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VISVESVARAYA TECHNOLOGICALUNIVERSITY,
BELGAUM-590018
SDM COLLEGE OF ENGINEERING & TECHNOLOGY,
DHARWAD-580002
PROJECT REPORT
ENTITLED
PERFORMANCE BASED ANALYSIS OF BRIDGE DECK FOR
DISTINCTIVE GIRDER TYPES
SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENT FOR
THE AWARD OF
MASTER OF TECHNOLOGY
IN
COMPUTER AIDED DESIGN OF STRUCTURES
SUBMITTED BY:
MR . PRATEEK HUNDEKAR
USN: 2SD12CCS12
UNDER THE GUIDANCE OF
Dr. D K. KULKARNI
PROFESSOR
DEPARTMENT OF CIVIL ENGINEERING
2013-2014
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I
ABSTRACT
Bridge decks must withstand one of the most damaging types of live load forces i.e.
vehicle loads. In this thesis the bridge deck is modeled as a simply supported beam with
the bridge deck slab spanning in one direction. The bending moment per unit width ofslab caused by the IRC vehicle loads is calculated by estimating the width of slab that
may be taken as effective in resisting the bending moment due to the loads, and
accordingly the deck slab is modeled for that bending moment. Analysis for discrete
model is done using the finite element method. This Thesis presents the results related to
finite element analysis (FEA) of simply supported reinforced concrete bridge deck of
different deck thicknesses (375mm to 825mm) and constant width of 12 m, without
footpath under Indian Road Congress (IRC) vehicle load classes. Hence, a total of 128
numbers of cases were analyzed. The Dimension of deck slabs are taken from standard
drawings of the Ministry of Road Transport & Highways-1991. And the deck was
supported by four distinct types of girders, i.e. Rectangular girder; Tee beam girder; I
section Concrete girder and ISMB600 steel girder for each load class that was considered
i.e. IRC Class 70R and IRC Class AA loading. Under condition, without footpath,
carriageway-width of 12 m. Due to edge loading, maximum FEA bending moments are
seen to vary linearly in case of both the load classes (Class 70R & Class AA) for the deck
supported by all the four type of girders. Under centered loading, the maximum
longitudinal bending moments caused due to IRC class 70R for deck slab with
rectangular girder and I- section concrete girder show a correlation between them. The
maximum bending moment values are seen to be nearly equal to each other with only
slight differences in the values. For Both the load classes and all the load cases
considered, ISMB-600 steel girder is seen to produce higher bending moment values for
both edge loading and center loading. The values for ISMB-600 girder are much greater
when compared with the other two types of girders. The thickness of deck slab
contributes a major role in carrying the vehicle loads. The increase in thickness reduces
the loss in ultimate Moment carrying capacity; decrease the maximum deck stress and
live load deflection; helps distribute deck live loads more evenly to the girders and
increases the deck service life.
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II
ACKNOWLEDGEMENT
The sense of contentment and elation that accompanies the successful completion of my task would be
incomplete without mentioning the names of the people who helped in accomplishment of this M.Tech
thesis, whose constant guidance, support and encouragement resulted in its realization.
I am grateful to our institution S.D.M. COLLEGE OF ENGINEERING &
TECHNOLOGY with its ideas and inspiration for having provided us the facilities that
have made this dissertation work a success.
I offer my sincerest gratitude to my guide Dr. D K. Kulkarni, Professor and PG.
Coordinator, Department of civil engineering, S.D.M.C.E.T, Dharwad, who has supported
me throughout my thesis with his patience and knowledge whilst allowing me the space
to work in my own way and allowing me to use all facilities available at S.D.M.C.E.T for
the successful completion of the project and my dissertation work.
I am greatly thankful to Mr. Kiran Malipatil, Asst. Professor, Department of civil
engineering, KLECET, Belgaum, for his timely help and guidance.
I gratefully acknowledge Dr. S. G Joshi, Head of Department, Civil Engineering,
S.D.M.C.E.T, for his encouragement and suggestions during the course of my dissertation
Work.
Also I would like to take this opportunity to thank Dr. S. Mohan Kumar, Principal,
S.D.M.C.E.T, for his encouragement during my dissertation work.
I thank all Teaching and non-teaching staff of the department who has helped me
successfully complete the thesis.
Above all, my heartfelt gratitude goes to my family, friends and Almighty for their
inspiration and constant support without which the thesis would not have accomplished.
PRATEEK S. HUNDEKAR
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III
TABLE OF CONTENTS
Chapter No. PARTICULARS Page No.
ABSTRACT I
ACKNOWLEDGEMENT II
LIST OF TABLES VI
LIST OF FIGURES VII
1 INTRODUCTION 1
2 LITERATURE SURVEY 3
2.1 Introduction 3
2.2 Literature review 3
2.3 Outcome of the Literature Review 8
3 PROJECT DESCRIPTION 9
3.1 Problem Formulation 9
3.2 Methodology 9
3.3 Objectives of the Thesis 9
3.4 Organization of the Report 10
4 ANALYTICAL APPROACH 11
4.1 Introduction 11
4.2 The FE Modeling Process 11
4.2.1 Idealization 12
4.2.2 Discretization 12
4.2.3 Element Analysis 13
4.2.4 Structural Analysis 13
4.2.5 Post Processing 13
4.2.6 Result Handling 13
5 FE MODELING OF SLABS 15
5.1 General 155.2 Structural Analysis with FEM 16
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IV
5.2.1 Element Types 17
5.2.2 FE Mesh 17
5.2.3 Support Conditions for Slab Bridges 18
5.3 Loads 19
5.3.1 Self-Weight 195.3.2 Traffic Loads 20
6 VERIFICATION STUDIES 24
6.1 Verification Studies 24
6.1.1 Reinforced-Concrete Beam 24
6.1.2 Reinforced-Concrete Slab 26
7 FINITE ELEMENT MODEL 28
7.1 Model Characteristics 28
7.1.1 FE Mesh 28
7.1.2 Model View Details 29
8 LOADS 34
8.1 Self-weight 34
8.2 Vehicle Loads 34
8.3 Load Combinations 37
9 INVESTIGATIONS 38
9.1 FE Analyses 38
9.1.1 Bridge Deck with Rectangular Girder 38
9.1.2 Bridge Deck with Prismatic Tee Beam Girder 43
9.1.3 Bridge Deck with I section concrete Girder 47
9.1.4 Bridge Deck with ISMB 600 Steel Girder 52
10 ANALYSYS RESULTS AND DISCUSSIONS 57
10.1 RESULTS 57
10.2 DISCUSSIONS 61
11 CONCLUSION 62
11.1 Summary 62
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V
11.2 Conclusion 63
11.3 Scope for Future Studies 64
REFERENCES 65
APPENDIX 67
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VI
LIST OF TABLES
Table No. PARTICULARS Page No.
5.1 Material Properties 195.2 Minimum clearance between passing vehicles 21
5.3 Load combinations 22
6.1 Bending moment along span (kNm/m) 27
8.1 Material properties 34
8.2 Minimum Carriageway Width 37
8.3 Live load combinations 37
9.1 Maximum Bending moment (kN-m/m) along span 39
9.2 Maximum Bending moment (kN-m/m) along span 43
9.3 Maximum Bending moment (kN-m/m) along span 48
9.4 Maximum Bending moment (kN-m/m) along span 52
10.1 Maximum Bending moment (kN-m/m) along span 58
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VII
LIST OF FIGURES
Figure No. PARTICULARS Page No.
5.1 Slab: thickness to panel dimension ratio 15
5.2 Sectional forces and stresses of a finite plate element 16
5.3 (a) Pin Support of One Node 18
5.3 (b) Coupling of Nodes 19
5.4 (a) Wheel arrangement for 70R (Wheeled Vehicle) 20
5.4 (b) Wheel arrangement for 70R (Tracked Vehicle) 20
5.4 (c) Clear Carriageway Width 21
5.5 IRC Class AA Tracked and Wheeled Vehicles (Clause 204.1) 23
6.1 Simply Supported Beam 24
6.2 SS beam carrying concentrated load 25
6.3 BMD for SS beam 25
6.4 SFD for SS beam 26
7.1 Isometric View of Model of Concrete Slab with supporting
girders
28
7.2 Bridge Deck Resting on Rectangular Girder 30
7.3 Bridge Deck Resting on Tee Girder 31
7.4 Sectional Properties of Prismatic Tee beam 31
7.5 Bridge Deck Resting on I section concrete Girder 32
7.6 Sectional Properties of I section concrete beam 32
7.7 Bridge Deck Resting on ISMB 600 steel Girder 33
7.8 Sectional properties of ISMB 600 steel Girder 33
7.9 Material Properties of ISMB 600 steel Girder 33
8.1 Class 70R Tracked & Wheeled Vehicles (Clause 204.1) 358.2 Class AA Tracked Vehicles (Clause 204.1) 35
8.3 Wheel Arrangement for 70R 36
8.4 Clear Carriageway width 36
9.1 Graphical representation 39
9.2 Stress contours due to self-weight of the structure 40
9.3 Stress contours due to IRC class 70R edge loading 41
9.4 Stress contours due to IRC class 70R center loading 41
9.5 Stress contours due to IRC class AA edge loading 42
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VIII
9.6 Stress contours due to IRC class AA center loading 42
9.7 Graphical representation 44
9.8 Stress contours due to self-weight of the structure 45
9.9 Stress contours due to IRC class 70R edge loading 45
9.10 Stress contours due to IRC class 70R center loading 469.11 Stress contours due to IRC class AA edge loading 46
9.12 Stress contours due to IRC class AA center loading 47
9.13 Graphical representation 48
9.14 Stress contours due to self-weight of the structure 49
9.15 Stress contours due to IRC class 70R edge loading 50
9.16 Stress contours due to IRC class 70R center loading 50
9.17 Stress contours due to IRC class AA edge loading 51
9.18 Stress contours due to IRC class AA center loading 51
9.19 Graphical representation 53
9.20 Stress contours due to self-weight of the structure 54
9.21 Stress contours due to IRC class 70R edge loading 54
9.22 Stress contours due to IRC class 70R center loading 55
9.23 Stress contours due to IRC class AA edge loading 55
9.24 Stress contours due to IRC class AA center loading 56
10.1Longitudinal Bending moments (kNm/m) for IRC Class 70R-
Center loading59
10.2Longitudinal Bending moments (kNm/m) for IRC Class AA -
center loading59
10.3Longitudinal Bending moments (kNm/m) for IRC Class 70R –
edge loading60
10.4
Longitudinal Bending moments (kNm/m) for IRC Class AA –
edge loading 60
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PERFORMANCE BASED ANALYSIS OF BRIDGE DECK FOR DISTINCTIVE GIRDER TYPES
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CHAPTER 1
INTRODUCTION
Bridge decks must withstand one of the most damaging types of live load forces
i.e., the concentrated and direct pounding of truck wheels. A primary function of the deck
is to distribute these forces in a favorable manner to the support elements below. The ratio
of live to total load stresses is high in bridge decks usually much higher than in most of
the other components of the bridge. Additionally, because of their exposed location,
temperature variations are large in bridge decks and restraints to the resulting volume
changes tend to cause early cracking of the concrete. Identification of Dynamic moving
vehicle loads is extremely important for not only the design of bridges and pavements but
also their monitoring and retrofitting in the transportation engineering. However, it is
difficult to directly measure the interaction forces between the vehicles and a bridge
because they are in motion and time varying. The dynamic load data are valuable because
the dynamic wheel loads might increase road surface damage by a factor of 2 – 4 over that
due to static wheel loads, the repeated application of moving heavier vehicles directly
contribute to fatigue failure and crack propagation in bridge structure, leading to a
reduction in useful life. In recent years, the technique of moving load identification has
been developing very rapidly. In some of the techniques, the bridge deck is modeled as a
simply supported beam or multi-span continuous beam, and the vehicle/bridge interaction
force is modeled as one-point or two-point loads at a fixed spacing moving at a constant
speed. In India, in the case of bridge deck slabs spanning in one direction, the bending
moment per unit width of slab caused by the IRC vehicle loads can be calculated by
estimating the width of slab that may be taken as effective in resisting the bending
moment due to the loads and accordingly the deck slab is designed for that bending
moment. Dynamic response analysis for discrete system can be found using the finite
element method, and the modeling accuracy can be studied against the degree of
discretization of the structure for a moving load analysis. The dynamic performance of
bridges can be affected by many factors. Different types of vehicles, vehicle speeds, and
road surface conditions could all contribute to different bridge dynamic performances.
