Studyonthe behaviorof box girder bridge

As indicated in fig 2-2 the movements of the plate elements of the cross section cause distortion stresses in the transverse direction and warping stresses in the longitudinal direction.

STUDY AND BEHAVIOUR OF

BOX GIRDER BRIDGE

A Project Report Submitted to

Nagarjuna University

In Partial fulfillment of the Requirements for the

Award of the Degree of

V.VICKRANTH (Y06CE060)

Under the Guidance of

V.RAMESH, Asst Professor

&

Special Thanks to

N.R.K.MURTHY, HEAD OF THE DEPARTMENT

DEPARTMENT OF CIVIL ENGINEERING

V.R.SIDDHARTHA ENGINEERING

COLLEGE KANURU, VIJAYAWADA-520007

APRIL -2010 STUDY AND BEHAVIOUR OF BOX GIRDER BRIDGE

DEPARTMENT OF CIVIL ENGINEERING V.R.SIDDHARTHA ENGINEERING COLLEGE

KANURU, VIJAYAWADA-520007

This is to certify that the project report entitled “STUDY AND BEHAVIOUR OF BOX GIRDER BRIDGE” is the bona fide work done by

Under guidance and supervision of V.RAMESH, Asst.Professor, submitted in

partial fulfillment of the requirements for the award of the Degree of Bachelor of

Technology, in Civil Engineering by the Acharya Nagarjuna University

GUIDE: HEAD OF THE DEPARTMENT Date Date:

ACKNOWLEDGEMENTS

We take this opportunity first to express our deep sense of gratitude and

gratefulness to our project guide, V.RAMESH, Asst.Professor, Department of Civil Engineering

for his expert guidance, constant encouragement and support during all phases of our work

We would also like to thank N.R.K.MURTHY, Professor, Department of Civil

Engineering, D Y NARASIMHA RAO, Senior Engineer, Bridges and B SRIKANTH, Design

Engineer, S.C.R Secunderabad for their valuable suggestions and encouragement in the

successful completion of this Report

We would also like to thank Dr N.R.K MURTHY, Professor and Head,

Department of Civil Engineering for his cooperation in providing facilities for the successful

completion of this Report

We would also like to thank Dr.K.MOHAN RAO, Principal,V.R.SIDDHARTHA

ENGINEERING COLLEGE for providing the state of the art facilities in the college We also

take this opportunity to thank everyone who helped either directly or indirectly in bringing out

the project report to the final form

PROJECT ASSOCIATES:

J.S.KALYANA RAMA (Y06CE050) V.R.RAGHAVA SUDHIR (Y06CE039) V.SAMPATH KUMAR (Y06CE044) V.VICKRANTH (Y06CE060)

ABSTRACT

“When tension flanges of longitudinal girders are connected

together, the resulting structure is called a box girder bridge”

