A046 code of practice for the design of steel bridges

Table 2.1 Various Parts of BS 5400 Issue Latest Amend’t 9.1 Code of Practice for the Design of Bridge Bearings9.2 Specification for Materials, Manufacture and Installation of Bridge Bea

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SCI PUBLICATION P295

Commentary on BS 5400-3: 2000 Code of practice for the design

© The Steel Construction Institute, 1991, 2000 Apart from any fair dealing for the purposes of research or private study or criticism or review, as permitted under the Copyright Designs and Patents Act, 1988, this publication may not be reproduced, stored or transmitted, in any form or by any means, without the prior permission in writing of the publishers, or in the case of reprographic reproduction only in accordance with the terms of the licences issued by the UK Copyright Licensing Agency, or in accordance with the terms

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Foreword to Commentary on BS 5400-3: 1982

This publication is one of a range of publications produced by The Steel ConstructionInstitute which relate specifically to the design of steel and composite bridge structures and

the use and interpretation of the various clauses within BS 5400: Part 3: 1982 It has been

edited by Dr D M Martin (The Steel Construction Institute) and Dr J Tubman (Scott WilsonKirkpatrick) The following Engineers contributed to the commentary on the variousclauses:

Dr M J Baker Imperial College of Science and Technology

Mr A Bannister British Steel Swinden Laboratories

Mr C W Brown The Steel Construction Institute

Mr B D Cheal Consultant

Dr P Davidson Imperial College of Science and Technology

Mr K Goodearl Consultant

Mr D C Iles The Steel Construction Institute

Dr W Manners University of Leicester

Dr D M Martin The Steel Construction Institute

Dr R Narayanan The Steel Construction Institute

Dr G W Owens The Steel Construction Institute

Dr J Spindel Consultant

Dr J Tubman Scott Wilson KirkpatrickOur particular thanks are due to Mr S Chakrabarti of the Department of Transport for hisvaluable advice and comments on the text

During the preparation of the Commentary many points of interpretation were resolved bydiscussion The document, therefore, represents a consensus of opinion on the variousclauses within the Code and it should act as both an authoritative guide and a referencedocument for practising Bridge Engineers

The work leading to this publication was funded by British Steel General Steels and theproject was managed by Dr D M Martin (The Steel Construction Institute)

Foreword to Commentary on BS 5400-3: 2000

The publication of a revised version of BS 5400-3 in 2000 has necessitated an update of theCommentary The editors, Mr D C Iles and Mr C W Brown of The Steel ConstructionInstitute, have endeavoured to retain as much as possible of the original text, but havebrought it into line with the new clauses Major revisions have been necessary to Sections

6 and 9, and the opportunity has been taken to add a commentary on Clauses 9.10 and 9.15,

which were not covered in the commentary on BS 5400-3: 1982

A summary of the clauses that have been amended in the 2000 version of BS 5400-3 isgiven in an Appendix The type of amendment (e.g editorial, major technical change, etc.)

is indicated in that Appendix

Further guidance on the use of BS 5400-3: 2000 can be found in two other SCI publications,

Design guide for composite highway bridges (P289) and Design guide for composite highway bridges: Worked Examples (P290) To buy a hardcopy version of this document call 01344 872775 or go to http://shop.steelbiz.org/ This material is copyright - all rights reserved Reproduced for IHS Technical Indexes Ltd under licence from The Steel Construction Institute on 15/8/2005

iv

5.6 Diaphragms and fixings required during construction 14

6.5 Notch toughness 19 To buy a hardcopy version of this document call 01344 872775 or go to http://shop.steelbiz.org/ This material is copyright - all rights reserved Reproduced for IHS Technical Indexes Ltd under licence from The Steel Construction Institute on 15/8/2005

8.3 Distortion and warping stresses in box girders 29

9.10 Flanges in longitudinally stiffened beams 79

9.13 Transverse web stiffeners other than at supports 95

9.15 Cross beams and other transverse members in stiffened flanges

1019.16 Intermediate internal cross frames in box girders 105

10.5 Effective section 11010.6 Compression members without longitudinal stiffeners 11010.7 Compression members with longitudinal stiffeners 113

10.10 Compression members connected by perforated plates 11910.11 Compression members with components back to back 120

11.8 Tension members connected by perforated plates 12611.9 Tension members with components back to back 127

v

The Commentary discusses in detail the provisions in the clauses of

BS 5400-3:2000, provides background information where appropriate andcomments on their practical application The comments and discussion representthe considered opinion of experienced engineers and researchers In some casesinformation about the basis of the clauses has been difficult to obtain; for suchcases, the commentary presents the consensus view of the background to theseclauses

The scope of this publication is limited to those aspects of BS 5400-3: 2000 mostcommonly used by bridge designers Comments are given on a clause-by-clausebasis The design of cross frames and diaphragms in box girder design (Clauses

9.16 and 9.17) is not discussed.

The Commentary is intended as a reference document to be used in conjunctionwith the Code References and comparisons are made to other codes whereappropriate (viz BS 5950, BS EN 10025 and BS 153) References are given atthe end of each principal Section and are referred to in the text in the form[2.3],where ‘2’ indicates Section 2 and ‘3’ is the third reference in that Section

BS 153 was restricted in its scope to simply supported steel bridges of up to 300 ft

in span and was primarily intended for plate girders and truss construction By

1967, continuous steel bridges, box girder bridges and cable stayed systems hadbeen designed and numerous long span bridges were in prospect The Code wastherefore being applied, and sometimes misapplied, beyond its intended bounds

The group of engineers referred to above recommended that limit state philosophyshould be adopted, so that there would be uniformity of reliability of service

This was the first time a British code was to be drafted using limit state concepts

The work of the drafting panels commenced in 1968 and an embryonic draft of theSteel Design Code existed in 1970 The collapse during erection of four steel boxgirder bridges (two of them British designed) triggered much research effort,which resulted in the production of the Interim Design and Workmanship Rules

by the Merrison Committee[2.1] These rules were rather severe - though at thetime they were regarded as essential, largely because of the anxiety about thesafety of the bridges in service

Following the publication of the Interim Design and Workmanship Rules, the SteelBridge Sub-Committee was reconvened in 1973 The intention was to base thenew Design Code on the Merrison Rules as regards the treatment of box girderstructures When the draft was presented in 1975, the Committee found itselfdissatisfied with its own brief for the Code Extensive modifications were madeunder the direction of Steering Panels Continuity of style was achieved by gettingthe drafts vetted by one person before the final draft was reviewed by a panel ofdesigners

The draft for public comment was eventually published in 1979 followed by aone-day Seminar (organised by IStructE) in January 1980 and a three-dayConference (organised by the University College, Cardiff) in March 1980

The Code of Practice for Steel Bridges (i.e BS 5400-3) finally appeared (aftersome modifications) in 1982 It should be noted that this was a new Code based

on the limit state approach; it was not a revision of an old one

Two official amendments have been issued since publication, AMD 4051 inAugust 1982 and AMD 6488 in April 1991 The former was comparativelyminor; the latter was a major revision, incorporating much (but not all of) of thematerial published in the Department of Transport’s (subsequently HighwaysAgency’s) Standard BD 13/90 By 1992 it was becoming apparent that a completeoverhaul of the Code was necessary It had been hoped to avoid this pending theissue of a Eurocode for steel bridges, but when it became obvious that such a To buy a hardcopy version of this document call 01344 872775 or go to http://shop.steelbiz.org/ This material is copyright - all rights reserved Reproduced for IHS Technical Indexes Ltd under licence from The Steel Construction Institute on 15/8/2005

Eurocode was a long way from completion, the BSI Bridge Code CommitteeB525/10 set up a Working Group (WG3) to update BS 5400-3 A draft of theproposed revisions was issued for public comment in 1995; after taking thesecomments into account a completely new version of BS 5400-3 was issued in2000.

