cap

e Tow

n

bull bull bull

3

Configuration 7

80 80 80

000 MaxW = 560kN


Univers

ity of

Cap

e Tow

nbull bull bull

bull bull bull


Configuration 1

80 80 80

Max W = 560kN

Configuration 2

80 80 80

eee Max W = 560kN

Configuration 3

80 80 80

eee MaxW = 560kN

Configuration 4

90 90

MaxW= 560kN


Univers

ity of

Cap

e Tow

n


bull bull bull


5


77 60 60 60 60 60 60 60 60

o 0000 0000 MaxW = 557kN

Configuration 2

80 80 80

000 MaxW = 560kN

Configuration 3

80 80 80



Configuration 4

48 48 48 48 48

00000 MaxW = 557kN


Univers

ity of

Cap

e Tow

n

bullbull bull

bull bull bull

bull bull bull

APPENDlXC

s Ii

~ [I $

~ 1- fl~


Configuration 1

90 90

Max W =560kN

Configuration 2

80 80 80

MaxW = 560kN

Configuration 3

90 90

00 0 MaxW = 560kN

Configuration 4

80 80 80

000 MaxW = 560kN

Configuration 5

80 80 80

Univers

ity of

Cap

e Tow

nAppendix B


bull

Appendix B


bull

Univers

ity of

Cap

e Tow

n

APPENDIXB


6 Axle Vehicles

2~ ------------------------------------

220+------+------+_----_+------+_--~~~--~

e ~200+------+------+------+----~~-----+----~

5 ~ 180 +_----_+------r---~~~----+-----_+----~ s =i 160 +_-----r----~~----_+------+_----_+----~ = I~+-----~------+------+------+------+----~

120 r------+------r-----+-----+------+--~ o 2 4 6 8 10 12

Reduced Variate

---6 Axle

Figure B I Sm span

o 2 4 6 8 0 12

Reduced Variate

-6 Axle

Figure B2 10m span

650

600

~ 550 o ~ 500 8 Q

~ 450 CgtII S 0 ~400 =

350

300

I

~

~

~

Univers

ity of

Cap

e Tow

n

APPENDIX B

1050

1000

9508 ~ 900

-= 850e Q

~ 800 c ~

a 750 ~ ~ 700

650

600

o 2 4 6 8 10 12

~

p y

r

V

Reduced Variate

--6 Axle

Figure B3 15m span

1600

1500 middotLL7 8 ~ 1400 r ~ ~ 1300 e Q

Ishy ~ 1200 ~ c V] 1100 ~ V ~ 1000

900

o 2 4 6 8 10 12

Reduced Variate

--6 Axle

Figure B4 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

3000

2800

8 ~ 2600 sect ~ 2400

E OIlca 2200 ==GI

=I

2000

1800

V

_V

Ijj


10 12

--6 Axle

Figure B5 30m span

Univers

ity of

Cap

e Tow

n

APPENDIXB


6 Axle Vehicles

24)

220

~ 200 180~ ca

c IIl 160

14)

120

0 2 4 6

Reduced Variate

8 10 12

---- 6 Axle

Figure B6 5m span

290

270

__ 250 Z ~ 2l 230 ~ 1 210

c IIl 190

170

150

~ b V

~

~ I

I o 2 4 6 8 10 12

Reduced Variate

--6 Axle

Figure B7 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

330

310

~ 290 Z ~ 270 Q

r 250 ~

c (IJ

230

210

190

o 2 4 6 8 10 12

V

J1V

I ~ I l

Reduced Variate

Figure B8 15m span


6 Axle

Figure B9 20m span

380

360

340

Z ~ 320 300 ~

01 280

c (IJ

260

240

220

--

V ~

~

)1

~

Univers

ity of

Cap

e Tow

n

APPENDIXB

430

410

390 Z 370 ltJ ~ =gt 350 ~ ~ 330c

00

310

290

270 o 2 4 6 12

r V

V ~

~V 1

8 10

I I

I I

1

I I I

i

I I i I

Reduced Variate

--6 Axle


Univers

ity of

Cap

e Tow

n

APPENDIXB


6 Axle Vehicles

200

195

e Z ~

190

-= S 185 ~

~ 011 9 180 0

= Ql

175

170

0 2 4 6

Reduced Variate

8 10 12

--6 Axle I

Figure B 11 5m span

530

520

e ~51O -= ~ 500 ~ 011

=a 490 =

Ql

480

470

V ~

~V ~

o

r

2 4 6 8 10 12

Reduced Variate

I --6 Axle I


Univers

ity of

Cap

e Tow

n

APPENDIXB

1000

950 5 ~ c 900 OJ e Q

~ C)I) 8509 -g c OJ = 800

750


o 2 4 6 8 10 12

Reduced Variate

--6 Axle I


0 122 4 6 8 10

Reduced Variate

--6 Axle

1550

1500

5 ~ 1450 a OJ

C 1400Q

~ C)I)