The behavior of box girder section for a general case of an

eccentric load has been studied and presented its studies in chapter 2 An

encompassing review of literature has been made regarding construction

and a summary of general specifications with reference to IRC:18 have

been discussed in chapter 3

Box girders can be universally applied from the point of view of

load carrying, to their indifference as to whether the bending moments are

positive or negative and to their torsional stiffness; from the point of view

of economy

An ongoing work has been taken as a case study for the present

work Analysis principles for torsion and distortion effects are applied to

the section selected, and found satisfactory Correspondingly, the problem

has been analyzed and designed for flexure and shear by giving due

considerations for torsional and distortional effects as a precautionary

measure

TABLE OF CONTENTS

CERTIFICATE

ACKNOWLEDGEMENTS

ABSTRACT

CONTENTS PAGE.NO

1 INTRODUCTION TO BOX

GIRDER BRIDGES 1

Introduction 2

Historical development 3

Evolution 4

Advantages 5

Disadvantages 5

Specifications 6

2 BEHAVIOUR OF BOX GIRDER 7

Flexure 9

Torsion 10

Distortion 16

Warping of Cross section 18

Shear lag 19

Diaphragms 22

3 CONSTRUCTION AND GENERAL

ARRANGEMENT 24

General Arrangement 25

Cast-in-situ Construction 26

Construction of Multi-cell

Beam On Elastic Foundation 35

Tabulation of Bending Moment

Prestressing forces and other

Prestress in service condition 54

Design of Elastomeric Bearing 58

Check for ultimate moment of

Design of cantilever deck

Design of cantilever deck

7 CONCLUSIONS 86

CONCLUSION AND

FUTURE WORK 87

CHAPTER 1

INTRODUCTION

Introduction

The continuing expansion of highway network throughout the

world is largely the result of great increase in traffic, population and

extensive growth of metropolitan urban areas This expansion has lead to

many changes in the use and development of various kinds of bridges The

bridge type is related to providing maximum efficiency of use of material

and construction technique, for particular span, and applications As Span

increases, dead load is an important increasing factor To reduce the dead

load, unnecessary material, which is not utilized to its full capacity, is

removed out of section, this Results in the shape of box girder or cellular

structures, depending upon whether the shear deformations can be

neglected or not Span range is more for box bridge girder as compare to

T-beam Girder Bridge resulting in comparatively lesser number of piers

for the same valley width and hence results in economy

A box girder is formed when two web plates are joined by a

common flange at both the top and the bottom The closed cell which is

formed has a much greater torsional stiffness and strength than an open

section and it is this feature which is the usual reason for choosing a box

girder configuration

Box girders are rarely used in buildings (box columns are

sometimes used but these are axially loaded rather than in loaded in

bending) They may be used in special circumstances, such as when loads

are carried eccentrically to the beam axis

“When tension flanges of longitudinal girders are connected

together, the resulting structure is called a box girder bridge”