The complete Standard is as shown in Table 2.1, produced in 10 parts which covervarious facets of bridge design

Table 2.1 Various Parts of BS 5400

Issue

Latest Amend’t

9.1 Code of Practice for the Design of Bridge

Bearings9.2 Specification for Materials, Manufacture and

Installation of Bridge BearingsCode of Practice for Fatigue

1988197820001990197919991978

1978

19831983

construction

Part 1 of the Standard is a General Statement of the concepts and limit stateprinciples common to the other parts It should be referred to for definitions, thegeneral procedures for limit state partial safety factor design and other commonrequirements, such as robustness and design life

Part 2 covers all aspects of design loading, other than fatigue, which is covered

by Part 10, for highway, railway and foot bridges including partial safety factors

on loads and load combinations Its scope is suited to the design of modern forms

of bridge having been particularly extended from BS 153 to provide more guidance

on the assessment of wind loading and temperature effects Various combinations

of loads together with the load factors to be used in the ultimate limit state, aswell as in the serviceability limit state, are prescribed For bridges in the UKunder the control or approval of the Highways Agency or for which the HighwaysAgency has a responsibility, the values of some loads (and in particular highwayloads) have been substantially increased in the Departmental Standard BD37/88,which effectively replaces Part 2

Part 3 contains recommendations for the design against collapse andunserviceability of steel bridges The design objectives (including partial factors

on strength) and limitations in design on construction and workmanship are setout Guidance is given on steel properties to be assumed in design or specified,including requirements for notch toughness The major part of the Code treats thedesign of tension and compression members, of beams (including plate and boxgirders), of trusses and of connections

Part 4 is the Code of Practice for the design of concrete bridges Thespecifications for the materials used in such bridges are contained in Part 7 andPart 8

Part 5 lays down extensive requirements for the design of composite bridges andcovers both serviceability and ultimate limit states Guidance is given about crackwidths allowed in concrete, the use of shear connectors, the influence of shear lagetc The requirements of composite box girders, cased and filler beams,composite columns and permanent formwork are all features covered in a codifiedform for the first time The Highways Agency have issued a modified version ofthis Part for use on bridges in the UK under their control or approval or for whichthey have a responsibility

Part 6 is a mandatory Specification for steel materials and workmanship Thematerials clauses cover requirements for structural steels, steels for rivets, pins,shear connectors and bolts, welding consumables, steel castings and forgings andcast iron Fabrication tolerances, preparation of materials, requirements forbolting, rivetting and welding, and other manufacturing limitations are defined

Inspection and testing procedures and general instruction on handling, transportand erection are provided

Part 9 is in 2 parts: The first part is a Code for design of bearings and the second

is a Specification for the materials, manufacture and installation of all types ofbridge bearings

Part 10 is a Code of Practice, concerned with fatigue life appraisal for steel,concrete and composite bridges Following general guidance on the approach todesign against fatigue, structural details are classified for defining their fatiguecharacteristics, with explanatory notes Design loading spectra are specified forhighway and railway bridges in the United Kingdom Acceptable methods ofstress calculation are set down The Code then sets out methods of life assessmentbased on the Palmgren-Miner damage summation Amendment No 1 was issued

in 1999

It should be noted that, for all bridges under the control or approval of one of thefour overseeing Organisations (the Highways Agency in England, the ScottishExecutive Development Department, the Welsh Assembly and the Department forRegional Development in Northern Ireland), the Departmental Standards in the

Design Manual for Roads and Bridges [2.2] effectively supersede certain clauses ofthe design Code(s).

BS 5400 is based on a partial safety factor/limit state philosophy The specifiedvalue of each type of load (given in Part 2) is multiplied by a partial factor toobtain a design value which has an appropriately small probability of beingexceeded in the design life of the bridge When two or more loads act together,the partial factors to be used allow for the fact that the peak values of the time-varying loads are unlikely to occur at the same instant in time

The factored loads, in different combinations, are applied to the structure and theload effects determined The latter are then compared with the design strength ofthe elements

This is expressed mathematically in BS 5400-3 as:

(f3 is a factor that takes account of inaccuracies in load assessment,

stress distributions and construction;

(m1(m2 is replaced by a single factor (m which takes account of uncertainty

in material strength and quality, and manufacturing tolerances; and

Qk is the specified nominal load

It should be noted that this expression differs from that given in Part 1 and Part 4,where the partial factor (f3 is included with the load effects rather than theassessment of strength This difference arose due to separate drafting of Parts 3and 4

It is clear that live loads will in general vary more than dead loads and hence ahigher load factor is assigned to live loading

The exception to this is superimposed dead load due to deck surfacing, which has

a very high load factor This is to allow for the possibility of resurfacing workbeing carried out on top of the original surfacing

2.5 Combinations of loads

The Code recognises that when loads are in combination, particularly combinationsinvolving wind or HB loads, they are unlikely to exceed their specified valuessimultaneously by large amounts, and hence load factors for such combinations arereduced

Table 2.2 Typical combinations of loads [Source: BD 37/88]

Combination 1 Combination 2

Dead (steel)Dead (concrete)Superimposed dead (deck surfacing)Superimposed dead (other)

Windwith dead + superimposed deadwith dead + superimposed dead + LiveVertical live load

HA alone

HA with HB or HB alone

1.051.151.751.20

1.501.30

1.051.151.751.75

1.401.10

1.251.10

The purpose of limit state design is to identify all the possible modes of failure foreach structure and all the ways in which it could become unserviceable and then

to proportion the structure so that these events are sufficiently unlikely to occur

In practice, the engineer does not have to carry out risk or probability calculationsdirectly since these were done by the Code drafting committee Appropriate levels

of safety and serviceability are achieved by using the partial factors given inParts 2 and 3 of the Code

2.1 Inquiry into the basis of design and method of erection of steel box

girder bridges Interim design and workmanship rules

HMSO, 1973

2.2 Design Manual for Roads and Bridges

The Highways Agency, the Scottish Executive, the Welsh Assembly andthe Department for Regional Development, Northern Ireland

3 PREAMBLE TO COMMENTARY

The Commentary is intended to be read in conjunction with BS 5400-3: 2000

References to tables and figures in the Code are made in italics, e.g “See

Figure 10” Figures and tables within this Commentary are numbered by

reference to the commentary clause to which they refer; for example Figure 9.5.5

is the fifth figure in the commentary to Clause 9.5 Reference should be made to

BS 5400-3: 2000 for details of definitions and nomenclature

The Commentary refers only to the Code of Practice published by the BritishStandards Institution It does not deal with Departmental Standards in the DesignManual for Roads and Bridges unless they are specifically relevant to thebackground of a particular aspect Armed with the background information to theoriginal clauses, users should be able to assess for themselves the implications ofany modest changes demanded by implementation documents

Even where no comment is considered necessary, the clause heading is

nevertheless given for reasons of uniformity of presentation Clauses 9.16 and

9.17 relate primarily to box-girder construction and are outside the scope of the

present work

of failure.

The Code lists three limit states: the ultimate limit state, the serviceability limitstate, and fatigue Leaving fatigue on one side for later discussion (Section 4.2.3below), the other two limit states can be defined as follows The ultimate limitstate represents conditions of total collapse which endanger the safety of peopleand/or require major or total reconstruction The serviceability limit staterepresents the limit of acceptable performance in service Hence the keydistinction between these limit states in practice is that serviceability limit statecalculations are made with loads factored to represent the worst loads that thebridge is expected to experience during its design life, while ultimate limit statecalculations are made with significantly greater factored loads representingextremely improbable occurrences

Since, in general, structures are susceptible to several different types of failure,and are subject to several different types of limitation on acceptable performance,

it is common in more recent codes (e.g BS 5950-1 and the design Eurocodes) touse the plural form and refer to ultimate limit states and serviceability limit states

Different ultimate limit states can be defined in terms of different failuremechanisms The most basic is the overturning or sliding of the whole structure,

or some part of it, when considered as a rigid body; this applies to structureswhich rely on only their self-weight for stability The more common failuremechanisms are those of yielding, buckling and brittle fracture Although it cansometimes be useful to think of these as separate limit states, the possibility ofstructural failure involving a combination of these failures mechanisms must also

be considered The serviceability limit states can include any requirement relevant

to the satisfactory performance of the structure in service, and are usuallyconcerned with limiting deflections and distortions, either permanent or temporary,

or vibrations

The way in which the Code handles these various limit states will be discussed inmore detail in the following pages, but it should be noted that, because of the longperiod of time over which BS 5400 was written, different parts of the Code refer

to limit states in different ways In particular, Part 1 uses the plural form ultimatelimit states and serviceability limit states, and list individual limit states under eachheading; however it goes on to list certain deflection limits, i.e those concerned To buy a hardcopy version of this document call 01344 872775 or go to http://shop.steelbiz.org/ This material is copyright - all rights reserved Reproduced for IHS Technical Indexes Ltd under licence from The Steel Construction Institute on 15/8/2005

with the appearance of the bridge, with clearances and with drainage of waterfrom bridge decks, under “Further Requirements”, rather than as serviceabilitylimit states.

The first consideration in creating and organising the rules for the ultimate limitstate is the extent to which different types of failure can be handled separately

One important principle of the Code, as of most steel design, is that ductilefailures are considered preferable to brittle failures The limit state of brittlefracture is therefore disposed of by ensuring that the steel used has sufficientductility and notch toughness so that brittle fracture does not govern the strength

of bridges; this is covered in 6.4 and 6.5

Certain aspects of local buckling are dealt with similarly, by means of the shape

limitations in 9.3 and 10.3 It would not, of course, be economic to proportion

steel bridges so that buckling never affected the strength; hence the major part ofthe Code consists of the calculations required to assess the strength of elements ofbridges failing due to the combined effects of yield and buckling; and all elements

of a bridge must be checked against these requirements

The requirement given in the Part 1 description of the ultimate limit state is thatthe structure should be checked for equilibrium as a rigid body, but this is notexplicitly repeated in Part 3 Where the forces acting on a structure are such thatits own self-weight is insufficient to guarantee that it always remains in overallequilibrium, then devices such as holding-down bolts or bearings that resist tensionare required, and the system of partial factors used in the Code ensures that theproper design of these elements will ensure the stability of the bridge as a whole

The design checks specifically listed under the serviceability limit state heading

are limited to six locations, as listed in Table 1 of the Code One of these arises

because slip in normal friction-grip bolted connections is defined as aserviceability limit state The others are all concerned with preventing excessivepermanent deformation of bridges under ‘normal’ loading Although the exactorigin of the cause for concern varies from case to case, it tends to arise from thepresence of certain forms of structural behaviour, such as shear lag, restraint ofwarping or stable elastic buckling, which can cause high local stresses to bepresent in the elastic stress distribution, but which may not significantly affect theultimate strength of the bridge In such cases, the process of structural failure will

be associated with large amounts of plastic yielding, which may start at relativelylow loads, causing parts of the bridge to distort significantly well before failureoccurs These serviceability limit state requirements therefore consist of checks

to ensure that yield is not exceeded under normal loading, including all thecomplications of the elastic stress distribution in the calculations By comparison,the ultimate limit state may usually be checked after redistributing peak stresses

to correspond more closely to the state of stress at failure

In clauses of the Code other than those in Table 1, serviceability limit state checks

are not required This is because the elastic stress distribution and the stressdistribution at failure are sufficiently similar for the ultimate limit state calculation

to ensure automatically that significant distortion does not occur under workingloads.

Other design requirements in the Code which could have been considered asserviceability limit states are those concerned with the effect of deflection on

clearance gauges (4.6) and on appearance (5.7) Part 1 also requires checks to

ensure that deflections do not affect drainage of water from bridge decks, andchecks for vibration of footbridges

Although Part 3 lists fatigue separately from the ultimate and serviceability limitstates, Part 1 lists it as one of the ultimate limit states If a sufficiently rigorousprogramme of periodic inspections were to be mounted to ensure that fatiguecracks were found and repaired before structural failure occurs, then fatigue could

be classified as a serviceability limit state BS 5950-1 mentions this possibility

It would not, in general, be considered acceptable practice for bridges

However it is classified, the nature of fatigue, in particular its dependence on theloading history, means that it requires calculation procedures which are quitedifferent from those used for other limit states In BS 5400 this is handled bydevoting Part 10 exclusively to fatigue

This approach can only be reasonable, however, if there is no significantinteraction between fatigue and other limit states On the face of it, suchinteraction is possible because the basis of Part 10 is that fatigue cracks will existand grow in bridge structures, although, of course, the predicted fatigue life must

be greater than the specified design life of 120 years

As far as interaction with brittle fracture is concerned, this is dealt with byensuring that the material toughness requirement is sufficiently stringent that agrowing fatigue crack will not precipitate brittle failure before ductile failure

In the case of interactions with ductile failures, the concern would be the effect

of reduction of cross-section area due to the growing crack However, fatiguecrack growth is non-linear, with cracks growing very slowly at first, andaccelerating during the course of the fatigue life It is therefore only close to theend of the fatigue life that there might be sufficient reduction of area to precipitate

a ductile failure at a load lower than the calculated failure load Since there is avery considerable amount of variation in experimental fatigue life data, calculatedfatigue life predictions are generally very conservative As a result it isconsidered acceptable to ignore the possibility of interactions between fatiguecrack growth and ductile failures

