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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



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.



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



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



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



V

11.2 Conclusion 63

11.3 Scope for Future Studies 64

REFERENCES 65

APPENDIX 67



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







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



VIII

9.6 Stress contours due to IRC class AA center loading 42




9.10 Stress contours due to IRC class 70R center loading 469.11 Stress contours due to IRC class AA edge loading 46














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



PERFORMANCE BASED ANALYSIS OF BRIDGE DECK FOR DISTINCTIVE GIRDER TYPES

Department of Civil Engineering, S.D.M.C.E.T, Dharwad. Page 1

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





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.





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.





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.





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





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





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.





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.





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.





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.





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.





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





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





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.





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.





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.





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





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





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





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)





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.





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.





Figure 5.5

WHEELED VEHICLE

Class AA Tracked and Wheeled Vehicles (Clause 204.1)





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





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





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





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.





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.





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





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.





Figure 7.3: Bridge Deck Resting on Tee Girder

Figure 7.4: Sectional Properties of Prismatic Tee beam






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.





Figure 7.5: Bridge Deck Resting on I section concrete Girder

Figure 7.6: Sectional Properties of I section concrete beam






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.





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






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.





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.





Figure 8.1: CLASS 70R TRACKED & WHEELED VEHICLES (CLAUSE 204.1)

Figure 8.2: CLASS AA TRACKED VEHICLES (CLAUSE 204.1)





Figure 8.3: Wheel arrangement for 70R

Figure 8.4: Clear Carriageway width





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





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.





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





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)






due to IRC class 70R edge loading. (Max BM= 121.92 kN-m/m)


due to IRC class 70R center loading. (Max BM= 96.15 kN-m/m)






due to IRC class AA edge loading. (Max BM= 133.9 kN-m/m)


due to IRC class AA center loading. (Max BM= 107.03 kN-m/m)





9.1.2 Bridge Deck with Prismatic Tee Beam Girder


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.


Span

(m)

Deck

Thickness

(mm)

Girder type

Prismatic Tee beam


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





Fig 9.7 Graphical representation





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


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






due Self-weight of the structure. (Max BM= 111.3 kN-m/m)


due IRC class 70R center loading. (Max BM= 100.3 kN-m/m)






due IRC class AA center loading. (Max BM= 111.3 kN-m/m)


due IRC class 70R edge loading. (Max BM= 127.75 kN-m/m)






due IRC class 7AA edge loading. (Max BM= 139.9 kN-m/m)

9.1.3 Bridge Deck with I section concrete Girder


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







Span

(m)

Deck

Thickness

(mm)

Girder type

I Section (Concrete)


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


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









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




9.16, 9.17 and 9.18.


due self-weight of the structure. (Max BM= 60.32 kN-m/m)








due IRC class AA edge loading. (Max BM= 133.8 kN-m/m)





9.1.4 Bridge Deck with ISMB 600 Steel Girder


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



Span

(m)

Deck

Thickness

(mm)

Girder type

ISMB 600 steel section


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










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




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






due to self-weight of the structure. (Max BM= 195.22 kN-m/m)








due IRC class AA edge loading. (Max BM= 161.6 kN-m/m)





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,





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


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 )





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)





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)





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.





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.





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.





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.





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.





[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.

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2D frame models‖, Master of Science Thesis in the Master‘s Programme,

Structural Engineering and Building Performance Design.

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Section: II – Loads and Stresses, Fifth Revision.

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[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

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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





Fig 2: Completed Bridge Model in STAAD.pro

1. Open STAAD.pro with the units of kN-M and use the Space option.





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.





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




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.

merged compressed thesis

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