Box girders can be universally applied from the point of view of

load carrying, to their indifference as to whether the bending moments are

positive or negative and to their torsional stiffness; from the point of view

of economy

1.1 Historical development and description:

The first box girder cross section possessed deck slabs that

cantilevered out only slightly from the box portion shown in figs a to e

With the prestressed concrete the length of cantilever could be increased

The high form work costs caused a reduction in the number of cells fig (f,

g, h) In order to reduce the construction loads to minimum possible extent

or to require only one longitudinal girder in working states even with

multiple traffic lanes

It was only with the development of high strength prestressing steel that it

became possible to span longer distances The first prestressed concrete

bridges, most of I-cross sections were built towards the end of the

1920’s.The great breakthrough was achieved only after 1945 “THE

SCLAYN” bridge over the river Maas, which was built by Magnel in

1948, was the first continuous prestressed concrete box-girder bridge with

2 spans of 62.70m In following years the ratio of wages to material costs

climbed sharply This thereby shifted the emphasis of development of

construction method The box girder cross-section evolved structurally

from the hollow cell-deck bridge or T-beam Bridge The widening of the

compression zone that began as a structural requirement at the central

piers was in the extended throughout the entire length of bridge because of

advantages transverse load-carrying characteristics

Fig:1-1

1.2 Evolution :

The spanning of bridges started with simple slabs As the spans

increased, the design depth of slab is also increased It is known that

material near centre of gravity contributes very little for flexure and hence

can be removed This leads to beam and slab systems The reinforcement

in bottom bulb of beam provided capacity for tensile forces and top slab

concrete, the capacity to resist the compression They formed a couple to

resist flexure

As the width of slab is increased more number of longitudinal girders are

required resulting in reduction of stiffness of beams in transverse direction

and relatively high transverse curvature The webs of beams get opened

out spreading radially from top slab Under high transverse bending these

will no longer be in their original position To keep it in their original

position the bulbs at bottom should be tied together which in-turn leads to

evolution of box girder Long spans with wider decks and eccentric

loading on cross-section will suffer in curvature in longitudinal and

transverse direction causing heavy distortion of cross-section Hence the

bridges should have high torsional rigidity in order to resist the distortion

of cross-section deck to a minimum

Accordingly box girders are more suitable for larger spans and wider

decks, box girders are to be suitable cross-section They are elegant and

slender Economy and aesthetics further lead to evolution of cantilevers in

top flanges and inclined webs in external cells of box girder The

dimension of cell could be controlled by prestressing

As the span and width increases the beams and bottom slabs are to be tied

to keep the geometry which in turn leads to evolution box girder

Any eccentric load will cause high torsional stresses which will be counter

acted by the box section The analysis of such sections are more

complicated due combination of flexure, shear, torsion, distortion But it is

more efficient section It is used for larger spans with wide

cross-section It can be used for spans up to 150m depending upon the

construction methods Cantilever method of construction is preferred

most

1.3 Advantages Associated with Box Girders:

 In recent years, single or multicell reinforced concrete box Girder

Bridge have been proposed and widely used as economic aesthetic

solution for the over crossings, under crossings, grade separation

structures and viaducts found in modern highway system

 The very large Torsional rigidity of the box girder‘s closed cellular

section provides structures beneath is more aesthetically pleasing than

open-web type system

 In case of long span bridges, large width of deck is available to

accommodate prestressing cables at bottom flange level

 Interiors of box girder bridges can be used to accommodate service

such as gas pipes, water mains etc

 For large spans, bottom flange could be used as another deck

accommodates traffic also

 The maintenance of box girder is easier in interior space is directly

accessible without use of scaffolding

 Alternatively space is hermetically sealed and enclosed air may be

dried to provide a non-corrosive atmosphere

 It has high structural efficiency which minimizes the prestessing

force required to resist a given bending moment, and its great Torsional

strength with the capacity this gives to re-centre eccentric live loads,

minimizing the prestress required to carry them

One of the main disadvantages of box decks is that they are

difficult to cast in-situ due to the inaccessibility of the bottom slab and the

need to extract the internal shutter Either the box has to be designed so

that the entire cross section may be cast in one continuous pour, or the

cross section has to be cast in stages

1.5 Specifications:

It can cover a range of spans from 25 m up to the largest

non-suspended concrete decks built; of the order of 300 m Single box girders

may also carry decks up to 30 m wide For the longer span beams, beyond

about 50 m, they are practically the only feasible deck section Below

30m precast beams or voided slab decks are more suitable while above

50ma single cell box arrangement is usually more economic

Single cell box-girder cast-in-situ are used for spans form 40m to

270m.The box arrangement is done in order to give aesthetic appearance

where the web of box will act as a slender appearance when combined

with a slim parapet profile Single box arrangements are efficient for both

the longitudinal and transverse designs, and they produce an economic

solution for mot medium and long span structures This type of deck is

constructed span-by-span, using full-height scaffolding or trusses, or as

balanced cantilever using form travelers This could be particularly

important for medium length bridges with spans between 40m and 55m

Such spans are too long for twin rib type decks, and too short for

cast-in-situ balanced cantilever construction of box girders, while a total length of

box section deck of less than about 1,000 m does not justify setting up a

precast segmental facility

Haunches:

The uprights have to carry the same bending moment as the haunch, but

with the benefit of a compression force due to the weight of the roof Thus

they may be slightly thinner than the haunches Haunches are always

economical They provide the twin benefits of attracting moment away

from mid-span and then providing a greater lever arm to resist this

moment economically Even very short haunches are valuable in reducing

the hogging reinforcement

CHAPTER 2

BEHAVIOUR OF BOX GIRDER BRIDGES

Fig:2-1

A general loading on a box girder, such as shown in fig 2-1

for single cell box, has components which bend, twist, and deform the

cross section Thin walled closed section girders are so stiff and strong in

torsion that the designer might assume, after computations based on the

elemental torsional theory, that the torsional component of loading in fig

2-1(c) has negligible influence on box girder response If the torsional

component of the loading is applied as shears on the plate elements that

are in proportion to St Venant torsion shear flows, fig 2-1 (e), the section

is twisted without deformation of the cross section The resulting

longitudinal warping stresses are small, and no transverse flexural

distortion stresses are induced However, if the torsional loading is applied

as shown in fig 2-1 (c), there are also forces acting on the plate elements

fig 2-1 (f), which tend to deform the cross section As indicated in fig 2-2

the movements of the plate elements of the cross section cause distortion

stresses in the transverse direction and warping stresses in the longitudinal

direction

Fig:2-2

A vehicle load, placed on the upper flange of box girder

can occupy any position, transverse as well as longitudinal This load is

transferred transversely by flexure of deck to the webs of box girder

For understanding the various stresses generated, initially consider that the webs of box girder are not allowed to deflect The

structure resembles a portal frame The flexure of deck would induce

transverse bending stresses in the webs, and consequently in the bottom

flanges of the girder Any vehicle load can thus be replaced by the forces

at the intersections of deck and web as shown in fig 2-3

Now the supports under the web are allowed to yield This results in deflection of web and consequently redistribution of forces

among web and flanges

Distortion of cross section occurs as a result of the fact that m1 and m2 are not equal resulting in sway of frame, due to eccentrically

placed load The section of box tries to resist this distortion, resulting in

the transverse stresses These stresses are called distortional transverse

stresses The distortion of cross section is not uniform along the span,

either due to non uniform loading or due to presence of diaphragms or due

to both However the compatibility of displacements must be satisfied

along the longitudinal edges of plate forming the box, which implies that

these plates must bend individually in their own plane, thus inducing

longitudinal warping displacements Any restraint to these displacements

causes stresses These stresses are called longitudinal warping stresses and

are in addition to longitudinal bending stresses

The main reason for box section being more efficient is that for

eccentrically placed live loads on the deck slabs, the distribution of

longitudinal flexural stresses across the section remains more or less

identical to that produced by symmetrical transverse loading In other

words, the high torsional strength of the box section makes it very suitable

for long span bridges

Investigations have shown that the box girders subjected to torsion

undergo deformation or distortion of the section, giving rise to transverse

as well as longitudinal stresses These stresses cannot be predicted by the

conventional theories of bending and torsion One line of approach to the

analysis of box girders subjected to torsion is based on the study of THIN

WALLED BEAM THEORY The major assumptions are:

a) Plate action by bending in the longitudinal direction for all plates

forming the cross section, namely webs, slabs is negligible

b) Longitudinal stresses vary linearly between the longitudinal joints,

or the meeting points of the plates forming the cross

section

Fig: 2-3

The kerb, footpath, parapet, and wearing coat generally

form the superimposed dead loads acting on the effective section which is

responsible for carrying all loads safely and transmitting them to the

substructure Because of symmetry, the self weight of the effective section

and the superimposed dead loads do not create any torsional effects

However the non-symmetrical live loads which consist of concentrated

wheel loads from vehicles on any part of carriage way and the equivalent

uniformly distributed load on one of the footpaths can subject the box

girder to torsion

Fig: 2-4

If the deck slab is considered to be resting on non

deflecting supports at A and B in fig 2-3(b), the vertical reactions and the

moments created by the live loads at these points can be computed The

effects of moments at this stage are treated as separately since they cause

only local transverse flexure fig 2-5 and can be evaluated by considering a

slice of unit length from the box girder The effect of superimposed and

dead loads should also be taken into account in such evaluations

Fig: 2-5

Coming to the vertical reactions, let equal and opposite vertical forces be applied at A and B In studying the longitudinal and

transverse effects, it should be noted that finally all longitudinal effects

have to be superimposed separately on the one hand, and transverse effects

on the other The vertical forces are denoted by P1 and P2 in fig 2-6 As

shown, (a) = (b) +(c) Since (c) = (d) + (e), it is evident that (a) = (b) + (d)

+ (e) Now (b) and (d) are symmetrical loads and, as in the case of

superimposed dead loads and self weight, do not create any torsional

effects Let the sum of all these symmetrical loads be denoted by Q, Q,

acting at A and B fig The loads Q, Q cause simple longitudinal flexure

only and the structural effects caused are illustrated in fig 2-4(a) The

loads P, P cause torsional effects in the box girder, and they are shown in

fig b, c The internal forces generated to counteract P, P are shown in fig

2-7

Fig: 2-6

Fig: 2-7

In ‘rigid body rotation’ or ‘pure torsion’ effects, the section merely twists or rotates causing St.Venant shear stresses and