a a 1350 OJ =

1300

1250

~7

shy

~ V

-~

~

Univers

ity of

Cap

e Tow

n

APPENDIX B

- ~

V d ~

AV V

I

-i

V

2 4 6 8 10 12

Reduced Variate

--6 Axle

2850

2800

e 2750 Z 0 2700 Se2650 Q

~ 2600 ~

5 2550-g ga 2500

2450

2400

o


Univers

ity of

Cap

e Tow

n

APPENDIXB


6 Axle Vehicles

185

180

~ 175 cJ ~

170~ -= en

165

160 0 2 4 6

Reduced Variate

I --6 Axle

8 IO 12

Figure B 16 5m span

250

245

240

235

~ 230

~ 225 ~ ~ 220 -= en

215

210

205

200 -

f

- I

~ ~

7 V


I --6 Axle I

12 o 8 IO


Univers

ity of

Cap

e Tow

n

APPENDIXB

305

300

295

290 ~ 285 0 ~ 280 ~

275 270

265

260 o

2

~

~ r It

V


--+-- 6 Axle I

FigureBl8 15m span


--+-- 6 Axle I


340

335

~ 330

u 3250 ~ 01

320

315

310

~ V V

J ~

~

L V

Univers

ity of

Cap

e Tow

n

APPENDIXB

405

400

395 -

~ 390

QI OJ

Q 385 ~

eo QI 380

c en 375

370

365 o 2 4 6 8 10 12

--~

V

~ V

~

-~

i I

I i i

l Reduced Variate

-+- 6 Axle I

Figure B20 30m span

Univers

ity of

Cap

e Tow

n

APPENDIXB


7 Axle Vehicles

240

220 a ~ 200


CQ

140

120 0 2 4 6

Reduced Variate

--+---7 Axle

Figure B21 Sm span

700

650

~ 600

- 550 ~

~ 500 ~ 450a = ~400

350

300 12o 2 4 6 8 10

4~

h 1

~

I t

I

I

~ -I I

I I I I

Reduced Variate

--+---7 Axle

Figure B22 10m span

8 10 12

Univers

ity of

Cap

e Tow

n

APPENDIXB

1200

1100 e z 0 1000 C a Q 900 1gt11 CIa 800 CI

cQ

700

600


-+--7 Axle

Figure B23 15m span

1800

1700

Le 1600

~ C 1500 sect 1400 ~ ~ 1300a ~ 1200cQ

1100

1000

o 2 4 6 8 10 12

~

d ~

~

7 bull

Reduced Variate

-+--7 Axle

Figure B24 20m span

8 10 12

Univers

ity of

Cap

e Tow

n

APPENDIXB

3200

3000 e 2 2800 CI OJ

e 2600Q


2200

2000


8 IO 12

--7 Axle

Figure B25 30m span

Univers

ity of

Cap

e Tow

n

APPENDIXB


7 Axle Vehicles

240 ----------- ----- ---------------------

220 +---~r_--_+----r----+_---r_--~

~200 +-----4------+----~------+-----~~~~ ~ ~ ~ 160+----~r_---_+-----_b~--+_-----r_--~

140 +----~r_-~~~---r------+-----r_--~

180 +---~r_--_+-----r----~~---r_--~

120+-----r_--_+---~---+------r_---_4

o 2 4 6

Reduced Variate

-+--7 Axle

8 10 12

Figure B26 5m span

270----~------_-------_----~

250+----~----+---~---~--~~--~

Z 230 +---middot~~---+---~----~~--~----~ C ~ 8 210 +-----4-----~---~~~-+---~---~ r ~ ~ 190 +------I-------t~---_t__----+_---__t---_i

170+---~~--~---_t__---+-----__t---_i

150+----~------_+------~------+-----_4-----~

o 2 4 6

Reduced Variate

-+--7 Axle

8 10 12

Figure B27 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

320

300

~ 280 - 41 OJ ~ 260 41

~ 240

220

200

V

V

V

~~

~ f7

I i I I I i

I i 1

o 2 4 6

Reduced Variate

--+-7 Axle

8 0 12

Figure B28 15m span

390

370

~ 350 Z 0 41 330OJ C ~

30 41

c (J 290

270

250

o

h pound

7 6A V I

~

V

4V 2 4 6 8

I r

I I I

I i I

i I


--+-7 Axle

Figure B29 20m span

Univers

ity of

Cap

e Tow

n

APPENDrxB

480

460

44)

Z 420 ~ ~ 400 0

380 os

CI 360(I)

340

320

300

~

)~

d ~ ~

~

k

o 2 4 6

Reduced Variate

-+-7 Axle

8 10 12

Figure B30 30m span

Univers

ity of

Cap

e Tow

n

APPENDIX B


7 Axle Vehicles

200

~ 195

e Z 190 e Jif75 185

8 Q 180 CD

a fS 175 =I 170

~ 165


I ---7 Axle

Figure B31 5m span

o 2 4 6 12

Reduced Variate

580

560

e 54)

~ 520

il 500 01

sect 480 ~ 460

]44) 01

=I 420

400

380

-

I

j ~

--~ ~ ~

I

L

4

8 10

I

I

I

i

---7 Axle

Figure B32 10m span

Univers

ity of

Cap

e Tow

n

APPENDIX 8

1100

1050

e ~ 1000

C 01 e 950 Q

011

= 900a I 01 ~

850

800 0 2 4 6 8 10 12

Reduced Variate

--7 Axle

Figure 833 15m span

1700

1650

e 1600

L ~ 1550 01= e f1500Q

011

= 1450 rIIa 01= ~ ~ 1400

~

1350 ~~

1300 o 2 4 6 8 10 12

Reduced Variate

--7 Axle

Figure 834 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

3000

2950

ez 2900 ~ 2850 e ~

~ 2800 = a ~ 2750 =

2700

2650


-+-7 Axle

4

v

- V

Figure B35 30m span

Univers

ity of

Cap

e Tow

n

APPENDIXB


7 Axle Vehicles

~ ltI ~ 1 -= C-I

190

185

180

175

170

165

160

155

150

145

140

--shy

J r

) -

i-~

~ J1V


I ---7 Axle I

Figure B36 5m span

260

~V250

Y240 ~ ~ 230 -~ 5 ~ -= C-I 220

~

210 ~

200 o 2 4 6 8 10 12

Reduced Variate

I ---7 Axle I

Figure B37 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

320

~ 310

~ 300 r ~ 290 1

~

280 ~

~ ~ CI 270 (I) 260 -

250

240


--+-7 Axle

Figure B38 15m span

355

350

345

340

~ 335 330 ~ 325 ~

CI 320 (I)

315

310

305

300


--+-7 Axle

~

( L

l

~ ~

gt

~ ~

L

~

Figure B39 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

420

415

410

~ 4tl5

tJ

or 400

z (Il

395

390

385


I --7 Axle

Figure B40 30m span

t ~ i-

~~

1pound J

Univers

ity of

Cap

e Tow

n

APPENDIX B


8 Axle Vehicles

o 2 3 4 5 6 7 8 9

Reduced Variate

--+- 8 Axle

Figure B41 Sm span

o 2 3 4 5 6 7 8 9

Reduced Variate

1 --+-8 Axle I

Figure B42 10m span

e 3

550

500

- 450 c e c ~400 OIlca ~

CQ 350

300

V V ~

~--shy V

~ V~

8 ~

550

500

- 450 c a V

V r shy --

V -c ~400 ~

-V a c=350

300

~ V

Univers

ity of

Cap

e Tow

n

1050

1000

8 950

Z 900~

C 850a 0

~ 800 Oilc

750ac =I 700

650

600

o 2 3 4 5

Reduced Variate

1 --+-8 Axle

Figure B43 15m span

1600

1500

e Z 1400 ~ C a 1300 0

~ Oilc 1200ac

=I 1100

1000

o 2 3 4 5

Reduced Variate

--+- 8 Axle

Figure B44 20m span

I

-~ ~

shy

~ ~

~ ~ shy

V

I

~ ~~

- ~

~ ~

~ ~

V III

~

6 7 8

APPENDIXB

9

6 7 8 9

Univers

ity of

Cap

e Tow

n

APPENDIXB

I 17 I

7 ~ ~ I-

I

1

-e ~ i i

~ shy I- I

~ ~ 1

f

~ ~

i

I 2 3 4 5 6 7 8 9

Reduced Variate

1 -+--8 Axle I

3000

2900

2800 8 2700 ~

2600 -= 8 ~

2500 = ~ 2400 0laquo1 = a 2300 = ~

~ 2200

2100

2000 o

Figure B45 30m span

Univers

ity of

Cap

e Tow

n

APPENDIXB


8 Axle Vehicles

260

240

~ 220

~

~V ~ 200 ~ c

IIl 180

160

140

~

~

V ~V

V-

~

o 2 3 4 5

Reduced Variate

I --8 Axle I

6 7 8 9

Figure B46 5m span

250 I

240

~ ~~

~

~

~ ~ I

~

~ I

I I

230

220

~ 210 ~ ~200

I 190 ~ IIl 180

I 1170

J160

150

o 2 3 4 5 6 7 8 9

Reduced Variate

I --8 Axle I

Figure B47 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

310

290

~ 270

0 250

gj I 230rJl

210

190 o 2 3 4 5 9

Reduced Variate

-+-- 8 Axle I

Figure B48 15m span

r-- i I

L i v

v ~

I

~ ~ I

-11 I

~ i j

6 7 8

V

I

360

340

320 Z o 300 ~ ~ 280

c rJl 260

240

220

10-shy

-~

-V

- ~

o 2 3 4 5

Reduced Variate

-+-- 8 Axle I

6 7 8 9

Figure B49 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

440

420

400

~ 380 Q 360 ~ ~ 340 c CIl

320

300

280 o 2 3 4 5 6 7 8 9

~ ~

---~VIII

~

I

L Y I

~ ~ I

~ ~- I

i I I I

1

I I i

Reduced Variate

-+- 8 Axle I

Figure B50 30m span

Univers

ity of

Cap

e Tow

n

APPENDIX B


8 Axle Vehicles

I

I

570

550

a ~ 530

-= ~ ~ 510 ~ 01)

9 ~ 490 OJ

I=Q

470

450

L

I

I i

~- ~

~

-~ shy i

~

I

I j i


--8 Axle I

6 7 8 9

Figure BS I Sm span

570

550

e ~ 530 -

~ -= E lt) 510 ~ 01)c 490ac ~

I=Q

470

~V

-~ ~ ~

~ shy-shy

~

450


I -shy 8 Axle I

6 7 8 9

Figure B52 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

1030 1 i1010

I990e IZ e 970 c ~ 95013 Q

~ 930 OIl

Is= 910 = I= ~

890 1

870 i

850

V ~

[i i

~ V I

~~ I I

~ ~ I I

I

I I

V

I

o 2 3 4 5 6 7 8 9

Reduced Variate

1 -+-8 Axle

Figure B53 15m span

1600 I

~ 15508 ~ z e ~ -c 1500 shy8 ~

~ Q OIl 1450 s= ~ =

V = 1400

1350 o 2 3 4 5 6 7 8 9

Reduced Variate

-+-8 Axle I

Figure B54 20m span

Univers

ity of

Cap

e Tow

n

APPENDIX 8

3000-----r-------------~----~----r---~----~----~

e ~ - 2900 E 8 Q

~ ~

aI 2800 I =

2700+---~~--~----~----~---+----~----~---+--~

o 2 3 4 5

Reduced Variate

-+-8 Axle

Figure 855 30m span

6 7 8 9

Univers

ity of

Cap

e Tow

n

APPENDIX B


8 Axle Vehicles

260

255

250

Z 245

~ ~

240 235= ~ 230~

c CIl 225

220

V

215

210

~ I

~~

~r V

~

~ ~r

I i I

l i

I

o

Figure 856 5m span

2 3 4 5

Reduced Variate

-+- 8 Axle

6 7 8 9

3000

~ --~ ~ 2900 V ~ V

~ V 01 41 ~c

CIl 2800

V ~

2700

o 2 3 4 5 6 7 8 9

Reduced Variate

1 -+-8 Axle I

Figure 857 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

-

o 2 3 4 5 6 7 8 9

Reduced Variate

-+- 8 Axle

Figure B58 15m span

305

300

295

~ 290 III ltJ 285Q ~ ~ 280 c rI)

275

270 I 265

L ~

~ ~

tr V

~

I-shyi-shy

I

I i I

I I I i i I

I

345

340

335

Z 330 ~ III 325 Qr 320 =OJ c 315IJ)

V

~

-U i-

~

310

305 V-300

shy

i I

I I I

I i i

i I


1 -+-8 Axle

6 7 8 9

Figure B59 20m span

Univers

ity of

Cap

e Tow

n

I

APPENDIXB

415

40

405 Z ~ 400 0 ~ 395 gJ

c (I)