For given structural properties of a bridge and road surface condition, the mechanical
properties (or dynamic characteristics) of the vehicles traveling on the bridge would playa very important role in affecting the dynamic performance of the bridge. Therefore, it
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would be very beneficial to be able to identify the parameters of vehicles traveling on
bridges. In safety evaluations the dynamic effect of traffic actions can be taken into
account using equivalent loads determined by multiplying the static loads by a so-called
dynamic amplification factor. The effects of heavily loaded trucks can be determinant forthe evaluation of deck slabs.
Bridge decks must withstand one of the most damaging types of live load forces i.e., the
concentrated and direct pounding of truck wheels. A primary function of the deck is to
distribute these forces in a favorable manner to the support elements below. The ratio of
live to total load stresses is high in bridge decks — usually much higher than in most of the
other components of the bridge and such fatigue-producing stresses tend to aggravate any
defects that might be present in the deck.
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Chapter 2
LITERATURE SURVEY
2.1 Introduction
It has been evident that many research papers have been published on the study of
dynamic, seismic and static response of the bridges. Many load cases were considered
including vehicle loads, self-weight, wind loads etc. for the evaluation of bridge-vehicle
interactions and the effects of them on the structure. In some of the techniques, the bridge
deck is modeled as a simply supported beam or multi-span continuous beam, and the
vehicle/bridge interaction force is modeled as one-point or two-point loads at a fixed
spacing moving at a constant speed. Dynamic response analysis for discrete system was
found using the finite element method, and the modeling accuracy can be studied against
the degree of discretization of the structure for a moving load analysis. The dynamic
performance of bridges can be affected by many factors. Different types of vehicles,
vehicle speeds, and road surface conditions could all contribute to different bridge
dynamic performances. It would be very beneficial to be able to identify the parameters
of vehicles traveling on bridges. In safety evaluations the dynamic effect of traffic actions
can be taken into account using equivalent loads determined by multiplying the static
loads by a so-called dynamic amplification factor. The effects of heavily loaded trucks
can be determinant for the evaluation of deck slabs.
The objective of this chapter is to give a brief overview of the literature on finite element
analysis of bridges and the loads acting upon them.
2.2 Literature review
L. Deng, C.S. Cai., [1] have presented a method for identifying the parameters of
vehicles moving on bridges. Two vehicle models, a single-degree-of-freedom model and
a full-scale vehicle model, are used. The vehicle bridge coupling equations are established
by combining the equations of motion of both the bridge and the vehicle using the
displacement relationship and the interaction force relationship at the contact point.
Bridge responses including displacement, acceleration, and strain are used in the
identification process.
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S.S. Law et al., [2] presented a new moving load identification method based on finite
element method and condensation technique. The measured displacements are formulated
as the shape functions of the finite elements of the structure which is modeled as a
straight beam. The measured responses can be limited to a small number of masterdegrees-of- freedom of the structural system. Numerical simulations and experimental
results demonstrate the efficiency and accuracy of the method to identify a system of
general moving loads or interaction forces between the vehicle and the bridge deck.
Adadrian Kidarsa et al., [3] Proposes an analysis method for moving loads computes
the internal force history in a structural member at the integration points of force-based
finite elements as opposed to the end forces of a refined displacement-based finite
element mesh. The force- based formulation satisfies strong equilibrium of internal
section forces with the element end forces and the moving load. This is in contrast with
displacement-based finite element formulations that violate equilibrium between the
section forces and the equivalent end forces computed for the moving load. A new
approach to numerical quadrature in force-based elements allows the specification of
integration point locations where the section demand is critical while ensuring a sufficient
level of integration accuracy over the element domain. Influence lines computed by
numerical integration in force-based elements converge to the exact solution and accurate
results are obtained for practical applications in structural engineering through the new
low-order integration approach. The proposed methodology for moving load analysis has
been incorporated in automated software to load rate a large number of bridges
efficiently.
L. Yu et al., [4] reviewed the current knowledge on factors affecting performance of
moving force identification methods under main headings below: background of moving
force identification, experimental verification in laboratory and its application in field. It
mainly focuses on the potential of four developed identification methods, i.e. Interpretive
Method I (IMI), Interpretive Method II (IMII), Time Domain Method (TDM) and
Frequency – Time Domain Method (FTDM). Some parameter effects, such as vehicle –
bridge parameters, measurement parameters and algorithm parameters, are also discussed.
Some conclusions that have been achieved on moving force identification are highlighted
and recommendations served as a good indicator to steer the direction of further work in
the field.
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Kanchan Sen Gupta et al., [5] presented the results related to finite element analysis
(FEA) of simply supported reinforced concrete bridge deck of different span lengths (3 m
to 10 m) and constant width of 12 m, with and without footpath under eleven possible
Indian Road Congress (IRC) vehicle load cases. So, in total 88 no of cases were analyzed.Dimension of deck slabs are taken from standard drawings of the Ministry of Road
Transport & Highways-1991. Under condition A (including footpath, carriageway-width
7.5 m), due to edge loading, maximum FEA bending moments are similar to IRC bending
moments for the span up to 4 m for few cases. However, for larger spans, the IRC
bending moments are less than FEA bending moments by 5 to 20%. Under condition B
(without footpath, carriageway-width 9.6 m), due to edge loading, IRC bending moments
are less than FEA bending moments by 4 to 30%.
Claude Broquet et al., [6] studied the dynamic effect of traffic actions on the deck slabs
of concrete road bridges using the finite-element method. All the important parameters
that influence bridge-vehicle interaction are studied with a systematic approach. An
advanced numerical model is described and the results of a parametric study are
presented. The results suggest that vehicle speed is less important than vehicle mass and
that road roughness is the most important parameter affecting the dynamic behavior of
deck slabs. The type of bridge cross section was not found to have a significant influence
on deck slab behavior. The dynamic amplification factor varied between 1.0 and 1.55 for
the bridges and vehicles studied.
Daniel M. Balmer et al., [7] This paper highlights about the thickness of the deck slab
suggesting that thicker bridge decks are stiffer, stronger, and should provide a longer
service life; however, they cost more and require a stronger and more costly support
girder system. All of the parameters investigated in the parameter sensitivity study, with
the exception of two (deck unit weight and initial cost), support increasing Alabama‘s
minimum bridge deck thickness. An increase in thickness from 178 to 203 mm would
cause the deck unit weight to increase 287 – 575 N/m2, depending on whether the concrete
is added to the top or the underside of the deck. However, increasing the deck thickness
from 178 to 203 mm would also increase the deck service life, which would reduce the
life-cycle cost of the deck/bridge.
Lina Ding et al., [8] stated that Vehicles generate moving dynamic loads on bridges. In
most studies and current practice, the actions of vehicles are modeled as moving static
loads with a dynamic increase factor, which are obtained mainly from field
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measurements. In this study, an evolutionary spectral method is presented to evaluate the
dynamic vehicle loads on bridges due to the passage of a vehicle along a rough bridge
surface at a constant speed. The vehicle – bridge interaction problem is modeled in two
parts: the deterministic moving dynamic force induced by the vehicle weight, and therandom interaction force induced by the road pavement roughness. Each part is calculated
separately using the Runge – Kutta method and the total moving dynamic load is obtained
by adding the forces from these two parts. Two different types of vehicle models are used
in the numerical analysis. The effects of the road surface roughness, bridge length, and
vehicle speed and axle space on the dynamic vehicle loads on bridges are studied. The
results show that the road surface roughness has a significant influence on the dynamic
vehicle – bridge interaction. The dynamic amplification factors (DAF) and dynamic load
coefficient (DLC) depend on the road surface roughness condition.
M. Mabsout et al., [9] presented the results of a parametric study related to the wheel
load distribution in one-span, simply supported, multilane, reinforced concrete slab
bridges. The finite-element method was used to investigate the effect of span length, slab
width with and without shoulders, and wheel load conditions on typical bridges. A total of
112 highway bridge case studies were analyzed. It was assumed that the bridges were
stand-alone structures carrying one-way traffic. The finite-element analysis (FEA) results
of one-, two-, three-, and four-lane bridges are presented in combination with four typical
span lengths. Bridges were loaded with highway design truck HS20 placed at critical
locations in the longitudinal direction of each lane. Two possible transverse truck
positions were considered: (1) Centered loading condition where design trucks are
assumed to be traveling in the center of each lane; and (2) edge loading condition where
the design trucks are placed close to one edge of the slab with the absolute minimum
spacing between adjacent trucks. FEA results for bridges subjected to edge loadingshowed that the AASHTO standard specifications procedure overestimates the bending
moment by 30% for one lane and a span length less than 7.5 m (25 ft.) but agrees with
FEA bending moments for longer spans. The AASHTO bending moment gave results
similar to those of the FEA when considering two or more lanes and a span length less
than 10.5 m (35 ft.). However, as the span length increases, AASHTO underestimates the
FEA bending moment by 15 to 30%. It was shown that the presence of shoulders on both
sides of the bridge increases the load-carrying capacity of the bridge due to the increase in
slab width. An extreme loading scenario was created by introducing a disabled truck near
the edge in addition to design trucks in other lanes placed as close as
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PERFORMANCE BASED ANALYSIS OF BRIDGE DECK FOR DISTINCTIVE GIRDER TYPES
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possible to the disabled truck. For this extreme loading condition, AASHTO procedure
gave similar results to the FEA longitudinal bending moments for spans up to 7.5 m (25
ft) and underestimated the FEA (20 to 40%) for spans between 9 and 16.5 m (30 and 55
ft), regardless of the number of lanes. The new AASHTO load and resistance factordesign (LRFD) bridge design specifications overestimate the bending moments for
normal traffic on bridges. However, LRFD procedure gives results similar to those of the
FEA edge1truck loading condition. Furthermore, the FEA results showed that edge beams
must be considered in multilane slab bridges with a span length ranging between 6 and
16.5 m (20 and 55 ft). This paper will assist bridge engineers in performing realistic
designs of simply supported, multilane, reinforced concrete slab bridges as well as
evaluating the load-carrying capacity of existing highway bridges.
I. K Fang et al., [10] conducted experimental and analytical investigation regarding the
behavior of Ontario-type reinforced concrete bridge decks. A full-scale bridge deck (both
cast-in-place and precast), detailed in accordance with the Texas State Department of
Highways provisions for Ontario-type decks, and having about 60% of the reinforcement
required by the current AASHTO code, performs well under current AASHTO design
load levels. Under service and overload conditions (about three times the current
AASHTO design wheel load), the behavior of the deck slab is essentially linear.
Membrane forces do not noticeably affect the performance of the bridge prior to deck
cracking. After cracking, significant compressive membrane forces are present in the
deck, and could significantly increase its flexural capacity. Detailed finite element models
of the specimen are developed for both the cast-in-place and precast panel deck cases.
Cracking of the deck is followed using sequential linear analyses with a smeared cracking
model. Analytical predictions agree well with experimental results.
L. Charlie Cao et al., [11] observed from test and analysis results that the differential
deflection between girders in a slab-on-girder bridge deck reduces the negative bending
moments in the deck slab. A simplified analysis method considering the effect of girder
deflection is developed, based on an analytical solution obtained with the elastic plate
theory. With this approach, the effects of the girder stiffness and spacing, and the span
length of the bridge on the maximum negative bending moments in a deck slab can be
assessed. The simplified analysis method is validated with finite-element models. It has
been shown that the maximum negative bending moment in a bridge deck can be
accurately evaluated with the proposed method.
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J.L. Zapico et al., [12] studied that, considerable experience was gained in model
updating, and the critical issues that remain are the choice of parameters and how to deal
with ill-conditioning. Although a number of theoretical tools exist to help with both of
these tasks, the techniques are advancing by gaining experience with a diverse range ofStructures. This paper adds to this debate by updating an experimental bridge model with
a geometric scale of 1:50 that represents a typical multi-span continuous-deck motorway
bridge. The bridge has four identical straight spans and an irregular distribution of piers
and the central pier is shorter than the others. Four configurations corresponding to
different pier stiffness and the inclusion of an isolation – dissipation device were
considered. An initial test without the piers present was also performed. The measurement
of data in these different configurations allows the model updating to be performed
sequentially, where parameters identified in earlier configurations maintain their
estimated values in subsequent configurations. This approach means that each
configuration has a small number of uncertain parameters to be identified,
Leading to a set of well-conditioned estimation problems based on predicting four natural
frequencies of the structure. The procedure was successful, and all of the measured
natural frequencies were estimated accurately with a maximum error of fewer than 2.5%.
2.3 Outcome of the Literature Review
No study has been reported in literature on comparison of the moments and
stresses produced in the bridge deck taking into account of various types of girder
supports. In the present study, girders of different sizes and shapes and also of different
materials have been considered into the study of performance of the bridge deck for a
constant span with increasing deck thickness for various girder supports using standard
drawings provided by MORT&H and loads specified by the Indian Road Congress,
standard specifications and code of practice for road bridges.
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CHAPTER 3
PROJECT DESCRIPTION
3.1 Problem Formulation
The important parameters that influence bridge-vehicle interaction are to be
studied with a systematic approach in identifying the parameters of vehicles moving on
bridges and to identify a system of various load classes. A finite element model is to be
described and the results of a parametric study are to be presented in a systematic manner
including displacements, forces, bending moments etc. finite element analysis (FEA) of
concrete bridge deck supported by distinctive girder types for a range of deck slab
thicknesses and load classes is to be carried out using a suitable FEA software package.
3.2 Methodology
The aim of the thesis work is to identify and analyze the bridge deck for various
types of loads and load classes, mainly live loads and self-weight of the structure. The
modeling is to be carried out by using a standard FEA package which helps in
proper modeling and accurate analysis of the bridge deck for various parameters
of loads, loading types and type of structural elements supporting the deck. An attempt
is made to develop a virtual model of the bridge deck system, using the software to
obtain results for forces, displacements, bending moments etc. The virtual model can
be simulated and modified for the application of various load classes and different
girder supports, and are used further for the purpose of analysis.
3.3 Objectives of the Thesis
To identify the load cases on the bridge deck. The important parameters that
influence bridge-vehicle interaction are to be studied.
To carry out a systematic approach in identifying the parameters of vehicles
moving on bridges and to identify a system of general moving loads and load
classes.
To model the bridge deck using surface meshing/discretization of the slab.
To carry out finite element analysis (FEA) of concrete bridge deck supported by
distinctive girder types using a suitable FEA software package.
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To study the moments acting on the deck slab for various types of girder supports.
3.4 Organization of the Report
The thesis is comprised of the following contents.
Chapter 1: INTRODUCTION
Chapter 2: LITERATURE SURVEY
Chapter 3: PROJECT DESCRIPTION
Chapter 4: ANALYTICAL APPROACH
Chapter 5: FE MODELING OF SLABS
Chapter 6: VERIFICATION STUDIES
Chapter 7: FINITE ELEMENT MODEL
Chapter 8: LOADS
Chapter 9: INVESTIGATIONS
Chapter 10: ANALYSYS RESULTS AND DISCUSSIONS
Chapter 11: CONCLUSION
In chapter 1, a brief introduction about the bridges and vehicles has been given. In
chapter 2, a literature survey has been carried out to obtain the data for the proposed
work. Chapter 3 summarizes about the description of the project that is done. While
chapter 4 gives the details of the analytical approach that is used in the thesis work.
Chapter 5 mainly focuses on the finite element modeling of the slab and the support
elements. Chapter 6 gives the information about the verification/ validation of the model
and the software. The finite element model details and detailed study is presented in
chapter 7. The loads and load combinations and load cases can be thoroughly understood
from chapter 8. The investigations on various studies, load cases and models are given in
detail in chapter 9. Chapter 10 gives the proper idea about the results obtained by analysis
and results are discussed in this chapter. Chapter 11 gives the information about the
conclusions drawn and also for the future scope of study.
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CHAPTER 4
ANALYTICAL APPROACH
4.1 Introduction
A finite element analysis (FEA) procedure which can effectively simulate slab
behavior is to be defined and validated against the manually calculated results to prove
the abilities. The purposes of the analysis are to develop an analysis approach which can
successfully predict the load resisting behavior of a restrained deck system; to extend the
model to simulate the proposed deck slabs on various type of girders, to predict behavior
of the decks on bridges without doing full-scale load testing of huge assemblages and to
verify the developed design method. The literature review and the experimental results
are the basis of the basic assumption of the material properties and verification of the
FEA technique.
4.2 The FE Modeling Process
The process involves various step by step procedure for mmodeling, simulation
and calculation which are as shown in figure 2.1.
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4.2.1 Idealization
In the first step of FE analysis an idealization and simplification of the real
structure is done by representing it with a structural model, for example by a 3D Shell
model. The model includes geometry, boundary conditions, loads etc. In design of
concrete structures it is commonly assumed that the material is linear elastic. Boundary
conditions at supports are often simplified as being 100% fixed or not fixed at all even
though in reality it is somewhere in-between. In some situations it is important to include
the support stiffness to give a good interpretation of reality. The designer should have in
mind that the interpretation of the reality gives rise to a variety of choices and selections.
This puts high demands on the structural engineer since wrong assumptions have a large
impact on the resulting outcome. Two theories that are often used for analyzing linear
plates are the Kirchhoff-Germain and the Reissner-Mindlin theories. Both theories can be
used for moderate thin plates, where the deflection is less than half of the plate‘s
thickness. Thin plates should preferably be calculated with Kirchhoff theory. Similar
result can be achieved with Mindlin theory but a much finer mesh is required. The
required element size in case of Krichhoff theory should not be larger than approximately
the plate thickness. However, for very thick plates, the Mindlin theory must be used. For
the Mindlin theory, the width of the edge zone is comparable to the thickness of the plate;
in this edge area a sufficiently fine mesh should be applied. In slab structures modeled
with linear plates, discontinuity regions may appear under point loads and at pin supports.
According to plate theory a point load is acting in a single point in which the shear force
and bending moment approaches infinity, One way to overcome this is to include the load
or support pressure distribution in the model.
4.2.2 Discretization
In the second step, the structural model is divided into finite elements. The results,
primarily in integration points, depend on the element size, the type and shape, and how
the load is applied. Consequently a denser element mesh and less distorted elements lead
to a more correct answer. Higher order elements often lead to a more correct result.
However, quadric shell and plate elements can lead to a large variation in sectional forces
at point loads and pin supports. Shell elements differ from plate element due to that shell
element can be curved and can carry both membrane and bending forces. Shell element
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needs larger computer capacity. A lower order element can in this case be favorable ,
even if the element size need to be smaller.
4.2.3 Element Analysis
Element approximation and element stiffness is calculated in this step. The
internal element stiffness in the element analysis is approximated with a base function. In
FE analysis, a numerical integration is used to get an accurate integration over the chosen
integration points in the elements. This integration is an approximation even if a sufficient
amount of integration points is used, due to the fact that integration of rational functions
does not give exact solutions.
4.2.4 Structural Analysis
A calculation of the stiffness matrix is done by paring the single elements‘
stiffness matrix with equilibrium conditions and geometry conditions. The equation
system can be solved for the whole structure. The computer can only use a certain amount
of significant numbers; thereby rounding errors can arise in this step.
4.2.5 Post Processing
In this step, the calculations of stress components in all the elements are
performed. The stress is calculated in the integration points. These points are generally
not situated in the elements nodes, but are situated a distance into the element with for
example Gauss integration. The values in the integration points are the most exact results
from the FE analysis. Nevertheless, the results are often showed in the element nodes.
The integration point results are extrapolated to the nodes with the element base
functions. Generally an element with high order produces a better approximation for a
linear elastic analysis. Every node is in general connected to more than one element. Due
to this, the node result is calculated as a mean value from the single elements
contributions. In other words all elements connected to the same node have an effect on
the node value. Hence, the results from the post processing as mentioned above are not
exact and contains rounding.
4.2.6 Result Handling
The results from the FE-analysis have to be further analyzed. This leads to large
uncertainties due to considerations of the structure`s real behavior. The analysis is
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dependent on choices made in Step 1. For 2D frame analysis the output data is
manageable for large models. Due to the increased complexity with 3D shell analysis, it is
very hard and sometimes practically impossible to analyze all output data. The use of
reviewing all the output from the analysis can also be questioned. Instead a combinationof words, numbers and iso-color plots gives a good description of the results.
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CHAPTER 5
FE MODELING OF SLABS
The definition of a slab is a thin plane spatial surface structure dominantly loaded
by forces normal to the plane of the plate. a slab is a member for which the minimum
panel dimension is not less than five times the overall slab thickness is shown in figure
5.1.
Figure 5.1 Slab: thickness to panel dimension ratio
5.1 General
To be able to understand the mode of action of a slab, a definition of the sectional
forces is made. First of all, a co-ordinate system (x, y) is introduced; see Figure 3.2. The
bending moment that gives bending around the x- axis is denoted mx and the bending
moment that gives bending around the y- axis my. The torsional moment that twists the
slab is denoted as mxy and the shear forces vx and vy. In a shell element there are also
membrane forces acting in the plane of the element.
Some additional assumptions are used together with the definitions. One
assumption is that the vertical stress in the slab cross-section sz is equal to zero. This is
considered valid as long as the thickness of the slab t is constant and much smaller than
the width, t<<b. Stresses in normal direction can be neglected which means that there are
no normal strains in the middle plane.
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Figure 5.2 Sectional forces and stresses of a finite plate element
Another assumption is that the displacements in vertical direction are considered to be
small, <<t. This means that the first order theory can be used. Also, the material is
assumed to exhibit a linear strain distribution over the section depth. One further
assumption is that the plane sections before loading remain plane after loading (Bernoulli-
Euler theory). In FE modeling of slabs, shell elements are often used. In this case,
membrane forces are included in the element definition. In this case also horizontal
loading can be taken into account. Some of the provided sectional forces from a 3D shell
analysis are the longitudinal- and transversal bending moments mx, my and the torsional
moment mxy. The reinforcement is designed is based on the assumption that the
reinforcement in a cracked concrete section cannot resist torsional moments. Instead, the
principal moments caused by the elastic moments mx, my and mxy are resisted by
reinforcement moments acting in pure bending in ultimate limit state. The torsional
moment will result in increased requirements of both top and bottom reinforcement.
Consequently, a positive reinforcement moment and a negative reinforcement moment
are derived.
5.2 Structural Analysis with FEM
This part treats literature recommendations of how to model slab frame bridges
and slab bridges in accurate ways. This underlying theory is used as a base for the choices
made for the FE-models in this thesis. The first parts about mesh and FE mesh are
common for all bridge models.
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5.2.1 Element Types
The choice of element type depends on the requested output. The main element
categories are continuum elements, structural elements and special purpose elements.
Within each of these categories, there is a range of various types of elements. Structural
elements are elements based on e.g. beam and shell theory. In contrast to continuum
elements they have rotational degrees of freedom in addition to the translational.
Furthermore, their response can be expressed in terms of cross-sectional forces and
moments. Due to the aim of the thesis, it is appropriate to use structural elements, more
specifically shell elements.
5.2.2 FE Mesh
Proper meshing is essential for obtaining accurate results. This has to do with how
finite element programs treat data and calculate the sectional forces. It is clear that for a
given type of element, the accuracy increases with decreasing element size. In general,
one could say that a denser mesh should be used in regions where the results of the
analysis changes rapidly like over the supports. Depending on how the support conditions
in the FE model are modeled, singularity problems can be obtained over the supports. In
this case, an increase of mesh density will lead to that the values will approach infinity.
With triangular elements a denser mesh is needed in order to obtain a more accurate
result. Distorted elements also give large errors in the results should be avoided. If
distorted elements still need to be used locally a compensation for the error can be made
by a denser mesh, within certain limits. A common perception is that a good mesh is a
uniform mesh with quadratic elements.
One reason for this is that the finite elements are derived for this shapes and that
this shape will give better approximation of the result in the integration points. Another
reason is that finite element programs extrapolate the results calculated in the Gauss
points to the nodes. This interpolation becomes more inaccurate for triangular and
rectangular elements compared to quadratic elements. In finite element analysis the slab
is divided into small elements which are connected by their nodes. By increasing the
number of elements and consequently increasing the density of the mesh, a more accurate
interpolation of the node displacement is obtained. Increasing the mesh density will lead
to a more accurate result. Although it is preferred to aim at a more accurate analysis, it
should not be more accurate than required. Despite the benefits with a finite element
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analysis, one should never underestimate the need of proper understanding of the method.
As will be discussed later in this chapter, it is essential that correct modeling of the
support conditions is made.
5.2.3 Support Conditions for Slab Bridges
Modeling the support conditions for a slab requires a great deal of consideration.
Depending on how various restraints are introduced, the properties of the connection will
change and the resulting outcome will be considerably influenced. A concentrated support
can be interpreted as a pin support on a column, e.g. for a flat slab. The line support can
instead be seen as a continuous support of the slab over a wall. A line support can also be
discontinuous where the wall ends inside the slab. Both concentrated supports andinterrupted line supports causes singularity problems since the shear force and bending
moment tend to go to infinity upon mesh refinement. However, this is only a numerical
problem and the slab should not be designed for the values obtained in the support points.
Instead the design should be based on reduced values take in critical sections adjacent to
the support points. The following subchapter will present appropriate ways to model
support conditions used for the slab bridge and frame slab bridge.
Pin Support of One Node
Pin support of one node refers to restraining a single node in the vertical direction;
see Figure 5.3 (a). Modeling the support this way will give rise to peak values in the
moment distribution which does not exist in reality. A way of treating this phenomena is
to use values in adjacent critical sections. Recommendations for this is being developed in
a currently ongoing project for the Swedish transport administration.
Figure 5.3 (a) Pin Support of One Node
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Coupling of Nodes
Coupling of nodes builds on the principle that the node in the center of the support
is connected to the other nodes representing the support, with infinitely stiff connections.
This connection can then be regarded as an infinitely stiff plate connected to the slab,
which is allowed to rotate around the center node; see Figure 5.3 (b). To couple the nodes
provides an advantage of not having to reduce the peak values, in contrast to the pin
support of one node.
5.3 (b) Coupling of Nodes
5.3 Loads
In reality a structure is loaded with many different loads. In this study, the load
types on the bridges studied were limited and a representative amount of loads were
selected in order to obtain a credible comparison. The loads included in the analysis are
the self-weight of the structure and traffic loads.
5.3.1 Self-Weight
The self-weight was calculated from the geometry of the bridge section. The
density of concrete was assumed to be 24 kN/m3 and Poisson‘s ratio 0.17. As shown in
table 5.1.
Table 5.1 Material Properties
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5.3.2 Traffic Loads
The vehicle traffic can differ between different bridges depending on how the
traffic is composed. The differences can include the proportion of heavy transport
vehicles (HTV‘s), the traffic density accounting for the average number of vehicles over a
year and the traffic conditions. The conditions can include a number of different factors
where one is the number of congestions. In addition, extremely heavy vehicles and their
axel loads need to be taken into account. These differences are taken into consideration
by using load models according to Indian Road congress (IRC: 6-2010) shown in figures
5.4 (a), 5.4(b) and 5.4 (c).
Figure 5.4 (a)
Figure 5.4 (b)
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Figure 5.4 (c)
Indian Road congress (IRC: 6-2010) specify that The minimum clearance, f, between
outer edge of the wheel and the roadway face of the kerb and the minimum clearance, g,
between the outer edges of passing or crossing vehicles on multi-lane bridges shall be as
given below in table 5.2 :
Table 5.2 minimum clearance passing vehicles
Vehicles in adjacent lanes shall be taken as headed in the direction producing maximum
Stresses. The spaces on the carriageway left uncovered by the standard train of vehicles
shall not be assumed as subject to any additional live load unless otherwise shown in
Table 5.3.
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Table 5.3 Load combinations
The minimum width of the two-lane carriageway shall be 7.5m as per Clause 112.1 of
IRC: 5.
The nose to tail spacing between two successive vehicles shall not be less than
90m.
For multi-lane bridges and culverts, each Class AA loading shall be considered to
occupy two lanes and no other vehicle shall be allowed in these two lanes. The
passing/crossing vehicle can only be allowed on lanes other than these two
lanes. Load combination is as shown in Table 2.
The maximum loads for the wheeled vehicle shall be 20 tonne for a single axle or
40 tonne for a bridge of two axles spaced not more than 1.2m centres.
Class AA loading is applicable only for bridges having carriageway width of
5.3m and above (i.e. 1.2 x 2 + 2.9 = 5.3). The minimum clearance between the
road face of the kerb and the outer edge of the wheel or track, ‗C‘, shall be 1.2m.
Axle loads in tone. Linear dimensions in meter.
The above mentioned points can be visualized from figure 5.5.
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Figure 5.5
WHEELED VEHICLE
Class AA Tracked and Wheeled Vehicles (Clause 204.1)
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Chapter 6
VERIFICATION STUDIES
The most important results and discussions of results are presented in this chapter.
The comparison among diffenent type of girders have been done and relevent graphs and
tables have been represented.
6.1 Verification Studies
6.1.1 Reinforced-Concrete Beam
As the software is well known for its accurate analyses and is widely used to
design various kinds of structures both simple and complicated, yet safe, A study for data
validation is to be carried to check the software generated results with the results obtained
by manual calculations.
A simply supported beam carrying a point load was analyzed with the known
formulas (Figure 6.1) manually and the same was modeled in the STAAD.Pro software
with the exact same parameters as were in manual calculations. For the horizontal
element, standard beam element was chosen and was used it as a beam, the supports were
assigned, a hinge at one end and a roller support on the other which simulate a simply
supported condition of the beam carrying point load.
Figure 6.1 Simply supported beam
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The model was then assigned with point load at the center of the beam and the analysis
was carried out. The following results were obtained from the software, which accurately
converged with the manual calculations and the exact values were found. The results and
graphs obtained by the software are shown in figure 6.2, 6.3 and 6.4.
Figure 6.2 SS beam carrying concentrated load
Figure 6.3 BMD for SS beam
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Figure 6.4 SFD for SS beam
In the above example, a 10 meter long beam having hinge and roller support, which is
also known as simple support, when the software was run, it yielded the results for
bending moments and shear forces which are represented in graphs as shown in the
previous figures. From which it is concluded that the finite element model shows
excellent correlation with the hand calculation and that it can be used to carry out further
work in this thesis.
6.1.2 Reinforced-Concrete Slab
Further verification of the validity of finite element models of reinforced-concrete
components may be demonstrated by comparing the predicted response of the model with
Analytical results obtained from ANSYS software of a simply supported.
Concrete slab Load deflection behavior, stress distribution, and crack initiation, three
important results obtained from the model, were compared to values for similar behavior
obtained for the Analytical model in ANSYS. The success of this analytical model will
serve as a precursor to subsequent research of bridge deck analysis.
Hence the Moments due to IRC class 70R and IRC class AA tracked vehicle loads
compared with the results obtained by Mr. Kanchan Sen Gupta et al., [5], were taken into
account for the verification of results. The FE model considered by Kanchan Sen Gupta et
al., [5], was referred and the same was modeled in STAAD.Pro considering all the
dimensions, loads, loading type and loading intensity as was given in the paper. The
analysis was done and the bending moments (kNm/m) generated by STAAD.Pro
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correlated with the results generated by ANSYS. The verified results can be seen in table
6.1 below.
Table 6.1: Bending moment along span (kNm/m)
Span (m)
Slab
Thickness
(mm)
Type of girder
FE Model Rectangular TeeI
section
ISMB
600
10 825
STAAD.Pro 96.1499 107.036 121.92 133.909
ANSYS 105.36 105.38 142.14 149.17
IRC 88.36 92.63 124.41 133.25
From the above table we can see the bending moment generated by both the software and
that specified by Indian Road Congress are tabulated. From the above table we can see
that the results generated by STAAD.Pro are correlating to the moments given by IRC
and converging nearer to the IRC values. Hence with the above verifications, further
work in the thesis is carried out for various girder and loading types.
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Chapter 7
FINITE ELEMENT MODEL
The modeling is to be carried out by using a standard FEA package which helps in
proper modeling and accurate analysis of the deck for various parameters of loads,
loading types and type of structural elements. An attempt is to be made to develop a
virtual model using the software to obtain the results for forces, displacements, bending
moments etc. in simulated models which can be used further for the purpose of analysis.
7.1 Model Characteristics
7.1.1 FE Mesh
The slab was modeled using a plate element and it was divided into finite element
mesh which consists of shell elements. The shell elements representing the slab were
0.5m by 0.5m quadrilateral shell elements with four nodes and six degrees of freedom per
node. The slab has constant length of 10m and constant width of 12m. This resulted in a
slab model with 525 nodes, 480 plates and 3,150 degrees of freedom. A sketch of the
finite element mesh is shown in Figure 7.1.
Figure 7.1: Isometric View of Model of Concrete Slab with supporting girders.
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In the model illustrated above, the horizontal elements used are the standard beam
elements, and the slab is modeled using the plate element. The plate element was divided
into fragments of size 0.5m X 0.5m quadrilateral shell elements. The whole slab is
divided into these quadrilateral elements which behave as individual plates adjacent toeach other. These plates have all the characteristics as same as the concrete slab as a
whole. These plates can handle stresses individually. The reason behind the discretization
of the plate is to simplify the study of stresses developed in the slab. The center stress and
the corner stress of each individual plate can be known and can be accounted for the
analysis of the deck.
7.1.2 Model View Details
A total of four types of girders were selected to model the bridge deck. The deck
was modeled with constant lateral dimensions of 10m long by 12m wide for all the girder
types. Thought the thickness of the deck varies from 375mm to 825mm according to the
standard drawings provided by Ministry of Road Transport & Highways (MORT&H).
The detailed models for each girder type are illustrated with the help of following figures.
As per the standard drawings by MORT & H the following parameters were considered in
modeling the structure.
• Span = 10 m.
• Slab thickness = 375mm To 825mm
• Type of support = Simple support
• Type of girder:
–
Rectangular Beam Girder
– Tee Beam Girder
– I section concrete girder
–
Indian Standard steel section girder
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Department of Civil Engineering, S.D.M.C.E.T, Dharwad. Page 30
Bridge Deck with Rectangular Girder
In this model, the slab is resting on a 10m long rectangular girder of size 1.2m
deep and 1m wide. The slab has constant lateral dimensions and varying thicknesses. A
total of 8 numbers of cases were considered with slab thicknesses being 375mm, 425mm,
475mm, 525mm, 575mm, 675mm, 745mm and 825mm. an illustrative example is shown
in figure 7.2 below. The Poisson‘s ratio is taken as 0.17 and modulus of elasticity of
concrete as 21.7kN/mm2.
Figure 7.2: Bridge Deck Resting on Rectangular Girder
The girders are simply supported i.e. hinge support at one end and roller support on the
other. This way the moments and forces along Z direction are released as one end of the
supports is free to move laterally along Z direction. The slab rests on top of the girders i.e.
the bottom fibers of the slab are in contact with the top fibers of the girders. This way the
forces imposing on the slab will have a continuous path of flow through the girders to the
supports.
Bridge Deck with Tee beam Girder
In this model, the slab is resting on a 10m long Tee-beam girder of size 1.2m deep
and 1m wide with 0.3m thick web. The slab has constant lateral dimensions and varying
thicknesses. A total of 8 numbers of cases were considered with slab thicknesses being
375mm, 425mm, 475mm, 525mm, 575mm, 675mm, 745mm and 825mm. an illustrativeexample is shown in figure 7.3 and 7.4 below. The Poisson‘s ratio is taken as 0.17 and
modulus of elasticity of concrete as 21.7kN/mm2.
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Figure 7.3: Bridge Deck Resting on Tee Girder
Figure 7.4: Sectional Properties of Prismatic Tee beam
The girders are simply supported i.e. hinge support at one end and roller support on the
other. This way the moments and forces along Z direction are released as one end of the
supports is free to move laterally along Z direction. The slab rests on top of the girders i.e.
the bottom fibers of the slab are in contact with the top fibers of the girders. This way the
forces imposing on the slab will have a continuous path of flow through the girders to the
supports.
Bridge Deck with I section concrete Girder
In this model, the slab is resting on a 10m long I section concrete girder of size
1.2m deep and 1m wide with 0.3m thick web. The slab has constant lateral dimensions
and varying thicknesses. A total of 8 numbers of cases were considered with slab
thicknesses being 375mm, 425mm, 475mm, 525mm, 575mm, 675mm, 745mm and
825mm. an illustrative example is shown in figure 7.5 and 7 .6 below. The Poisson‘s ratio
is taken as 0.17 and modulus of elasticity of concrete as 21.7kN/mm2.
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PERFORMANCE BASED ANALYSIS OF BRIDGE DECK FOR DISTINCTIVE GIRDER TYPES
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Figure 7.5: Bridge Deck Resting on I section concrete Girder
Figure 7.6: Sectional Properties of I section concrete beam
The girders are simply supported i.e. hinge support at one end and roller support on the
other. This way the moments and forces along Z direction are released as one end of the
supports is free to move laterally along Z direction. The slab rests on top of the girders i.e.
the bottom fibers of the slab are in contact with the top fibers of the girders. This way the
forces imposing on the slab will have a continuous path of flow through the girders to the
supports.
Bridge Deck with Indian Standard ISMB 600 steel Girder
In this model, the slab is resting on a 10m long ISMB 600 steel girder of size 0.6m
deep and 0.21m wide with 0.012m thick web. The slab has constant lateral dimensions
and varying thicknesses. A total of 8 numbers of cases were considered with slab
thicknesses being 375mm, 425mm, 475mm, 525mm, 575mm, 675mm, 745mm and
825mm. an illustrative example is shown in figure 7.7, 7.8 and 7.9 below. The Poisson‘s
ratio is taken as 0.17 and modulus of elasticity of concrete as 21.7kN/mm2.
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PERFORMANCE BASED ANALYSIS OF BRIDGE DECK FOR DISTINCTIVE GIRDER TYPES
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Figure 7.7: Bridge Deck Resting on ISMB 600 steel Girder
Figure 7.8: Sectional properties of ISMB 600 steel Girder
Figure 7.9: Material Properties of ISMB 600 steel Girder
The girders are simply supported i.e. hinge support at one end and roller support on the
other. This way the moments and forces along Z direction are released as one end of the
supports is free to move laterally along Z direction. The slab rests on top of the girders i.e.
the bottom fibers of the slab are in contact with the top fibers of the girders. This way the
forces imposing on the slab will have a continuous path of flow through the girders to the
supports.
A total of 32 numbers of models were created for the purpose of analysis for
banding moments and stresses. The models were then subjected to self-weight and
various vehicle loads moving over the deck in the direction along span. Which arediscussed in detail in the following chapters.
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PERFORMANCE BASED ANALYSIS OF BRIDGE DECK FOR DISTINCTIVE GIRDER TYPES
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Chapter 8
LOADS
8.1 Self-weight
The self-weight of the structure was calculated from the geometry of the bridge
section. The modulus of elasticity of concrete was taken as 21.7kN/m3 and Poisson‘s
ratio 0.17. As shown in table 8.1.
Table 8.1: Material properties
8.2 Vehicle Loads
The deck was subjected to vehicle loads. Mainly two kinds of loads were chosen
from the standard specifications of IRC: 6 – 2010, Standard specifications and code of
practice for Road Bridges, Section: II – Loads and Stresses, Fifth Revision. [13]. Shown
in figures 8.1 and 8.2.
– IRC Class 70R Tracked load
– IRS Class AA Tracked load
The loads were placed one by one on the deck for each model. The loads were placed
mainly in two forms.
– Edge Loading
– Center loading
The edge loading is primarily a load which is placed on the edge of the deck with
minimum clear edge distance specified in IRC: 6 – 2010. [13]. the details for minimum
edge distance and the minimum distance between adjacent vehicles for IRC class 70Rtracked and wheeled vehicle and IRC class AA tracked and wheeled vehicle are shown in
figure 8.4 and figure 8.5 below.
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PERFORMANCE BASED ANALYSIS OF BRIDGE DECK FOR DISTINCTIVE GIRDER TYPES
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Figure 8.1: CLASS 70R TRACKED & WHEELED VEHICLES (CLAUSE 204.1)
Figure 8.2: CLASS AA TRACKED VEHICLES (CLAUSE 204.1)
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Figure 8.3: Wheel arrangement for 70R
Figure 8.4: Clear Carriageway width
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PERFORMANCE BASED ANALYSIS OF BRIDGE DECK FOR DISTINCTIVE GIRDER TYPES
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The minimum clearance, f, between outer edge of the wheel and the roadway face of the
kerb and the minimum clearance, g, between the outer edges of passing or crossing
vehicles on multi-lane bridges shall be as given in table 8.2 below:
Table 8.2: minimum carriageway width
8.3 Load Combinations
Vehicles in adjacent lanes shall be taken as headed in the direction producing maximum
Stresses. The spaces on the carriageway left uncovered by the standard train of vehicles
shall not be assumed as subject to any additional live load unless otherwise shown in
Table 8.3.
Table 8.3: Live load combinations
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PERFORMANCE BASED ANALYSIS OF BRIDGE DECK FOR DISTINCTIVE GIRDER TYPES
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Chapter 9
INVESTIGATIONS
The most important results and discussions of the analysis are presented in this
chapter. The results of deck slab analyses have been tabulated. The comparison among
diffenent type of girders have been done and relevent graphs and tables have been
represented.
9.1 FE Analyses
Finite element analysis has been carried out with the following considerations.
1. IRC Class 70R Loading on the Edge and at the Centre.
2. IRC Class AA Loading on the Edge and at the Centre.
The above mentioned load classes are considered for different thickness of the deck slab
varying from 375mm to 825mm and also for different type of girders supporting the deck
slab for a constant span of 10m.
A total of 128 numbers of load cases were analyzed and maximum bending
moments along span were compared with those obtained from Cl. 305.16.2. (1) Of IRC:
21 – 2000.
The results are tabulated in a systematic manner in this chapter. We can see the
variation of maximum bending moments acting on the deck along span for the two IRC
load classes and for different girder types. Tables, stress contours and graphs help
understand the results better, which are as shown in the following part of this chapter.
9.1.1 Bridge Deck with Rectangular Girder
The load classes, Class 70R and Class AA are considered for different thickness
of the deck slab varying from 375mm to 825mm with 4 numbers of rectangular girders of
1.2m deep and 1m wide, supporting the deck slab for a span of 10m and carriageway
width of 12m. The results obtained are tabulated in table 9.1, and the graphical
representation is shown in figure 9.1.
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Table 9.1: Maximum Bending moment (kN-m/m) along span
Span
(m)
Deck
Thickness
(mm)
Girder type
Rectangular
Centered Loading Edge Loading
70R AA 70R AA
10
375 91.72 102.45 115.37 127.17
425 92.18 102.93 116.04 127.86
475 92.65 103.42 116.74 128.57
525 93.14 103.92 117.45 129.30
575 93.63 104.43 118.17 130.05
675 94.63 105.47 119.65 131.58
745 95.34 106.20 120.71 132.66
825 96.15 107.04 121.92 133.91
Figure 9.1 Graphical representation
90.00
95.00
100.00
105.00
110.00
115.00
120.00
125.00
130.00
135.00
375 425 475 525 575 675 745 825
Class AA-Edge
70R-Edge
Class AA-Center
70R center
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From the above table and graph, we can see that the maximum bending moment along the
span increases with the increasing thickness of deck slab.
For both the classes i.e. class 70R as well as class AA, the bending moment is
seen to have higher values for Edge loading and comparatively lower values for Centered
loading. This is caused because the vehicle load placed on the slab is eccentric and the
load is placed at a distance from the center and hence the axle load is not distributed
equally among all the girders.
The stress contour diagrams show a visual representation of the stresses caused due to the
vehicle loads placed on the edge and at the center as shown in figure 9.2, 9.3, 9.4, 9.5 and
9.6.
Fig 9.2: Stress contours showing bending moment pattern across the deck area caused
due to self-weight of the structure. (Max BM= 147.3 kN-m/m)
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Fig 9.3: Stress contours showing bending moment pattern across the deck area caused
due to IRC class 70R edge loading. (Max BM= 121.92 kN-m/m)
Fig 9.4: Stress contours showing bending moment pattern across the deck area caused
due to IRC class 70R center loading. (Max BM= 96.15 kN-m/m)
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Fig 9.5: Stress contours showing bending moment pattern across the deck area caused
due to IRC class AA edge loading. (Max BM= 133.9 kN-m/m)
Fig 9.6: Stress contours showing bending moment pattern across the deck area caused
due to IRC class AA center loading. (Max BM= 107.03 kN-m/m)
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9.1.2 Bridge Deck with Prismatic Tee Beam Girder
The load classes, Class 70R and Class AA are considered for different thickness
of the deck slab varying from 375mm to 825mm with 4 numbers of prismatic Tee beam
girders of 1.2m deep and 1m wide with 0.3m thick web, supporting the deck slab for a
span of 10m and carriageway width of 12m. The results obtained are tabulated in table
9.2, and the graphical representation is shown in figure 9.7.
Table 9.2: Maximum Bending moment (kN-m/m) along span
Span
(m)
Deck
Thickness
(mm)
Girder type
Prismatic Tee beam
Centered Loading Edge Loading
70R AA 70R AA
10
375 92.62 103.38 116.65 128.48
425 93.37 104.16 117.74 129.60
475 94.17 104.98 118.89 130.78
525 95.01 105.84 120.09 132.02
575 95.87 106.73 121.33 133.29
675 97.63 108.55 123.88 135.92
745 98.88 109.84 125.69 137.78
825 100.30 111.31 127.75 139.90
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Fig 9.7 Graphical representation
From the above table and graph, we can see that the maximum bending moment along the
span increases with the increasing thickness of deck slab.
For both the classes i.e. class 70R as well as class AA, the bending moment is
seen to have higher values for Edge loading and comparatively lower values for Centered
loading. This is caused because the vehicle load placed on the slab is eccentric and theload is placed at a distance from the center and hence the axle load is not distributed
equally among all the girders.
The stress contour diagrams show a visual representation of the stresses caused
due to the vehicle loads placed on the edge and at the center as shown in figure 9.8, 9.9,
9.10, 9.11 and 9.12.
90.00
100.00
110.00
120.00
130.00
140.00
150.00
375 425 475 525 575 675 745 825
Class AA-Edge
70R-Edge
Class AA-Center
70R center
Thickness (mm)
Prismatic Tee beam
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Fig 9.8: Stress contours showing bending moment pattern across the deck area caused
due Self-weight of the structure. (Max BM= 111.3 kN-m/m)
Fig 9.9: Stress contours showing bending moment pattern across the deck area caused
due IRC class 70R center loading. (Max BM= 100.3 kN-m/m)
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Fig 9.10: Stress contours showing bending moment pattern across the deck area caused
due IRC class AA center loading. (Max BM= 111.3 kN-m/m)
Fig 9.11: Stress contours showing bending moment pattern across the deck area caused
due IRC class 70R edge loading. (Max BM= 127.75 kN-m/m)
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Fig 9.12: Stress contours showing bending moment pattern across the deck area caused
due IRC class 7AA edge loading. (Max BM= 139.9 kN-m/m)
9.1.3 Bridge Deck with I section concrete Girder
The load classes, Class 70R and Class AA are considered for different thickness
of the deck slab varying from 375mm to 825mm with 4 numbers of I section concrete
girders of 1.5m deep and 1m wide with 0.3m thick web, supporting the deck slab for aspan of 10m and carriageway width of 12m. The results obtained are tabulated in table
9.3, and the graphical representation is shown in figure 9.13.
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Table 9.3: Maximum Bending moment (kN-m/m) along span
Span
(m)
Deck
Thickness
(mm)
Girder type
I Section (Concrete)
Centered Loading Edge Loading
70R AA 70R AA
10
375 91.66 102.40 115.30 127.09
425 92.11 102.86 115.95 127.76
475 92.58 103.34 116.63 128.46
525 93.05 103.83 117.33 129.18
575 93.54 104.34 118.05 129.92
675 94.53 105.37 119.52 131.44
745 95.25 106.10 120.58 132.53
825 96.07 106.96 121.82 133.80
Fig 9.13 Graphical representation
90.00
100.00
110.00
120.00
130.00
140.00
150.00
375 425 475 525 575 675 745 825
Class AA-Edge
70R-Edge
Class AA-Center
70R center
Thickness (mm)
I Section Concrete
Girder
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From the above table and graph, we can see that the maximum bending moment along the
span increases with the increasing thickness of deck slab.
For both the classes i.e. class 70R as well as class AA, the bending moment is
seen to have higher values for Edge loading and comparatively lower values for Centered
loading. This is caused because the vehicle load placed on the slab is eccentric and the
load is placed at a distance from the center and hence the axle load is not distributed
equally among all the girders.
The stress contour diagrams show a visual representation of the stresses caused
due to the vehicle loads placed on the edge and at the center as shown in figure 9.14, 9.15,
9.16, 9.17 and 9.18.
Fig 9.14: Stress contours showing bending moment pattern across the deck area caused
due self-weight of the structure. (Max BM= 60.32 kN-m/m)
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Fig 9.15: Stress contours showing bending moment pattern across the deck area caused
due IRC class 70R center loading. (Max BM= 96.0 kN-m/m)
Fig 9.16: Stress contours showing bending moment pattern across the deck area caused
due IRC class AA center loading. (Max BM= 106.96 kN-m/m)
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Fig 9.17: Stress contours showing bending moment pattern across the deck area caused
due IRC class 70R edge loading. (Max BM= 121.8 kN-m/m)
Fig 9.18: Stress contours showing bending moment pattern across the deck area caused
due IRC class AA edge loading. (Max BM= 133.8 kN-m/m)
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9.1.4 Bridge Deck with ISMB 600 Steel Girder
The load classes, Class 70R and Class AA are considered for different thickness
of the deck slab varying from 375mm to 825mm with 4 numbers of I section concrete
girders of 1.5m deep and 1m wide with 0.3m thick web, supporting the deck slab for a
span of 10m and carriageway width of 12m. The results obtained are tabulated in table
9.4, and the graphical representation is shown in figure 9.19.
Table 9.4: Maximum Bending moment (kN-m/m) along span
Span
(m)
Deck
Thickness
(mm)
Girder type
ISMB 600 steel section
Centered Loading Edge Loading
70R AA 70R AA
10
375 98.99 109.94 125.56 137.64
425 101.23 112.25 128.68 140.86
475 103.45 114.53 131.77 144.03
525 105.59 116.74 134.73 147.08
575 107.62 118.83 137.55 149.97
675 111.27 122.60 142.62 155.18
745 113.50 124.90 145.76 158.38
825 115.74 127.20 148.98 161.60
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Fig 9.19 Graphical representation
From the above table and graph, we can see that the maximum bending moment along the
span increases with the increasing thickness of deck slab.
For both the classes i.e. class 70R as well as class AA, the bending moment is
seen to have higher values for Edge loading and comparatively lower values for Centered
loading. This is caused because the vehicle load placed on the slab is eccentric and theload is placed at a distance from the center and hence the axle load is not distributed
equally among all the girders.
The stress contour diagrams show a visual representation of the stresses caused
due to the vehicle loads placed on the edge and at the center as shown in figure 9.20, 9.21,
9.22, 9.23 and 9.24.
90.00
100.00
110.00
120.00
130.00
140.00
150.00
160.00
170.00
375 425 475 525 575 675 745 825
Class AA-Edge
70R-Edge
Class AA-Center
70R center
Thickness (mm)
ISMB 600 Steel
girder
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Fig 9.20: Stress contours showing bending moment pattern across the deck area caused
due to self-weight of the structure. (Max BM= 195.22 kN-m/m)
Fig 9.21: Stress contours showing bending moment pattern across the deck area caused
due IRC class 70R center loading. (Max BM= 115.74 kN-m/m)
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Fig 9.22: Stress contours showing bending moment pattern across the deck area caused
due IRC class AA center loading. (Max BM= 127.2 kN-m/m)
Fig 9.23: Stress contours showing bending moment pattern across the deck area caused
due IRC class 70R edge loading. (Max BM= 148.98 kN-m/m)
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Fig 9.24: Stress contours showing bending moment pattern across the deck area caused
due IRC class AA edge loading. (Max BM= 161.6 kN-m/m)
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Chapter 10
ANALYSYS RESULTS AND DISCUSSIONS
10.1 RESULTS
The above results obtained from analysis output given by STAAD.Pro software
are studied and they are tabulated together to know the differences of bending moments
between the four type of girders which were considered i.e. rectangular girder, prismatic
Tee beam, I section concrete girder and ISMB 600 steel girder.
The thesis presents the results of an investigation of concrete bridge deck slabsusing finite-element analysis. Simply supported deck slabs were considered for various
girder types & load cases. Total 128 load cases were analyzed and maximum bending
moments along span were compared.
The comparison among all 128 cases is shown in a tabular form as well as in
graphical representation for better understanding of result values generated by the
software.
Table 10.1 shows the systematic arrangement of result values obtained from
analyses results, which show maximum bending moment occurred due to the two load
classes considered i.e. IRC 70R load class and IRC AA load class, loaded on the edge and
at the center for all four girder types.
The span of slab was taken as 10m for all load cases as well as lateral dimension
of the slab (length and width) was kept same (10m X 12m) for each load case. And the
thickness of deck was varied from 375mm to 825mm for each load case. The results areshown in table 10.1 below followed by graphical representation of result comparison
shown in fig 10.1,
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7 0 R
A A
7 0 R
A A
7 0 R
A A
7 0 R
A A
7 0 R
A A
7 0 R
A A
7 0 R
A A
7 0 R
A A
3 7 5
9 1 . 7 2
1 0 2 . 4 5
1 1 5 . 3 7
1 2 7 . 1 7
9 2 . 6 2
1 0 3 . 3 8
1 1 6 . 6 5
1 2 8 . 4 8
9 1 . 6 6
1 0 2 . 4 0
1 1 5 . 3 0
1 2 7 . 0 9
9 8 . 9 9
1 0 9 . 9 4
1 2 5 . 5 6
1 3 7 . 6 4
4 2 5
9 2 . 1 8
1 0 2 . 9 3
1 1 6 . 0 4
1 2 7 . 8 6
9 3 . 3 7
1 0 4 . 1 6
1 1 7 . 7 4
1 2 9 . 6 0
9 2 . 1 1
1 0 2 . 8 6
1 1 5 . 9 5
1 2 7 . 7 6
1 0 1 . 2 3
1 1 2 . 2 5
1 2 8 . 6 8
1 4 0 . 8 6
4 7 5
9 2 . 6 5
1 0 3 . 4 2
1 1 6 . 7 4
1 2 8 . 5 7
9 4 . 1 7
1 0 4 . 9 8
1 1 8 . 8 9
1 3 0 . 7 8
9 2 . 5 8
1 0 3 . 3 4
1 1 6 . 6 3
1 2 8 . 4 6
1 0 3 . 4 5
1 1 4 . 5 3
1 3 1 . 7 7
1 4 4 . 0 3
5 2 5
9 3 . 1 4
1 0 3 . 9 2
1 1 7 . 4 5
1 2 9 . 3 0
9 5 . 0 1
1 0 5 . 8 4
1 2 0 . 0 9
1 3 2 . 0 2
9 3 . 0 5
1 0 3 . 8 3
1 1 7 . 3 3
1 2 9 . 1 8
1 0 5 . 5 9
1 1 6 . 7 4
1 3 4 . 7 3
1 4 7 . 0 8
5 7 5
9 3 . 6 3
1 0 4 . 4 3
1 1 8 . 1 7
1 3 0 . 0 5
9 5 . 8 7
1 0 6 . 7 3
1 2 1 . 3 3
1 3 3 . 2 9
9 3 . 5 4
1 0 4 . 3 4
1 1 8 . 0 5
1 2 9 . 9 2
1 0 7 . 6 2
1 1 8 . 8 3
1 3 7 . 5 5
1 4 9 . 9 7
6 7 5
9 4 . 6 3
1 0 5 . 4 7
1 1 9 . 6 5
1 3 1 . 5 8
9 7 . 6 3
1 0 8 . 5 5
1 2 3 . 8 8
1 3 5 . 9 2
9 4 . 5 3
1 0 5 . 3 7
1 1 9 . 5 2
1 3 1 . 4 4
1 1 1 . 2 7
1 2 2 . 6 0
1 4 2 . 6 2
1 5 5 . 1 8
7 4 5
9 5 . 3 4
1 0 6 . 2 0
1 2 0 . 7 1
1 3 2 . 6 6
9 8 . 8 8
1 0 9 . 8 4
1 2 5 . 6 9
1 3 7 . 7 8
9 5 . 2 5
1 0 6 . 1 0
1 2 0 . 5 8
1 3 2 . 5 3
1 1 3 . 5 0
1 2 4 . 9 0
1 4 5 . 7 6
1 5 8 . 3 8
8 2 5
9 6 . 1 5
1 0 7 . 0 4
1 2 1 . 9 2
1 3 3 . 9 1
1 0 0 . 3 0
1 1 1 . 3 1
1 2 7 . 7 5
1 3 9 . 9 0
9 6 . 0 7
1 0 6 . 9 6
1 2 1 . 8 2
1 3 3 . 8 0
1 1 5 . 7 4
1 2 7 . 2 0
1 4 8 . 9 8
1 6 1 . 6 0
I S M B 6 0
0 S t e e l
C e n t e r e d L o a d i n g
E
d g e L o a d i n g
C e n t e r e d L o a d i n g
E d g e L o a d i n g
C e n t e r e d L o a d i n g
E d g e L o a d i n g
C e n t e r e d L o a d i n g
E d g e L o a d i n g
S p a n ( m )
D e c k
T h i c k n e s s
( m m )
R e c t a n g u l a r
P r i s m a t i c T e e B e a m
I s e c t i o n ( C
o n c r e t e )
1 0
G i r d e r t y p e
T a b l e 8 . 1 : M a x i m u m l o n g i t u d i n a l b e n d i n g m o m e n t ( k N - m / m )
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Figure 10.1: Longitudinal Bending moments (kNm/m) for IRC Class 70R-center loading.
Figure 10.2: Longitudinal Bending moments (kNm/m) for IRC Class A - center loading.
85.00
90.00
95.00
100.00
105.00
110.00
115.00
120.00
125.00
375 425 475 525 575 675 745 825
ISMB 600
I section
Tee
Rect
70R center70R
Class 70R
center
loading
70R
Thickness(mm)
95.00
100.00
105.00
110.00
115.00
120.00
125.00
130.00
375 425 475 525 575 675 745 825
ISMB 600
I section
Tee
Rect
Class AA
center
loading
Thickness
(mm)
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Figure 10.3: Longitudinal Bending moments (kNm/m) for IRC Class 70R – edge loading
Figure 10.4: Longitudinal Bending moments (kNm/m) for IRC Class AA – edge loading
105.00
115.00
125.00
135.00
145.00
155.00
165.00
375 425 475 525 575 675 745 825
ISMB 600
I section
Tee
Rect
Class
70R- edge
loading
Thickness(mm)
115.00
120.00
125.00
130.00
135.00
140.00
145.00
150.00
155.00
160.00
165.00
375 425 475 525 575 675 745 825
ISMB 600
I section
Tee
Rect
Class AAEdge loading
Thickness
(mm)
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10.2 DISCUSSIONS
The maximum longitudinal bending moments were obtained at the critical cross
section of each slab/ load case, typically located at or near mid span and edge, for the
various cases considered. Figure 10.1, 10.2, 10.3 and 10.4 show the maximum
longitudinal moment distribution across the critical width of two-lane bridges with no
shoulders for the various girder types analyzed, and considering centered and edge loads
for IRC Class 70R loading and IRC Class AA loading. It is worth noting that under edge
load condition, the maximum FEA design bending moment in the slab was defined as the
first maximum peak value after the edge moment value. This maximum design moment
near the edge is assumed to be resisted by the deck slab. Figures 10.3 and 10.4 compare
the results of the maximum FEA longitudinal moment distributions due to edge loading
of IRC Class 70R loading and IRC Class AA loading placed 1.2m from the edge of deck
slab.
Figures 10.1 and 10.2 compare the results of the maximum FEA longitudinal
moment distributions due to center loading of IRC Class 70R loading and IRC Class AA
loading placed at the center of deck slab.
The average bending moment in the middle strip is essentially the same regardless
to the position of wheel loads from the edge i.e. center loading, as the loads are equally
distributed over each girder, supporting the deck. Slab bridges subject to centered load
and edge load for IRC class 70R and IRC class AA and the maximum FEA bending
moments due to these loads are summarized in Table 9.1, 9.2, 9.3 and 9.4.
The comparison among Maximum bending moments due to all the load cases and
all the girder types are combined and summarized in Table 10.1. And also the graphical
representation for all the cases is shown in Figure 10.1, 10.2, 10.3 and 10.4.
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Chapter 11
CONCLUSION
11.1 Summary
This Thesis presented the results of an investigation of reinforced concrete slab
bridges using finite-element analysis. Simply supported one-span bridges were considered
with constant span lengths, various girder supports and various loading conditions for
cases without shoulders.
The most important results and discussions of analysis are presented in the thesis.A total of 128 case study bridges were analyzed. The results obtained from analysis
output given by STAAD.Pro software are studied and they are tabulated together to know
the differences of bending moments between the four type of girders which were
considered i.e. rectangular girder, prismatic Tee beam, I section concrete girder and
ISMB 600 steel girder.
The maximum longitudinal bending moments were compared with IRC design
procedures for verification of the results and further study was carried out considering
various types of girders and load classes. The maximum longitudinal bending moments
were obtained at the critical cross section of each slab/ load case, typically located at or
near mid span and edge, for the various cases considered.
The comparison is done among results of the maximum FEA longitudinal moment
distributions due to center loading of IRC Class 70R loading and IRC Class AA loading
placed at the center of deck slab. Slab bridges subject to centered load and edge load for
IRC class 70R and IRC class AA and the maximum FEA bending moments due to these
loads are summarized.
The comparison among Maximum bending moments due to all the load cases and
all the girder types are combined and summarized and also the graphical representation
for all the cases is shown in appropriate tables and figures in respective chapters. The
main interest of this report was to study the difference between the bending moments of
various girder types supporting the bridge deck.
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11.2 Conclusion
Based on the results of this investigation, the following conclusions can be drawn
regarding the maximum longitudinal bending moments:
The accuracy of the model was validated. The STAAD.Pro software calculates
accurate results and predicts behavior not generally obtained through manual
calculations. The capability of the software is to represent the model to predict
deflections, strains, and stresses while minimizing unnecessary complexities.
The maximum longitudinal bending moments caused due to IRC class 70R center
loading for deck slab with rectangular girder and I section concrete girder show a
correlation between them. The maximum bending moment values are seen to be
nearly equal to each other with only slight differences in the values.
For IRC class AA edge loading and IRC class AA center loading, the maximum
bending moments along span for rectangular girder converge with I section
concrete girder.
In case of IRC class 70R Edge loading, the moments are seen to vary with the
type of girder as well as the thickness of the girder. No moment value is
converging with other in this case. Also the maximum bending moment values
increase with the increasing thickness of the deck slab.
For Both the load classes and all the load cases considered, ISMB-600 steel girder
is seen to produce higher bending moment values for both edge loading and center
loading. The values for ISMB-600 girder are much greater when compared with
the other two types of girders.
The thickness of deck slab also contributes a major role in carrying the vehicle
loads. The increase in thickness will reduce the loss in ultimate Moment carryingcapacity of the deck.
Other positive effects will be in the deck-girder system. There will be increase in
section Modulus; hence there will be decrease in the maximum deck stress and
live load deflection.
Increasing the deck thickness will also help distribute deck live loads more evenly
to the girders.
The only negative effects of increasing the deck thickness will be increases in thedeck unit Weight. However, increasing the deck thickness would also increase the
deck service life. This should increase the durability and longevity of the decks.
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11.3 Scope for Future Studies
As one part, future studies can be performed as a continuation on this thesis. The
results obtained and conclusions drawn were based on several assumptions regarding
geometry and boundary conditions. As a future study, these boundary conditions can be
varied in order to find an improved way of modeling. In this thesis a rather limited
evaluation of boundary conditions was performed, which can be further refined. Also the
geometry should be varied in order to verify that the conclusions are valid for geometrical
variations for bridges of the same type. This could be made as a parameter study where
the slab bridge and frame slab bridge are modeled with varying length and width and also
with various other types of supporting elements. As another part of further studies, a
continuation on existing research fields can be resumed.
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REFERENCES
[1] L. Deng, C.S. Cai., ―Identification of parameters of vehicles moving on bridges‖,
Engineering Structures 31 (2009) 2474_2485.[2] S.S. Law., J.Q. Bu., X.Q. Zhu., S.L. Chan., ―Vehicle axle loads identification
using finite element method‖, Engineering Structures 26 ( 2004) 1143 – 1153.
[3] Adrian Kidarsa., Michael H. Scott., Christopher C. Higgins., ―Analysis of moving
loads using force- based finite elements‖, Finite Elements in Analysis and Design
44 (2008) 214 – 224.
[4] L. Yu., Tommy H.T. Chan., ―Recent research on identification of moving loads on
bridges‖, Journal of Sound and Vibration 305 (2007) 3– 21.
[5] Kanchan Sen Gupta., Somnath Karmakar., ―Investigations on simply supported
concrete bridge deck slab for IRC vehicle loadings using finite element analysis‖,
International Journal of Earth Sciences and Engineering ISSN 0974-5904, Volume
04, No 06 SPL, October 2011, pp 716-719.
[6] Claude Broquet., Simon., Bailey., Mario Fafard., and Eugen Bruhwiler.,
―Dynamic behavior of deck slabs of concrete road‖, Journal of Bridge
Engineering, Vol. 9, No. 2, March 1, 2004. ©ASCE, ISSN 1084-0702/2004/2-
137 – 146.
[7] Daniel M. Balmer., and George E. Ramey., ―Effects of bridge deck thickness on
properties and behavior of bridge decks‖, Practice Periodical on Structural Design
and construction, Vol. 8, No. 2, May 1,2003. ©ASCE, ISSN 1084-0680/2003/2-
83 – 93.
[8] Lina Ding., Hong Hao., Xinqun Zhu., ―Evaluation of dynamic vehicle axle loads
on bridges with different surface conditions‖, Journal of Sound and Vibration 323
(2009) 826 – 848.
[9] M. Mabsout., K. Tarhini., R. Jabakhanji., E. Awwad., ―Wheel Load Distribution
in Simply Supported Concrete Slab Bridges‖, Journal of Bridge Engineering, Vol.
9, No. 2, March 1, 2004. ©ASCE, ISSN 1084-0702/2004/2-147 – 155.
[10] I.K. Fang., Member, ASCE, J. Worley., N. H. Burns., Member, ASCE, R. E.
Klingner., Member, ASCE, ―Behavior Of Isotropic R / C Bridge Decks On Steel
Girders‖, Journal of Structural Engineering, Vol. 116, No. 3, March, 1990.
©ASCE, ISSN 0733-9445/90/0003-0659. Paper No.24413.
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PERFORMANCE BASED ANALYSIS OF BRIDGE DECK FOR DISTINCTIVE GIRDER TYPES
Department of Civil Engineering, S.D.M.C.E.T, Dharwad. Page 66
[11] L. Charlie Cao., P. Benson Shing., Member, ASCE., ―Simplified Analysis
Method For Slab-On-Girder Highway Bridge Decks‖, Journal of Structural
Engineering, Vol. 125, No. 1, January, 1999. ASCE, ISSN 0733-9445/99/0001-
0049 – 0059. Paper No. 16124.[12] J.L. Zapico., M.P. Gonzalez., M.I. Friswell., C.A. Taylor., A.J. Crewe., ―Finite
element model updating of a small scale bridge‖, Journal of Sound and Vibration
268 (2003) 993 – 1012 Journal of Sound and Vibration 268 (2003) 993 – 1012.
[13] Y.B. Yang., C.W. Lin., ―Vehicle– bridge interaction dynamics and potential
applications‖, Journal of Sound and Vibration 284 (2005) 205– 226.
[14] R. Michael Biggs, Graduate Research Assistant; Furman W. Barton, Ph.D., P.E.
Faculty Research Scientist; Jose P. Gomez, Ph.D., P.E, Senior Research Scientist;
Peter J. Massarelli, Ph.D., Faculty Research Associate; Wallace T. McKeel, Jr.,
P.E., Research Manager, ―Final Report, Finite Element Modeling of Reinforced
Concrete Bridge Decks ", Virginia Transportation Research Council In
Cooperation with the U.S. Department of Transportation Federal Highway
Administration, Charlottesville, Virginia, September 2000, VTRC 01-R4.
[15] Adnan Jukic., Kristoffer Ekfeldt., ―A comparative analysis between 3D shell and
2D frame models‖, Master of Science Thesis in the Master‘s Programme,
Structural Engineering and Building Performance Design.
[16] IRC: 6 – 2010, Standard specifications and code of practice for Road Bridges,
Section: II – Loads and Stresses, Fifth Revision.
[17] IRC: 21 – 2000, Standard specifications and code of Practice for Road Bridges,
Section: III – Cement Concrete (Plain and Reinforced), Third Revision.
[18] Ministry of Road Transport & Highway (MORT &H) (1991), ―Standard
Drawings for Road Bridges ", Drg. Nos. SD/107 to SD/122.
[19]
Leslaw Kwasniewski., Hongyi Li., JerryWekezer., Jerzy Malachowski., ―Finite
element analysis of vehicle –bridge interaction‖, Finite Elements in Analysis and
Design 42 (2006) 950 – 959.
[20] Junbo Jia., Anders Ulfvarson., ―Dynamic analysis of vehicle–deck interactions‖,
Ocean Engineering 33 (2006) 1765 – 1795.
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APPENDIX
BRIDGE DESIGN USING THE STAAD.PRO/BEAVA
The combination of STAAD.pro and STAAD.beava can make your bridge design and
analysis easier. STAAD.pro is first used to construct the bridge geometry and
STAAD.beava is used to find the IRC load positions that will create the maximum load
response. The maximum load response could be any of the following:
1. Maximum plate stresses, moment about the local x axis of a plate (Mx), moment
about the local y axis of a plate (My) etc. used to design for concrete deck
reinforcement.
2.
Maximum support reactions to design isolated, pile cap, and mat foundations.
3. Maximum bending moment or axial force in a member used to design members as
per the IRC code.
4. Maximum deflection at mid span.
These loads that create the maximum load responses can be transferred into STAAD.pro
as load cases to load combinations for further analysis and design.
Creating the Bridge Geometry/Structural Analysis
Fig 1: Bridge Dimensions
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Fig 2: Completed Bridge Model in STAAD.pro
1. Open STAAD.pro with the units of kN-M and use the Space option.
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2. Click the Next button and select the Add Beam mode. Click Finish .
3. The goal of the next few steps is to draw the stick model of the Bridge Structure (i.e.
the beams and the girders). Select the X-Z grid option. Create two grid lines in the x
direction at 10m spacing. Create four grid lines in the z direction at 3m spacing.
4. Click on the Snap Node/Beam button and draw the beams and the girders as shown
below. First draw five 20m girders. Then draw the 9m beams in the z direction.
5. Click on Geometry->Intersect Selected Members->Highlight. STAAD.pro will
highlight all the beams that intersect each other no common nodes. To break these beams
at the intersection point, click on Geometry->Intersect Selected Members->Intersect.
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6. The beams have been created. The columns will now be created using the translational
repeat command. Select nodes 6, 14, and 7 using the nodes cursor as shown below. The
node numbers may vary depending upon how the model was constructed. Select
Geometry->Translational Repeat from the menu. Select the y direction for the
translational repeat and select enter a Default Step Spacing
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7. Click on the View->3D Render ing in the menu.
8. Run Analysis If the analysis completed successfully, you should look at the
exaggerated deflected shape of the bridge under the action of self-weight. Try to find out
any connectivity problems etc. You can go to the Post-Processing mode by clicking on
Mode- >Post-processing command in the menu.
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