associated warping stresses which can be evaluated by the elemental

theory of torsion as applied to closed sections of thin walled members It

may be emphasized that due to very high stiffness in ‘pure torsion’, the

box girder will twist very little, and that the webs will remain almost

vertical in their original unloaded position Also the associated

longitudinal stresses due to warping restraint when present are negligible

as compared to those induced by the longitudinal flexure due to forces Q,

Q

The theoretical behavior of a thin-walled box section subject to

pure torsion is well known For a single cell box, the torque is resisted by

a shear flow which acts around the walls of the box This shear flow

(force/unit length) is constant around the box and is given by q = T/2A,

where T is the torque and A is the area enclosed by the box The shear

flow produces shear stresses and strains in the walls and gives rise to a

Or,

Where J is the torsion constant

However, pure torsion of a thin walled section will also

produce a warping of the cross-section, Of course, for a simple uniform

box section subject to pure torsion, warping is unrestrained and does not

give rise to any secondary stresses But if, for example, a box is supported

and torsionally restrained at both ends and then subjected to applied torque

in the middle, warping is fully restrained in the middle by virtue of

symmetry and torsional warping stresses are generated Similar restraint

occurs in continuous box sections which are torsionally restrained at

intermediate supports

This restraint of warping gives rise to longitudinal warping

stresses and associated shear stresses in the same manner as bending

effects in each wall of the box The shear stresses effectively modify

slightly the uniformity of the shear stress calculated by pure torsion

theory, usually reducing the stress near corners and increasing it in

mid-panel Because maximum combined effects usually occur at the corners, it

is conservative to ignore the warping shear stresses and use the simple

uniform distribution The longitudinal effects are, on the other hand

greatest at the corners They need to be taken into account when

considering the occurrence of yield stresses in service and the stress range

under fatigue loading But since the longitudinal stresses do not actually

participate in the carrying of the torsion, the occurrence of yield at the

corners and the consequent relief of some or all of these warping stresses

would not reduce the torsional resistance

Fig 2-8 Warping of rectangular box subjected to pure torsion

If torsional loading is applied, there are forces acting on the plate

of elements, which tend to deform the cross section The movements of

the plate elements of the cross section cause distortion stresses in

transverse direction and warping stresses in longitudinal direction

2.3 DISTORTION:

Fig 2-9: Distortional effects

When torsion is applied directly around the perimeter of a box

section, by forces exactly equal to the shear flow in each of the sides of the

box, there is no tendency for the cross section to change its shape Torsion

can be applied in this manner if, at the position where the force couple is

applied, a diaphragm or stiff frame is provided to ensure that the section

remains square and that torque is in fact fed into the box walls as a shear

flow around the perimeter Provision of such diaphragms or frames is

practical, and indeed necessary, at supports and at positions where heavy

point loads are introduced But such restraint can only be provided at

discrete positions When the load is distributed along the beam, or when

point loads can occur anywhere along the beam such as concentrated axle

loads from vehicles, the distortional effects must be carried by other

means

The distortional forces shown are tending to increase the length of

one diagonal and shorten the other This tendency is resisted in two ways,

by in-plane bending of each of the wall of the box and by out-of-plane

bending, is illustrated in Figure

Fig 2-10 Distortional displacements in box girder

In general the distortional behavior depends on interaction between the

two sorts of bending The behavior has been demonstrated to be analogous

to that of a beam on an elastic foundation (BEF), and this analogy is

frequently used to evaluate the distortional effects

If the only resistance to transverse distortional bending is

provided by out-of-plane bending of the flange plates there were no

intermediate restraints to distortion, the distortional deflections in most

situations would be significant and would affect the global behavior For

this reason it is usual to provide intermediate cross-frames or diaphragms;

consideration of distortional displacements and stresses can then be

limited to the lengths between cross-frames

The distortion of section is not same throughout the span It may

be completely nil or non-existent at points where diaphragms are

provided, simply because distortion at such points is physically not

possible The warping stresses produced by distortion are different from

those induced by the restraint to warping in pure torsion which is

encountered in elementary theory of torsion The compatibility of

displacements must be satisfied along the longitudinal edges of the plate

forming the box, which implies that these plates must bend individually in

their own plane, thus inducing longitudinal warping displacements Any

restraint to this displacement causes stresses These stresses are called

longitudinal warping stresses and are in addition to longitudinal bending

stresses A general loading on a box girder such as for a single cell box,

has components, which bend twice and deform the cross section Using

the principles of super position, the effects of each section could be

analyzed independently and results superimposed

Distortional stresses also occur under flexural component,

due to poisson effect and the beam reductance of the flange in multi

cellular box, the symmetrical component also gives rise to distortion

stresses and it is significant percentage of total stresses With increase in

number of cells, the proportion of transverse distortional stresses also

increase How ever for a single cell box the procedure of considering only

the distortional component of loading for evaluation of distortional

stresses in adequate for practical purposes

The concrete boxes in general have sufficient distortional

stiffness to limit the warping stresses to small fraction of the bending

stresses, without internal diaphragms But for steel boxes either internal

diaphragms or stiffer transverse frames are necessary to prevent buckling

of flanges as well as of webs and in most cases these will be sufficient to

limit the deformation of the cross section

Sloping of the webs of box girder increase distortional

stiffness and hence transverse load distribution is improved If section is

fully triangulated, the transverse distortional bending stresses are

eliminated This form could be particularly advantageous for multicell

steel boxes Therefore distortion of box girder depends on arrangement of

load transversely, shape of the box girder, number of cells and their

arrangement, type of bridge such as concrete or steel, distortional stiffness

provided by internal diaphragms and transverse bracings provided to

check buckling of webs and flanges

Warping is an out of plane on the points of cross section, arising due to torsional loading Initially considering a box beam whose

cross section cannot distort because of the existence of rigid transverse

diaphragms all along the span These diaphragms are assumed to restrict

longitudinal displacements of cross sections except at midspan where, by

symmetry the cross section remains plane The longitudinal displacements

are called torsional warping displacements and are associated with shear

deformations in the planes of flanges and webs

In further stage assume that transverse diaphragms other than those at supports are removed so that the cross section can

distort (Fig) It results in additional twisting of cross section under

torsional loading The additional vertical deflection of each web also

increases the out of plane displacements of the cross sections These

additional warping displacements are called distortional warping

displacements/

Thus concrete box beams with no intermediate diaphragms when subjected to torsional loading, undergo warping

displacements composing of two components viz, torsional and

distortional warping displacements Both these give rise to longitudinal

normal stresses i.e warping stresses whenever warping is constrained

Distortion of cross section is the main source of warping stresses in

concrete box girders, when distortion is mainly resisted by transverse

bending strength of the walls and not by diaphragms

In a box girder a large shear flow is normally

transmitted from vertical webs to horizontal flanges, causes in plane shear

deformation of flange plates, the consequence of which is that the

longitudinal displacements in central portion of flange plate lag behind

those behind those near the web, where as the bending theory predicts

equal displacements which thus produces out of plane warping of an

initially planar cross section resulting in the “SHEAR LAG" Another

form of warping which arises when a box beam is subjected to bending

without torsion, as with symmetrical loading is known as “SHEAR LAG

IN BENDING”