390

385

380

o 2 3 6 7 8 9

I

~ V

~

~ ~

~ ~

~

4 5 Reduced Variate

I --8 Axle

k I L

-I

i

I i

i

i

i I

Figure B60 30m span

Univers

ity of

Cap

e Tow

n

APPENDIX B


6 Axle Vehicles

295---------~----------~----------~--_

275

e 255

~ lt11

C 235 e ~ Q

~ 215

195

--t-- i

i-----i---

175 +-----r-----r-------------------r----~

-100 100 300 500 700 900 1100 1300

Reduced Variate

Figure B61 5m span



bull

Univers

ity of

Cap

e Tow

n

APPENDIX 8

1500~----~----------~----r---~~--------~

I I I1400 -1 shy --+-__--_1shy

~ 1300 --~-~---j---+I -

i 1200 -1-shy - -+-shy - -+-shy8 Q


~ ~~~-- I I I 900 r-- ---t---T 800+-----+-----~----r_----r_----r-----~--~

-100 100 300 500 700 900 11 00 1300

Reduced Variate


Figure 863 15m span

2200

2100

~2000 a ~ 1900

i 1800 g1700

~1600 = i 1500

11 1400

1300

1200

I 1

-1 I I

I I I

L---shyI

___shy---- shy

-100 100 300 500 700 900 1100 1300

Reduced Variate


Figure 864 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

3800

3600

e 3400Z e I 3200 QI e

3000Q

~

2800a QI 2600=

2400

2200

-100 100 300 500 700 900 1100 1300

Reduced Variate


Figure B65 30m span

Univers

ity of

Cap

e Tow

n

APPENDIXB


6 Axle Vehicles

300

280

Z 260

0 240 ~ 220i ~ fIJ

200

180

160

I--I-shy

I --shy

i

I

-100 100 300 500 700 900 1100 1300

Reduced Variate


--Nonnal Gumbel

Figure B66 5m span

340

~ - Q CIS ~ fIJ

200

Reduced Variate

320 ~-l--middot- 1 --300

280

260

240 i

220 I T

I

-100 100 300 500 700 900

-I 1100 1300


--Nonnal Gumbel

Figure B67 10m span

Univers

ity of

Cap

e Tow

n

390

370

350

~ 330 r 0

310 ~

CI rJl

290

270

250

i -i----~--~middot~--- -+ -- ---~-- ----~--shy




-100 100 300 500 700 900 1100 1300

Reduced Variate


-- Normal Gwnbel

Figure B68 15m span

440

420

400

~ 380 0 r 01 360

CI rJl

340

320

300

-100 100 300 500 700 900 1100 [300

Reduced Variate


--Normal Gwnbel

Figure B69 20m span

APPENDIXB

Univers

ity of

Cap

e Tow

n

APPENDIXB

510

490

470

~ 450 Ol _ e

430~ 01 41 410

CIl

390

370

350

-100 100 300 500 700 900 1100 1300

Reduced Variate


-- Normal - Gumbel

1 _ - --1-

j ---+--~~I i

-1----1-----

-+-------tli

- -+---~ I - i - --L-- -l- - -l

-I -+---1-- 1


Univers

ity of

Cap

e Tow

n

APPENDIXB


6 Axle Vehicles

220

215


ltgt 200 I~ ~


I 185 19----1----1- -------------r

180

-100 100 300 500 700 900 1100

Reduced Variate


Normal -It- Gwnbel

Figure B71 Sm span

670

650

e 630 Z e 610 7 ltI 590S ltgt ~ 570

cI ~

550 I ltI

cQ 530

510

490

I +---+--+---shy- T - shy -

1 ------

-100 100 300 500 700 900 1100

Reduced Variate



Figure B72 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

1450 -r------------------------

e z 13502 1250

ltII

C e 0 1150 5 ~

1050 c CQ

950

I

~-+_____ I

850+----r---r----~--~---+----~

-100 100 300 500 700 900 1100

Reduced Variate



Figure B73 15m span

1910

1860

e 1810 Z 2 1760l c

1710e 0

1660

5 ~

1610 c CQ 1560

1510

1460

-100 100 1100

--------1 ---

~-r---~-- ----shy- 1- --1-- - -I-

I i

300 500 700 900

Reduced Variate



Figure B74 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

3150 ----------------------------

3100

3050

3000

2950

2900

2850

2800



i I I i -

- i

i

I--I - - -1-shy

I -LOO 100 300 500 700 900 1100

Reduced Variate


-- Normal --Gumbel

Figure B75 30m span

Univers

ity of

Cap

e Tow

n

190

APPENDIXB


6 Axle Vehicles

Z 186 Cshy Ol

184 01 Olc 182

CIl

180

178

-100

I 188 +---1-shy

t-+----shy

100 300 500 700 900 1100 1300

Reduced Variate


-- Normal ~Gumbel

Figure B76 5m span

290

280

270Z e ~ 260 lt=

250 ~ c

rJ)

240

230

220

-100 100 300 500 700 900 1100 1300

Reduced Variate


--Normal ~Gumbel

Figure B77 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

325 i

--------------t------~t__-__I320

315

Z 310cshy 305 Q

300 = c (JJ 295

290

285

280

-100 100 300 500 700 1100 13 00

+--------+--- +-----i---Le----+- -I

=---=------- ------I

j-__+--_ - i___ __ I

900

+-_-I- shyI

Reduced Variate


-- Normal --Gumbel

Figure B78 15m span

355~----~----~----~--~~--------------~

350 +shy

345

340 -Jshy

335

- -I I II

--J---- t---j---- k-- ------------I_____I

---l-

330~~--T----r-----~--~~--~----_----__t

-100 100 300 500 7 00 900 1100 13_00 Reduced Variate


-- Normal Gumbel

Figure B79 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

420

415

410

~ 405 ~ 400 ~ c CIl 395

390

385

-100 100

---1shy--T

I 3_00 500 700 900 11 00 1300

Redoced Variate


Figure B8D 30m span

Univers

ity of

Cap

e Tow

n

APPENDIXB


7 Axle Vehicles

310

--L290

e 270Z ~ l 250c a 230Qa 01)


170 I I i

150

-100 100 300 500 700 900 1100 1300

Reduced Variate


--Normal Gwnbel

Figure B81 5m span

i

600 +----

850~----~--~----~----------------T_--~

800

750 ----1 -1-1-1 -+1-----gt+-1 700 --------I----b---i------ -t-- i_ _ 650 -I- ----+---- +- - -- - --=L--+---tI

~ ac ~ 550

500

450+-----r---~----_+----_r----~----~--~

-100 100 300 500 700 900 1100 1300

Reduced Variate


-- Nonnal Gwnbel

Figure B82 10m span

Univers

ity of

Cap

e Tow

n

1350 ~-+ ~ -1250 - i - ishy1150

I 1050 I 950 I

APPENDIX B

1450 ~--~------------------r----------

850+----r---~----_r---4_----r_-~---~

-100 100 300 500 700 900 1100 1300

Reduced Variate


Normal --Gwnbel

Figure B83 ISm span

2150

2050

E 1950 z ~ 1850 l I 1750S ~

~ 1650 toll

aI 1550 I = 1450

1350

1250

-100 100 300 500

Reduced Variate

__1__ _

i ~~----- --~I -----

700 900 1100 1300


Normal --Gwnbel

Figure B84 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB


2650 f----i~-_+---r---i---+---ir-----l

-100 100 300 500 700 900 lUXgt 13 00

Reduced Variate



Figure B85 30m span

3850 ------1----------------------

3650

3450

3250

3050

2850

Univers

ity of

Cap

e Tow

n

APPENDIXB


7 Axle Vehicles

~ Qj e r ltII Qj

-= CIl

280

260

24)

220

I I +---+-----l-- -+_-+--~I- --


200

180 -l--~_-__+- ------L--__+------ shyt----shy160+-----r---------+-----r-----r----~--~

-100 100 300 500 700 900 1100 1300

Reduced Variate


Normal -+-Gumbel

Figure B86 5m span

320 I

300 1___

I I ~ 280 I Qj

--t-~-- - e 260r g

-= 24) -CIl

220

200

-100 100 300 500 700 900 1100 1300

Redoced Variate



Figure B87 10m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

360

350

340

~ 330 - 320~ ltJ ~ 310 01 300 -= rIl

290


280

270

260

-100 100 300 500 700 900 1100 1300

Reduced Variate


Normal Gwnbe1

Figure B88 15m span

450r-----~----r_----~----~----~--~----_

430 ~---+_---+_--_+_--_+_--_+--_=_+--_l

Z 410

0 ~ 390ltJ ~ 37001 ~

-= rIl 350

330


310

-100 100 300 500 700 900 1100 1300

Reduced Variate


Normal Gwnbel

Figure B89 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

~ y Q ~ CII d rJJ

560

540

520

500

480

460

440

420

400

380

360

I I



+----+ishy - ---- -+------L shy-shy-----~--___l I I -

-100 100 300 500 700 900 1100 1300

Reduced Variate


Normal --- Gwnbel

Figure B90 30m span

Univers

ity of

Cap

e Tow

n

APPENDIXB


7 Axle Vehicles

210

205 5 z e 200 ~ c e ~ 195

E till ca 190 c

=

185

180

-100 100 300 500 700 900 11 00 1300

Reduced Variate

I r----+-I-- ---~-------+---t---I I


Normal Gumbel

Figure B9 I Sm span

5 Z e l c e ~

E

aC till

c =

535

530

525

520

515

510

505

500


Normal Gumbel


-100 100 300 500 700 900 1100 1300

Reduced Variate

Figure B92 10m span

Univers

ity of

Cap

e Tow

n

1150

1100 - middot 1050

1000 r --

950

900


i I

- 1i

APPENDIX B

1200 -------~----____--____----_

850+---r-----r--~--~---~--_T----~

-100 100 300 500 700 900 1100 1300

Reduced Variate



Figure 893 15m span

e

1650

1630

1610

~ 1590 ~ c 1570 e Q 1550 ~ ell 1530= a c 1510 = 1490

1470

1450

I I -~-t-shyI

i il )

l--shy

-100 100 300 500 700 900 1100 1300

Reduced Variate



Figure 894 20m span

Univers

ity of

Cap

e Tow

n

APPENDIXB

I i I

-~-+--1-1 ~ I-1--

2820+-----r---~~--~----~----_+----_+----~

-100 100 300 500 700 900 1100 1300

Reduced Variate


-- Normal Gumbel

Figure B95 30m span

2940

2920 e Z 2900ltII

I -OJ

8 ltgt 2880 ~ OG Ia 2860 I OJ

CQ

2840

Univers

ity of

Cap

e Tow

n

APPENDIXB


7 Axle Vehicles

210

205 +---f---l----I I---r----f-----

----- -JbI~__+ - I

--~-l ---- - ---+----+-- i

200 -J-- -+- - - j--shy

~ 195 -- ---1- -+----

ltj 41 190

ri I II i __ J ---r--shy 185

41 -= I ~ I - I ~+---r---rIl 180

175 +-ltSgt---- - +-i--i---T --+--shy i

170

-100 100 300 500 700 900 1100 1300

Reduced Variate


-- Normal --Gumbel

Reduced Variate


--Normal --Gumbel

Figure B97 10m span

Univers

ity of

Cap

e Tow

n

360

+ JiUO--t---

-j---t----+--- -~-- - T -3S0

-340 r- -r- I ~- -1- -shy~ 330 ltJ ~ Q 320 +---h-=-~~--1 ~~-Ib~01

310c ~ -- I-- r-----1-shyen


280

-100 100 300 Soo 700 900 1100 1300

Reduced Variate


-- Normal Gumbel

Figure B98 ISm span

390r---~----~----~-----1

~ 370

~

----------~--~

380 +--------- I - ---r ---+- - - - ------- ---+-- - - - - --1

I - +1--- -+-

3S0 +----+

330+-----r---~----_+---_r----~----~-~

~ 360 +--shygj t3

340



Figure B99 20m span

APPENDIXB

Univers

ity of

Cap

e Tow

n

APPENDIX B

423

421

419

417Z 415 Q

413 ltlI c 411 (IJ

409

407

405

-100 100 300 500 700 900 1100 1300

Reduced Variate



Univers

ity of

Cap

e Tow

n

APPENDIXB


8 Axle Vehicles

240

230

e 220

~ - 210 -= 200e 0

E 190 011c a 180 c = 170

160

150

-100

-I----tl ---+shy

I

-r I i-----1L-~II --_t_

_ -+shy _ _ i

100 300 500 700 900 1100 1300

Reduced Variate


Normal Gumbel

Figure BIOI Sm span

650

8 600 z -I - I c 550 e 0

E 011 500ca I = 450

4OO+-----r---------+-----r-----r----~--~

-II

-100 100 300 500 700 900 1100 1300

Reduced Variate


Normal Gumbel


Univers

ity of

Cap

e Tow

n

APPENDIXB

1200 ----------~r_-r_--__r--____--__


= --+1- ~ l -~ a = CQ

850 q - -I--middot-~ -1

800 I

750 +-----~----~----_----~----_r----~---~

-100 100 300 500 700 900 1100 1300

Reduced Variate




1900

1800

S Z 1700 l = 1600 8 c ~ 1500 OJ)

= a = 1400

CQ

1300

1200

-100 100 300 500 7 00 9 00 1100 1300

Reduced Variate




Univers

ity of

Cap

e Tow

n

APPENDIXB

3350 I

I

I

3250

1-~ --

- 3150S

z --1-shy ~c 3050 1

II I 2950e iQ

2850 011 s 27501l c

I = 2650

2550 -I middot I

2450

-100 100 300 500 700 900 1100 1300

Reduced Variate


-- Normal Gumbel


Univers

ity of

Cap

e Tow

n


8 Axle Vehicles

210----------~------_----~----~----~

200~-----~-----4------~----~-----+--~~

190

~

~


I~+_-----r----_------r-----~-----+----~

I f----- -I shy

180 +---------------

170 -t------------+-~

I I-shy ----------- 1 160 +-------1----4-----

-100 100 300 500 700 900 1100

Reduced Variate


-- Nonnal - Gumbel

Figure B106 5m span

290

280

270

260 ~ - ~ 250 Q 240 ~ 230 ~

rIl 220

210

200

190 -00 100 300


-- Normal -Gumbel


-1---1--shy-1----1-1--shy


500 700 900 11 00

Reduced Variate

APPENDIXB

Univers

ity of

Cap

e Tow

n

APPENDTXB

370


~ 330

01 310

- - --~---t-shy--


270

250

230

-100 100 300 500 700 900 1100

Reduced Variate


-- Normal Gwnbel


~o----~-----------~-----------------_

380

~ 360 01 Q 3~ ~ ~ c 320()

300

280

-100 100 300 500 700 900 1100

Reduced Variate


-- Normal Gumbel


Univers

ity of

Cap

e Tow

n

APPENDIXB

500

480

460

~ 440 OIl

~ Q 420 ~ ltII OIl 400d

(I)

380

360

340

-100 100 300 500 700 900 1100

Reduced Variate


-- Normal Gwnbel


Univers

ity of

Cap

e Tow

n

APPENDIXB


8 Axle Vehicles

210~----~-------~----~--------------

205 ~---l-

200 -j---l-----

195 -+----l~oP ---1-shy +---1------1


185 -t------t----i---i------r----

-100 100 300 500 700 900 1100 1300

Reduced Variate


-- Normal Gumbel

Figure BIll 5m span

545

540

S Z 535 i 530 GI a 0 525 ~ ~ c a 520

C GI

IQ 515

510

505

-t-+---t-I-L I I

-100 100 300 500 700 900 1100 1300

Reduced Variate


-- Normal Gumbel


Univers

ity of

Cap

e Tow

n

APPENDIX B

104)

1030

e 1020Z e l 1010c e 1000=gt OG

990c s c 980=I

970

960

-100 100 300 500 700 900 1100 13 00

Reduced Variate


-- Nonna --- Gumbel


1620-----~--~----~~--_----~----~--~


ac

c =I

1500+-----r---~----_T----_r----~----_--~

1600

1580

1560 l

i 154)

1520

-100 100 300 500 700 900 1100 1300

Reduced Variate


--Nonna --- Gumbel


Univers

ity of

Cap

e Tow

n

APPENDIX B

2970

~ 2950

S z 0 2930 (I)

is e 2910Q

~ 1gt11 Ca 2890 c

al

2870

2850+-----r-----~--~r_--~r_--~----_+----~

-100 100 300 500 700 900 IUlO 1300

Reduced Variate


--Normal -Gwnbel


Univers

ity of

Cap

e Tow

n

--

APPENDIXB


8 Axle Vehicles

200

195

Z ~ 190 ~ ~ 185 ~ -= (I)

180

i i I I ~ E bull

175

c_---+-__---_ ~--_f

~-+-----il-_+ _-+t_i ---t-I-I -100 100 300 500 700 900 1100 1300

Reduced Variate




~ ~

= ~ -= ~ (I)

275-----------~--------~----------~----_

270

265

260

- shy -- ----- shy ----1---shy

I 2S5 -t shy250

245

240

-100 100 3 00 500 700 900 1100 1300

Reduced Variate


--Normal ---Gumbel


Univers

ity of

Cap

e Tow

n

APPENOIXB

325

320 I-- -I ~

315

310OJ ~ 305~ -= (I)

300

295

290

-100 100 300 500 700 900 1100 1300

Reduced Variate



Z e ~ Q

~

~ -= (I)

360~----------------~----~---------------

355

350

345

340

335

330

--+----~-- ~--- i shy - ---+-----1

i I I I -100 100 300 500 700 900 1100 1300

Reduced Variate


-Nannal Gwnbel


Univers

ity of

Cap

e Tow

n

APPENDIXB

QI ~ 415 +---f--shy

-~--t-I I

I -=r-i--- II

I 400+-----~----+_----+_----r_----+_----r_--~

430~----~----~----------~----~----~--~

425 --f ~ r - ~ 420 -I---~---li-- --- --t-shyZ I ==- i

~ o

lltU 410 +-- -r shy

~ ~-----------l405 -1--061+--1-----+ I

i i

-100 100 300 500 700 900 1100 1300

Reduced Variate



Univers

ity of

Cap

e Tow

nAppendix C


II

II

Univers

ity of

Cap

e Tow

n

APPENDIX C

Page No




Univers

ity of

Cap

e Tow

n


Univers

ity of

Cap

e Tow

n




















Univers

ity of

Cap

e Tow

n




I 022

2 23E-05 3


4 46E-09 (2)(3) 5



6 (I) (4)IOE-09


7 47E-18 (6) (4)



9 10E-18 (1)(7)


10 47E-27 (9)(4)








3

Univers

ity of

Cap

e Tow

n


4

Univers

ity of

Cap

e Tow

n

A-1

APPENDIX A

Univers

ity of

Cap

e Tow

nAppendix D

Impact Formula I

bull bull

Univers

ity of

Cap

e Tow

n

APPENDIX 0

Page No







Univers

ity of

Cap

e Tow

n





Where













3J =shy

b L


J =~ b Lf





Where













3 J =shy

b L


J =~ b Lf

Univers

ity of

Cap

e Tow

n



therefore used











response

2



therefore used











response

2

Univers

ity of

Cap

e Tow

nAppendix E


bull

Univers

ity of

Cap

e Tow

n

1

APPENDIX E

Page No









Univers

ity of

Cap

e Tow

n

























III 2

I ~


























W~ I i I

WI 2

I I ~


Univers

ity of

Cap

e Tow

n


















2

Univers

ity of

Cap

e Tow

n









moments





















3

E13








moments













E14 Simulation








3

Univers

ity of

Cap

e Tow

n






(i) Maximum W

(ii) Shortest b

(iii) Centred x =05












limits





legal vehicles





4

Univers

ity of

Cap

e Tow

n







5 197 189 4

10 547 562 3 15 1054 1054 0 20 1582 1626 3)

7


0 Connor Difference

5 184 173 -6

10 252 258 3 15 308 304 -1 20 347 346 0





simulations









5

Univers

ity of

Cap

e Tow

n

Bending Moments kNm


5 293 301 -3 10 800 812 -1 15 1262 1364 -7 20 1903 2097 -9 30 3526 3631 -3








6

Univers

ity of

Cap

e Tow

nAppendix F


Visual Bas

Univers

ity of

Cap

e Tow

n


Sub centralloadO









Univers

ity of

Cap

e Tow

n




pos = inc n







+


pos = inc n



10) lt= 0 Or

+ + +


Then Then Then





+ + spaclO



Univers

ity of

Cap

e Tow

n






n=n+1 Loop



Next z


Univers

ity of

Cap

e Tow

n




Nexty








Next s


End Sub




Nexty








Next s


End Sub