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COMPARATIVE STUDY OF RCC TBEAM BRIDGE

BY IRC 112:2011 & IRC 21:2000

A DISSERTATION

SUBMITTED IN PARTIAL FULFILLIMENT OF THE REQUIRMENTS

FOR

THE AWARD OF THE DEGREE OF

MASTER OF TECHNOLOGY

IN

STRUCTURAL ENGINEERING

BY

A V PRANAY KUMAR REDDY

Roll No: 12011D2002

DEPARTMENT OF CIVIL ENGINEERING

JNTUH COLLEGE OF ENGINEERING, KUKATPALLY

HYDERABAD500 085, A.P, INDIA


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JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY COLLEGE OF

ENGINEERING(AUTONOMOUS) Kukatpally, Hyderabad-500 085.

CERTIFICATE

This is to certify that the dissertation work entitled COMPARATIVE STUDY OF RCC T-

BEAM BRIDGE BY IRC 112 :2011 &IRC 21:2000being submitted by Mr. A V PRANAY

KUMAR REDDY, Regd.No.12011D2002in partial fulfillment of the requirements for the

award of the degree of MASTER OF TECHNOLOGYin STRUCTURAL ENGINEERING

to the JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY, HYDERABADis a

record of bonafide work carried out by him under my guidance and supervision.

Mr. A V PRANAY KUMAR REDDYhas worked on this project for a

period of two semester and in my opinion this thesis attains the standard requirements for the

award of Masters Degree. The results embodied in this dissertation have not been submitted to

any other University or Institution for the award of any Degree or Diploma.

Project Guide Head of the Department

Mrs.P. Srilakshmi Dr.K.M. Lakshmana Rao

Assoc.Professor in Civil Engineering Dept., Professor in Transportation Engg.

Dept. of Civil Engineering, Head of the Department,JNTUH College of Engineering, Dept. of Civil Engineering,JNTUH

Hyderabad. Hyderabad


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.

DECLARATION

I, the undersigned A V PRANAY KUMAR REDDY bearing Regd. No: 12011D2002

here by certify that the project entitled COMPARATIVE STUDY OF RCC T-BEAM

BRIDGE BY IRC 112 :2011 &IRC 21:2000 which is being submitted to the Jawaharlal

Technological university Hyderabad,in partial fulfillment of the requirements for the award of

the Degree of Master of Technology in Structural Engineering,Department of civil

engineering, is a bonafide work carried out by me and the results embodied in this Project report

have not been reproduced or copied from any source. The results embodied in this Project report

have not been submitted to any other university or Institute for the award of any Degree or

Diploma.

A V PRANAY KUMAR REDDY

Regd. No: 12011D2002

JNTUCE, Kukatpally,

Hyderabad- 500 085.

PLACE : Hyderabad

DATE :


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CHAPTER 1

INTRODUCTION

1.1 GENERAL

Bridge construction has been one of the important engagements of mankind from the earliest

days and today. It has achieved a world-wide level of importance. Bridges are one of the most

challenging of all civil engineering works. The numbers and sizes of bridges have continuously

increased in the last fifty years. Man's increasing mobility through railway and motorized

transport has caused such complex forms of bridges to be built, which has seemed unrealistic

earlier. To cope up with this demand, tremendous efforts all over the world in the form of activeresearch in analysis, design and construction of bridges is continuing.

1.1Definition

A bridge is a structure which maintains the communications such as the road and railway traffic

and other moving loads over an obstacle, namely a channel, a road, a railway or a valley. The

structure is termed as a "Bridge" when it carries road and railway traffic or a pipe line over a

channel or a valley and an over bridge" when it carries the traffic or pipe line over a

communication system like roads or railways. A viaduct is also a bridge constructed over a

busy locality to carry the vehicular traffic over the area keeping the activities of the area below

the is duct uninterrupted.

1.2Components of a bridge:-

The main parts of a bridge structure are as below:

a) Decking Consisting of a slab, girders, trusses etc.

b) Bearings for the decking

c) Abutments and piers

d) Foundations for abutments and piers.


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e) River training works, like revetment for slopes at abutments,aprons at bed level,etc.

f) Approaches to the bridge to connect the bridge proper to the roads on either side and

g) Hand rails, guard stones etc.

The components above the level of bearings are grouped as superstructure,while the parts below

the bearing level are classed as sub- structure.

1.3 Structural forms of bridge decks:-

A bridge may be classified in many ways depending up on its function,

material of construction, form or type of superstructure, plan geometry, support conditions or

span. They are:

1) Form of construction or type of deck

2) Plan- geometry or plan form

3) Support conditions

Over the years, a number of methods of analysis of bridge superstructures have been evolved and

are being used.Courbon's method, Hendry Jaeger method and Morice and Little methods are

some of the methods which have been in use since long, and are still popular, as they are found

to be easy, amenable to design graphs and also reasonably accurate for bridge decks of simple

configurations. But these methods are being gradually replaced where computer facilities are

available or more accurate analysis is desired or the cross section and/or layouts of the bridge

decks are complex.