Shear lag can also arise in torsion when one end of box

beam is restrained against warping and a torsional load is applied from the

other end fig 2-11 The restraint against warping induces longitudinal

stresses in the region of built-in-end and shear stresses in this area are

redistributed as a result which is an effect of shear deformation sometimes

called as shear lag Shear distribution is not uniform across the flange

being more at edges and less at the centre fig 2-13

Fig:2-11

In a box beam with wide, thin flanges shear strains may be sufficient to

cause the central longitudinal displacements to lag behind at the edges of

the flange causing a redistribution of bending stresses shown in fig 2-12

This phenomenon is termed as “STRESS DIFFUSION”

The shear lag that causes increase of bending stresses near

the web in a wide flange of girder is known as positive shear lag Whereas

the shear lag, that results in reduction of bending stresses near the web

and increases away from flange is called negative shear lag fig 2-12

When a cantilever box girder is subjected to uniform load, positive as well

as negative shear lag is produced However it should be pointed out that

positive shear lag is differed from negative shear lag in shear deformations

at various points across the girder

At a distance away from the fixed end in a cantilever box

girder say half of the span; the fixity of slab is gradually diminished, as is

the intensity of shear From the compatibility of deformation, the negative

shear lag yields Although positive shear lag may occur under both point

as well as uniform loading, negative shear lag occur only under uniform

load

Fig:2-12

It may be concluded that the appearance of the negative

shear lag in cantilever box girder is due to the boundary conditions and the

type of loading applied These are respectively external and internal

causes producing negative shear lag effect

Negative shear lag is also dependent upon ratio of span to

width of slab The smaller the ratio, the more severe are the effects of

positive and negative shear lag

Fig:2-13

The more important consideration regarding shear lag is that

it increases the deflections of box girder The shear lag effect increases

with the width of the box and so it is particularly important for modern

bridge designs which often feature wide single cell box cross sections The

shear lag effect becomes more pronounced with an increase in the ratio of

box width to the span length, which typically occurs in the side spans of

bridge girders The no uniformity of the longitudinal stress distribution is

particularly pronounced in the vicinity of large concentrated loads Aside

from its adverse effects on transverse stress distribution it also alters the

longitudinal bending moment and shear force distributions in redundant

structural systems Finally, the effect of shear lag on shear stress

distribution in the flange of the box, as compared to the prediction of

bending theory is also appreciable A typical situation in which large stress

redistributions are caused by creep is the development of a negative

bending moment over the support when two adjacent spans are initially

erected as separate simply supported beams and are subsequently made

continuous over the support In the absence of creep, the bending moment

over the support due to own weight remains zero, and thus the negative

bending moment which develops is entirely caused by creep

Fig 2-14 Effect of shear lag on distribution of stresses

at the support of a box girder

Advantage of closed section is realized only when distortion of

cross section is restricted Distortion could be checked by two ways: First

by improving the bending stiffness of web and flanges by appropriate

reinforcement, so as additional stresses generated due to restraint to

distortion are within safe limits The Second alternative to check distortion

may be to provide diaphragms as shear walls at the section where it is to

be checked These diaphragms distribute the differential shears of web to

flanges also by bending in plate ad by shear forces in diaphragm

The introduction of diaphragms into box girders will have two effects on transverse moments in slabs:

1) If the diaphragm spacing is approximately equal to transverse

spacing of webs, transverse bending moments may be reduced as a result

of two way slab action of diaphragm support

2) The moments caused by differential deflection will be eliminated

over the region influenced by diaphragms

By the provision of diaphragms, transverse bending stresses

caused by the moments, resulting from differential deflection of top and

bottom slabs are eliminated Proper spacing of diaphragms can be

determined by the use of beam on elastic foundation concept to effectively

control differential deflection The use of diaphragms at supports which

are definite locations of concentrated loading significantly diminishes the

differential deflections near the supports and should always be provided

As far as possible interior diaphragms are avoided as they not only result in additional load but also disrupt and delay the casting

cycle resulting in overall delay in construction In general interior

diaphragms would be needed for the box section, which has light webs

and supported by relatively stiff slabs Such a form of cross section is not

appropriate for concrete box girders, although prestressing is done

externally this type of cross section is not justified

Diaphragms which are stiff out of their planes, when provided at the supports, restrain warping in continuous spans, resulting in