Most of the partial safety factors given in the Code have been determined by aprocess of probabilistic calibration, using structural reliability theory, to ensurethat each structural component has an acceptably small risk of failure during thedesign life of the bridge, taken as 120 years Details of the procedures that wereused are described in references 4.1 to 4.4 In general, safety factors are needed

in design to take account of the various uncertainties that may affect theperformance of the structure as built These include both the physical variability To buy a hardcopy version of this document call 01344 872775 or go to http://shop.steelbiz.org/ This material is copyright - all rights reserved Reproduced for IHS Technical Indexes Ltd under licence from The Steel Construction Institute on 15/8/2005

of quantities such as loads and material properties, causing deviations fromspecified or characteristic values, and the inability of the relatively simple Codeequations to predict exactly the load-carrying capacity of the various structuralcomponents - known as model uncertainties In Part 3, the statistical variability

of material properties was assessed from test data and, where possible, modeluncertainties were determined by the analysis of experimental results It should

be noted that the partial factors given in Part 3 are not intended to allow for thepossibility of gross errors in design calculations or analysis, or fabrication errors,

or misuse of the structure during its service life, nor for the effects of corrosion

These effects should be guarded against by appropriate quality assurance measures,maintenance procedures and other allowances

Part 1 states that a satisfactory design is one in which the design resistance R*

exceeds the design load effects S* for each relevant limit state, where R* and S*

are calculated from expressions involving the partial factors (fL, (f3, (m1 and (m2.The partial factors have been evaluated to allow for the various uncertaintiesmentioned above and in 2.3 of Part 1, but it is incorrect to think that theindividual partial factors allow separately for each uncertainty A betterinterpretation is that the sets of partial factors, when used together, provideacceptable standards of safety or serviceability over the range of designs for whichthe Code of Practice is intended to be used

The partial factors in Part 3 were obtained by probabilistic calibration to the oldbridge design code BS 153 so that, on average, designs to Part 3 have the samelevel of safety as designs to BS 153 However, the partial factors in Part 3 whenused with the new design clauses lead to much less scatter in safety levels thandesigns to the earlier standard In addition, the elimination of some aspects ofover-conservative design provides a saving in steel weight for many structuralcomponents

The safety factor format of a design code is defined as the way in which thepartial factors are introduced into the design equations It defines how manypartial factors are used, how they are combined and where they are placed in theequations There are both theoretical and practical advantages in placing thepartial factors next to the variables containing the major sources of uncertainty

The safety factor format given in the Code (see Section 2.3 of Commentary)differs slightly from the format which was used to evaluate the factors:

/

However, it was found that the simpler format finally given in Part 3 could beadopted without significant loss of accuracy This is possible since, for manystructural components, strength can be assumed to be proportional to yield stress

4.3.3 Values of partial safety factors

The partial factors on individual loads and for combinations of loads, (fL, aregiven in Part 2 (as modified by BD 37/88 for structures within the scope of theDesign Manual for Roads and Bridges) and were assessed mainly by judgementrather than by statistical means In a similar manner, the value of (f3 was chosen

to be 1.1 for the ultimate limit state and 1.0 for the serviceability limit state, butallowance for this is made in the values specified for the partial factors onmaterials

For both the ultimate and serviceability limit states, the partial factors (m1, on thecharacteristic yield stress, and (m2, allowing for modelling uncertainty, arecombined into a single factor (m (= (m1 (m2) The values assigned to (m reflectthe different modelling uncertainties and are intended to achieve the same risk offailure for each It is worth noting that some of the (m values have beensignificantly changed in the 2000 version of BS 5400-3 from what they were in the

1982 version The most important change is possibly in the bending resistance ofbeams where (m has been reduced from 1.20 to 1.05 for all beams; this reflectsthe improved level of reliability of the revised method of calculating the resistance

given in 9 In addition, the (m value for fillet welds has been increased, notbecause of doubts on reliability but because a more logical and consistent, but lessconservative, approach to the calculation of the strength has been included

The lower values of (fL, (f3 and (m for the serviceability limit state reflect the factthat the acceptable risk of unserviceability is higher than that for reaching anultimate limit state In addition, in some circumstances, the prediction ofserviceability limits is associated with less uncertainty than the prediction ofultimate behaviour

Finally, it should be noted that the aim of equal safety levels for all types ofstructural component in a bridge is not an entirely logical goal This is becausethe safety of a bridge as a whole depends not only on the strength of the individualcomponents, but also on the way in which they are inter-connected and theredistribution of load that can take place In general, it is the safety of the wholestructural system which needs to be considered, and not that of individualcomponents However, simplified Code rules for achieving this objective have notyet been formulated

Where it cannot be guaranteed that there will be no loss, an additional thickness

to allow for it must be added in design; this is particularly relevant in the case of

weathering steel, which is covered in the new sub-clause 4.5.6. To buy a hardcopy version of this document call 01344 872775 or go to http://shop.steelbiz.org/ This material is copyright - all rights reserved Reproduced for IHS Technical Indexes Ltd under licence from The Steel Construction Institute on 15/8/2005

CIRIA, London, 19774.2 FLINT AND NEILL PARTNERSHIP and IMPERIAL COLLEGE

Derivation of safety factors for BS 5400: Part 3Final report to the Department of Transport, August 19804.3 FLINT, A.R., SMITH, B.W., BAKER, M.J and MANNERS, W

The derivation of safety factors for design of highway bridges Thedesign of steel bridges

Proceedings of the conference on the new code for the design andconstruction of steel bridges, Cardiff 1980, Granada Publishing, 19814.4 THOFT-CHRISTENSEN, P and BAKER, M.J

Structural reliability theory and its applicationsSpringer-Verlag, 1982

5 LIMITATIONS ON CONSTRUCTION AND WORKMANSHIP

Whilst the clause itself suggests universal compatibility between BS 5400- 5: 1979and BS 5400-3: 2000, the Foreword to the latter lists a small number of points to

be borne in mind by the designer when using Parts 3 and 5 in conjunction

Numerous inconsistencies between these parts of the Code were subsequentlyuncovered as their combined use in practice increased

BS 5400-5 is implemented by the UK highway authorities through BD 16/82 (part

of the Design Manual for Roads and Bridges) That document makes a significantnumber of technical changes to BS 5400-5 and they should be taken into account

by designers of composite bridges BSI have not responded to the changes;

BS 5400-5 is effectively not being maintained, although it has not been withdrawn

For the purpose of fatigue assessment to Part 10 of the Code, the precise function

of the attachment is often irrelevant; it is the nature and quality of the fabricated

detail which dictates its fatigue classification; moreover, the stress fluctuations inthe parent material (to which the fixing is attached), rather than in the fixing itself,will normally be critical for fatigue.

Implicit in the provisions of Part 10 is the assumption that fatigue damage may gounnoticed during routine inspections Potential problems should therefore be

‘designed out’ before fabrication commences

In addition to fatigue considerations, another aspect of this clause worthy ofattention is the possibility of the “proper functioning of the completed structure”

being impaired by, for example, failure to remove temporary bracing Depending

on the configuration of such bracing, the load distribution characteristics of thedeck could be significantly different from those assumed in global analysis

6 PROPERTIES OF MATERIALS

Introductory comments

The purpose of Clause 6 is to ensure that the properties of the particular steel used

are appropriate to the intended operating conditions in terms of strength andtoughness, so that the probability of failure, by whatever cause, is acceptably low

This is accomplished by assessing the potential material properties of a given steelgrade together with the effect of thickness on toughness, strength and residualstresses These factors are then combined with the typical potential design stressesand service conditions that the part will be subjected to, in order to ensure thatadequate margins of safety will be achieved

In the original version of Clause 6 of the Code (published in 1982) the material

properties were specified by reference to BS 4360: 1979[6.1] Following theintroduction of BS 4360: 1986[6.2] and the first version of the European Standardfor structural steels, EN 10 025: 1990[6.3], most of the 1979 version of BS 4360was effectively superseded In February 1991, section 6 of the Department ofTransport’s Departmental Standard BD13/90 (subsequently part of the DesignManual for Roads and Bridges)[6.4] largely replaced clause 6 of BS 5400-3: 1982

in order to:

(a) bring Clause 6 up to date, by referencing BS 4360: 1986 and BS EN 10025:

1990, thus superseding all references to the 1979 version of BS 4360

(b) bring certain clause requirements of Clause 6 more into line with actual

design situations

Subsequent to the issue of BD 13/90, a short-term revision of BS 4360 was issued

in 1990, but that has now been withdrawn In addition, BS EN 10025 was revisedand reissued in 1993 using completely new designations of steel grades inaccordance with BS EN 10027 Further European Standards have been issued,covering all grades of structural steel suitable for bridges designed to BS 5400-3except for hot finished hollow sections in weather resistant steel It should benoted that when a European Standard is issued in the UK, it is prefixed with theletters ‘BS’ and contains a National Foreword; it may also include a NationalAnnex Further references in this publication to (for example) EN 10 025 will begiven as BS EN 10 025

The materials Standards current in September 2000 are as follows:

BS 7668 Specification for weldable structural steels Hot finished hollow

sections in weather resistant steels[6.5]

BS EN 10025 Hot rolled products of non-alloy structural steels [6.6]

BS EN 10113 Hot rolled products in weldable fine grain structural steels[6.7]

BS EN 10137 Plates and wide flats made of high yield strength structural

steels in the quenched and tempered or precipitation hardenedcondition[6.8]

BS EN 10155 Structural steels with improved atmospheric corrosion

resistance[6.9]

BS EN 10210 Hot finished structural hollow sections of non-alloy and fine

grain structural steel[6.10] To buy a hardcopy version of this document call 01344 872775 or go to http://shop.steelbiz.org/ This material is copyright - all rights reserved Reproduced for IHS Technical Indexes Ltd under licence from The Steel Construction Institute on 15/8/2005

Whilst the BS EN Standards largely replace the old British Standards such as

BS 4360, some designers may still be more familiar with the old standards, andmaterial manufactured to the old standards Hence comparisons are useful,although it must be stressed that the new steels are not simply the old steels withnew names - there are some differences in production and properties It must also

be emphasised that the new Standards must be used - the old BS 4360 designationssuch as 50D etc are no longer permitted As a guide, however, the grades in thenew Standards which correspond most closely to some of the old familiar grades

in BS 4360:1986 are given in Table 6.0.1

More detailed information on the selection of steel grade is given Guidance Note

3.01 of the SCI publication Guidance Notes on Best Practice in Steel Bridge

* indicates that the grade is covered in the UK National Annex

Section 6 of BS 5400-3 has therefore been completely rewritten to take intoaccount the current steel Standards At the same time, recent work has shown thenecessity of modifying the technical approach to certain requirements (in particularnotch toughness), and this has been reflected in the revised clauses To buy a hardcopy version of this document call 01344 872775 or go to http://shop.steelbiz.org/ This material is copyright - all rights reserved Reproduced for IHS Technical Indexes Ltd under licence from The Steel Construction Institute on 15/8/2005

6.1 General

There is now a recommendation that all steels should comply with the performancerequirements of 6.3 and 6.4; previously, it was assumed that a steel complyingwith BS 4360: 1979 (or, later, BS 4360: 1986 or BS EN 10025: 1990)automatically satisfied 6.3 and 6.4 The change is deliberate, since the newStandards cover a much wider range of steels, some of which may be unsuitablefor use in bridges

The minimum yield strengths of structural steels given in the Standards of 6.1.2

decrease with increasing section thickness for various reasons allied to theproduction process However, tolerances on section thickness, as a proportion ofthe thickness, also decrease with increasing thickness Thus, when BS 5400-3:

1982 was written it was argued that these effects largely cancelled each other out,

so that using the same value of nominal yield stress for all thicknesses would lead

to designs for which reliabilities would be acceptably uniform over the full range

of section thicknesses in use at the time The nominal yield stresses to be used indesign were fixed at the value for minimum yield strength specified in

BS 4360 (1979) for a thickness of 16 mm, or 12 mm for weather resistant steel

In BD 13/90, the nominal yield stress was taken to follow more closely thedecrease of minimum yield strength in BS 4360 or BS EN 10025, and this hasbeen taken to its logical conclusion in the current revision of BS 5400-3 by takingthe nominal yield stress as the minimum specified yield strength for the

appropriate thickness, provided that the tolerances used are as specified in 6.1.2.

The calculation of nominal yield stress for steels to specifications other than those

listed in 6.1.2 utilises a formula which takes into account both the percentage

tolerance below the specified plate or section thickness permitted by the relevantstandard and the statistical variation of yield stress about a mean value Theclause makes use of confidence levels and statistical tables, which are contained

in BS 2846[6.12] The net result of this approach is that the derived value of nominalyield stress is representative of the actual value likely to be found in a particulargrade of steel

6.3 Ultimate tensile stress

Research has been carried out in recent years on the effect of the ratio of theultimate tensile stress to the yield stress of steel components The view in the pasthas been that a value significantly above 1.0 was needed to ensure adequate plasticredistribution of peak stresses, and to protect against brittle fracture; BS 5400-3:

1982 specified a ratio of 1.4 for steels with a nominal yield stress below

390 N/mm2, or 1.2 for higher nominal yield stress It is probable that these were

‘pragmatic’ values, since they were what was actually attained by steel to

BS 4360: 1979 This is no longer the case with steels to the new EuropeanStandards, and in any case the general view is now that this ratio plays little part

in either plasticity or brittle fracture, which are primarily controlled by ductility

(6.4) and notch toughness (6.5) respectively ENV 1993-2 [6.13] specifies a valuefor the ratio of 1.10 (‘boxed’), and recent research suggests that the reduction inreliability by reducing the ratio to 1.0 would be negligible However, it has stillbeen deemed advisable to limit the ratio in BS 5400-3 to at least 1.2

It should be noted that there are some clauses (for example 11.3.2) where the

strength of a component is governed by the ultimate tensile strength but where thedesign rule is written in terms of the nominal yield strength, with a factorintroduced which is based on the above ratio Such rules have been revised to

take account of the change to the ratio in 6.3.

Steels intended for use in bridge construction should have a ductility not less thanthat corresponding to an elongation, based on the standard proportional gaugelength of 5.65%S0, of 15%, or 19% where plasticity is relied on (for example inutilising the plastic moment of resistance of a compact section, or redistributingstresses from the tension flange of a beam) Provision is made for conversion inaccordance with BS EN ISO 2566-1[6.14] if a non-proportional gauge length is used

Note that this rules out the use of material of over 100 mm thick (and possibly ofover 63 mm thick for compact sections) if it is not possible to determine whichwill be the transverse direction (see Table 5 of BS EN 10025)

Traditional limit state design methods are based on the avoidance of failure bygeneral plastic collapse; in such methods the design stress must be limited to thatwhich would cause unacceptable deformation or collapse of the structure, divided

by appropriate partial safety factors These factors are described in the

commentary on 2.3; they allow for considerably more than just deficiencies in

material properties However, they do not allow for the possibility of brittlefracture Experience has shown that brittle fracture can occur at a stress muchlower than the design stress and without any warning or prior plastic deformation

Brittle fractures usually stem from the presence of a stress concentration, such as

a notch or sharp corner Whilst such stress concentrations can usually be avoided

by following good detailing practice, the possibility of a crack-like defectoccurring within the material of a structural member cannot be entirely eliminatedthrough design This potential problem is overcome by ensuring adequate notch

toughness of the steel In this way, the safety margin against brittle fracture isincorporated in the material specification The Charpy test can be used as anindirect measure of material toughness and therefore provides an indication of asteel's resistance to brittle fracture The Charpy requirements for structural steelshave been introduced to ensure that adequate toughness can be guaranteed at agiven service temperature, thus reducing the probability of brittle fracture to anacceptably low level.

The required toughness of a steel part depends on a number of factors:

(a) the design minimum temperature of the part (6.5.2) (b) the types of steel product and construction detail used in the part (6.5.3) (c) the stress level expected in service (6.5.3)

(d) the strength grade of the steel (6.5.4) (e) the thickness of the stress carrying part (6.5.4)

The method adopted in BS 5400-3 for achieving these objectives is to determinethe maximum thickness at which a particular steel can be used, taking into account

its toughness and the factors (a) to (d) above The formula quoted in 6.5.4 for

determining this thickness has been derived by TWI and UMIST and is based onthe results of a large number of detailed calculations using ‘state-of-the-art’

fracture mechanics, leading to a formula which gives a best fit to the results withadequate safety margins

It is worth noting the physical reason why the apparent toughness of a platedecreases with increasing thickness A thick plate is highly restrained and doesnot allow much plastic deformation at a defect tip; thus the driving force forfracture is concentrated at this point Thin plates are much more likely to deformplastically, thus causing local yielding at the defect tip

The “Design minimum temperature” is a starting point for the determination oftoughness requirements

For most bridge elements, the design minimum temperature is taken to be theminimum effective bridge temperature as specified in BS 5400-2

Those parts of a bridge which are designed primarily to resist thermal movement(for instance, tie-backs for long continuous bridges) require an additional safetymargin and hence their design minimum temperature is taken to be 5°C lower thanthe minimum effective bridge temperature

The importance of the design minimum temperature arises from the relationshipbetween notch toughness and temperature for a particular steel The change from

‘tough’ behaviour to ‘brittle’ behaviour with decreasing temperature is fairlyabrupt (at the so-called ‘transition temperature’) in modern structural steels

The method in which this relationship is built into the design rule is described

further in the discussion on 6.5.4 below.

The formula for the permissible thickness in 6.5.4 requires the application of a

factor k which is the product of four further factors kd, kg, kF and ks which allow,

respectively, for the constructional details (6.5.3.2), any gross stress concentrations (6.5.3.3), the stress levels (6.5.3.4) and the rate of loading (6.5.3.5), all of which influence the required toughness of the steel.

6.5.3.2 Constructional details

The value of the factor kd to be used for various details is given in Table 3a of

BS 5400-3 This takes account of the potential fracture initiation site; it has beenfound realistic (and convenient) to relate the details to the familiar types listed in

Tables 17a, b and c of BS 5400-10 Attention is drawn, however, to the fact that

this may not be the end of the matter, since some detail types (marked with a

single asterisk in Table 3a of BS 5400-3) may require stress concentration factors

kg less than unity, whilst others (marked with two asterisks) will require suchstress concentration factors Note 3 to this table draws attention to the benefitswhich may be obtained by stress-relieving any welds

6.5.3.3 Geometrical stress concentrations

Whilst, in may cases, the effects of stress concentrations have been taken intoaccount implicitly in the use of the kd factors in Table 3a, there are some cases

where an additional factor kg less than unity may have to be taken into account

These include the details marked with one or two asterisks in Table 3a; guidance

on them, and other details, is given in BS 5400-10 Table 17 under “special design stress parameter”, and in figures 21 and 22 of that Part Whilst queries have been

raised in the past on whether fatigue concentration factors given in these figuresare appropriate for brittle fracture calculations, it is accepted that they givesufficient accuracy for this clause

The possibility of brittle fracture in a component increases with increasing

principal tensile stress The basic formula in 6.5.4 for thickness, however,

assumes that the part carries significant tension (> 0.5 Fy) and hence the table of

kF factors (Table 3b) gives a relaxation (kF > 1) for all cases when the part is notfully stressed in tension It should also be noted that the stress level includesresidual stress; hence most welded details (unless stress relieved) willautomatically have a kF factor of unity (even if the applied stress is compressive)

Attention is drawn to the fact that parts may be stressed more severely in tensionduring erection than in-service

The rate of loading can affect the proneness to brittle fracture, but generally only

if it is extremely rapid Hence provision is made for a ks factor of 0.5 for parts

of a bridge subject to impact loading (such as deck details close to parapet fixings)but 1.0 elsewhere Special considerations would apply if design against explosionwere required

6.5.4 Maximum permitted thickness

This clause gives a formula for the maximum permitted thickness t of a steel part

where U < T27J ! 20, not permitted

It is useful to examine the sensitivity of this formula to the various effectsdescribed above In the ‘normal’ case of a steel part with a nominal yield stress

of 355 N/mm2 and a Charpy energy value of 27 J at -20oC, fully stressed intension, with no serious stress raisers, and for a design minimum temperature of-20oC, the formula limits the thickness to 50 mm

The k value described in 6.5.3 is a straightforward multiplication factor which can

vary from 0.25 or less to 4, so can have a profound effect on the permittedthickness

The term (355/Fy)1.4 shows that as the nominal yield stress increases, so thepermitted thickness decreases This is simply because members constructed inhigher yield steels are likely to be stressed more highly than those in steels with

a lower yield, and the kF factor (6.5.3.4) is based on the stress as a proportion of

the nominal yield stress

The final term in the formula is perhaps the most complicated, and reflects thevariation in notch toughness of the steel with temperature It is based on T27J, thetemperature at which a Charpy energy Cv of 27 Joules is specified in the productstandard For many steels, evaluation of T27J is simple; for example J0 gradesspecify 27 Joules at 0oC, J2 grades specify 27 Joules at -20oC It is less obviousfor K2 grades, which specify 40 Joules at -20oC, and to get over this problem thecode assumes that for energy values other than 27 Joules, the temperatures aremodified as follows:

For Cv = 30 Joules, T27J / T30JFor Cv = 40 Joules, T27J / T40J - 10oCWhere T30J and T40J are the specified test temperatures for energy values of 30Jand 40J respectively Hence T27J for K2 grade is -30oC

The final term in the formula therefore can be seen to decrease the permittedthickness as the value of T27J goes up and also as the design minimum temperature

U goes down This therefore implicitly takes into account the effect of thetransition curve of figure 6.5.1 Note that care should be taken to insert thecorrect signs for T27J and U in the formula To see quickly the effect, the value

of this last term for various values of T27J and U is shown in table 6.5.4.1

Note that if U < T27J - 20, the steel may not be used at all This reflects the viewthat the transition curve cannot be predicted with any confidence at temperaturesmore than 20oC below that at which the Charpy energy is 27 Joules To buy a hardcopy version of this document call 01344 872775 or go to http://shop.steelbiz.org/ This material is copyright - all rights reserved Reproduced for IHS Technical Indexes Ltd under licence from The Steel Construction Institute on 15/8/2005

Table 6.5.4.1 Thickness factor for various values of U and T 27J

Table 3c of BS 5400-3 gives a full table of permitted thickness of steel parts of the

various grades in the European Standards, based on a k factor of 1 For other kfactors, the appropriate maximum permitted thickness can be determined bymultiplying the tabulated value by the factor

6.1 BRITISH STANDARDS INSTITUTION

BS 4360: 1979 Specification for weldable structural steelsBSI, London, 1979 (superseded)

6.2 BRITISH STANDARDS INSTITUTION

BS 4360: 1986 Specification for weldable structural steelsBSI, London, 1986 (superseded)

6.3 BRITISH STANDARDS INSTITUTION

BS EN 10025: 1990 Hot rolled products of non-alloy structuralsteels and their technical delivery conditions

BSI, London, 1990 (superseded)6.4 DESIGN MANUAL FOR ROADS AND BRIDGES

BD 13/90, Design of steel bridges - Use of BS 5400: Part 3: 1982Department of Transport, 1990

6.5 BRITISH STANDARDS INSTITUTION

BS 7668: Specification for weldable structural steels Hot finishedstructural hollow sections in weather resistant steels

BSI, London, 1994 To buy a hardcopy version of this document call 01344 872775 or go to http://shop.steelbiz.org/ This material is copyright - all rights reserved Reproduced for IHS Technical Indexes Ltd under licence from The Steel Construction Institute on 15/8/2005

6.6 BRITISH STANDARDS INSTITUTION

BS EN 10025: 1993 Hot rolled products of non-alloy structuralsteels Technical delivery conditions

BSI, London, 19936.7 BRITISH STANDARDS INSTITUTION

BS EN 10113: 1993 Hot rolled products in weldable fine grainstructural steels

BSI, London, (three parts, all 1993)6.8 BRITISH STANDARDS INSTITUTION

BS EN 10137: 1996 Plates and wide flats made of high yieldstrength structural steels in the quenched and tempered or precipitationhardened conditions

BSI, London, (three parts, all 1996)6.9 BRITISH STANDARDS INSTITUTION

BS EN 10155: 1993 Structural steels with improved atmosphericcorrosion resistance Technical delivery conditions

BSI, London, 19936.10 BRITISH STANDARDS INSTITUTION

BS EN 10210: 1994 and 1996 Hot finished structural hollow sections

of non-alloy and fine grain structural steelsBSI, London, (three parts; part 1, 1994; parts 2 and 3, 1996)6.11 THE STEEL CONSTRUCTION INSTITUTE

Guidance Notes on Best Practice in Steel Bridge ConstructionSCI, Ascot, 1998, (Second Issue, 2000)

6.12 EUROPEAN COMMITTEE FOR STANDARDISATION

ENV 1993-2: 1997

Eurocode 3: Design of steel structures

Part 2: Steel bridgesCEN, Brussels, October 19976.13 BRITISH STANDARDS INSTITUTION

BS 2846: Guide to statistical interpretation of dataPart 3: 1975 (1985) Determination of a statistical tolerance intervalBSI, London, 1975 (1985)

6.14 BRITISH STANDARDS INSTITUTION

BS EN ISO 2566: 1999 Steel Conversion of elongation valuesPart 1: Carbon and low alloy steels

BSI, London, 1999

7 GLOBAL ANALYSIS FOR LOAD EFFECTS

Linear elastic analysis will prove satisfactory as a method of determining theglobal distribution of bending moments, shear forces, etc in the vast majority ofshort to medium span bridge decks This is fortunate, as the principle ofsuperposition then allows stress resultants from individual load cases to becombined in an attempt to identify the most critical of the load combinations inPart 2 or BD 37/88

Where the material exhibits a non-linear stress-strain characteristic or whereapparently secondary effects give rise to internal forces of the first order (e.g the

P-) effect in the case of a cable-stayed or suspended structure), then anappropriate non-linear analysis may be employed

It should be noted that the use of non-linear or plastic methods of analysisgenerally prohibits the principle of superposition being employed for thesummation of load effects In some cases (for example the so-called ‘gravitystiffness’ of a suspension bridge), the non-linearity of the response may be verysmall for normal levels of loading and can often be ignored

In the design of composite beams, the provisions of this clause should be read inconjunction with those of Part 5, particularly with regard to the treatment ofconcrete in tension in hogging moment regions

The clause generally allows gross rather than ‘shear lagged’ section properties to

be used This is because the relative stiffnesses of members are virtuallyunchanged by making allowance for shear lag effects in all members Someexceptions are, however, noted:

For beams on flexible supports (including cable-stayed bridges) ‘shear lagged’

properties should be used since in such cases the global distribution of bendingmoments is more sensitive to the relative stiffnesses of the members Also,continuous box girders, or girders with integral decks, during erection should beanalysed using ‘shear lagged’ properties since they are sensitive to variations instiffness

Finally, if deflections have to be calculated, they depend on absolute stiffness and

so require the use of ‘shear lagged’ properties

Where allowance has to be made for shear lag as in 7.2, this is done by using an

effective breadth It is sufficiently accurate to use the quarter span valuesthroughout the spans of the beams for global analysis, including calculation ofdeflections (but not, of course for stress analysis - see 8.2 below)

8 STRESS ANALYSIS

There are three main reasons why the distribution of bending stress in a girdercross-section may differ from that given by the elementary theory of bending andthe assumption that plane sections remain plane

The first reason is the influence of local buckling in the compression regions ofthe cross-section, which will generally reduce the compression in the region ofmaximum buckling displacement This phenomenon is discussed in the

commentary on 9.4.2.

The second reason is that, even in the absence of local bucking, flange stresseswill reduce at a distance from the web due to shear lag effects These are

discussed below in the commentary on 8.2.

The third reason is that plastic straining in the web, in the presence of bending andshear, can give rise to a reduction in the bending stress carried on the web, and

an increase in the shear stress[8.1] This has the consequence that some of thebending moment in the web is shed plastically to the flanges It is usuallyconservative to assume that the redistribution does not occur, but the Code doesallow a certain amount of redistribution, which is more fully described in the

commentary on 9.5.4.

Elementary bending theory assumes that sections that are plane before bendingremain plane after bending, which implies that the axial strain in the flanges isuniform across their breadth However, because of the in-plane shear flexibility

of the flange, this may not be valid for flanges which are reasonably broad relative

to their length[8.2] The reason for this can readily be visualised by imagining abroad plate compressed along its short edges, giving rise to a non-uniformdistribution of longitudinal compressive strains across the breadth of the plate

The strains (and stresses) will be at their maximum at the short edges where thecompressive load is applied, and will gradually reduce to a minimum at the middle

of the plate, similar to the distribution of stress shown in Figure 8.2.1, which is

taken from Figure 56 of the Code Clearly if the flange was infinitely rigid in

shear, notwithstanding a finite axial rigidity, then axial stresses and strains in theflange would have to be uniform

b x b

Midpoint between webs

or free edge

e

1

max σ σ

L C

Figure 8.2.1 Distribution of longitudinal stress in the flange of a beam

In the context of girder flanges, this means that axial stresses and strains will begreatest at the connection to the web(s), and they will be at a minimum farthestfrom the web(s) The implications are twofold Firstly, any calculation of flangestress which was based on the full flange breadth straining uniformly (planesections remaining plane), would underestimate the flange stress in the region ofthe web Secondly, since shear lag means that the full axial stiffness of the flange

is not being mobilized, then it implies a reduction in the effective bending stiffness

of the girder, and an increase in the girder deflections The variation in stress andthe increase in deflection resulting from shear lag can be quantified directly byfinite element analysis, and the Code makes provision for this However, theusual method of allowing for shear lag effects when calculating stresses anddeflections in a standard analysis based on plane sections remaining plane, is toassume reduced effective breadths of flange, such that the flange, and thedeflections of the effective girder are the same as in the real girder In general,the effective breadths for these two purposes will not be the same As subsequent

calculations in the Code (e.g in 9.4.2) are carried out using effective breadths,

rather than the direct stress or deflection output from finite element analysis,guidance is given on how to convert the results of such an analysis into aneffective breadth, by taking the actual breadth times mean stress divided by peakstress The ratio of the effective breadth to the actual breadth is denoted as R inthe Code

The significance of shear lag depends on a number of factors The most importantfactor is the ratio of the flange breadth to its length, b/L Long narrow flanges(b/L less than 0.05, say) will have a high shear rigidity, and will therefore havenegligible shear lag effects Wide flanges, on the other hand will have much less

shear rigidity, and will be more susceptible to shear lag Examination of Tables

4 to 7 of the Code shows how the shear lag effective breadth reduces dramatically

as b/L is increased

The second factor is the form of loading It is found that the rate of change ofshear is important in determining the amount of shear lag Concentrated (or point)loads give rise to a much greater rate of change of shear in the region of the loadthan do more distributed loads, and will have, in consequence, a reduced shear lageffective breadth Standard highway or railway loads are reasonably distributed, To buy a hardcopy version of this document call 01344 872775 or go to http://shop.steelbiz.org/ This material is copyright - all rights reserved Reproduced for IHS Technical Indexes Ltd under licence from The Steel Construction Institute on 15/8/2005

so Tables 4 to 7 are for the typical situation of a distributed load Reduced values

of R, appropriate to situations with significant point loads, are given in

Appendix A.

The third important influence on shear lag effective breadths is the degree oforthotropy in the flange An unstiffened and perfectly isotropic flange will besubject to shear lag in accordance with the previous two paragraphs If the sameamount of flange material is distributed between a reduced thickness of flange andits longitudinal stiffeners, then there will be an even greater reduction in the flangestress remote from the web(s) This can be visualised by taking the redistribution

of flange material to its limits, so that the flange plate thickness reduces to zeroand all the flange material is in the stringers In this case, none of the internalstringers will carry any load at all In other words, as the shear rigidity of theflange reduces to zero, so the shear lag effective breadth reduces to zero TheCode allows for orthotropy by defining shear lag effective breadths as a function

of ", the ratio of the stiffener area to the flange plate area A value of " equal

to zero equates to an unstiffened flange, and typical stiffened flanges will have an

" value between zero and one R is given in Tables 4 to 7 for these two values

only, and the designer should use linear interpolation (or extrapolation) betweenthem for the value of " appropriate to the actual flange Inspection of the tableswill show that shear lag is more significant for " = 1 than it is for " = 0, asexpected

The final main influence on shear lag phenomena is the support conditions of the

girder In 8.2 this is allowed for by providing different tables of R values, for 4

basic support conditions - simply supported, fixed-ended, propped cantilever and

unpropped cantilever (Tables 4 to 7, respectively) The fixed-ended table is

described as being appropriate to internal spans of continuous beams, and is a

reasonable approximation Appendix A.2, on the other hand adopts a more

accurate approach for the real support conditions found in a girder, by allowingthe portions of the girder between points of contraflexure to be treated asequivalent simply supported spans Analysis has shown this to be a very goodapproximation, for the purposes of calculating R

The shear lag effective breadth is found to be fairly uniform along the length of

a uniformly loaded span, except in the regions of low or zero moment Spanssubjected to point loads, however, have a much greater variation in R along theirlength The tables give values of R at the mid-span and quarter span positions,

as well as at the supports, and allow linear interpolation between these positions

in order to calculate stresses at all points along the length of the girder A singlevalue of effective breadth is used for deflection calculations, and this is taken to

be the value given in the tables at the quarter span position

Although shear lag has a generally detrimental effect on stresses and deflections,there may be situations where it can offer some advantage, for instance where thereduced stress in the middle of a wide flange can be beneficial when designing the

flange for local bending due to wheel loads For this purpose, Appendix A.6 gives

an expression which defines the distribution of longitudinal stress across thebreadth of the flange

The final point to note is that, for typical values of b/L (i.e b/L<<1.0), it has

been found from elasto-plastic analysis that shear lag has almost no effect on theultimate strength of flanges[8.3] The reason for this is that the yielding whichoccurs first of all at the edges of the flanges, is able to spread away from the web

until the whole flange is fully mobilised The Code therefore requires shear lag

to be taken into account for the serviceability limit state only

girders

The torsional and distortional behaviour of box girders is generally outside thescope of this publication However, a useful description of the behaviour is given

in Section 3 of Design guide for composite box girder bridges[8.4] Nevertheless,

it should be noted that the distinction between torsional and distortional warping

has been clarified in the revised clauses 8.3, 9.2.1.3 and 9.2.3.2, and the

determination of distortional effects in accordance with Appendix B has beensimplified by the inclusion of general expressions as alternatives to interpolation

between curves on Figures Additionally, Table 17 has been revised and extended

after reference to the original research on which it was based

Typical double flanged sections, such as I, channel or box sections, whensubjected to shear, have a distribution of shear on the web which is very nearlyuniform, and as a result, the Code assumes a uniform shear distribution in thewebs of such sections

Other types of cross-section will have a much less uniform shear flow in the web,

and 8.4 requires the distribution of shear in the web to be calculated from the

theory of bending

The effects of certain imperfections, such as some bearing misalignments and

errors in level and inclination (8.5.1(a)), and imperfections in straightness and flatness of members (8.5.1(b)), are assumed to have been allowed for in the design

rules in the Code, provided they are within the tolerances of their respectiveworkmanship specifications

On the other hand, 8.5.2 lists a number of imperfections which have to be allowed

for explicitly; for example, lack of common planarity of bearings under torsionallystiff girders, and columns on bearings which may apply eccentricity of loading

The general approach is that where an absolute error may give rise to widelydiffering results, depending on the structural properties and response, it has to beallowed for explicitly

Residual stresses are a self-equilibrating system of compressive and tensile stressesdistributed throughout the cross-section of a member, which arise due todifferential cooling rates after welding or hot-rolling, or from permanentdeformations due to cold-rolling, or handling and transportation These locked-instresses will have some effect on the strength and stiffness of the member, and To buy a hardcopy version of this document call 01344 872775 or go to http://shop.steelbiz.org/ This material is copyright - all rights reserved Reproduced for IHS Technical Indexes Ltd under licence from The Steel Construction Institute on 15/8/2005