Following the advent of digital computers, computer-aided methods like Finite Element, Finite

Difference, Finite Strip have been developed and are in use to analyse intricate forms of skew,

curved, bifurcated and arbitrary shapes of bridges having usual support conditions and cross

sections. But these methods are highly numerical and always carry a heavy cost-penalty.

Grillage Analogy is probably one of the most popular computer-aided methods for analyzing

bridge decks. The method consists of representing the actual decking system of the bridge by an

equivalent grillage of beams. The dispersed bending and torsional stiffness of the decking system


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are assumed, for the purpose of analysis, to be concentrated in these beams. The stiffnesses of

the beams are chosen so that the prototype bridge deck and the equivalent grillage of beams are

subjected to identical deformations under loading. The actual deck loading is replaced by an

equivalent nodal loading. The method is applicable to bridge decks with simple as well as

complex configurations with almost the same ease and confidence. The method is easy to

comprehend and use. The analysis is relatively inexpensive and has been proved to be reliably

accurate for a wide variety of bridges. The grillage representation helps in giving the designer a

feel of the structural behavior of the bridge and the manner in which loading is distributed and

eventually taken to the supports.

As the present topic is Concerned essentially with the analysis of highway bridge decks and

hence the main factors which govern and influence the choice of analytical technique, tio be

discussed, are only identified.

1.3.1Although there is a wide choice in classification but the description will be limited to only

those types of bridges which can be gainfully handled by employing the method of grillage

analogy.

(1) Form of construction

Broadly the forms of construction can be divided into(1) Slab Decks

(a) Solid slab deck

(b) Voided slab deck

(c) Pseudo slab deck

(2) Slab on girder deck

(a) T beam

(b) I beam

(3) Box girder bridges

(a) Single box girder

(b) Multi-cell box girder

(c) Singlecell trapezoidal box girder


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1.3.1(a) Slab decks:-

The slab deck behaves like a flat plate, which is a structural continuum for

transferring moments, shears and torsion in all directions in the plane of the plate. Based on

support conditions the slab deforms. Normally in a bridge deck two sides will be supported On

bearings over piers and the remaining two sides will be either free or stiffened by edge beams

corresponding to elastic supports.

The slab deforms locally in the form of a dish causing two dimensional moments, which share

the load from the deck. The deformation is a function of the stiffness of the slab in the

corresponding direction. Concrete slab decks are normally used for span upto 10m. For higher

spans the required thickness of the slab becomes large and accordingly the self weight becomes

large.

A Slab is isotropic when its stiffness is the same in all directions in the plane of the slab.It is

orthotropic when the stiffnesses are different in two directions at right angles.

Slab decks can conviently be analysed using the computer grillage analysis.

Solid slab

1.3.2 Slabon-Girders Bridge:-

Slab on girders bridges are by far the most commonly adopted type in the span range

of 10 to 50 m. The majority of beam and slab decks have number of beams spanning

longitudinally between abutments with a thin slab spanning transversely across the top. T beam

bridges are one of the most common examples under this category and are very popular because

of their simple geometry, low fabrication cost, easy erection or casting and smaller dead loads.

Usually I section or T section is used for the beam. But T section is found to be more efficient. T

beams are economical where depth of section is not a controlling factor from


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Head room coosiderations.The T beam bridge superstructure may consist of either girders and

slab or girders, slab and diaphragms at the supports or girders, slab, intermediate cross beams

and diaphragms. However. T-beam bridge with cross beam extending into and cast

monolithically with the deck slab is found to be more efficient and is recommended for adoption.

Simply supported RC T beam is normally adopted for spans upto 25m, Span depth ratio is

generally kept as 12 and 15 for continuous spans. Higher ratios are possible but riding qualities

are affected by creep characteristics of concrete. The girders spacing h, may vary justified by

comparing the cost of corresponding slab thickness. The usual range of spacing h is between 2 to

3m for these bridges. The stem width, *b', is about 300 mm. This stem or web is increased to B

at the bottom, forming a bulb to accommodate a large number of reinforcement bars there. This

B may be kept between 500 to 625 mm. The stem width is increased to B in the end region to

take care of large shears occurring there.

1.3.3 Box-Girder bridge

Now a days, single or multi cell reinforced and pre-stressed concrete box girder bridge have

been widely used as economic and aesthetic solutions for over crossing, under crossing,

separation structures and viaducts found in todays modern highway systems. The main

advantage of this type of bridges lies in the high torsional rigidity available because of closed

box section and convenience in varying the depth along the span.

In the span range of 20-30m, cast in situ multi cell reinforced concrete box girder bridges

are used. The span depth ratio of RC box girder bridges is generally adopted as 16 for simple

spans and 18 for continuous spans.

1.3

Plan Geometry or Plan Forms:-

The horizontal and vertical alignments of a bridge are governed by the

Geometrics of highway,roadway or channel it crosses.A bridge may be either be right or

skew,straight or curved or any combination thereof.


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.

1.4Support Configurations:-

The simple supports are common with slab bridges or with slab-on-girders

bridges of smaller spans. Cantilever and Balanced cantilever bridges are constructed for span

range of 35 to 60 m having T-beam or box-girder as their cross-section. Fully continuous bridges

are advantageous for spans over 35m and are suitable with pre-stressed concrete girders.

Further, the bridge may be placed on rigid supports or flexible (yielding)

supports. The conventional plate, rocker or rocker-cum-roller bearings provide rigid supports.

However, the recent trend is to favour elastomeric bearings. This provides yielding supports.

These are preferred because of their low height and low cost and require practically no

maintenance. Also, they are easy to replace. These bearings can cope up with complex

deformations of skew and curved geometry.

1.5

OBJECTIVES OF STUDY:

The aim of this project work is simply to know which method requires

more materials when all other factors such as length and width of the bridge as well as other

difficulties arise during the construction of bridge are assumed to be same for both Working

stress method and Limit state method.


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CHAPTER-2

DESIGN APPROACH

CHAPTER-3

BRIDGE LOADING

3.1 Introduction:

The loading has profound effect upon the design, construction and eventually upon the cost of

any bridge of a give span. Besides carrying their own weight, the decks are designed for certain

loadings imposed partly by the vehicles and the users and partly by the nature. In order to

maintain uniformity in design, loading standards have been laid down for the guidance of

engineer. Different countries, including India, have their own loading standards.

In India, these standards for Railway bridges are formulated by the Research Design and

Standards Organization (RDSO) of the Indian Railways. For highway bridges, Indian Road

Congress (IRC), a statutory body formed by the Government of India under the Ministry of

Surface Transport, prepares the Codes of Practices(5). These codes are compiled faithfully in

the design of bridges. The Bureau of Indian Standards (BIS), a body responsible for the

"Standardization" in the country, also brings out specifications for bridges. But the

specifications laid down by IRC supersede those of the BIS, wherever at variance.

2.2 Loading requirements:

The deck of the highway bridge has to support moving loads in the form of vehicles, men and

materials and transmit their effects to the foundation. It has also to support and carry the self

weight of its various components. The structure is also subjected to vibrations under moving

loads giving rise to what is known as impact loading. The details of some other loads and forces


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such as earthquake, wind etc., which also become important in some cases could be referred

from the Codes of Practice. Only the important loads to be used in the analysis of decks are

briefly described here.

2.3 Dead Loads:

The bridge superstructure is to be analysed for its self weight and dead loads imposed on it as

well. The dead loads imposed on the bridge consist of permanent load such as that of wearing

coat, kerb, parapets stationary etc. The dead load can be estimated fairly accurately during

design and can be controlled during construction and service.As a guidein estimating the dead

loads the unit weight of materials may be assumed as given in IRC :6-2000.

2.4 Live Loads:

The main loading on highway bridges is due to the vehicles moving on it,which are transient and hence

difficult to estimate accurately and the designs has very little control over them once the bridge is

opened to traffic. In order to analyse the bridge for these moving loads,IRC code recommends certain

standard hypothetical loading systems. The bridge is then designed for the maximum response values

under these standard loads.

The live loads usually consist of a set of wheel loads which are patch loads due to tyre contact area.

These patch loads may be treated as point loads acting at the centre of the contact area. The

simplification is found to be acceptable in the analysis.

Accordingly to Indian Roads Congress classification, the main live loads for road bridges can be put into

the following four types.

I) IRC Class A Loading Single Lane and Two Lanes:

Single lane Class A loading is a train load of eight axles of two wheels each thus having sixteen wheels in

total. The total load of the train is 55.4 tonnes. The nose to tail length of the train is 20.3 m and the

distance between the first and the last axle is 18.8 m. The minimum clear longitudinal distance between

two successive trains is 18.5m. The minimum center line distance of the wheel line from the edge of the

kerb works out to 400mm. The configuration of the loads as well as the portion of each wheel is given in*******

Class A two lanes loading consists of two Class A-Single lane trains placed side by side at specified

minimum clearance. Class A loading is adopted on all permanent bridges and culverts to be constructed

on State and National Highways


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ii) Class B Loading:

The Class B loading is identical to Class A loading as far as positions of axles are concerned but the

magnitude of axle loads is 60% of the corresponding loads in Class A Vehicles (Figs. 2.1 a, b). This loading

is intended for temporary structures, timber bridges and bridges in specified areas.

iii) IRC Class AA Loading:

This loading is to be adopted within certain municipal limits, in certain existing or contemplated

industrial areas, in other specified areas. and along certain specified highways.

The loading is an alternate loading and one train of Class AA vehicle is to be considered for every two

lanes of Class A loading. It consists of either a tracked vehicle of 70 tonnes or a two axle wheeled vehicle

of 40 tonnes.

Detailed dimensions, kerb distances etc., arc given in ******* Bridges designed for Class AA loading

should also be checked for equivalent lanes of Class A loading since under certain conditions, heavier

stresses are obtained under such equivalent Class A loading. The nose to tail spacing between two

successive vehicles is specified as 90m. For each standard vehicle as train, all the axles of a unit of

vehicles shall be considered as acting simultaneously in a position causing maximum stresses.

iv)Class 70 R Loading:

This is the revised version of Class AA loading and consists of tracked and wheel loadings. The minimum

clearance between the road face of the kerb and the outer edge of the track or wheel is same as for

Class AA loading. The spacing between successive vehicles is 30m this spacing is measured from the rear

most point of ground contact of the leading vehicle to the forward most point of ground contact of the

following vehicle.

70R loading, as before, weights 70 tonnes. The track dimensions are slightly different than those of Class

AA track loading. For design purposes, wherever required, each strip loading could be idealized into a

suitable number of point loads say 8 or 10.

70 R Wheel loading is of two types:-

1. 70R Bogie loading weighing 40 tonnes through two axles each weighing 20 tonnes.

2. 70R train loading weighing 100 tonnes through seven axles, one axle of 8 tonnes, two axles of 12

tonnes each and four axles of 17 tonnes each.


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An axle may have four or eight wheels on it. There are two, four wheel arrangements and one, eight

wheel arrangement leading to three alternate wheel arrangements termed as col. '1', col. 'm', col. 'n'

arrangements. All axles will have the same arrangement of wheels at a time and all wheels on an axle

will have equal loads. The two alternate four wheel arrangement namely col. '1', col. 'm' are given in

figs. 2.3 (a), (b), (c).

2.5 Impact loads

Another major loading on the bridge superstructure is due to vibrations caused when the vehicle is

moving over the bridge. The theoretical estimation of this load is quite complex as it depends upon a

variety of factors such as roughness of the surface, spring system of the vehicle, condition of expansion

joints at the entry of the bridge etc.

The IRC code however, recommends definite values of impact factors for the vehicles for simplifying the

analysis. The value of impact load is expressed as percentage of the live load, depending upon the

material used in the construction of deck of the bridge, type of loading and the bridge span.The

percentage can be calculated using suitable formulae or could be directly read from fig given page no.

23 of IRC:6-2000.

The impact fraction shall be determined from the following equations which are applicable for spans

between 3 m and 45 m.

i) Impact factor fraction for reinforced concrete bridge =

ii) Impact factor fraction for steel bridges =

Where L, is length in metres of the span.

2.6 Foot way, Kerb, Railing and Parapet Live Loads:

The following provisions have been made for footpath, kerb, railing and parapet live loadings in

IRC :6-2000.

i)

For all parts of bridge floors accessible only to pedestrians and animals and for all footways

the loading shall be taken as 400 Kg/m2, where crowd loads are likely to occur such as on

bridges located near towns which are either centres of pilgrimage or where large


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congregational fairs are held seasonally, the intensity of footway loading be increased from

400 kg/m2 to 500 kg,/m2.

ii)

Kerbs, 0.6 in or more in width, shall be designed for the above loads and for a local lateral

force of 750 kg per metre, applied horizontally at the top or the kerb. If the kerb width is

less than 0.6 in, no live load may be necessary in addition to the lateral load specified above.

The horizontal force need not be considered in the design of the main structural members

of the bridge.

iii)

In bridges designed for IRC vehicular loadings, the members supporting the footways shall

be designed for the following live load per square metre of footway area, the loaded length

of footway taken in each case being such as to produce the worst effects on the member

under construction.

a)

For effective span of 7.5 m or less, 400 kg/m2 or 500 kg/m2as the ease may be as per (i)

above.

b)

For effective spans of over 7.5 m but not exceeding 30 m, the into-v4y or load shall be

determined according to the equation.

P =P'[ ]

c) For effective spans of over 30 m, the intensity of load shall be determined according to

the equation.

P = [P1-260+ ][ ]

P = The live load in Kg/m2.

L = The effective span of the main girder in m.

W = width of the footway in m.

iv)

Each part of the footway shall be capable of carrying a wheel load of 4 tonnes, which

shall be deemed to include impact, distributed over a contact area, 300 mm in diameter, the

permissible working stresses shall be increased by 25% to meet his provision.

v)

The railings or parapets shall be designed to resist a lateral horizontal force and a vertical

force each of 150 kg/m applied simultaneously at the top of the railing or parapet. These

forces need not be considered in the design of the main structural members if footpaths are

provided, the effect of these forces shall be considered in the design of the structural

system supporting the railings and the footpath upto the face of the footpath kerb only.


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CHAPTER 4

Method of grillage Analysis

4.1 Introduction:-

In recent years, the Grillage Analogy Method,which is a computer-oriented technique,is increasingly

being used in the analysis and design of bridges.The method is also suitable in cases where bridge

exhibits complicating features such as heavy skew,edge stiffening and isolated supports.The use of

computer facilities the investigation of several load cases in shortest possible time.The method is

versatile in nature and the contribution of kerb beams and the effect of differential sinking of girder

endsover yielding bearings (such as neoprene bearing) can also be taken into account abd large

variety of bridge decks can be analysed with sufficient practical accuracy.Further more,the grillagerepresentationis conducive to give the designer a feel for the structural behavior of the bridge and

the manner in which the bridge loadings are distributed and eventually taken to the supports.

This method of analysis, based on stiffness matrix approach,was made amenable to computer

programming by Lightfoot and Sawko. West made recommendations backed by carefully conducted

experiments on the use of grillage analogy. Gibb developed a general computer program for grillage

analysis of bridge decks using direct stiffness approach that takes into account the shear deformation

also,Martin then followed by Sawko derived stiffness matrix for curved beams and proclaimed a

computer program for a grillagefor the analysis of decks, curved in plan.

Method of Grillage Analogy

The grillage analogy method can be applied to the bridge decks exhibiting complicated features such

as heavy skew, edge stiffening, deep haunches over supports,continuous and isolated supports etc.,

with ease. The method is versatile, in that ,the contributions of kerb beams and footpaths and the

effect of differential sinking of girder ends over yielding supports such in the case of neoprene bearing

can be taken into account.Further it is easy for an engineer to visualize and prepare the data for a

grillage. Also,the grillage analysis programs are more generally available and can be run on personal

computers. The method has proved to the reliably accurate for a wide varietyof bridge decks.

The method consists of 'converting the bridge deck structure into a network of rigidly connected

beams at discrete node i.e. idealizing the bridge by an equivalent grillage.

The deformations at the two ends of a beam element are related to the bending and to moments

through their bending and torsional stiffnesses. The load deformation relationship at the two ends of

a skeletal element with reference to the member axis is expressed in terms of its stiffness


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property.This relationship which is expressed with reference to the member coordinate axis, is then

transferred to the structure or global axis using transformation matrix, so that the equilibrium

condition that exist at each node in the structure can be satisfied.

These moments are written in terms of the end-deformations employing slope-deflection

and torsional rotation-moment equations. The shear force in the beam is also related to the bendingmoment at the two ends of the beam and can again be written in terms of the end-deformations of

the beam. The shear and moment in all the beam elements meeting at a node and fixed end reactions,

if any, at the node, are summed-up and three basic statical equilibrium equations at each node

namely Fz= 0,Mz= 0 and My= 0 are satisfied.

The bridge structure is very stiff in the horizontal plane due to the presence of decking

slab. The transitional displacements along the two horizontal axes and rotation about the vertical axis

will be negligible and may be ignored in the analysis. Thus a skeletal structure will have three degrees

of freedom at each node i.e., freedom of vertical displacement and freedom of rotations about two

mutually perpendicular axes in the horizontal plane. In general, a grillage with n nodes will have 3ndegrees of freedom or 3n nodal deformations and 3n equilibrium equations relating to these.

All span loadings are converted into equivalent nodal loads by computing the fixed end

forces and transferring them to global axes. A set of simultaneous equations are obtained in the

process and their solutions result in the evaluation of the nodal displacements in the structure. The

member forces including the bending and the torsional moments can then be determined by back

substitution in the slope deflection and torsional rotation moment equations.

When a bridge deck is analysed by the method Grillage Analogy, there are essentially

five steps to be followed for obtaining design responses:

(i) Idealisation of physical deck into equivalent grillage

(ii)

Evaluation of equivalent elastic inertias of members of grillage

(iii) Application and transfer of loads to various nodes of grillage

(iv)

Determination of force responses and design envelopes

(v)

Interpretation of results.

Bridges are frequently designed with their decks skew to the supports, tapered or curved

in plan. The behavior and rigorous analysis are significantly complicated by the shapes and support

conditions but their effects on grillage analysis are of inconvenience rather than theoretical

complexity.

3.2 Idealization of Physical deck into equivalent Grillage:-

The method of grillage analysis involves the idealization of the bridge deck

as a plane grillage of discrete inter-connected beams. This is the first important step to be taken by


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the designer and needs utmost care and understanding of the structural behavior of the bridge decks.

It is difficult to make precise general rules for choosing a grillage mesh and much depends upon the

nature of the deck to be analysed, its support conditions, accuracy required, quantum of computing

facility available etc., and only a set of guidelines can be suggested for setting grid lines. It may be

noted that such idealization of the deck is not without pitfalls and the grid lines adopted in one case

may not be efficient in another similar case and the experience and judgment of the designer will

always play a major role.

3.2.1 General Guidelines for Grillage Lay-out:-

Some basic guidelines regarding the location, direction, number, spacing etc. of the

longitudinal and transverse grid lines forming the idealized grillage mesh, are given bellow. But each

type of deck has its own special features and may need some particular arrangements for setting

idealized grid lines and therefore has been discussed separately also.

(a) Location and Direction of Grid lines

In the longitudinal direction, these should be along the centre line of girders, longitudinal webs or

edge beams, wherever these are present. Where isolated bearings are adopted, the grid lines are also

to be chosen along the lines joining the centers of bearings. In the transverse direction, the grid lines

are to be adopted, one at each ends connecting the centers of bearings and along the centre lines of

transverse beams, wherever these exist. Ordinarily the Grid lines should coincide with the centre of

the sections but some shift is permissible, if this simplifies the grid layout.

(b) Number and Spacing of Grid Lines

Wherever possible, an odd number of longitudinal and transverse grid lines are to

be adopted. The minimum number of longitudinal grid lines may be three and the minimum number

of transverse grid lines per span may be five.

The ratio of spacing of transverse grid lines to those of longitudinal grid lines may be chosen between

1.0 and 2.0. The ratio should also, ordinarily, reflect the span-width of the bridge.Thus, for a short

span and wide bridge, it should be close to 1.0 and for long span and narrow bridge ,this ratio may be

closer to 2.0.

Grid lines are usually uniformly placed, but their spacings can be varied, if the situation so demands.

For example, closer transverse grid lines should be adopted near a continuous support as the

longitudinal moment gradient is steep at such locations.

It may be noted that with an increase in number of grid lines, the accuracy of computation increases,

but the effort involved is also more and soon it becomes a case 'of diminishing return. In a contiguous

girder bridge, more than one longitudinal physical beam can be represented by one grid line. For slab

bridges, the grid lines need not be closer than two to three times the depth of slab.


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3.3 Grillage idealization of slab on girder bridges:-

The idealization of beam and slab bridge by an assembly of interconnected

beams seems to confirm more readily to engineering judgment than for slab bridges. The T and I

beams are by far the most commonly adopted type of bridge decks, consisting of longitudinal girders

at definite spacing connected by top slab, with or without transverse cross beams. Usually, thediaphragms connecting the longitudinal girders are provided at the supports.In longer spans

intermediate cross girders are also provided.

The logical choice of longitudinal grid lines for T-Beam or I Beam decks are to make them coincident

with the centre lines of physical girders and the longitudinal members are given the properties of the

girder plus associated portions of the Slab,which they represent. Additional grid lines between

physical girders may also be set in order to improve the accuracy of the result. Edge grid lines may be

provided at the edges of the deck or at suitable distance from the edge. For bridge with footpaths

,one extra longitudinal grid along the centre line of each foot path slab is provided. The above

procedure for choosing longitudinal grid lines is applicable to both right and skew decks.

3.4 Evaluation of equivalent elastic properties:-

After the actual bridge structure is simulated into equivalent grillage, consisting of

longitudinal and transverse grid lines meeting at discrete nodes,the second important step in grillage

analogy method is to assign appropriate elastic properties i.e. flexural and torsional stiffnesses to

each member of the grillage so idealized. This needs the computation equivalent flexural moment of

inertia I and torsional inertia J for the members of the grillage mesh. This is accomplished by

considering isolated sections of the deck as if they are individual beams and the inertias are calculatedfor each section.

3.5 Flexural and Torsion inertias of Grillage Analysis for slab on girder decks:-

Slab-on-Girders bridge decks consist of a number of beams spanning

longitudinally between abutments with a thin slab spanning transversely across the top. T-beam

bridges are the common examples under this category. When such I or T-beams bend, the flanges are

subjected to flexural stresses. An element of the flange away from the rib or stem of the beam has

less stress than the one directly over the rib due to shearing deformations of the flange. Sheardeformation relieves some amount of compressive stress in more distant elements. This phenomenon

is known as shear lag.

For the purpose of calculation of flexural and torsional inertias, the effective width of

slab, to function as the compression flange of T-beam or L-beam, is needed. A rigorous analysis for its

determination is extremely complex and in absence of more accurate procedure for its evaluation, IRC


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recommendations are followed. IRC: 21-2000 recommends that the effective width of the slab should

be the least of the following:

I . In case of T-beams

(i) One-fourth the effective span of the beam

(ii) The distance between the centers of the ribs of the beams

(iii) The breadth of the rib plus twelve times the thickness of the slab

2. In case of L-beams

(i) One-tenth the effective span of the beam

(ii) The breadth of the rib plus one-half the clear distance between he ribs

(iii) The breadth of the rib plus six times the thickness of slab

The flexural inertia of each grillage member is calculated about its centroid.

Often the centroids of interior and edge member sections are located at different levels.The effect of

this is ignored as the error involved is insignificant.

Once the effective width of slab acting with the beam is decided, the deck is

conceptually divided into number of T or L-beams as the case may be. Some portion of the slab may

be left over between the flanges of adjacent beams in either directions. In the longitudinal direction,

it is sufficient to consider the effective flange width of T,L or composite sections, in order to account

for the effects of shear lag and ignore the left over slab should be considered by introducing

additional grid lines at the centre of each left over slab portion.

The section properties of grid lines representing the slab may be calculated as:

I = bd3 and J = bd3

If the construction materials have different properties in the longitudinal and

transverse directions, care must be taken to apply correction for this. For example ,in a reinforced

concrete slab on pre-stressed concrete beams or on steel beams, the inertia of the beam element (I or

J) is multiple by the ratio of modulus of elasticities of beams Eb and Es materials to convert it into the

inertia of slab material.


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3.5 Evaluation and Application of Loads:-

The bridge is mainly subjected to vertical loads comprising dead, live and impact

loads. Grillage analysis requires these loads on the bridge superstructure, are to be evaluated into

equivalent loads appropriately distributed to the nodes of the grillage.

a) Dead load

The deck of a bridge is subjected to dead loads comprising of its self weight and

weights due to wearing coat, parapet, kerb etc. which are of permanent stationary nature. The dead

loads act on the deck in the form of distributed load. These dead loads are customarily considered to

be borne by the longitudinal grid members only giving rise to distributed loads on them. This

distributed load on a longitudinal grid member is idealized into equivalent nodal loads. This is

specially required to be done when the distributed load is non-uniform. On the other hand, if the self

load is uniform all along the length of the longitudinal grid line then it is not necessary to find the

equivalent nodal load and instead it can be handled as a uniformly distributed load (u.d.I.) itself.

Further, if the dead load is u.d.l. but its centre is non coincident with the longitudinal grid line then it

is substituted by a vertical u.d.l. together with a torsional u.d.l.

The self weight of cross-beams and diaphragms needs further

considerations. These beams, located at specific intervals, are actually small discrete loads on the

longitudinal girders. However, for simplicity of computation, the total weight of all the cross-beams

per span should be calculated and equally divided in the form of distributed loads to various

longitudinal members of the grillage. The dead weight of railings, kerbs, footpaths etc. is lumped on

the edge longitudinal grid lines.

b) Live Load

The mains live loading on highway bridges is of the vehicles moving on it. The details of these loading

is given in IRC :6-2000 code. The vehicular live loads consist of a set of wheel loads. These are

distributed over small areas of contacts of wheels and form patch loads. These patch loads are treated

as concentrated loads acting at the centres of contact areas. This is a conservative assumption and is

made to facilitate the analysis. The effect of this assumption the result is very small and does not

make any appreciable change in the design.

The wheel loads of the vehicle will be either in the panels formed by the longitudinal and transverse

grid lines, or on the nodes. The wheel loads falling in the panels are to be transferred to the

surrounding nodes of the panels to facilitate the analysis.

To obtain the maximum response resultants for the design, different positions of each type of loading

system are to be tried on the bridge deck. For this purpose, the wheel loads of a vehicular loading

system are placed on the bridge and moved longitudinally and transversely in small steps to occupy a

large number of different positions on the deck. The largest force response is obtained at each node.


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c)Impact Load

Another major loading on the bridge superstructure is due to the

vibrations caused when the vehicle is moving over the bridge. This is considered through impact

loading. IRC gives impact load as a percentage of live load. As per IRC 6-2000, impact load varies with

type of live loading, span length of the bridge and whether it is steel or a concrete bridge. The impactload can be calculated using formulae or could be directly read from read to use graphical plot (Fig '5'

of IRC 6-2000). The impact load, so evaluated, is directly added to the corresponding live load.

3.6 IDENTIFICATION OF PANELS IN THE GRILLAGE

When longitudinal and transverse members of the grillage form panels and the grillage is therefore

divided into number of such panels. All the wheels of the vehicular loading system may not come

directly on the nodes of the grid but usually majority of the wheels fall inside the panels.These wheel

loads acting on the panels are to be transferred to the contiguous nodes forming the panel,before the

grid is analysed by the grillage analogy .Therefore,it is essential to identify the panels of the idealized

grillage deck in which a particular wheel load is lying.

3.7 TRANSFER OF LOADS TO THE NODES

The grillage analysis requires that loads be transferred to the corresponding nodes in the form of

equivalent loads. These equivalent nodal loads can be computed using any one of the following two

approaches:

(i)

Simple statical approach where the load is apportioned in the form of equivalent

vertical shear assuming that the panel between contiguous grillage elements is simply

supported along its boundary.

(ii) Another approach is where the equivalent load consists of vertical shear and

moments assuming that the panel between the contiguous grillage elements is clamped at

its edges.

Although the first approach is simpler, the neglect of fixed end moments will lead to some

error. The neglect of fixed end moments in the longitudinal direction does not usually give rise to any

significant error but their neglect in transverse direction can result in some inaccuracy in transverse

moments.

The second approach, where the loads arc distributed in the form of vertical shear and moments, is

more tedious but theoretically superior, As the computer is invariably used in the analysis of grillage,

this tediousness may not be considered an impediment to its use. However, both the approaches are

in practice and if the grillage mesh size is small, the results given by both will be close. But if the mesh

size is coarse, only the second approach is recommended.


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3.8 GRILLAGE ANALYSIS AND FORCE RESPONSES

After the loads are transferred to the nodes of the grillage in the form of equivalent

forces, the grillage may now be analysed to determine nodal deformations and member forces.

Analysis of Grillage

Direct stiffness method is an effective tool in analyzing the grillage on a computer. As mentioned

earlier, there are three possible displacements at each joint of the grillage. These, for a grid in X-Y

plane, are joint rotations about X and Y axes and joint translation in Z-direction, normal to X-Y plane.

The displacements in its own plane and rotation about Z-axis are small and are ignored. The analysis

of grillage by the stiffness method involves the following steps.

1. Formulation of Stiffness Matrix

2.Formulation of Load Vectors

3.Identification of Support Conditions

4. Solution of simultaneous Equations

5. Determination of Nodal and Member Deformations and Forces

Force Responses

As discussed above, the solution of equations yields nodal deformations i.e.

deflection,slope and rotation at each end of the member. The shear force for a member,the bending

moments at the two ends of the member, the torsional moment in a member and reactions at the

supported nodes are the usual output. However, these outputs can be modified and more details are

possible. Ordinarily the output is obtained for various longitudinal and transverse positions of different

types of live loading. Invariably the output obtained is very large. Scanning this output, for a grillage of

even moderate size, is a problem. Therefore, to reduce the output data,only the critical values of the

force responses need to be retained.

For the design of any bridge structure we need the envelope diagrams of various responses

on it. The envelope diagrams are the response diagrams drawn along the longitudinal grid lines with thelargest values of responses picked up under live load. This may be achieved for a particular live load by

moving it over the deck in small increments both longitudinally and transversely and for each of the load

positions, the deck is analysed. When the load moves from one position to the next position, the

responses are again obtained for this new position of load and these values are compared with the

previous values. The larger values of each force responses like shear force, bending moment and

torsional moment for each grid member are required along with the corresponding load position,


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deleting the smaller values. The process is repeated till the whole length and breadth of the bridge is

covered by the live load.

The load position for each critical value is given through the coordinates of the left

most wheel of the leading axle. This information of load position could be used for positioning the live

load on the deck and carrying out a manual check if so desired.

The number of movements of loads in longitudinal and transverse directions will

depend upon the factors like span, carriageway width, type of live loading, extent of accuracy desired,

available computer time, etc. However, as a preliminary guidance, the movements of loads in

increments equal to about 1 /15th

of span length or half the size of the mesh in longitudinal direction is

chosen.

The initial and final positions of the live loading on the deck should be so chosen that no critical

response is missed out. The initial and final positions of wheels in longitudinal direction (Xminand Xmax)

and in transverse direction (Yminand Ymax).

3.9 Design Envelopes

In order to design a bridge for IRC loading, it is not sufficient to analyse the grillage for any one type of

live load only and obtain response envelope diagrams for it. The maximum responses due to one

particular type of live load may not be critical at all the points on the deck and it has to be scanned for

other types of live loads also to obtain the largest design responses.

To achieve this each live load system is moved longitudinally and transversely in small increments to

cover the entire deck. The grillage is analysed for each of these positions and the maximum values of

responses are retained along with the corresponding load positions; the maximum response results of

various types of live loads are compared with each other and the highest values along with their load

positions and type of loading are retained giving an overall envelope diagram for each response

separately.

3.10 1NTERPRETAION OF RESULTS

The output or the result obtained from the analysts of grillage consists of vertical

deflections and X and Y rotations of each node. shear force and torsional moment of each beam

element,bending moments at the two ends of each beam element and reactions at each support.

The output or the result obtained from the analysis of grillage consists of vertical deflections and X

and Y rotations of each node, shear force and torsional moment of each beam element, bending

moments at the two ends of each beam element and reactions at each support.

The above results are to be judiciously used while designing a bridge deck. Since the deck has been

initially idealized as a grillage and the analysis has been performed on the idealized grid, the results


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may sometimes need modifications and proper interpretations before they are finally used in design.

Some of the important interpretations of the Output and its modifications due to the local effects for

slab bridges and slab-beam bridges are discussed below.

3.10.1 Slab Bridges

The computer output for deformations like deflection and rotation and force responses like bending

moment, shear force and torsional moment are to be thoroughly examined and judiciously

interpreted in slab bridges. Modifications in the output results are made, if necessary, due to local

effects which are not considered earlier in the grillage analysis and the modified responses are to be

used in the design for better accuracy. Some of the significant observations pertaining a to force

responses for slab bridges are discussed here.

The slabs are designed on the basis of per unit force response. The computer gives

response for the width which is represented by a particular grillage member. Hence, these responses

should be converted into per unit width before these values are considered for design.

Only one value of the shear force for a member of the grillage is obtained from the

output and the same may be used in as such. Similarly, maximum reactions printed, are taken a

design values for reaction at supported nodes.

In reinforced concrete bridges, the direction of reinforcement may not always coincide with the

direction of principal moment. This is more so with skew slab bridges. In such a case, it should be

ensured that reinforcement component in the direction of each principal moment is adequate.

3.10.2 Slab-on-Girders Bridges

In beam and slab decks also, the stepping of moments in members on either side of a node occur. Thedifference in bending moments in two adjacent members meeting at a node will generally be large in

exterior girders. Where all the members meeting at the node are physical beams, the actual values of

bending moment output from the program should be used. If' at a node there are no physical beams in

the other direction and the grid beam elements represent a slab, the bending moments on either side of

the node should he averaged as there is no real beam of any significant torsional strength


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