stresses These stresses add to longitudinal bending stresses As conditions

of maximum torque do not generally coincide with conditions of

maximum bending, and the warping stresses, if they occur, may not

therefore increase bending stresses to unacceptable values

CHAPTER 3

CONSTRUCTION AND

GENERAL ARANGEMENT

OF BOX GIRDER

3.1 GENERAL ARRANGEMENT:

The deck arrangement is similar to a voided slab, but with

the voids occupying a larger proportion of deck area and usually being

rectangular in section The outer webs are often sloped and side

cantilevers made longer to improve the appearance The web thickness is

governed by the shear requirements, but they must be wide enough to

provide space for reinforcement and concrete to be placed around

pre-stressing ducts This usually requires a minimum web thickness of

300mm, but may be wider if larger tendons are used The deck slab size is

governed by web spacing and live load carried and is typically between

150mm and 200mm being sufficient Transverse diaphragms are provided

across the full width of the box at each of the support locations The

diaphragms provide rigidity to the box assist in transferring the loads in

the webs to the supports Intermediate diaphragms are often placed at ¼

or 1/3 points along the span to stiffen up the box and to help distribute the

loading between the webs

Access into box cells is achieved through soffit access holes

of a minimum of 600mm diameter, and is located near the abutments

Similar sized holes are provided through each of diaphragms and webs, as

required to give access into each section of deck Small drainage holes,

typically 50mm diameter, are provided through bottom slab at the low

point in each section of deck to ensure that water cannot collect inside box

cells

Concreting and construction restraints dictate a minimum

deck depth of 1200mm; although for reasonable inspection and

maintenance access a depth of at least 1800mm is needed With an

optimum span –to-depth ratio of between 18:1 and 25:1 the preferred span

lengths are usually greater than 30m

Multi-strand tendons are used following a draped profile,

and are located in the bottom of the webs in the mid span and at the top of

webs over the supports For decks with a overall length less than 80m and

fully cast before applying prestress, the tendons would usually extend over

the full deck length and be anchored on the end diaphragms Longer decks

are cast in stages on span-by-span basis, with the prestress tendons

anchored on the webs at the construction joint The tendons are then

continued into next stage of deck by using couplers

CODAL PROVISIONS

COARSE AGGREGATES

IRC:18 recommends the nominal size of coarse aggregate shall usually be

restricted to 10mm less than the minimum clear distance between the individual

cables or un-tensioned steel reinforcement or 10mm less than the minim um clear

cover to un-tensioned steel reinforcement, whichever is less A nominal size of

20mm coarse aggregate is used for pre-stressed concrete work

Concrete shall be used in accordance with clause 302.6 of IRC21

A) Casting the cross section in one pour

B) Casting the cross section in stages

A) Casting the cross section in one pour:

Fig:3-1 Wide bottom slab cast through trunking

Fig:3-2 Narrow bottom slab with concrete cast down webs

There are two approaches to cast a box section in one pour

The bottom slab may be cast first with the help of trucking passing

through temporary holes left in the soffit form of top slab This requires

laborers to spread and vibrate the concrete, generally possible for decks

that are at least two meters deep The casting of webs must follow closely,

so that cold joints are avoided The fluidity of the concrete needs to be

designed such that the concrete will not slump out of the webs This is

assisted if there is a strip of top shutter to bottom slab about 500mm wide

along web This method of construction is most suitable for boxes with

relatively narrow bottom flanges The compaction of bottom slab concrete

needs to be effected by external vibrates, which impels the use of steel

shutters The concrete may be cast down both webs , with inspection holes

in the shutter that allow air to be expelled and the complete filling bottom

slab to be confirmed Alternatively concrete may be cast down first with

the second web being cast only when concrete appears at its base,

demonstrating that the bottom slab is full The concrete mix design is

critical and full-scale trials representing both the geometry of the cross

section and density of reinforcement and prestress cables are essential

However the section is cast, the core shutter must be dismantled and

removed through a hole in the top slab, or made collapsible so it may be

withdrawn longitudinally through the pier diaphragm

Despite these difficulties, casting the section in one pour is

under-used The recent development of self-compacting concrete could

revolutionize the construction of decks in this manner This could be

particularly important for medium length bridges with spans between 40 m

and 55 m Such spans are too long for twin rib type decks, and too short

for cast-in-situ balanced cantilever construction of box girders, while a

total length of box section deck of less than about 1,000 m does not justify

setting up a precast segmental facility Currently, it is this type of bridge

that is least favorable for concrete and where steel composite construction

is found to be competitive

B) Casting the cross section in stages

Fig:3-3 Alternative positions of construction joint

The most common method of building box decks in situ is

to cast the cross section in stages Either, the bottom slab is cast first with

the webs and top slab cast in a second phase, or the webs and bottom slab

constitute the first phase, completed by the top slab When the bottom slab

is cast first, the construction joint is usually located just above the slab,

giving a kicker for the web formwork, position 1 in Figure A joint in this

location has several disadvantages

Alternatively, the joint may be in the bottom slab close to the webs, or at

the beginning of the haunches, position 2 The advantages of locating the

joint in the bottom slab are that it does not cross prestressing tendons or

heavy reinforcement; it is protected from the weather and is also less

prominent visually The main disadvantage is that the slab only constitutes

a small proportion of the total concrete to be cast, leaving a much larger

second pour The joint may be located at the top of the web, just below the

top slab, position 3 This retains many of the disadvantages of position 1,

namely that the construction joint is crossed by prestressing ducts at a

shallow angle, and it is difficult to prepare for the next pour due to the

presence of the web reinforcement In addition, most of the difficulty of

casting the bottom slab has been re-introduced The advantages are

that the joint is less prominent visually and is protected from the weather

by the side cantilever, the quantity of concrete in each pour is similar and

less of the shutter is trapped inside the box Casting a cross section in

phases causes the second phase to crack due to restraint by the hardened

concrete of the first phase Although the section may be reinforced to limit

the width of the cracks, it is not desirable for a prestressed concrete deck

to be cracked under permanent loads Eliminating cracks altogether would

require very expensive measures such as cooling the second phase

concrete to limit the rise in temperature during setting or adopting crack

sealing admixtures

Most in situ multi-cell box girders are cast on full height

scaffolding built up from the ground Where good access exists this form

of construction provides flexibility in the construction sequence and deck

layout Obstructions under the deck, such as live loads, railways or small

rivers, are overcome by spanning with temporary works to support the

false work

After erecting the scaffolding the formwork is placed to the

required shape and profile Timber formwork, consisting of a plywood

facing supported by timber studding, Steel forms are used when long

lengths of decks are to be cast in stages and the shutters are used many

times With timber forms it is easier to have squarer angled corners and

flat faces while steel forms are able to incorporate curved and sides

Casting the deck section in several stages simplifies the

formwork This also makes the concreting operations much simpler and

easier to control The bottom slab, outer webs and diaphragms are cast

first, followed by the inner webs and top slab soon after The time delay

between castings should be kept to a minimum to reduce any early thermal

and differential shrinkage effects

It is preferable to cast the outer webs with the bottom slab so

that the construction joint is at the top of web and hidden in the corner

with top slab A construction joint between the bottom slab and the webs

is difficult to hide on the concrete surface and, although this is not

important for the inner webs, it marks the appearance on the outer webs

The form work for the inner webs and top slab is supported off the bottom

slab concrete, simplifying the overall arrangement

With the formwork in position, the next activity is the fixing of

the reinforcement, prestressing ducts and anchorages Short shutters are

being installed along the bottom of the webs to form kickers when the

webs are cast in next stage

Without the inner web and top slab formwork in place the access for

placing, compacting and finishing the concrete in the bottom slab is

improved The subsequent concreting of inner webs and top slab is done

from above the deck without needing access to the void

At this stage the deck is still fully supported by the false work

which remains in place until the concreting is completed and the tendons

installed

Either permanent formwork panels or removable table forms are used

between the webs to support the wet deck slab concrete The removal of

formwork from inside the voids, after the deck is completed, requires it to

be broken down into small sections are passed out through the access

holes in the diaphragms and bottom slabs alternatively, a larger temporary

access hole is left in the top slab at one end of the deck slab which is

concrete after the rest of the formwork has been removed

Longer girder bridge decks, extending over several spans, are

usually cast in sections on a span-by-span basis This has several benefits

including reducing the size of concrete pours to a more manageable

quantity, optimizing the length of pre stress tendons and permitting the

maximum re –use of false work and formwork The first section cast is a

complete span plus part of the adjacent spans to give short cantilevers

This moves the construction joints away from the highly stressed region at

the pier and helps to balance the deck in temporary and permanent

situations To optimize the overall moment distribution the construction

joint is placed between the ¼ or 1/3 points of span Subsequent sections of

deck extend from the construction joint over the next pier with a short

cantilever, as before This process is continued until the end of deck is

reached

During concreting of deck slab the level and finishing of the top

surface has to be carefully controlled On smaller decks this is achieved by

placing leveling timbers on the reinforcement and screeding the concrete

to the top of these For larger areas of slab a finishing machine is used to

assist accurately leveling of top surface

When the concrete has attained the required strength the pre stress tendon

are installed and stressed The deck tends to lift up along its span and

reduce the load on the false work as the pre stress applied The false work

is removed after sufficient tendons have been stressed to carry dead load

of deck

CHAPTER 4

ANALYSIS OF BOX GIRDER

BRIDGE: