bridge rating

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Bridge Rating


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ISO BRG083110M4 Version 15.0.0Berkeley, California, USA February 2011

CSiBridge

Bridge Rating


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Copyright

Copyright Computers & Structures, Inc., 1978-2011All rights reserved.

The CSI Logo is a registered trademark of Computers & Structures, Inc.CSiBridge

TMand Watch & Learn

TMare trademarks of Computers &

Structures, Inc. Adobe and Acrobat are registered trademarks of AdobeSystems Incorported. AutoCAD is a registered trademark of Autodesk, Inc.

The computer program CSiBridgeTM

and all associated documentation areproprietary and copyrighted products. Worldwide rights of ownership restwith Computers & Structures, Inc. Unlicensed use of this program orreproduction of documentation in any form, without prior writtenauthorization from Computers & Structures, Inc., is explicitly prohibited.

No part of this publication may be reproduced or distributed in any form orby any means, or stored in a database or retrieval system, without the priorexplicit written permission of the publisher.

Further information and copies of this documentation may be obtained from:

Computers & Structures, Inc.1995 University AvenueBerkeley, California 94704 USA

Phone: (510) 649-2200FAX: (510) 649-2299e-mail: [email protected] (for general questions)e-mail: [email protected] (for technical support questions)web: www.csiberkeley.com


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DISCLAIMER

CONSIDERABLE TIME, EFFORT AND EXPENSE HAVE GONE INTO

THE DEVELOPMENT AND TESTING OF THIS SOFTWARE.

HOWEVER, THE USER ACCEPTS AND UNDERSTANDS THAT NO

WARRANTY IS EXPRESSED OR IMPLIED BY THE DEVELOPERS

OR THE DISTRIBUTORS ON THE ACCURACY OR THE

RELIABILITY OF THIS PRODUCT.

THIS PRODUCT IS A PRACTICAL AND POWERFUL TOOL FOR

STRUCTURAL DESIGN. HOWEVER, THE USER MUST EXPLICITLY

UNDERSTAND THE BASIC ASSUMPTIONS OF THE SOFTWARE

MODELING, ANALYSIS, AND DESIGN ALGORITHMS AND

COMPENSATE FOR THE ASPECTS THAT ARE NOT ADDRESSED.

THE INFORMATION PRODUCED BY THE SOFTWARE MUST BE

CHECKED BY A QUALIFIED AND EXPERIENCED ENGINEER. THE

ENGINEER MUST INDEPENDENTLY VERIFY THE RESULTS AND

TAKE PROFESSIONAL RESPONSIBILITY FOR THE INFORMATION

THAT IS USED.


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i

Contents

1 Introduction

1.1 Organization 1-2

1.2 Recommended Reading 1-2

2 Concrete Box Girder Bridges

2.1 Load Rating - Flexure 2-1

2.1.1 Rating Factor 2-1

2.1.2 Flexural Resistance 2-22.1.3 Flexural Resistance Algorithm 2-3

2.1.4 Rating Factor Algorithm 2-6

2.2 Load Rating Min Rebar for Flexure 2-7

2.2.1 Min Rebar for Flexure Algorithm 2-8

3 Multicell Concrete Box Girder Bridges

3.1 Load Rating - Flexure 3-2


3.1.2 Flexural Resistance 3-3

3.1.3 Flexural Resistance Algorithm 3-3

3.1.4 Live Load Distribution into Girders 3-7



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CSiBridge Bridge Rating

ii

3.2 Load Rating Min Rebar for Flexure 3-83.2.1 Live Load Distribution into Girders 3-9


3.3 Load Rating - Shear AASHTO-LRFD-2007 3-10



3.3.3 Shear Resistance 3-11

3.3.4 Shear Resistance Parameters 3-12

3.3.5 Shear Resistance Variables 3-13

3.3.6 Shear Resistance Algorithm 3-15


4 Precast Concrete Girder Bridges with

Composite Slabs

4.1 Load Rating Flexure 4-2


4.1.2 Flexural Resistance 4-3

4.1.3 Flexural Resistance Algorithm 4-3



4.2 Load Rating Min Rebar for Flexure 4-84.2.1 Live Load Distribution Into Girders 4-9


4.3 Load Rating - Shear AASHTO-LRFD-2007 4-10



4.3.3 Shear Resistance 4-12

4.3.4 Shear Resistance Parameters 4-12

4.3.5 Shear Resistance Variables 4-14

4.3.6 Shear Resistance Algorithm 4-16



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Contents

iii

5 Steel I-Section with Concrete Slab

5.1 Load Rating 5-2


5.1.2 Rating Factor Algorithm Flexure 5-2

5.1.3 Rating Factor Algorithm Shear 5-3

5.2 Section Properties 5-3

5.2.1 Section Proportions 5-3

5.2.2. Yield Moments 5-4

5.2.3 Plastic Moments 5-6

5.2.4 Section Classification and Factors 5-10

5.2.5 Unbraced Length Lb

and Section Transitions 5-14

5.3 Demand Sets 5-14

5.3.1 Composite Sections 5-14

5.3.2 Non-Composite Sections 5-18

5.4 Strength Rating Request 5-19

5.4.1 Flexure 5-19

5.4.2 Shear 5-26

5.5 Service Rating Request 5-28

5.5.1 Composite Sections 5-285.5.2 Non-Composite Sections 5-30

5.6 Section Optimization 5-30


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Organization 1 - 1

Chapter 1 Introduction

CSiBridge is the ultimate integrated tool for modeling, analysis,

and design of bridge structures. The ease with which all of these

tasks can be accomplished makes CSiBridge the most versatile

and productive bridge design package in the industry. CSi-

Bridge offers an easy-to-use tool for load rating in accordance

with the AASHTO Manual for Condition Evaluation and Load

and Resistance Factor Rating (LRFR) of Highway Bridges Octo-

ber 2003 with 2005 Interim Revisions. This manual describes the

algorithms applied to concrete box, multicell, and precast I or Ugirder deck superstructure bridge models.

In the case of concrete box bridges, CSiBridge applies an algo-

rithm that idealizes the superstructure as a torsionally stiff single-

spine beam, as defined in AASHTO LRFD Section 4.6.1.1.

In the case of a multicell concrete box bridge, CSiBridge analyzes

the superstructure on a girder-by-girder (web-by-web) basis while

ignoring the effects of torsion. The user has the option to use the

individual girder demands directly from the CSiBridge model

(available only for Area and Solid models) or use Live Load Dis-

tribution (LLD) factors. CSiBridge gives the user a choice of

methods to address distribution of live load to individual girders.


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1 - 2 Organization

In the case of precast I or U girder bridges, CSiBridge analyzes

the superstructure on a girder-by-girder (beam-by-beam) basis

while ignoring the effects of torsion. The user has the option to

use the individual girder demands directly from the CSiBridge

model (available only for Area and Solid models) or use Live

Load Distribution (LLD) factors. CSiBridge gives the user a

choice of methods to address distribution of live load to individual

girders.

The evaluation and application of LLD factors is described in de-

tail in Chapter 3 of theBridge Superstructure Design manual.

1.1 OrganizationThis chapter identifies the applicable code and describes addi-

tional sources of information about CSiBridges many features

and advantages. Chapter 2 describes the algorithms for concrete

box deck superstructures. Chapter 3 describes the algorithms for

multicell concrete box deck superstructures. Chapter 4 describes

the algorithms when the deck superstructure is comprised of pre-

cast I or U girders with composite slab.

1.2 Recommended ReadingIt is strongly recommended that you read this manual and review

any applicable Watch & Learn Series tutorials, which are

found on our web site, http://www.csiberkeley.com, before at-

tempting to determine the bridge rating for a concrete box girder

or precast concrete bridge using CSiBridge. Additional informa-

tion can be found in the on-line Help facility available from

within the softwares main menu.

Also, other bridge related manuals include the following:

Defining the Work Flow - Provides an overview of the workflow when using CSiBridge. That manual includes a descrip-


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Chapter 1 Introduction

Recommended Reading 1 - 3

tion of the Bridge Wizard, a step-wise guide through the en-

tire model creation, analysis, and design process, and explains

the various tabs, panels, and commands of the user interface

that can be used independently of or in concert with the

Bridge Wizard.

Introduction to CSiBridge Introduces CSiBridge designwhen modeling concrete box girder bridges and precast con-

crete girder bridges. The basic steps involved in creating a

bridge model are described. Then an explanation of how loads

are applied is provided, including the importance of lanes, ve-

hicle definitions, vehicle classes, and load cases. The Intro-

duction concludes with an overview of the analysis and dis-

play of design output.

Superstructure Design Describes using CSiBridge tocomplete bridge design in accordance with the AASHTO

STD 2002 or AASHTO LRFD 2007 code for concrete box

girder bridges or the AASHTO 2007 LRFD code for bridges

when the superstructure includes Precast Concrete Box

bridges with a composite slab. Loading and load combina-

tions and well as Live Load Distribution Factors are de-

scribed. The manual explains how to define and run a design

request and provides the algorithms used by CSiBridge in

completing concrete box girder, cast-in-place multi-cell con-crete box, and precast concrete bridge design in accordance

with the AASHTO code. The manual concludes with a de-

scription of design output, which can be presented graphically

as plots, in data tables, and in reports generated using the Ad-

vanced Report Writer feature.

Seismic Analysis and Design Describes the eight simplesteps needed to complete response spectrum and pushover

analyses, determine the demand and capacity displacements,

and report the demand/capacity ratios for an Earthquake Re-

sisting System (ERS).


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Load Rating - Flexure 2 - 1

Chapter 2 Concrete Box Girder Bridges

This chapter describes the algorithm CSiBridge applies when load

rating concrete box deck superstructures in accordance with the

AASHTO Manual for Condition Evaluation and Load and Resis-

tance Factor Rating (LRFR) of Highway Bridges October 2003

with 2005 Interim Revisions.

This algorithm idealizes the superstructure as a torsionally stiff

single-spine beam, as defined in AASHTO LRFD Section 4.6.1.1.

For load rating of multicell concrete boxes using live load distri-bution factors, see Chapter 3.

2.1 Load Rating - Flexure2.1.1 Rating Factor

n DC DC DW DW P P

L LL IM

M M M MRF

M

AASHTO LRFR eq. 6-1

RF = Rating factor calculated by CSiBridge

Mn

= Nominal moment resistance calculated by CSiBridge


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2 - 2 Load Rating - Flexure

The following values are specified by the user in the Rating Re-

quest:

= Resistance factor for flexure; Default Value = 1.0,

Typical value(s): 1.0. The factor is specified in the

Rating Parameters form.

DC

MDC

= Factored moment demand due to dead load of struc-

tural components and attachments. The DC

factor

shall be included in the combo specified in the DC

Combo demand set.

DWMDW = Factored moment demand due to dead load of wear-ing surface and utilities. The

DWfactor shall be in-

cluded in the combo specified in the DW Combo de-

mand set.

PM

P= Factored moment demand due to permanent loads

other than dead loads. The P

factor shall be included

in the combo specified in the P Combo demand set.

LM

LL+IM= Factored moment demand due to live load. The

Lfac-

tor shall be included in the combo specified in the

LL+IM Combo demand set.

2.1.2 Flexural ResistanceThe flexural resistance is determined in accordance with ASHTO

LRFD 2007 paragraph 5.7.3.2. The resistance is evaluated only

for bending about horizontal axis 3. Separate resistance is calcu-

lated for positive and negative moment.

The moment resistance is based on bonded tendons and longitudi-

nal mild steel reinforcement defined in the Bridge Object. It is as-

sumed that all defined tendons in a section, stressed or not, have

fpe (effective stress after loses) larger than 0.5 fpu (specified tensilestrength). If a certain tendon should not be considered for the

flexural resistance calculation, its area must be set to zero.


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Only reinforcement in the tensile zone of the section is assumed to

contribute to the moment resistance of the section; reinforcement

in the compression zone is ignored.

2.1.3 Flexural Resistance AlgorithmAt each section:

All section properties and demands are converted from CSi-Bridge model units to N, mm.

The equivalent slab thickness is evaluated based on slab areaand slab width assuming a rectangular shape.

slabslabeq

slab

At

b

The equivalent web thickness is evaluated as the summationof all web horizontal thicknesses.

web

webeq web

1

n

b b

1

stress block factor is evaluated in accordance with 5.7.2.2

based on section cf

if cf > 28 MPa, then 128

max 0 85 0 05 0 657

cf. . ; .

else 1 0 85. .

The tendon location, area, and material are read. Only bondedtendons are processed; unbonded tendons are ignored.

The longitudinal rebar area and material are read.Tendons and longitudinal reinforcement bars are split into twogroups depending on which sign of moment they resistnegativeor positive. A tendon or rebar is considered to resist a positive


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moment when it is located outside of the top fiber compression

stress block and is considered to resist a negative moment when it

is located outside of the bottom fiber compression stress block. In

accordance with the code, the compression stress block extends

over a zone bounded by the edges of the cross-section and a

straight line located parallel to the neutral axis at the distance a =

1c from the extreme compression fiber. The distance c is meas-

ured perpendicular to the neutral axis.

Since at the time of tendon and rebar sorting into positive and

negative groups the distance c is unknown, it is assumed to be

equal to the distance between the neutral axis and the extreme

compression fiber. The distance c is later revaluated in accordance

with the code equation, but rebar and tendons are not re-checked

for their positive or negative group assignments.

For each tendon group, an area weighted average of the following

values is determined:

sum of the tendon areas,APT

distance from the center of gravity of the tendons in the ten-sile zone to the compression fiber, d

P

specified tensile strength of prestressing steel,fpu

constant k(eq. 5.7.3.1.1-2)

2 1.04py

pu

fk

f

For each rebar group the following values are determined:

sum of rebar areas,AS

distance from the center of gravity of the rebar in the tensilezone to the compression fiber, d

s

specified minimum yield strength rebar,fy

The distance c between the neutral axis and the compressiveface is evaluated in accordance with (eq. 5.7.3.1.1-4).


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1 slab0 85

PT pu s y

pu

c PT

PT

A f A fc

f. f b kA

y

The distance c is compared to distance ds. Ifc > 0.6d

sandA

s> 0,

then stress in the rebar is recalculated

1 slab0 6 0 85pu

s c PT PT pu

PTs

s

f. d . f b kA A f

yf

A

Iffs< 0, thenf

sis set to zero.

Distance c is recalculated by substitutingfy

withfs.

The distance c is compared to the equivalent slab thickness todetermine if the section is a T-section or a rectangular section.

If 1 slabeq ,c t the section is a T-section.

If the section is a T-section, the distance c is recalculated in

accordance with (eq. 5.7.3.1.1-3).

slab webeq slabeq

1

0 85

0 85

PT pu S y c

pu

c webeq PT

PT

A f A f . f b b tc

f. f b kA

y

The distance c is compared to distance ds. Ifc > 0.6 d

sandA

s> 0,

then stress in the rebar is recalculated as follows:

1 webeq slab webeq slabeq

s

0 6 0 85 0 85

A

pu

s c PT PT pu c

PT

s

f. d . f b kA A f . f b b t

yf

Iffs< 0, thenf

sis set to zero.


withfs.


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The extent of compression block a is evaluated as a = c1. It

is limited to the end of the web where the web enters the ten-

sile flange/slab.

Average stress in prestressing steel fps

is calculated in accor-

dance with (eq. 5.7.3.1.1-1).

1ps pupt

cf f k

y

Nominal flexural resistance Mn is calculated in accordance

with (eq. 5.7.3.2.2-1)

If the section is a T-section,

slabeqslab webeq slabeq0 852 2 2 2

n PT ps p s s s c

ta a aM A f d A f d . f b b t

else

2 2n PT ps p s s s

a aM A f d A f d

Factored flexural resistance is obtained by multiplying Mnby

.

Mr= M

n

2.1.4 Rating Factor AlgorithmIn case any of the user-defined combos for demands sets

DCM

DC,

DW

MDW

, or pM

pcontain multiple StepTypes, the M3 demands

from Max and Min StepTypes are consolidated into one ABS

StepType. This is accomplished by selecting the maximum abso-

lute from the two StepType values while preserving the sign.

The rating factor is calculated for each StepType present in the

LM

LL+IMdemand set. The StepType that produces the smallest rat-

ing factor is reported in the output table.


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Load Rating Min Rebar for Flexure 2 - 7

For each StepType, one of the section flexural capacities (positive

or negative), to be used in the rating factor equation, is selected to

match the sign of the LM

LL+IMmoment. Then the sign of the sum

of the moments DC

MDC

+ DW

MDW

+ pM

pis determined. If the sign

of the sum matches the sign of the LM

LL+IM, the moment resistance

is reduced by the sum; if the sign of the sum is opposite, the mo-

ment resistance is increased by the sum.

2.2 Load Rating Min Rebar for FlexureIn this rating request, CSiBridge verifies if the minimum rein-

forcement requirement is satisfied in accordance with AASHTOSection 5.7.3.3.2. The code states that the calculated flexural re-

sistance Mr, based on the provided PT and longitudinal rebar,

must satisfy the following requirement:

Mr> min(1.2M

cr, 1.33M

u)

whereMcr

= Sc (fr +fcpe) Scfr (calculated by CSiBridge)

Sc

= section modulus for the extreme fiber of the section where

tensile stress is caused by externally applied loads. The

value is calculated by CSiBridge and reported in the output

table.

fcpe

= compressive stress in concrete due to effective prestress

force only (after allowance for all prestress losses) at the ex-

treme fiber of the section where tensile stress is caused by

externally applied loads. The user specifies the name of the

combo for thefcpe

demand set in the definition of the Bridge

Rating Request.

fr

= modulus of rupture. The user specifies this value in the Rat-

ing Parameters.

Mu

= factored moment required by the applicable strength load

combinations specified in AASHTO Table 3.4.1-1. The user


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2 - 8 Load Rating Min Rebar for Flexure

specifies the name of the combo for the Mu

demand set in

the definition of the Bridge Rating Request.

2.2.1 Min Rebar for Flexure AlgorithmAt each section, the resistances for both positive and negative

moments are determined using the procedure outlined in Section

2.1.2. The fcpe

stresses at the top and bottom of the extreme fiber

are read, and Mcr

values for both positive and negative moments

are evaluated.

For each StepType present in the Mu

combo, the sign and magni-

tude of the M3 moment is read. If the Mu

sign is negative, the

minimum rebar equation is checked for negative flexural resis-

tance, and if the Mu

sign is positive, the minimum rebar equation

is checked for positive flexural resistance. If both StepTypes pre-

sent in the Mu

combo have the same sign, the minimum rebar for

the opposite sign moment is not checked and the note Not appli-

cable is reported in the output table.


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Chapter 3 Multicell Concrete Box Girder Bridges


rating multicell concrete box deck superstructures in accordance

with the AASHTO Manual for Condition Evaluation and Load

and Resistance Factor Rating (LRFR) of Highway Bridges Octo-

ber 2003 with 2005 Interim Revisions.

This algorithm analyzes the superstructure on a girder-by-girder

(web-by-web) basis while ignoring the effects of torsion. For load

rating of concrete box bridges where the superstructure is ideal-

ized as a torsionally stiff, single-spine beam as defined in

AASHTO LRFD Section 4.6.1.1, see Chapter 2.

The user has the option to use the individual girder demands di-

rectly from the CSiBridge model (available only for Area and

Solid models) or use Live Load Distribution (LLD) factors. CSi-

Bridge gives the user a choice of methods to address distribution

of live load to individual girders. The evaluation and application

of LLD factors is described in detail in Chapter 3 of the Bridge

Superstructure Design manual.

It is important to note that to obtain relevant results, the definition

of a Moving Load case must be adjusted depending on which

method is selected. Refer to Chapter 3, Section 3.1 of the BridgeSuperstructure Design manual.


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Legend:

Girder = the web + the tributary area of the top and bottom slabSection Cut = all girders present in the cross-section at the cut lo-

cation


n DC DC DW DW P P

L LL IM

M M M MRF

M

AASHTO LRFR eq. 6-1


Mn



quest:




DCMDC = Factored moment demand due to dead load of struc-


factor


Combo demand set.

DW

MDW

= Factored moment demand due to dead load of wear-

ing surface and utilities. The DW

factor shall be in-


mand set.

PM

P= Factored moment demand due to permanent loads

other than dead loads. The P factor shall be includedin the combo specified in the P Combo demand set.


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LM


Lfac-



3.1.2 Flexural ResistanceThe flexural resistance of each girder is determined in accordance

with AASHTO LRFD 2007 paragraph 5.7.3.2. The resistance is

evaluated only for bending about horizontal axis 3. Separate resis-

tance is calculated for positive and negative moment.




fpe

(effective stress after loses) larger than 0.5 fpu

(specified tensile

strength). If a certain tendon should not be considered for the



contribute to the moment resistance of the section; reinforcement

in the compression zone is ignored.

3.1.3 Flexural Resistance AlgorithmAt each section and each girder:


The equivalent slab thickness is evaluated based on slab areaand slab width assuming a rectangular shape.

slabslabeq

slab

At

b

1

stress block factor is evaluated in accordance with 5.7.2.2

based on section cf


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If cf > 28 MPa, then 128

max 0 85 0 05 0 657

cf. . ; .

else 1 0 85. .

The tendon location, area and material are read. Only bondedtendons are processed; unbonded tendons are ignored.

The longitudinal rebar area and material are readTendons and longitudinal reinforcement bars are split into two

groups depending on what sign of moment they resistnegative

or positive. A tendon or rebar is considered to resist a positivemoment when it is located outside of the top fiber compression

stress block and is considered to resist a negative moment when it

is located outside of the bottom fiber compression stress block.

Per code the compression stress block extends over a zone

bounded by the edges of the cross-section and a straight line lo-

cated parallel to the neutral axis at the distance a = 1c from the

extreme compression fiber. The distance c is measured perpen-

dicular to the neutral axis.



equal to the distance between the neutral axis and the extreme

compression fiber. The distance c is later revaluated in accordance

with the code equation, but rebar and tendons are not re-checked

for their positive or negative group assignments.

For each tendon group, an area weighted average of the following

values is determined:



P




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2 1.04py

pu

fk f




s


The distance c between neutral axis and the compressive face isevaluated in accordance with (eq. 5.7.3.1.1-4).

1 slab0 85

PT pu s y

pu

c PT

PT

A f A fc

f. f b kA

y


sandA

s> 0,


1 slab0 6 0 85pu

s c PT PT pu

PTs

s

f. d . f b kA A f

yf

A

Iffs< 0, thenf

sis set to zero.


withfs.

The distance c is compared to the equivalent slab thickness todetermine if the section is a T-section or rectangular section.

If 1 slabeq ,c t the section is a T-section.

If the section is a T-section, the distance c is recalculated in ac-cordance with (eq. 5.7.3.1.1-3).


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slab webeq slabeq

1

0 85

0 85

PT pu S y c

pu

c webeq PT

PT

A f A f . f b b tc f

. f b kAy


sandA

s> 0, then

stress in the rebar is recalculated

1 webeq slab webeq slabeq

s

0 6 0 85 0 85

A

pu

s c PT PT pu c

PT

s

f. d . f b kA A f . f b b t

yf

Iffs < 0, thenfs is set to zero.


withfs.

The extent of compression block a is evaluated as a = c1. It is

limited to end of web where the web enters the tensile flange/

slab.

Average stress in prestressing steelfps


dance with (eq. 5.7.3.1.1-1).

1ps pupt

cf f k

y

Nominal flexural resistanceMnis calculated in accordance with

(eq. 5.7.3.2.2-1)


slabeq

slab webeq slabeq0 852 2 2 2

n PT ps p s s s c


else

2 2n PT ps p s s s

a aM A f d A f d


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Factored flexural resistance is obtained by multiplyingMnby .

Mr= M

n

3.1.4 Live Load Distribution Into GirdersThe M3 demands on the section cut specified in the LL+IM de-

mand set are distributed into individual girders in accordance with

the Live Load Distribution method specified in the Rating Re-

quest. The evaluation and application of live load distribution fac-

tors is described in detail in Chapter 3 of the Bridge Superstruc-

ture Design manual.

M3 demands on the section cut specified in the DC, DW and P

Combo demand sets are distributed evenly to all girders unless

live load distribution Method 3 is used (CSiBridge reads the cal-

culated live load demands directly from individual girders --

available for Area and Solid models only). In that case, forces

from CSiBridge are read directly on a girder-by-girder basis.

3.1.5 Rating Factor AlgorithmIn case any of the user defined combos for demands sets

DCM

DC,

DW

MDW

, or pM





The girder rating factor is calculated for each StepType present in

the LM

LL+IMdemand set. The StepType that produces the smallest

rating factor is reported in the output table.

For each StepType, one of the girder flexural capacities (positive

or negative), to be used in the rating factor equation, is selected to

match the sign of the LMLL+IM moment. Then the sign of the sum ofthe moments

DCM

DC+

DWM

DW+

pM

pis determined. If the sign of

the sum matches the sign of the LM

LL+IM, the moment resistance is


27/88



reduced by the sum; if the sign of the sum is opposite, the moment

resistance is increased by the sum.

3.2 Load Rating Min Rebar for FlexureIn this rating request, CSiBridge verifies if minimum reinforce-

ment requirement is satisfied in accordance with AASHTO Sec-

tion 5.7.3.3.2. The code states that the calculated flexural resis-

tance Mr, based on the provided PT and longitudinal rebar, must

satisfy the following requirement:

Mr> min(1.2Mcr, 1.33Mu)

whereMcr

= Sc (fr +fcpe) Scfr (calculated by CSiBridge)

Sc

= section modulus for the extreme fiber of the section where

tensile stress is caused by externally applied loads. The

value is calculated by CSiBridge and reported in the output

table.

fcpe

= compressive stress in concrete due to effective prestress

force only (after allowance for all prestress losses) at the ex-

treme fiber of the section where tensile stress is caused by

externally applied loads. The user specifies the name of thecombo for thef

cpedemand set in the definition of the Bridge

Rating Request.

fr

= modulus of rupture. The user specifies this value in the Rat-

ing Parameters.

Mu

= factored moment required by the applicable strength load

combinations specified in AASHTO Table 3.4.1-1. The user

specifies the name of the combo for the Mu

demand set in

the definition of the Bridge Rating Request.


28/88



3.2.1

Live Load Distribution into GirdersThe M3 demands on the section cut specified in the M

udemand

set are distributed into individual girders in accordance with the

Live Load Distribution method specified in the Rating Request.

The evaluation and application of live load distribution factors is

described in detail in Chapter 3 of the Bridge Superstructure De-

sign manual.

M3 demands on section cut specified infcpe

combo demand set are

distributed evenly to all girders unless live load distribution

Method 3 is used (CSiBridge reads the calculated live load de-

mands directly from individual girders -- available for Area andSolid models only). In that case, forces from CSiBridge are not

read on a section-cut basis but directly on a girder-by-girder basis.

3.2.2 Min Rebar for Flexure AlgorithmAt each girder, the resistances for both positive and negative mo-

ments are determined using the procedure outlined in Section

3.1.2. The fcpe

stresses at the top and bottom of the extreme fiber

are read, and Mcr

values for both positive and negative moments

are evaluated.

For each StepType present in Mu

combo, the sign and magnitude

of the M3 moment is read. If theMu

sign is negative, the minimum

rebar equation is checked for negative flexural resistance and if

theMu

sign is positive, the minimum rebar equation is checked for

positive flexural resistance. If both StepTypes present in the Mu

combo have the same sign, the minimum rebar for the opposite

sign moment is not checked and the note Not applicable is re-

ported in the output table.


29/88


3 - 10 Load Rating - Shear AASHTO-LRFD-2007

3.3

Load Rating - Shear AASHTO-LRFD-2007

3.3.1 Rating Factorn DC DC DW DW p p

L LL IM

V V V V RF

V

AASHTO LRFR eq. 6-1

RF= Rating factor calculated by CSiBridge

Vn= Nominal shear resistance calculated by CSiBridge

The user specifies the values for the following in the Rating Re-

quest:

= Resistance factor for shear; Default Value = 0.9,

Typical value(s): 0.9 for normal weight concrete, 0.7

for light-weight concrete. The factor is specified in

the Rating Parameters form.

DC

VDC

= Factored shear demand due to dead load of structural

components and attachments. The DC

factor shall be

included in the combo specified in the DC Combo

demand set.

DW

VDW

= Factored shear demand due to dead load of wearing

surface and utilities. The DW


in the combo specified in the DW Combo demand set.

PV

P = Factored shear demand due to permanent loads other

than dead loads. The P

factor shall be included in the

combo specified in the P Combo demand set.

LV

LL+IM = Factored shear demands due to live load. The

Lfactor

shall be included in the combo specified in the



30/88


Load Rating - Shear AASHTO-LRFD-2007 3 - 11

3.3.2

Live Load Distribution Into GirdersThe V2 demands on the section cut specified in the LL+IM and

Mu

demand sets are distributed into individual girders in accor-

dance with the Live Load Distribution method specified in the

Rating Request. The evaluation and application of live load distri-

bution factors is described in detail in Chapter 3 of theBridge Su-

perstructure Design manual.

V2 demands on the section cut specified in the DC, DW and P



culated live load demands directly from individual girders --available for Area and Solid models only). In that case, forces


3.3.3 Shear ResistanceThe shear resistance is determined in accordance with paragraph

5.8.3.4.2 (derived from the Modified Compression Field Theory).

The procedure assumes that the concrete shear stresses are dis-

tributed uniformly over an area bvwide and d

vdeep, that the direc-

tion of principal compressive stresses (defined by angle and

shown as D) remains constant over dv, and that the shear strengthof the section can be determined by considering the biaxial stress

conditions at just one location in the web. The user should select

for design only those sections that comply with these assumptions

by defining appropriate station ranges in the design request (see

Chapter 4 of theBridge Superstructure Design manual).

The effective web width is taken as the minimum web width,

measured parallel to the neutral axis, between the resultants of the

tensile and compressive forces as a result of flexure. In determin-

ing the effective web width at a particular level, one-quarter of the

diameter of the grouted ducts at that level is subtracted from theweb width.


31/88



All defined tendons in a section, stressed or not, are assumed to be

grouted. Each tendon at a section is checked for presence in the

web and the minimum controlling effective web thicknesses are

evaluated.

The tendon duct is considered as having effect on the web effec-

tive thickness even if only part of the duct is within the web

boundaries. In such cases, the entire one-quarter of the tendon

duct diameter is subtracted from the element thickness

If several tendon ducts overlap in one web (when projected on

vertical axis), the diameters of ducts are added for the sake of

evaluation of the effective thickness. The effective web thicknessis calculated at the top and bottom of each duct.

Shear design is completed on a per-web (girder) basis; torsion is

ignored.

Transverse reinforcement specified in the Bridge Object is used to

verify if minimum shear reinforcement is provided. It is also used

to calculate the Vsshear resistance component. The density (area

per unit length) of provided transverse reinforcement in a given

girder is averaged based on values specified in the Bridge Object

over a distance 0.5 dv

cot measured down-station and up-station

from a given section cut.

3.3.4 Shear Resistance ParametersThe following parameters are considered during shear design:

Mu Combo Demand Set the forces in the specified combo areused in the Modified Compression Field Theory (MCFT) equa-

tions to determine shear resistance of the girder.

PhiC Resistance Factor; Default Value = 0.9, Typicalvalue(s): 0.7 to 0.9. The nominal shear resistance of normalweight concrete sections is multiplied by the resistance factor to

obtain factored resistance.


32/88



PhiC(Lightweight) Resistance Factor for light-weight con-crete; Default Value = 0.7, Typical value(s): 0.7 to 0.9. The

nominal shear resistance of light-weight concrete sections is

multiplied by the resistance factor to obtain factored resistance.

Check Sub Type Typical value: MCFT. Specifies whichmethod for shear design will be used: either MCFT in accor-

dance with 5.8.3.4.2; or the Vci/V

cwmethod in accordance with

5.8.3.4.3 Currently only the MCFT option is available.

Negative limit on strain in nonprestressed longitudinal rein-forcementin accordance with section 5.8.3.4.2; Default Value =

0.4x10-3

, Typical value(s): 0 to 0.4x10-3

Positive limit on strain in nonprestressed longitudinal rein-forcementin accordance with section 5.8.3.4.2; Default Value =

6.0x10-3, Typical value(s): 6.0x10

-3

PhiC for Nu Resistance Factor used in equation 5.8.3.5-1; De-

fault Value = 1.0, Typical value(s): 0.75 to 1.0

Phif for Mu Resistance Factor used in equation 5.8.3.5-1; De-

fault Value = 0.9, Typical value(s): 0.9 to 1.0.

sx = Maximum distance between layers of longitudinal crackcontrol reinforcement in accordance with AASHTO LRFD5.8.3.4.2-5. This parameter is used only when a girder does not

contain the code-specified minimum amount of shear rein-

forcement.

ag = Maximum aggregate size, Eq 5.8.3.4.2. This parameter isused only when a girder does not contain the code-specified

minimum amount of shear reinforcement.

3.3.5 Shear Resistance Variables

V= Resistance factor for shear

P

= Resistance factor for axial load


33/88



F

= Resistance factor for moment

= Multiplier of sqrt fcfor light-weight concrete in accor-

dance with 5.8.2.2

Vu

= Factored shear demand per girder excluding force in

tendons

Nu

= Applied factored axial force, taken as positive if tensile

Mu

= Factored moment at the section

V2c

= Shear in section cut excluding force in tendons

V2Tot

= Shear in section cut including force in tendons

Vp

= Component in the direction of the applied shear of the

effective prestressing force; if Vp

has the same sign as

Vu, then the component is resisting the applied shear

a = Depth of equivalent stress block in accordance with

5.7.3.2.2. Varies for positive and negative moment.

dv

= Effective shear depth in accordance with 5.8.2.9

dgirder = Depth of girder

dp

= Distance from compression face to center of gravity of

tendons in the tensile zone

ds = Distance from compression face to center of gravity of

longitudinal reinforcement in the tensile zone

b = Minimum web width

bv

= Effective web width adjusted for the presence of

prestressing ducts in accordance with section 5.8.2.9

Aps

= Area of prestressing steel on the flexural tension side of

the member


34/88



fpu

= Specified tensile strength of prestressing steel

Ep

= Prestressing steel Youngs modulus

Avl

= Area of nonprestressed steel on the flexural tension sideof the member at the section under consideration

Es

= Reinforcement Youngs modulus

s

= Strain in nonprestressed longitudinal tension reinforce-ment eq. 5.8.3.4.2-4

Limi tPos Limi tNeg,s s = Max and min value of strain in nonprestressed

longitudinal tension reinforcement as specified in theDesign Request

Ec

= Youngs modulus of concrete

Ac

= Area of concrete on the flexural tension side of themember

Avprov

= Area of transverse shear reinforcement per unit lengthas specified in the Bridge Object. The transverse rein-forcement density is averaged over a distance 0.5 cotmeasured up-station and down-station from the currentsection cut.

AVSmin

= Minimum area of transverse shear reinforcement perunit length in accordance with eq. 5.8.2.5

3.3.6 Shear Resistance AlgorithmAll section properties and demands are converted from CSiBridge

model units to N, mm.

If the combo specified in theMu

demand set contains envelopes, a

new force demand set is generated. The new force demand set is

built up from the maximum tension values of P and the maximum

absolute values of V2 and M3 of the two StepTypes (Max and

Min) present in the envelope COMBO case. The StepType of this

new force demand set is named ABS and the signs of the P, V2


35/88



and M3 are preserved. The ABS case follows the industry practice

where sections are designed for extreme shear and moments that

are not necessarily corresponding to the same design vehicle posi-

tion. The section cut is designed for all three StepTypes in the

COMBOMax, Min and ABSand the controlling StepType is

reported.

In the case when the demand moment u u p vM V V d , two

new force demand sets are generated where pos posu u p vM V V d

and neg negu u p vM V V d . The acronyms -CodeMinMuPos

and -CodeMinMuNeg are added to the end of the StepType

name. The signs of the P and V2 are preserved.

The shear resistance is evaluated for every force demand set de-

scribed previously and the smallest value is used in evaluation of

the rating factor.

The component in the direction of the applied shear of the effec-tive prestressing force, positive if resisting the applied shear, is

evaluated:

2 2Tot

girders

cp

V VV

n

Depth of equivalent stress block a for both positive and nega-tive moment is evaluated in accordance with eq. 5.7.3.1.1. See

section 3.1.2

Effective shear depth is evaluated.ps ps p vl y s

e

ps ps vl y

A f d A f dd

A f A f

girdermax 0 72 0 9 0 5v e ed . d , . d , d . a

Evaluate numerator and denominator of (eq. 5.8.3.4.2-4)


36/88



numerator 0 5 0 7u

s u u p ps pu

V

M. N V V A . f d

denominators p ps s vlE A E A Adjust denominator values as follows

If denominator 0s and numerator 0s , then LimitPoss s

If numerator 0s then denominators p ps s vl c cE A E A E A

Evaluate (eq. 5.8.3.4.2-4)numerator

denominator

ss

s

Check if axial tension is large enough to crack the flexuralcompression face of the section.

Ifgirder

0 52u cN

. f ' ,A

then 2s s

Check against the limit on the strain in non-prestressed longitu-dinal tension reinforcement specified in the Design Request

LimitNegmax( , )s s s and LimitPosmin( , )s s s

Evaluate the angle of inclination of diagonal compressivestresses as determined in Article 5.8.3.4

18 29 3500 45s (5.8.3.4)

Evaluate minimum transverse reinforcement density required inaccordance with the code

min 0 083v

v c

y

bA . f

f (5.8.3.4)


37/88



Check if the provided girder transverse reinforcement densityA

vprovaveraged over distance 0.5 cot measured up-station and

down-station from the current section cut satisfies minimum

specified by code and evaluate the factor indicating the ability

of diagonally cracked concrete to transmit tension and shear, as

specified in Article 5.8.3.4

IfAvprov

Avmin

, then4 8

1 750 s

.

else

4 8 51 25 41 750 39 25 4s xe

. .. s

where35

16

xxe

g

ss

a

(eq. 5.8.3.4)

Evaluate nominal shear resistance provided by tensile stresses inthe concrete (eq. 5.8.3.3-3)

0 083c c vV . f ' b d

Evaluate nominal shear resistance provided by tensile stresses inthe transverse reinforcement (eq. 5.8.3.3-4)

prov cots v y vV A f d (eq. 5.8.3.3-4)

Evaluate total factored shear resistance and check against amaximum specified in 5.8.3.3-2

min 0 25r v c s c v vV V V ; . f b d

Note: The shear resistance evaluated here purposely ignores the

effect of the component in the direction of the applied shear of the

effective prestressing force Vp. This is to ensure that the prestress-

ing effect is not double counted when evaluating the load rating


38/88



factor. The name of the combo that contains the prestressing loads

is specified in the Demand Set P Combo in the Rating Request.


DCV

DC,

DW

VDW

, or PV

Pcontain multiple StepTypes, the V2 demands from

Max and Min StepTypes are consolidated into one ABS Step-

Type. This is accomplished by selecting the maximum absolute

from the two StepType values while preserving the sign.


the LV



The sign of the sum of shear demands DC

VDC

, DW

VDW

, or PV

Pis de-

termined. If the sign of the sum matches the sign of the LV

LL+IM;

the shear resistance is reduced by the sum; if the sign of the sum is

opposite, the shear resistance is increased by the sum.


39/88


Chapter 4 Precast Concrete Girder Bridgeswith Composite Slabs


rating deck superstructures comprised of precast I or U girders

with composite slabs. The load rating is in accordance with the

AASHTO Manual for Condition Evaluation and Load and Resis-

tance Factor Rating (LRFR) of Highway Bridges October 2003

with 2005 Interim Revisions.

This algorithm analyzes the superstructure on a girder-by-girder

(beam-by-beam) basis while ignoring the effects of torsion. The

user has the option to use the individual girder demands directly

from the CSiBridge model (available only for Area and Solid

models) or use Live Load Distribution (LLD) factors. CSiBridge

gives the user a choice of methods to address distribution of live

load to individual girders. The evaluation and application of LLD

factors is described in detail in Chapter 3 of the Bridge Super-

structure Design manual.

It is important to note that to obtain relevant results, the definition

of a Moving Load case must be adjusted depending on whichmethod is selected. Refer to Chapter 3 Section 3.1 of the Bridge

Superstructure Design manual.


40/88



Legend:

Girder = beam + tributary area of the top of the slab

Section Cut = all girders are present in the cross-section at the cut

location


n DC DC DW DW P P

L LL IM

M M M M

RF M

AASHTO LRFR eq. 6-1


Mn



quest:




DC

MDC

= Factored moment demand due to dead load of struc-


factor


Combo demand set.

DW

MDW

= Factored moment demand due to dead load of wear-

ing surface and utilities. The DW

factor shall be in-


mand set.

PMP = Factored moment demand due to permanent loadsother than dead loads. The

Pfactor shall be included

in the combo specified in the P Combo demand set.


41/88

Chapter 4 Precast Concrete Girder Bridges with Composite Slabs


LM


Lfac-



4.1.2 Flexural ResistanceThe flexural resistance of each girder is determined in accordance

with AASHTO LRFD 2007 paragraph 5.7.3.2. The resistance is

evaluated only for bending about horizontal axis 3. Separate resis-

tance is calculated for positive and negative moment.




fpe

(effective stress after loses) larger than 0.5 fpu

(specified tensile

strength). If a certain tendon should not be considered for the



contribute towards the moment resistance of the section; rein-

forcement in compression zone is ignored.

4.1.3 Flexural Resistance AlgorithmAt each section and each girder:


The equivalent slab thickness is evaluated based on slab areaand slab width assuming rectangular shape.

1 stress block factor is evaluated in accordance with 5.7.2.2based on section cf

If cf > 28 MPa, then 128

max 0 85 0 05 0 657

cf. . ; .


42/88



else 1 0 85.

The tendon location, area, and material are read. Only bondedtendons are processed; unbonded tendons are ignored.

The longitudinal rebar area and material are readTendons and longitudinal reinforcement bars are split into two

groups depending on what sign of moment they resistnegative

or positive. A tendon or rebar is considered to resist a positive

moment when it is located outside of the top fiber compression

stress block and is considered to resist a negative moment when

it is located outside of the bottom fiber compression stressblock. In accordance with code, the compression stress block

extends over a zone bounded by the edges of the cross-section

and a straight line located parallel to the neutral axis at the dis-

tance a = 1c from the extreme compression fiber. The distance

c is measured perpendicular to the neutral axis.



equal to a distance between the neutral axis and the extreme

compression fiber. The distance c is later re-evaluated in accor-

dance with the code equation, but rebar and tendons are not re-checked for their positive or negative group assignments.

For each tendon group, an area weighted average of the follow-

ing values is determined:



P



2 1.04py

pu

fk

f


43/88






s


Positive moment resistance first it is assumed that the equiva-lent compression stress block is within the top slab. The dis-

tance c between neutral axis and the compressive face is evalu-

ated in accordance with (eq. 5.7.3.1.1-4).

1 slab0 85

PT pu s y

pu

c PT

PT

A f A fcf

. f b kAy


sandA

s>

0, then stress in the rebar is recalculated

1 slab0 6 0 85pu

s c PT PT pu

PTs

s

f. d . f b kA A f

yf

A

Iffs< 0, thenfs is set to zero.Distance c is recalculated by substitutingf

ywithf

s.

The distance c is compared to the slab thickness. If the distance

to the neutral axis c is larger than the composite slab thickness,

the distance c is re-evaluated. For this calculation, the beam

flange width and area are converted to their equivalents in slab

concrete by multiplying the beam flange width by the modular

ratio between the precast girder concrete and the slab concrete.

The web width in the equation for c is substituted for the effec-

tive converted girder flange width. The distance c is recalcu-

lated in accordance with (eq. 5.7.3.1.1-3).


44/88



slab webeq slabeq

1

0 85

0 85

PT pu S y c

pu

c webeq PT

PT

A f A f . f b b tc f

. f b kAy

The distance c is again compared to distance ds. Ifc > 0.6ds and

As> 0, then stress in the rebarf

sis recalculated. Iff

s< 0, thenf

sis

set to zero.


withfs.

If the calculated value ofc exceeds the sum of the deck thickness

and the equivalent precast girder flange thickness, the section is

designated as a T-section. The program assumes the neutral axis is

below the flange of the precast girder and recalculates c. The term

0.85 c wf b b in the calculation is broken into two terms: one

refers to the contribution of the deck to the composite section

flange and the second refers to the contribution of the precast

girder flange to the composite girder flange.


sandA

s> 0,


Iffs< 0, thenf

sis set to zero.


withfs.

The extent of compression block a is evaluated as a = c1. It is

limited to the end of the web where the web enters the tensile

beam flange

Average stress in prestressing steelfps


dance with (eq. 5.7.3.1.1-1).

1ps pupt

cf f k

y

Nominal flexural resistanceMnis calculated in accordance with

(eq. 5.7.3.2.2-1)


45/88




slabeq

slab webeq slabeq0 852 2 2 2

n PT ps p s s s c


else

2 2n PT ps p s s s

a aM A f d A f d

Factored flexural resistance is obtained by multiplyingMnby .

Mr = Mn

The process for evaluating negative moment resistance is analo-

gous.

4.1.4 Live Load Distribution into GirdersThe M3 demands on the section cuts specified in the LL+IM de-

mand set are distributed into individual girders according to the




sign manual.

M3 demands on the section cut specified in the DC, DW and P




available for Area and Solid models only). In that case, the forces



DCM

DC,

DW

MDW

, or pM




46/88






the LM



For each StepType, one of the girder flexural capacities (positive

or negative) to be used in the rating factor equation is selected to

match the sign of the LM

LL+IMmoment. Then the sign of the sum

of moments DC

MDC

, DW

MDW

, or pM

pis determined. If the sign of

the sum matches the sign of the LM

LL+IM, the moment resistance is

reduced by the sum; if the sign of the sum is opposite, the momentresistance is increased by the sum.

4.2 Load Rating Min Rebar for FlexureIn this rating request, CSiBridge verifies if the minimum rein-

forcement requirement is satisfied in accordance with AASHTO

Section 5.7.3.3.2. The code states that the calculated flexural re-

sistanceMrbased on the provided PT and longitudinal rebar must

satisfy the following requirement:

Mr> min(1.2M

cr, 1.33M

u)

where 1ccr c r cpe dnc c r nc

SM S f f M S f

S

(calculated by

CSiBridge)

Sc

= Section modulus for the extreme fiber of the composite

girder where tensile stress is caused by externally applied

loads. The value is calculated by CSiBridge and reported

in the output table.

Snc = Section modulus for the extreme fiber of the noncompo-site beam where tensile stress is caused by externally ap-


47/88



plied loads. The value is calculated by CSiBridge and re-

ported in the output table.

fcpe

= Compressive stress in concrete due to effective prestress

force only (after allowance for all prestress losses) at the

extreme fiber of the girder where tensile stress is caused

by externally applied loads. The user specifies the name

of the combo for thefcpe

demand set in the definition of the

Bridge Rating Request.

fr

= Modulus of rupture. The user specifies in this value in the

Rating Parameters.

Mdnc

= Total unfactored dead load moment acting on the non-

composite beam. The user specifies the name of the

combo for theMdnc

demand set in the definition of the B-

ridge Rating Request.

Mu

= Factored moment required by the applicable strength load

combinations specified in AASHTO Table 3.4.1-1. The

user specifies the name of the combo for the Mu

demand

set in the definition of the Bridge Rating Request.

4.2.1 Live Load Distribution into GirdersThe M3 demands on the section cut specified in the M

udemand

set are distributed into individual girders according to the Live

Load Distribution method specified in the Rating Request. The

evaluation and application of live load distribution factors is de-

scribed in detail in Chapter 3 of theBridge Superstructure Design

manual.

M3 demands on the section cut specified in thefcpe

andMdnc

combo

demand set are distributed evenly to all girders unless live load

distribution Method 3 is used (CSiBridge reads the calculated live

load demands directly from individual girders -- available for

Area and Solid models only). In that case, forces from CSiBridge


48/88


49/88



The user specifies the values for the following in the Rating Re-

quest:

= Resistance factor for shear; Default Value = 0.9,

Typical value(s): 0.9 for normal weight concrete, 0.7

for light-weight concrete. The factor is specified in

the Rating Parameters form.

DC

VDC

= Factored shear demand due to dead load of structural

components and attachments. The DC

factor shall be

included in the combo specified in the DC Combo

demand set.

DW

VDW

= Factored shear demand due to dead load of wearing

surface and utilities. The DW


in the combo specified in the DW Combo demand set.

PV

P = Factored shear demand due to permanent loads other

than dead loads. The P

factor shall be included in the

combo specified in the P Combo demand set.

LV

LL+IM = Factored shear demands due to live load. The

Lfactor

shall be included in the combo specified in the


4.3.2 Live Load Distribution into GirdersThe V2 demands on section cut specified in the LL+IMand M

u

demand set are distributed into individual girders according to the




sign manual.

V2 demands on the section cut specified in the DC, DW and P

Combo demand sets are distributed evenly to all girders unlesslive load distribution Method 3 is used (CSiBridge reads the cal-



50/88



available for Area and Solid models only). In that case, forces


4.3.3 Shear ResistanceThe shear resistance is determined in accordance with paragraph

5.8.3.4.2 (derived from Modified Compression Field Theory). The

procedure assumes that the concrete shear stresses are distributed

uniformly over an area bvwide and d

vdeep, that the direction of

principal compressive stresses (defined by angle and shown as

D) remains constant over dv, and that the shear strength of the sec-

tion can be determined by considering the biaxial stress conditionsat just one location in the web. The user should select for design

only those sections that comply with these assumptions by defin-

ing appropriate station ranges in the design request (see Chapter 4

of theBridge Superstructure Design manual).

It is assumed that the precast beams are pre-tensioned, and there-

fore, no ducts are present in webs. The effective web width is

taken as the minimum web width, measured parallel to the neutral

axis, between the resultants of the tensile and compressive forces

as a result of flexure

Shear design is completed on a per-web (girder) basis; torsion is

ignored.

Transverse reinforcement specified in the Bridge Object is used to

verify if minimum shear reinforcement is provided. It is also used

to calculate Vsshear resistance component. The density (area per

unit length) of provided transverse reinforcement in a given girder

is averaged based on values specified in the Bridge Object over

distance 0.5 dvcot measured down-station and up-station from a

given section cut

4.3.4 Shear Resistance ParametersThe following parameters are considered during shear design:


51/88



Mu

Combo Demand Set the forces in the specified combo are

used in the Modified Compression Field Theory (MCFT) equa-

tions to determine shear resistance of the girder

PhiC Resistance Factor; Default Value = 0.9, Typicalvalue(s): 0.7 to 0.9. The nominal shear resistance of normal

weight concrete sections is multiplied by the resistance factor to

obtain factored resistance.

PhiC (Lightweight) Resistance Factor for light-weight con-crete; Default Value = 0.7, Typical value(s): 0.7 to 0.9. The

nominal shear resistance of light-weight concrete sections is

multiplied by the resistance factor to obtain factored resistance.

Check Sub Type Typical value: MCFT. Specifies whichmethod for shear design will be used: either MCFT in accor-

dance with 5.8.3.4.2; or the Vci/V

cw method in accordance with

5.8.3.4.3 Currently only the MCFT option is available.

Negative limit on strain in nonprestressed longitudinal rein-forcementin accordance with section 5.8.3.4.2; Default Value =

0.4x10-3, Typical value(s): 0 to 0.4x10

-3

Positive limit on strain in nonprestressed longitudinal rein-forcementin accordance with section 5.8.3.4.2; Default Value =6.0x10

-3, Typical value(s): 6.0x10

-3

PhiC for Nu Resistance Factor used in equation 5.8.3.5-1; De-


Phif for Mu Resistance Factor used in equation 5.8.3.5-1; De-


sx = Maximum distance between layers of longitudinal crackcontrol reinforcement in accordance with AASHTO LRFD

5.8.3.4.2-5. This parameter is used only when a girder does not

contain the code-specified minimum amount of shear rein-

forcement.


52/88



ag = Maximum aggregate size, Eq 5.8.3.4.2. This parameter isused only when a girder does not contain the code-specified

minimum amount of shear reinforcement.

4.3.5 Shear Resistance Variables

V= Resistance factor for shear

P

= Resistance factor for axial load

F

= Resistance factor for moment

= Multiplier of sqrt fc for light-weight concrete in accor-dance with 5.8.2.2

Vu

= Factored shear demand per girder excluding force in

tendons

Nu

= Applied factored axial force, taken as positive if tensile

Mu

= Factored moment at the section

V2c

= Shear in section cut excluding force in tendons

V2Tot

= Shear in section cut including force in tendons

Vp

= Component in the direction of the applied shear of the

effective prestressing force; if Vp

has the same sign as

Vu, then the component is resisting the applied shear

a = Depth of equivalent stress block in accordance with

5.7.3.2.2. Varies for positive and negative moment.

dv

= Effective shear depth in accordance with 5.8.2.9

dgirder

= Depth of girder

compslabd Depth of composite slab (includes concrete haunch t2)


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dp

= Distance from compression face to center of gravity of

tendons in the tensile zone

ds = Distance from compression face to center of gravity of

longitudinal reinforcement in the tensile zone

b = Minimum web width

Aps

= Area of prestressing steel on the flexural tension side of

the member

fpu

= Specified tensile strength of prestressing steel

Ep = Prestressing steel Youngs modulus

Avl

= Area of nonprestressed steel on the flexural tension sideof the member at the section under consideration

Es

= Reinforcement Youngs modulus

s

= Strain in nonprestressed longitudinal tension reinforce-ment eq. 5.8.3.4.2-4

Limi tPos Limi tNeg,s s = Max and min value of strain in nonprestressed

longitudinal tension reinforcement as specified in theDesign Request

Ec

= Youngs modulus of beam concrete

Ac

= Area of concrete on the flexural tension side of themember

Avprov

= Area of transverse shear reinforcement per unit lengthas specified in the Bridge Object. The transverse rein-forcement density is averaged over a distance 0.5 cotmeasured up-station and down-station from the currentsection cut.

AVSmin

= Minimum area of transverse shear reinforcement perunit length in accordance with eq. 5.8.2.5


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4.3.6

Shear Resistance AlgorithmAll section properties and demands are converted from CSiBridge

model units to N, mm.

If the combo specified in theMudemand set contains envelopes, a

new force demand set is generated. The new force demand set is

built up from the maximum tension values of P and the maximum

absolute values of V2 and M3 of the two StepTypes (Max and

Min) present in the envelope COMBO case. The StepType of this

new force demand set is named ABS and the signs of the P, V2,

and M3 are preserved. The ABS case follows the industry practice

where sections are designed for extreme shear and moments thatare not necessarily corresponding to the same design vehicle posi-

tion. The section cut is designed for all three StepTypes in the

COMBOMax, Min and ABSand the controlling StepType is

reported.

In the case when demand moment u u p vM V V d , two new

force demand sets are generated where vpospuupos dVVM

and vnegpuuneg dVVM . The acronyms -CodeMinMuPos

and -CodeMinMuNeg are added to the end of the StepType

name. The signs of the P and V2 are preserved.

The shear resistance is evaluated for every force demand set de-scribed previously. and the smallest value is used in evaluation

of the rating factor.

The component in the direction of the applied shear of the effec-tive prestressing force, positive if resisting the applied shear, is

evaluated:

2 2Tot

girders

cp

V VV

n


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Depth of equivalent stress block a for both positive and nega-tive moment is evaluated in accordance with eq. 5.7.3.1.1. See

section 4.1.2.

Effective shear depth is evaluated.ps ps p vl y s

e

ps ps vl y

A f d A f dd

A f A f

girdermax 0 72 0 9 0 5v e ed . d , . d , d . a

Evaluate numerator and denominator of (eq. 5.8.3.4.2-4)numerator 0 5 0 7

u

s u u p ps pu

V

M. N V V A . f

d

denominators p ps s vlE A E A

Adjust denominator values as followsIf denominator 0s and numerator 0s , then LimitPoss s

If numerator 0s , then denominators p ps s vl c cE A E A E A

Evaluate (eq. 5.8.3.4.2-4)numerator

denominator

ss

s

Check if axial tension is large enough to crack the flexuralcompression face of the section.

Ifgirder

0 52u cN

. f ' ,A

then 2s s

Check against the limit on the strain in non-prestressed longitu-dinal tension reinforcement specified in the Design Request


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LimitNegmax( , )s s s and LimitPosmin( , )s s s

Evaluate the angle of inclination of diagonal compressivestresses as determined in Article 5.8.3.4

18 29 3500 45s (5.8.3.4)

Evaluate minimum transverse reinforcement density required inaccordance with code

min 0 083v

v c

y

bA . f

f (5.8.3.4)

Check if the provided girder transverse reinforcement densityA

vprovaveraged over distance 0.5cot measured up-station and

down-station from the current section cut satisfies the minimum

specified by code and evaluate the factor indicating the ability

of diagonally cracked concrete to transmit tension and shear, as

specified in Article 5.8.3.4

IfAvprov

Avmin

, then

4 8

1 750 s

.

else

4 8 51 25 4

1 750 39 25 4s xe

. .

. s

where35

16

xxe

g

ss

a

(eq. 5.8.3.4)

Evaluate nominal shear resistance provided by tensile stresses inthe concrete eq. 5.8.3.3-3

0 083c c vV . f ' b d

Evaluate nominal shear resistance provided by tensile stresses inthe transverse reinforcement eq. 5.8.3.3-4


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prov cots v y vV A f d (eq. 5.8.3.3-4)

Evaluate total factored shear resistance and check against amaximum specified in 5.8.3.3-2

min 0 25r v c s c v vV V V ; . f b d

Note: The shear resistance evaluated here purposely ignores the

effect of the component in the direction of the applied shear of the

effective prestressing force Vp. This is to ensure that the prestress-

ing effect is not double counted when evaluating the load rating

factor. The name of the combo that contains the prestressing loads

is specified in the Demand Set P Combo in the rating request.


DCV

DC,

DW

VDW

, or PV

Pcontain multiple StepTypes, the V2 demands from

Max and Min StepTypes are consolidated into one ABS Step-

Type. This is accomplished by selecting maximum absolute from

the two StepType values while preserving the sign.


the LVLL+IM demand set. The StepType that produces the smallestrating factor is reported in the output table.


VDC

, DW

VDW

, or PV

Pis de-

termined. If the sign of the sum matches the sign of the LV

LL+IM,

the shear resistance is reduced by the sum; if the sign of the sum is

opposite, the shear resistance is increased by the sum.


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Load Rating 5- 1

Chapter 5 Steel I-Section with Concrete Slab

This chapter describes the algorithm CSiBridge applies when load rating deck

superstructures comprised of steel I-beam with concrete slab. The slab can be

non-composite or composite. The load rating is in accordance with the

AASHTO Manual for Bridge Evaluation First Edition 2008 with 2010 Interim

Revisions (AASHTO MBE). The user has an option to set determination of

flexural capacity of qualifying sections in accordance with AASHTO LRFD

Section 6 or with Appendix A.

This algorithm analyzes the superstructure on a girder-by-girder (beam-by-

beam) basis while ignoring the effects of torsion. The user has the option to usethe individual girder demands directly from the CSiBridge model (available

only for Area and Solid models) or use Live Load Distribution (LLD) factors.

CSiBridge gives the user a choice of methods to address distribution of live

load to individual girders. The evaluation and application of LLD factors is de-

scribed in detail in Chapter 3 of the Bridge Superstructure Design manual. It is

important to note that to obtain relevant results, the definition of a Moving

Load case must be adjusted depending on which method is selected. Refer to

Chapter 3 Section 3.1 of theBridge Superstructure Design manual.


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5- 2 Load Rating

5.1 Load Rating

5.1.1 Rating Factor

DC DW

L

DC DW

LL IM

c s nRRF

AASHTO MBE eq. 6A.4.2.1-1

RF Rating factor calculated by CSiBridge

Rn Nominal resistance calculated by CSiBridge

Values specified by the user in the Rating Request:

c

Condition factor; Default Value = 1.0, Typical value(s): 1.0. The fac-tor is specified in the Rating Parameters form.

s

System factor; Default Value = 1.0, Typical value(s): 1.0. The factoris specified in the Rating Parameters form.

Resistance factor taken as flex

or shear

depending on type of rating

flex

Resistance factor for flexure; Default Value = 1.0, Typical value(s):1.0. The factor is specified in the Rating Parameters form.

shear

Resistance factor for shear; Default Value = 1.0, Typical value(s):1.0. The factor is specified in the Rating Parameters form.

DCDC Factored moment demand due to dead load of structural componentsand attachments. The

DCfactor shall be included in the combo speci-

fied in the DC Combo demand set.

DW

DW Factored moment demand due to dead load of wearing surface and

utilities. The DW

factor shall be included in the combo specified inthe DW Combo demand set.

LLIM Factored demand due to live load. The L

factor shall be included inthe combo specified in the LL+IM Combo demand set.

5.1.2 Rating Factor Algorithm - Flexure

The rating factor is calculated for each StepType present in the LLLIM de-mand set. The StepType that produces the smallest rating factor is reported in

the output table.


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Chapter 5 Steel I-Section with Concrete Slab

Section Properties 5- 3

For each StepType one of the sections flexural capacities (positive or negative)

to be used in the rating factor equation is selected to match the sign of theLLLIM moment. Then the sign of the sum of moments

DCDC +

DWDW is de-

termined. If the sign of the sum matches the sign of the LLLIM, the moment

resistance is reduced by the sum; if the sign of the sum is opposite, the moment

resistance is increased by the sum.

When the AASHTO LRFD code prescribes flange lateral bending stresses flto

be considered, the specified fraction of the absolute value offlcaused by DC

and DW is deducted from resistance, and fl

caused by LLIM is added to the

LLIM demand.

5.1.3 Rating Factor Algorithm - Shear

In case any of the user defined combos for demands sets DC

VDC

or DW

VDW

contain multiple StepTypes, the V2 demands from the Max and Min StepTypes

are consolidated into one ABS StepType. This is accomplished by selecting the

maximum absolute from the two StepType values while preserving the sign.

The girder rating factor is calculated for each StepType present in the LV

LL+IM

demand set. The StepType that produces the smallest rating factor is reported

in the output table.


VDC

+ DW

VDW

is determined. If the sign

of the sum matches the sign of the LV

LL+IM, the shear resistance is reduced by

the sum; if the sign of the sum is opposite the sign of the LV

LL+IM, the shear re-

sistance is increased by the sum.

5.2 Section Properties

5.2.1 Section Proportions

When the rating parameter Ignore Proportion Limits = No, the program veri-

fies each section cut for cross-section proportion limits in accordance with

AASHTO LRFD Section 6.10.2. If any of the girders in the section cut do not

satisfy the limits, the section cut is flagged as not valid, and the rating is not

calculated at that cut. To avoid flagging the section as not valid, set the rating

parameter to Yes. In that case, it is the responsibility of the user to verify that

the resistance formulas, as specified in AASHTO LRFD Section 6.10, are still

applicable.


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5- 4 Section Properties

5.2.2 Yield Moments

5.2.2.1.1 Composite Section in Positive Flexure

The positive yield moment, My, is determined by the program in accordance

with section D6.2.2 of the code. For the purpose of determining positive yield

moment,My, the program decomposes load cases present in combo DC to two

Bridge Design Action categories: non-composite and

bridge rating

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