PRACTICALSTEEL TUB GIRDER DESIGN

April 2005

AUTHORS

Domenic Coletti, P.E.HDR

Zhanfei “Tom” Fan, P.h.D., P.E.Texas Department of Transportation

Walter GattiTensor Engineering

John Holt, P.E.Texas Department of Transportation

John Vogel, P.E.Texas Department of Transportation

The National Steel Bridge Alliance has published this document inits continuing effort to enhance state-of-the-art steel bridge designand construction in the United States.

DISCLAIMERAll data, specifications, suggested practices and drawings presented herein, are based on thebest available information, are delineated in accordance with recognized professionalengineering principles and practices, and are published for general information only.Procedures and products, suggested or discussed, should not be used without first securingcompetent advice respecting their suitability for any given application.

Publication of the material herein is not to be construed as a warranty on the part of theNational Steel Bridge Alliance – or that of any person named herein – that these data andsuggested practices are suitable for any general or particular use, or of freedom frominfringement on any patent or patents. Further, any use of these data or suggested practicescan only be made with the understanding that the National Steel Bridge Alliance makes nowarranty of any kind respecting such use and the user assumes all liability arising therefrom.

TAB

LE OF C

ON

TENTS

ii

TABLE OF CONTENTS

INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1STEEL TUB GIRDER APPLICATION ISSUES . . . . . . . . . . . . . . . . . . . . . . . .2Span Ranges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3Curvature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3Aesthetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4Durability/Maintainability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4Economy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4Application Issues References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5DEPTH, WIDTH AND SPACING OF TUB GIRDERS . . . . . . . . . . . . . . . . . . .6Depth-to-Span Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7Tub Girder Width and Spacing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7ANALYSIS AND DESIGN METHODS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9Tangent Tub Girder Design Techniques and Tools . . . . . . . . . . . . . . . . . . . . . .10Approximate/Preliminary Curved Girder Design . . . . . . . . . . . . . . . . . . . . . . .11Effects of Curvature, M/R Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11Grid Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .123-D FEA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12GIRDER DESIGN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .14Bottom Flanges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15Webs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16Top Flanges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17DIAPHRAGMS AND BRACING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18General Guidelines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19Internal Intermediate Diaphragms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19External Intermediate Diaphragms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20Internal Diaphragms at Supports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .22External Diaphragms at Supports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23Top Flange Lateral Bracing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .24MISCELLANEOUS DETAILS AND ISSUES . . . . . . . . . . . . . . . . . . . . . . . .26Flange-to-Web Welds and Shear Studs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .27Bearings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .27Bridge Decks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .28Field Splices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .28Detailing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .29Material Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .30Painting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .31PRACTICAL EXAMPLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .32IH-35/US 290 Interchange, Austin, Texas . . . . . . . . . . . . . . . . . . . . . . . . . . . .33Various TxDOT Houston Projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .33US 75 Underpass at Churchill Way, Dallas, Texas . . . . . . . . . . . . . . . . . . . . . .34CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .36REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .38APPENDIX A: Computer Design Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .42APPENDIX B: Example Design Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . .43

Steel tub girder use is becoming morecommonplace in modern infrastructuredesign. They offer advantages over othersuperstructure types in terms of span range,stiffness, and durability – particularly incurved bridges. In addition, steel tub girdershave distinct aesthetic advantages, due totheir clean, simple appearance. Steel tubgirder design is in many ways more complexthan steel plate girder design, especially forconstruction loading stages. Yet there is nosingle, comprehensive source of informationon steel tub girders. Instead, bits and piecesof layout, design, detailing and constructionguidance are scattered among a broad anddisconnected collection of designspecifications, guidebooks, textbooks, articlesand formal design examples, many of whichare out of print or otherwise difficult to obtain.Designers faced with the task of preparingplans for a steel tub girder bridge often have tostart with an extensive – sometimesfrustrating – literature search, hoping to findenough advice from among several sourcesto guide them from preliminary designthrough final detailing.

A much anticipated tub girder publicationis forthcoming from the University of Texasand the University of Houston (25) but wasnot available at the time of publication ofthis book. Another much anticipatedpublication is the upcoming 2005 InterimRevisions to the AASHTO LRFD BridgeDesign Specifications (26), in which thedesign provisions for straight and curvedsteel girder bridges (both I girders and tubgirders) are “unified” into a single designspecification document.

This book addresses the entire designprocess for a steel tub girder bridge andoffers a list of pertinent references for eachphase, including suggestions on how to findsome hard-to-locate documents. The bookpresents preliminary design considerations,including: appropriate applications for steeltub girders; preliminary girder sizing andspacing guidelines; framing plan layoutconsiderations; and suggestions related topreliminary (approximate) design. The bookalso discusses issues related to final,

detailed design, including various availableanalysis tools (the M/R Method, grid analysis,and three-dimensional finite elementanalysis); specifics on design of thenumerous components of a steel tub girderbridge (girders, internal and externaldiaphragms, lateral bracing members,stiffeners, bearings, deck, field splices, etc.);suggestions on steel tub girder detailing; andspecial considerations for construction of asteel tub girder bridge.

While this book is not a stand-alone steel tubgirder design manual, it endeavors to coverthe entire design process in outline form inone document, while providing an extensivelist of references that the designer canconsult. Because nearly every steel tubgirder bridge is unique in terms ofconfiguration, site conditions, local fabricationand construction preferences, and myriadother factors, the book will typically outlineissues and considerations related to specificquestions rather than attempting to providehard and fast rules, in the hopes of leavingdesigners better informed to make their ownfinal decisions for their project. Finally, somerecent steel tub girder bridge experience inTexas is presented, with key issues andlessons learned highlighted.

This bookaddresses theentire designprocess for a steeltub girder bridge...

INTR

OD

UC

TION

1

INTRODUCTION

Figure 1: A bold statement in modernhighway bridge design, steel tub girders offeradvantages in span range, ability toaccommodate curvature, and aesthetics.

STEEL TUB GIRDER APPLICATION ISSUES

STEELTU

B G

IRD

ER A

PPLICATIO

N ISSU

ES

2

There are manyreasons to choosesteel tub girders,which offer manydistinct advantagesover steel plategirders and othersuperstructuretypes...

STEELTU

B G

IRD

ER A

PPLICATIO

N ISSU

ES

3

There are many reasons to choose steeltub girders, which offer many distinctadvantages over steel plate girders andother superstructure types. However, steeltub girders are not a panacea. Designersshould carefully consider each bridge on acase-by-case basis to determine if steeltub girders are an appropriate superstructurechoice. Several keys issues to evaluateare listed below.

SPAN RANGESSteel tub girders can potentially be moreeconomical than steel plate girders inlong-span applications, due to theincreased bending strength offered bytheir wide bottom flanges and thanks toless field work associated with handlingfewer pieces. However, their use in long-span applications should be evaluatedwith due consideration given to increasedfabrication costs of tub girders, particularlyif bottom flange longitudinal stiffeners orother complicated details are required.Also, lifting weights may be higher with tubgirders. Spans in excess of 500 feet havebeen successfully constructed; forinstance, in October 1998 the WestVirginia Department of Transportationcompleted the Lower Buffalo River Bridgecarrying WV 869 over the Kanawha River.That bridge features a five-span tangenttub girder unit with a 525-foot-long centerspan, the third longest tub girder span inthe United States.

In short span ranges, steel tub girders canbe an economical solution, particularly ifconsiderations such as aestheticpreferences preclude other structuretypes. However, it is increasingly difficultto design efficient steel tub girders forspan lengths shorter than those requiringthe rule-of-thumb 5-foot minimum webdepth (minimum depth needed to provideaccessibility for future inspection). Thislimit works out to be below approximately150 feet for simple spans and 200 feet forcontinuous spans. One writer hassuggested a desirable lower span lengthlimit of 120 feet (1). In lower span ranges,and/or when curvature is slight, othershapes may prove to be more efficientthan steel tub girders.

CURVATUREWhile steel tub girder use is not limited tocurved structures, they do offer definiteadvantages in curved bridge applications.Torsional stiffness of tub girders is manytimes greater than that of plate girders,resulting in superior transverse loaddistribution characteristics. Tub girders arealso extremely efficient in carryingtorsional loads found in curved bridges,requiring far fewer diaphragms betweengirders. Steel tub girders accommodateextremely tight radii of curvature and have

STEEL TUB GIRDER APPLICATION ISSUES

Figure 2: Steel tub girders under constructionfor a new Automated People Mover system.Tight curvature and clean appearance werekey factors in choosing steel tub girders.

Figure 3: For slight curvature and spansbelow approximately 120 feet, othersuperstructure types, such as the curved steelplate girders in this shallow depth curvedgrade separation bridge, may be a betterchoice than steel tub girders.

Steel tub girdersaccommodateextremely tightradii of curvatureand have beenused in this rolefrom their earliestapplications...

STEELTU

B G

IRD

ER A

PPLICATIO

N ISSU

ES

4

been used in this role from their earliestapplications. Among the earliest uses ofsteel tub girders in the United States weretwo bridges built on horizontal radii of 150feet in Massachusetts in the early 1960s(2). Later, a series of steel tub girderswere constructed at the Dallas/Fort WorthInternational Airport in the late 1970s on175-foot horizontal radii. On the downside, the complexity of fabricatingtrapezoidal box shapes to accommodatevertical curvature, horizontal curvature,super-elevation transitions, and/or skewsis challenging and contributes to a costpremium versus other structure types.

AESTHETICSOne of the reasons most often cited forusing steel tub girders is aesthetics.Bracing, stiffeners, utilities, and othercomponents are typically hidden within thebox, resulting in a smooth, unclutteredform. Because a single tub girder canessentially take the place of two plategirders, the number of visible componentsis minimized, again leading to a reductionin visual clutter.

DURABILITY/MAINTAINABILITYSteel tub girders offer advantages indurability and maintainability. The steelsurface area exposed to the environmentis greatly reduced, since half of the weband flange surfaces are enclosed. Inaddition, elements routinely subjected todebris buildup (and thus corrosion anddeterioration) in plate girders – such asbottom flanges, diaphragms, and bracingmembers – are protected in tub girders.Furthermore, reduced numbers ofdiaphragms result in reduced paintingcosts. Tub girders are also easier toinspect, since much inspection isperformed from inside the tub, whichserves as a protected walkway. However,it should be noted that bridges with onlyone or two tub girders (such as directconnector ramp structures) may beconsidered fracture critical, requiringadditional inspection.

ECONOMYSteel tub girders are more costly tofabricate than plate girders. Theirgeometry is complex, making it difficult tofabricate and assemble individual piecesin the shop and at bridge sites. It takeshighly skilled workers to fabricate anderect steel tub girders, resulting in apremium on labor costs even if materialcosts are competitive with plate girderalternates. Individual tub girders are alsobigger and heavier than plate girders,increasing equipment costs for erection.

However, well-conceived and carefullydetailed steel tub girders offer someeconomic advantages over plate girders. Theneed for fewer diaphragms reducesfabrication costs. Furthermore, fewer

Figure 4: Steel tub girders built on horizontalradii as tight as 175 feet were constructed atthe Dallas/Fort Worth International Airport inthe late 1970s.

Figure 5: Simple lines, smooth surfaces, andfewer parts visible; the clean appearance oftub girders offers distinct aestheticadvantages.

Figure 6 (nearright): Modernhighwayconstructioninvolves workingaround manyconstraints; steeltub girders canhelp solve toughproblems.

STEELTU

B G

IRD

ER A

PPLICATIO

N ISSU

ES

diaphragms and fewer girders versus plategirder alternates can speed erection, a criticaladvantage in urban highway reconstructionprojects where traffic interruptions (andassociated contractor “lane rental” penalties)dramatically affect construction costs andpose economic impacts to the community.

While steel tub girders are notinexpensive, when efficiently designed,carefully detailed, and used in the rightapplication, they represent a reasonablyeconomical, aesthetically pleasingsolution that will compete favorably withother superstructure types.

APPLICATION ISSUES REFERENCESThere are several good references thatdiscuss steel tub girder application issues.The article “Why Steel Box Girders?” (2)offers a concise overview of many keyissues. Both “Section 12, Beam and GirderBridges,” of the Structural Steel Designer’sHandbook (1) and “Section 21, Curved SteelBox Girder Bridges,” of the StructuralEngineer’s Handbook (3) touch on some ofthese issues as well. The introduction toVolume II, Chapter 7, “Composite Box GirderLoad Factor Design,” of the United StatesSteel (USS) Highway Structures DesignHandbook (4), also provides a succinctdiscussion of many key issues.

5

6

DEPTH, WIDTH AND SPACING OF TUB GIRDERS

DEPTH

, WID

TH A

ND

SPAC

ING

OF TU

B G

IRD

ERS

DEPTH-TO-SPAN RATIOSThe traditional rule of thumb for steelbridge girder depths of L/25 is a goodstarting point for steel tub girders. TheL/25 guideline is mentioned in Section 12of the latest version of the AASHTO GuideSpecifications for Horizontally CurvedSteel Girder Highway Bridges (5).However, designers should not be afraidto exceed this ratio; tangent steel tubgirders have approached L/35 and stillmet all code requirements for strength anddeflection control. Keep in mind theminimum recommended web depth for tubgirders is 5 feet, as cited by several writers(2, 6). Note that steel tub girder depthaffects more than just the commonlyconsidered implications, such as verticalclearance below a bridge. Because mosttub girders use sloped webs (typicallysloped at 1H:4V), web depth also directlyaffects bottom flange width (as will bediscussed later).

TUB GIRDER WIDTH AND SPACINGAs a lower bound, at least one writer hassuggested a minimum width of 4 feet bemaintained for tub girders (6) to allowsufficient room for workers to completefabrication of various internal girderdetails. As an upper bound, there are nohard and fast rules. Upper limits on tubgirder width (and also on tub girderspacing) are often controlled indirectly bythree central issues:

• Bottom Flange Width – Extremelywide bottom flanges will likelyrequire the addition of longitudinalstiffeners and/or transversestiffeners for stability (see furtherdiscussion below).

• Deck Transverse Span – Someowners (e.g., state departments oftransportation) are uncomfortablewith wide girder spacings, bothwithin each tub girder and betweengirders. One concern isconstructability. Wider deck spansare more difficult to form, and some

owners have very economical deckdetails – including permanent metaldeck forms or stay-in-place precastconcrete deck panels – which maynot be suited for wider girder widthsand spacings. Another issue is theability of wide span decks toaccommodate certain overloadconditions. Finally, redecking whilemaintaining traffic may be quitedifficult on bridges with wider girderwidths and spacings.

• Transportation Limits – Note that tubgirder widths above approximately12 feet present transportationdifficulties; widths above 14 feetmay require provisions for alongitudinal bottom flange splice sothat the tub can be transported tothe bridge site in two sections.

The ratio of the width of an individual tubgirder to the spacing between tub girdersshould also be considered. Article10.39.1.1 of the AASHTO StandardSpecifications for Highway Bridges (7)states: “The average distance center tocenter of flanges of adjacent boxes shallnot be greater than 1.2 times and not lessthan 0.8 times the distance center tocenter of the flanges of each box.”However, note that the main purpose ofthis limit is to keep the width/spacing ratio

As an upperbound, there areno hard and fastrules...

DEPTH

, WID

TH A

ND

SPAC

ING

OF TU

B G

IRD

ERS

7

DEPTH, WIDTH AND SPACING OF TUB GIRDERS

Figure 7: Maintain a minimum width of 4 feetfor tub girders to allow room for workers tocomplete fabrication of various internaldetails.

Overall width of abridge is also acontrolling factorin settingindividual tubgirder widths andspacings...

8

within the bounds of applicability for theempirical live load distribution factorsprovided in the AASHTO StandardSpecifications for Highway Bridges (7).Exceeding these limits may beacceptable, provided a more refinedanalysis is performed that more rigorouslyquantifies live load distribution. Designersshould take care to consider all theimplications if they choose to exceedthese limits.

Overall width of a bridge is also acontrolling factor in setting individual tubgirder widths and spacings. In manynarrower bridges carrying only one lane oftraffic plus shoulders (such as directconnector ramp structures in multilevelinterchanges), total out-to-out deck widthmay be as narrow as 28 feet or less. Inlonger spans requiring deep girders, twotub girders with webs sloped at 1H:4Vmay end up with overly narrow bottomflange widths. Single tub girder bridgeshave been successfully used in thesesituations, but beware that using a singletub girder may result in an excessivelywide bottom flange as well as design,detailing, and construction complexitiesassociated with providing two bearings pertub girder (see bearing discussions later).

Designers are advised to evaluate theseconsiderations early on, before evenpreliminary structural design calculationsare performed.

DEPTH

, WID

TH A

ND

SPAC

ING

OF TU

B G

IRD

ERS

AN

ALY

SIS AN

D D

ESIGN

METH

OD

S

9

ANALYSIS AND DESIGN METHODS

Final design of steel tub girder bridges is adetailed and intensive process. Caretaken during the preliminary design phasewill pay dividends many times over lateron. Thorough consideration of design,detailing, and construction issues up frontwill result in better, more efficient, andeasier-to-construct bridges in the end.Before beginning to run numbers, designersare advised to consider numerous framingplan issues discussed throughout this book.

While some simple rules of thumb exist tohelp guide the designer through thepreliminary design phase, each steel tubgirder bridge is unique. Additionally,because so many design, detailing andconstruction issues overlap, no hard andfast laws always govern. The most reliablerule is to take time during the preliminarylayout and design phase to identify andevaluate these issues.

In this section, the tools and techniquesfor overall tub girder superstructure designare discussed. However, it must be notedthat virtually all components of tub girderbridges require design. Some moresophisticated computer analysis tools(discussed below) can calculate many orall loads needed, but no program willperform all necessary design checks andmany require supplemental hand analysisto quantify loads in secondary members.

Because tub girders are often used in curvedbridges, much of the discussion of tub girderdesign is presented in a curved girdercontext. Furthermore, even tangent tubgirders are subject to torsional loading andthus deserve many of the sameconsiderations as for curved tub girders.However, discussion of tangent tub girderanalysis is worthwhile both for directapplications to tangent tub girder bridges andfor use of tangent girder design tools as partof approximate preliminary design.

TANGENT TUB GIRDER DESIGNTECHNIQUES AND TOOLSStraight bridges containing multipletangent tub girders can be designed using

a single girder model. Dead loads can beanalyzed assuming tributary loaddistribution, and live loads analyzed withappropriate live load distribution factors.Tub girder live load distribution factorswere developed by Mattock in the early1970s (8) and are still included in thecurrent AASHTO Standard Specificationsfor Highway Bridges (7) and AASHTOLRFD Bridge Design Specifications (9).Sennah and Kennedy (10) discussrecently completed research into live loaddistribution factors for tub girders,including recommended distributionformulas, but these have not beenincorporated into the AASHTO designspecifications. Designers are advised toalways verify the applicability of any codeor research recommendations bychecking the scope and assumptions ofthe background research.

Design can be facilitated using any of severalcommonly available tangent girderprograms, some of which are specificallydeveloped for tub girder design. Others arenormally only applicable to plate girder orrolled beam design, but can provide sufficientdesign information to shortcut some tediousanalysis steps. See Appendices A.1 and A.2for further information.

For shear design, designers must rememberthat all tub girders carry torsion, whichincreases effective design shear in one web.In most straight bridges, web shears due totorsion are significantly smaller than thosedue to bending. Torsional analysis may bewarranted for fascia girders and for girders atconstruction phase lines. If a single girdermodel is used, torsional moments can beapproximated by hand. If a multiple girdercomputer analysis model is used, torsionalmoments should be available from theanalysis, and additional web shears canbe derived.

In addition, because most tub girder websare sloped, the designer must account forthe increase in resultant web shear due toweb slope, as well as the increase in webdepth along the slope.

While somesimple rules ofthumb exist tohelp guide thedesigner throughthe preliminarydesign phase, eachsteel tub girderbridge is unique...

AN

ALY

SIS AN

D D

ESIGN

METH

OD

S

10

ANALYSIS AND DESIGN METHODS

APPROXIMATE/PRELIMINARY CURVEDGIRDER DESIGNAccording to the AASHTO GuideSpecifications for Horizontally CurvedSteel Girder Highway Bridges (5), theeffects of curvature on primary bendingloads can be neglected for slightly curvedbridges (see the code for the exactdefinitions and limits). That is, the “loadshifting” phenomenon in curved girderbridges (described below) can beneglected when curvature is slight.However, in all cases torsional effectsshould be examined. In many cases,these torsional effects only influence thedesign of the diaphragms and bracing.

In cases where the effects of curvature onprimary bending loads can be safelyneglected, the straight girder methodspreviously mentioned in this book shouldproduce a design very close to the finaldesign where torsion is considered, andthe resulting cross-section sizes should begood candidates for the trial member sizesin the final design model. When analyzinga curved bridge using tangent girdermethods, developed span lengths of thetub girders should be used. Live loaddistribution factors can be found in thecommentary to the ASD provisions of theprevious edition of the AASHTO GuideSpecifications for Horizontally CurvedHighway Bridges (11). Impact factors forsteel tub girders are found in the currentAASHTO Guide Specifications forHorizontally Curved Steel GirderHighway Bridges (5).

In cases where the effects of curvature onprimary bending loads cannot beneglected, approximate analysis can stillbe performed using straight girdermethods as the basis, but with the straightgirder results amplified with factors toaccount for curvature as described below.

EFFECTS OF CURVATURE, M/R METHODDesigners must remember that tangentgirder programs do not account for loadshifting and torsion effects caused by

horizontal curvature. It is up to designers toaccount for these effects in order to correctlyquantify design loads on a tub girder.

In general terms, an overturning moment(moment about the longitudinal axis of thebridge) occurs in curved bridges, since thecenters of gravity of each girder – and ofthe bridge as a whole – are offset from achord line drawn between support pointsof each span. When girders actindependently of each other (for example,in the case of self load of an individualgirder or the case of deck placement if nointermediate external diaphragms areprovided), this effect results in torsion ineach tub girder. These torsional momentscan be determined using the M/R Method,an approximate, hand calculation methodfor torsional analysis of single curved tubgirder bridges developed by Tung andFountain (3, 12, 13).

When girders are connected either bydiaphragms or by a hardened deck, thiseffect results in a tendency for load shiftingto the outside girders of the curve, due tothe global overturning moment present incurved spans; that is, girders on theoutside of the curve carry more load thangirders on the inside of the curve. Forpreliminary design of curved tub girders,this effect can be approximated usingguidance in the Federal HighwayAdministration (FHWA) “Curved GirderWorkshop Lecture Notes” (12), whichpresents graphs for quantifying increases indesign vertical moments due to curvature.

The M/R Method can be applied toeffectively calculate the torsional momentin single girders, or in girders underconstruction before adjacent tub girdersare tied together by intermediatediaphragms and slab. Because cross-sectional rotations can also be obtainedusing the M/R Method, it is possible that themethod can be applied to multiple girdersconnected by intermediate diaphragms tosolve the load shifting by iterations.However, the process would be too

Designers mustremember thattangent girderprograms do notaccount for loadshifting andtorsion effectscaused byhorizontalcurvature...

AN

ALY

SIS AN

D D

ESIGN

METH

OD

S

11

In a grid analysis,a two-dimensionalgrid is used todefine the overallgeometry, withline elements usedto model thegirders anddiaphragms...

12

complicated without additionalcomputational aids. More effective methodsto consider the interaction of the girders aregrid analysis and Three-DimensionalFinite Element Analysis (3-D FEA).

GRID ANALYSISMultiple girders and diaphragms can bemodeled in a grid analysis; mostcommercial programs for curved tub girderdesign are based on this method.Appendices A.3 and A.4 provideinformation on two of these programs. Atwo-dimensional grid is used to define theoverall geometry, with line elements usedto model the girders and diaphragms.Most programs distribute live loads togirders using the lever rule.

Because girders and diaphragms aremodeled by line elements, the elementsshould be able to account for all relateddeformations, including bending, shear,torsion, axial deformation and cross-sectional distortion. Numerous elementshave been developed, but commercialprograms currently available in the marketdo not cover all types of deformation.Engineers should ensure that the programemployed is at least able to model thebending, shear and pure torsion correctly,since warping stresses are usually smallin properly braced box girders. Cautionshould be exercised in modeling trusses(such as external K-frames) as equivalentline elements. Additional calculations are

required after the analysis to account forsuch items as brace forces and lateralbending stresses.

One major difficulty in grid analysis ismodeling the concrete slab under liveloads. Some programs and researchinvestigations use line elements – alignedtransversely like diaphragms – to modelslab action. Be aware that validation of thissimplification is not available from research.

For preliminary design, using these toolsmay be a more involved undertaking thanperforming a tangent girder analysis,because much more input is required tofully define a framing plan. However, thereis a definite benefit to avoiding performingmanual approximations to addresscurvature and/or perform design checksspecific to tub girders. Note that at thepreliminary design phase, it is both difficultand not valuable to perform detailed sizingof diaphragms and lateral bracingmembers beyond perhaps cursoryevaluations to verify the soundness of aproposed framing plan.

For final design of curved or severely skewedtub girders, a grid analysis is the minimumlevel of analysis that should be considered.

3-D FEA3-D FEA is a method in which girder platesare modeled using plate/shell elements,while a concrete slab is modeled either

AN

ALY

SIS AN

D D

ESIGN

METH

OD

S

using plate/shell elements or solid brickelements. Bracing members are alsoincluded in the analysis, usually modeledwith either truss or beam elements.

3-D FEA methods are intended to createhighly inclusive and accurate models thatcan replace all other methods. However,implementation of 3-D FEA into commonengineering practice still has manychallenges. Comparisons between fieldmeasurements and analysis – including3-D FEA – continue to show disparity,because many aspects of tub girders aredifficult to accurately model. Because 3-DFEA is still a simplification of actualstructure and load history, the necessity ofdetailed 3-D FEA is disputable if onlymarginal improvement is achieved, whilethe investment of computer and humanresources is increased significantly. Also,some engineers still prefer to perceive tubgirder bridges as beams and grids ratherthan a special assembly of plates andblocks. Finally, 3-D FEA generally requiresadditional efforts to convert stress resultsback to member forces (such as momentsand shears) as are used in design.

This method, however, remains aneffective tool in research and in studyingbridge behavior under isolated load cases.If interpreted properly, 3-D FEA results cancontribute to a better understanding ofcurved bridge behavior. Three-dimensional analysis programs orservices exist that include code-checkingprocedures for main girders (see AppendixA.5 for information). These are powerfulanalysis tools if used properly; however,design procedures still require othersupplemental structural analysis asdemonstrated in the design example inthe current AASHTO GuideSpecifications for Horizontally CurvedSteel Girder Highway Bridges (5).

Comparisonsbetween fieldmeasurements andanalysis – including3-D FEA –continue to showdisparity, becausemany aspects of tubgirders are difficultto accuratelymodel...

AN

ALY

SIS AN

D D

ESIGN

METH

OD

S

13

GIRDER DESIGN

14

GIR

DER

DESIG

N

Figure 8 (nearright): Thevarious parts ofa typical tubgirder.

15

The girder design process for tub girdersshould begin with development of aframing plan. Many decisions made earlyin the design process can have significantimpacts later on; some basic issues arepresented below. Structural analysis asdiscussed above must be performed to derivethe load effects, which are subsequentlychecked with the code provisions.

Tub girder bridges must always bedesigned considering constructionsequence. Some structural members,such as lateral bracing, are provided onlyfor construction purposes. Their design isconsequently controlled by constructionloading. The analysis must therefore beperformed on the partially completedstructure, simulating the sequence ofconstruction loading. Total stresses arethe sum of those generated due to loadson the complete bridge and those locked-in during construction.

Numerous guides and design examplesare available that specifically discussgirder design and code provisions in detail(1, 3, 4, 5, 7, 14, 15).

BOTTOM FLANGESBottom flange thickness and b/t ratios mayseem like minor details better left to finaldesign. However, designers of steel tubgirders are well-advised to consider thisissue up front while developing a framingplan, because many potentially complex

and costly ramifications may result fromthe simple choice of bottom flange widthand thickness.

The AASHTO Standard Specifications forHighway Bridges (7) suggest that for b/tratios greater than 45, “longitudinalstiffeners be considered,” and that b/tratios greater than 60 are not permitted forcompression flanges. The b/t limit of 45 forconsideration of longitudinal stiffeners isintended to be a rule of thumb; with a b/tabove 45, it may be more economical toadd a longitudinal stiffener to the bottomflange to increase bottom flange capacitywithout thickening the flange. Becausethey are a costly addition and their usemay result in undesirable fatigue details,careful consideration should be givenbefore adding longitudinal stiffeners.Engineers often find it more economical tosimply thicken the bottom flange in lieu ofusing longitudinal stiffeners.

Even in positive moment regions, there arelower bound limits for bottom (tension)flange thickness. As stated in the PreferredPractices for Steel Bridge Design,Fabrication, and Erection prepared by theTexas Steel Quality Council (16):

“For wide bottom flanges, platedistortion during fabrication anderection can be a problem. Designersshould check with fabricators whenusing bottom tension flange plates less

GIR

DER

DESIG

N

Internal IntermediateDiaphragm (Typ)

Bottom Flange (Typ)

Top Flange (Typ)

External IntermediateDiaphragm (Typ)

Web (Typ)

Shear Studs (Typ)

Stiffener (Typ)

Top Flange LateralBracing (Typ)

than 1-inch thick to determine whetherpractical stiffness needs are met. In nocase should bottom tension flanges beless than 1/2-inch thick. Anothersuggested guideline is that the bottomtension flanges have a b/t ratio of 80 orless.”

Other writers have suggested a maximum b/tratio of 120 for bottom flanges in tension (17).

For extremely wide and/or slender bottomflanges, transverse stiffeners may berequired. Bottom flange transversestiffeners serve several purposes, includingbracing bottom flange longitudinal stiffenersand stiffening bottom flanges for torsionalshear stresses. Again, care should be takenbefore adding transverse stiffeners tobottom flanges, since they will be costlyand may result in constructability andfatigue problems if not carefully detailed.

Some detailing guides, such as thePreferred Practices for Steel BridgeDesign, Fabrication, and Erection (16),provide more detailed suggestionsregarding tub girder bottom flangethickness and b/t ratios. These issues arealso discussed in the Commentary toSection 10.4.2.4 of the AASHTO GuideSpecification for Horizontally CurvedSteel Girder Highway Bridges (5).Designers should carefully review theissues presented in these documents andseek guidance from local steel bridgefabricators with tub girder experience

regarding relative cost issues beforemaking hasty assumptions regardingbottom flange thickness.

WEBSAlthough tub girders carry vertical shearsimilar to plate girders, they also carrytorsional shear stress. Tub girders arevery efficient in carrying torsion, so thisgenerally does not present a significantdesign challenge. The shear flow can beobtained from the torsional moment usingthe formulation q = T/2A, where A is thearea enclosed by the tub girder webs,flanges and slab (or lateral bracing, ifinvestigating girder prior to deckhardening). However, designers shouldremember early on that the webs will carrymore shear than what might be predictedby an approximate, tangent girderanalysis, and thus increased thickness oradditional transverse stiffeners may berequired. Recent experience has shownthat providing a reasonable number oftransverse stiffeners is currently moreeconomical than providing either a thinnerweb with extensive transverse stiffeners ora thicker web without.

It should be noted that all tub girders havetorsion; even tangent tub girders will besubject to some level of torsion from avariety of causes. Some potential sourcesof torsion in tangent (and curved) tubgirders include:

• Skew – Skew increases torsion intub girders, because web span

Figure 9 (nearright): Webs fortub girders carryboth verticalshear and sheardue to torsion,and are oftenhorizontallycurved, slopedand cambered.

GIR

DER

DESIG

N

16

positions relative to various loadpoints are no longer symmetricalfrom one web to the next.

• Asymmetrical Non-CompositeLoading – External girders inparticular can be subject toasymmetrical loading during deckplacement, since overhang widthsare often not equal to the tributarydeck width between adjacentgirders and at phased constructionlines. This effect can becontrolled/reduced by use ofintermediate external diaphragmsand/or lateral bracing.

• Asymmetrical Live Loading – TheCommentary to Article 9.7.2.4 ofthe AASHTO LRFD Bridge DesignSpecifications (9) offers a gooddiscussion of this issue. Becausetub girders have very high torsionalstiffness, they can developtorsional loading duringasymmetrical application of liveload. Plate girders do notexperience this phenomenon, sincethey are very flexible torsionallyand twist or rotate to accommodatethe deck behavior. For tub girders,this phenomenon is more importantfor deck design (it can control thedesign of the deck slab), but it isworth noting here as anothersource of torsion in tangent andcurved tub girders.

Occasionally, project requirements dictatethe need to use dapped girder ends.These complicate design, detailing andfabrication of the girders and their useshould not be undertaken lightly.Reference 27 has current guidance on thedesign of dapped girder ends for bothsteel plate and steel tub girders.

TOP FLANGESTop flanges of tub girders are designedprimarily to carry the girder bendingstresses. Additional longitudinal stressesdue to torsion exist, as the flanges alsoserve as members of the truss system

used for lateral bracing. Top flanges arealso subjected to significant lateralbending stresses. These lateral bendingstresses can be generated by horizontalgirder curvature (4), sloping webs (18),and temporary supporting brackets forslab overhangs (5). In addition, forcesfrom lateral bracing systems mayrepresent a major source of lateral flangebending stresses and should also beconsidered in design (see the recentarticle by Fan and Helwig [18] for a moredetailed discussion).

Design provisions (5) suggest that lateralbending of top flanges can greatly affectthe portion of capacity allocated tobending stresses. Increasing top flangewidth is generally more effective forresisting the lateral bending stresses thanincreasing top flange thickness. Sufficienttop flange width is also necessary toprovide room for connection of lateralbracing members. However, therecommended b/t ratio for top flanges intension or compression should becarefully followed.

Critical design stages for top flanges oftenoccur during construction prior to the deckcuring, when the flanges are laterallybraced only at the K-frame locations.Lateral bending stresses due to live loadeffects can be neglected in the capacitycheck when top flanges are embedded inthe hardened concrete with shear studs,except in areas where shear studs are notprovided. However, curved tub girders aretypically provided with shear studs alongthe entire girder length to achieve thedesired torsional rigidity from a closedcross-section.

In addition, top flanges are also subjectedto erection loads, as most contractors liftsteel girder sections by clamping the topflanges. Ideally, local stresses in the topflanges, including stresses in the weldbetween the flanges and web, should bechecked for these erection loads.

Critical designstages for topflanges oftenoccur duringconstructionprior to the deckcuring, when theflanges arelaterally bracedonly at the K-framelocations...

GIR

DER

DESIG

N

17

DIAPHRAGMS AND BRACING

DIA

PHR

AG

MS A

ND

BR

AC

ING

18

GENERAL GUIDELINESSection 10.2 (and the associatedCommentary) in the AASHTO GuideSpecifications for Horizontally CurvedSteel Girder Highway Bridges (5) offersdiscussion of framing plan issues such asdiaphragm and top flange lateral bracingconfigurations, spacing and proportioning.Other good discussions can be found inthe Bethlehem Steel Designer’s Guide toBox Girder Bridges (19) and the USSSteel / Concrete Composite Box-GirderBridges – A Construction Manual (20).More current sources for guidance includearticles by Fan and Helwig (18, 21);although the articles focus more on theanalytical aspects of determiningdiaphragm and bracing forces, they alsoprovide insights valuable for establishingeffective, efficient framing plans. “Section21, Curved Steel Box Girder Bridges,” ofthe Structural Engineering Handbook (3)also touches on some of these issues.

INTERNAL INTERMEDIATEDIAPHRAGMSInternal intermediate diaphragms areprovided in tub girders to control cross-sectional distortion, which introducesadditional stresses in box girders andshould be minimized. Cross-sectionaldistortion is caused by torsional loads thatdo not act on boxes in the same pattern asthe St.-Venant shear flow, which isuniformly distributed along the

circumference of the tub girder cross-section. Unfortunately, most torsionalloads on box girder bridges – such aseccentric vertical loads and curvature –induced torsion-fall in this category andwill introduce distortion. Because a true3-D FEA analysis using plate/shellelements will give total stresses inducedby bending, torsion and distortion, aseparate distortional analysis is notneeded. However, all design programsbased on grid analysis using line elementsare unable to predict distortional behaviorof box girders.

Distortional stresses can be neglected indesign, if a sufficient number of internaldiaphragms with adequate stiffness areprovided. Research efforts in the early1970s resulted in guidelines for spacingand stiffness requirements of internaldiaphragms. While there might beconceptual deficiencies in these previousinvestigations, experience in the pastthree decades has proven that theseguidelines are, in general, conservative.Those studies focused primarily on X-typecross frames. Most cross frames inmodern box girder bridges are K-frames,allowing better access for constructionand inspection. With very narrow boxes,consideration of X-frame or Z-frameconfigurations might be warranted. Until

Internalintermediatediaphragms areprovided in tubgirders to controlcross-sectionaldistortion, whichintroducesadditional stressesin box girders andshould beminimized...

DIA

PHR

AG

MS A

ND

BR

AC

ING

19

DIAPHRAGMS AND BRACING

Figure 10: Connection of K-frame diagonalsto top chord. Tub girders have many partsand pieces; try to keep the details simplewith clean load paths

Figure 11: Stiffeners to which bracingmembers are attached should be connectedto girder flanges to reduce local distortion.Shown is a typical detail for connection tothe bottom flange.

more studies on K-frames are available,previous data for X-type cross frames canbe judiciously used for K-frames. It shouldbe noted that the current AASHTO GuideSpecifications for Horizontally CurvedSteel Girder Highway Bridges (5) has omittedthese previously published guidelines.

Spacing of internal diaphragms is part ofthe framing process, and should bedetermined by also considering factorssuch as the angle and length of lateralbracing members, as discussed below.The stiffness requirement often results invery small sizes of cross frame members,which typically are structural angles.Members are sometimes selected basedon handling considerations; cross framemembers must also be checked to meetstrength requirements. Large brace forcescan develop inside cross frames,particularly when they are spacedrelatively far apart in curved bridges.Approximate design equations haverecently been developed to estimate theseforces (21). Strength verification should beconducted on diaphragms with controlling(largest) brace forces, usually located inthe largest bending moment regions. Theabove-mentioned guides (3, 5, 19, 20, 21)offer good discussions on sizing andspacing issues.

Internal cross frames also act as braces toprevent girder top flanges from buckling.However, the flange stability issue has notbeen well addressed in previous research.Current design guidelines based ondistortional stresses will likely continue to bethe primary approach in the years to come.

Internal cross frames should be detailed tominimize fatigue concerns. Stiffeners towhich bracing members are attachedshould be connected to girder flanges toreduce local distortion.

EXTERNAL INTERMEDIATEDIAPHRAGMSIt is widely known that intermediatediaphragms in curved I-shaped plate

girder bridges are primary structuralmembers and are always needed.Intermediate diaphragms prevent theindividual girders from rotatingindependently under torsional loads andtie the girders together such that torquesare resisted by a structural system with alarge rotation arm and are thus muchstiffer than individual girders. IndividualI-shaped plate girders have low torsionalstiffness and can develop significantrotation if not restrained.

Tub girders, on the other hand, possesslarger rotational stiffness and are muchmore capable of carrying external torquesindividually. In finished bridges, when tubsare fully closed and the concrete deckeffectively ties the girders together,transverse rotations of tubs are expectedto be small and external intermediatediaphragms are typically not warranted.During construction, however, therotational rigidity of tub girders is not ashigh. Steel tubs at this stage are quasi-closed, and their rotational behavior is notfully understood or predictable. Researchrecently performed at the University ofTexas (25) will provide more insight intothis behavior; publication is expected bysummer 2005. The main reason forconcern is the consequence of transverserotations. Because a girder’s two topflanges are spaced apart but still rotatetogether, resulting differential deflectionsat the top flanges would be large, evenwith a small girder rotation. Reasonable fit-up may become impossible, and differentialslab thickness will result at the top flangelocations if girder rotation is not controlled.

Consequently, external intermediatediaphragms are used to control differentialdisplacement and rotation of individual tubgirders during slab placement. In tangenttub girders, external intermediatediaphragms can sometimes be omitted orminimized if individual tub rotation anddifferential displacements are expected tobe relatively small and manageable.External intermediate diaphragms often

Internal crossframes also act asbraces to preventgirder top flangesfrom buckling...

DIA

PHR

AG

MS A

ND

BR

AC

ING

20

utilize a K-frame configuration, with depthclosely matching girder depth for efficiencyand simplification of supporting details.

The necessity of external diaphragms hasbeen a debated topic for years, and tubgirder bridges have been built with andwithout external diaphragms. Problemswith slab placement on curved girderswithout external intermediate diaphragmshave occurred.

Many previous and current researchinvestigations report that externalintermediate diaphragm forces are small,and concluded that they are not needed.Yet, girder rotations in curved bridges arefrequently observed. For example, boltholes do not align during installation. Manyengineers and contractors tend to beconservative with this issue and like theadditional stiffness and rotation controlthat external intermediate diaphragmsbring to structures. It is likely they willcontinue to be used unless strongevidence suggests otherwise, or aconvenient, reliable tool becomesavailable to predict girder rotation.

There is also ongoing debate regardingexternal intermediate diaphragm removalafter the deck has cured. Some advocateremoval of these diaphragms for aestheticreasons. However, care should be taken inevaluating the effects of removing“temporary” external intermediate

diaphragms; at a minimum, five issuesshould be addressed:

• Safety – Removing temporaryexternal intermediate diaphragmscan be difficult and potentiallyhazardous, due to falling debrisconcerns, or if members arecarrying significant load. Craneaccess is limited once the deck isin place.

• Deck Stresses – Loads carried bytemporary external intermediatediaphragms will shift to the deckwhen the diaphragms areremoved, adding to deck stressesand potentially leading to deckcracking if this effect is notcarefully evaluated in the deckdesign.

• Future Redecking – In locationswhere future redecking of thebridge is likely (for example, toaddress deck deterioration inregions where the heavy use ofdeicing salts is routine),consideration should be given toretaining external intermediatediaphragms, since they wouldlikely be required during redeckingfor the same reasons they wererequired during the originalconstruction.

• Traffic Control – If lane closuresare required to remove external

Figure 12 (nearright): Externalintermediatediaphragmscontroldifferentialdisplacementand rotation oftub girdersduring slabplacement.

DIA

PHR

AG

MS A

ND

BR

AC

ING

21

diaphragms, salvage value ofremoved diaphragms will be farless than costs to close lanes.

• Fatigue – Leaving externaldiaphragms in place may presentfatigue concerns, since connectionof diaphragm bottom chords to thegirder bottom flanges isproblematic and connection to theweb with stiffener backups mayresult in a poor fatigue detail.

In Texas, external K-frames are currentlyprovided every two to three internalK-frames, and are typically removed afterslab construction.

One related question is whether (and how)to include external intermediate diaphragmsin analysis models. External intermediatediaphragms are typically installed aftergirders are erected, so they do not carryload due to girder self-weight. Once thedeck is hardened, it serves as a moreeffective load path between girders fordistributing live loads; consequently,external intermediate diaphragms carrylittle or no load due to live load. Careshould be taken to properly address theseissues in tub girder analysis models.

INTERNAL DIAPHRAGMS AT SUPPORTSPier and end diaphragms are generallyfull-depth plate girder sections. Particularcare should be taken in detailing enddiaphragms for constructability, becausethe presence of abutment backwalls, othergirders, or pier cap stems will limit accessto one side of the diaphragm duringerection. Note that pier diaphragms (andsometimes end diaphragms) requireaccess manholes for future inspection.

Internal diaphragms at supports aredesigned as deep beams subjected to1) bending loads, which are the shearforces from the girder webs; and 2)torsion-induced shear flow along thecircumference of the diaphragms, due to thetorsional moment reactions on box girders.

Internal diaphragms typically consist of avertical plate. Top flanges can be providedfor the diaphragm to increase the bendingcapacity of the diaphragms, as pointed outabove, and can also provide support forthe slab at girder ends. Bearing stiffenerscan be attached to diaphragms and aredesigned as columns subjected to an axialload equal to the reaction. Access holesshould be provided for inspectionpurposes; in determining the location andsize of the holes, it is important to considerthe stress flow due to bending andtorsional moments.

Diaphragms are supported by one or twobearings. Two-bearing supports providebetter torsional resistance and induce lessbending stress. However, two-bearingsupports are not often recommended, dueto width limitations of bottom flanges andhigh demand for construction accuracy.Single supports are more widely used, andthe torsional resistance – as well as thedistributional reactions – resulting from thelarge bearing contact area is oftenconservatively neglected. Bearing designis discussed in more detail later.

Pier and enddiaphragms aregenerally full-depth plate girdersections...

DIA

PHR

AG

MS A

ND

BR

AC

ING

22

Figure 13: Internal diaphragms at supportsgenerally use full-depth solid webs, withaccess manholes between the bearingstiffeners.

EXTERNAL DIAPHRAGMS AT SUPPORTSIf dual bearings or other measures (suchas anchor bolts or shims) under the girderare able to prevent transverse rotation,external diaphragms should betheoretically stress free. If single-pointsupport is used, however, torsionalmoments must be resisted by externaldiaphragms that bend vertically.

Large torsional reactions may be neededat the end of the girder support points,which results in the use of solid plategirders for the diaphragms in many curvedbridges. With only one point support undereach girder, the internal end diaphragmsin adjacent girders combine with theexternal diaphragms to form a beam toresist the torsional moments fromindividual girders (Fig. 15). Because thetotal torque may be resisted by differentialreactions at the bearings of differentgirders, the diaphragms are subjected toboth bending and shear, as shown in Fig.15. If the torsional reaction on each of thetwin girders is T, the moment and shear onthe diaphragm can be derived from staticsas M = Tb/L and V = 2T/L, where L is thegirder spacing and b is the average lengthof the diaphragm. More complex systems,including multiple girders and unequaltorsional reactions, can be solved similarly.

The above procedure would result in abending moment at the end of diaphragms(M) smaller than the torque on the girder(T). However, the resultant reaction maynot be at the center of the girder width,due to rotation of the bearings. A largermoment may result at one end of thediaphragm than at the other. Aconservative approach is to simplyassume the moments at the diaphragmends to be equal to the torsional reactionof the box girder (M = T), while shears arestill calculated using the above method.These moment and shear values areimportant to the design of the plate girderdiaphragms, and to the design of theconnections between the diaphragms andthe girders.

Large moments at diaphragms oftenrequire the use of a moment connection tothe girder (diaphragm flanges are also

Large torsionalreactions may beneeded at thegirder supportpoints, whichresults in the useof solid plategirders for thediaphragms inmany curvedbridges...

DIA

PHR

AG

MS A

ND

BR

AC

ING

23

Figure 14: Full-depth plate girder sections aretypically used for external end diaphragms.Access holes are sometimes required tofacilitate field connection, but they were notused for this particular bridge.

Figure 15: Freebody diagrams for calculatingdiaphragm forces.

Figure 16: At supports, full-depth plate girdersections are often used for externaldiaphragms.

connected to the girders); the connectionmay be designed in a similar manner tothe splice design for the girders. Torsionalreactions at girder supports should beavailable from analysis results. Thelargest torsion is very likely to occur duringthe construction stage. Torsional momentsin straight girders are significantly smaller,and a plate girder may not be warrantedfor external diaphragms.

Avoid skews in tub girder bridges if at allpossible – especially at girder ends –since skewed end diaphragms areenormously complicated to detail,fabricate and erect. Pier diaphragms canpotentially be detailed as pairs of right(nonskewed) diaphragms to work aroundthe problems of skewed diaphragms.

TOP FLANGE LATERAL BRACINGTop flange lateral bracing is required in tubgirders to form the “fourth side” of the boxuntil the slab is in place. The previouslymentioned guides (3, 5, 18, 19, 20) offergood discussions on sizing and spacingissues. This bracing is typically formed withWT or angle sections, often configured in asingle diagonal (Warren truss) or doublediagonal (X-bracing truss) arrangement.

The purpose of providing a lateral bracingsystem is to increase the torsionalstiffness of tub girders. However, therelationship between torsional stiffnessand lateral bracing systems (includingconnection) has not been well studied.Analytical formulas are available to

calculate the thickness of an equivalentplate converted from the horizontal truss,although there is no experimentalverification on the stiffness aspect of thismethod. Rotation of tub girders is alsolikely to occur if bolted connections of thelateral bracing members experience slip. Abetter understanding of the quasi-closed tubgirder stiffness would impact the analyticalmethod and the use of external diaphragms.

Design of a top lateral bracing systemconsists of three major steps:

1. Framing The angle between diagonal lateralbracing members and the top flange, α, isan important design parameter. Ideally, anα around 45 degrees is desired. A small αleads to larger cross frame spacing andfewer bracing panels and connections.However, larger brace forces and girderstresses result from a small α. Engineersshould plan the framing using bothstructural and economical considerations.

Diagonal lateral bracing members areframed into the intersection of the girdertop flange and internal diaphragm(guidelines for the spacing of the internalcross frames were discussed earlier). Fornarrow girders, these guidelines maysuggest a cross frame spacing muchlarger than the girder width, which wouldresult in a small α. Therefore, the locationof the internal diaphragms should beplanned with consideration of lateral bracing.

Top flange lateralbracing is requiredin tub girders toform the “fourthside” of the boxuntil the slab is inplace...

DIA

PHR

AG

MS A

ND

BR

AC

ING

24

An alterative is to divide the spacingbetween two consecutive cross frames intomore than one lateral bracing panel. Singlelateral members (typically angle sections)are used at those dividing lines. Attachingtwo more members to the single lateral toform a vertical K-frame does notsignificantly increase steel weight, but doesadd cost, due to increased fabrication laborrequirements. Note that doing so alsomakes the structure stiffer, and brace forcesin both the lateral bracing members andinternal diaphragms may be slightly larger.

It is suggested to keep the plane of the topflange lateral bracing reasonably close tothe plane of the top flanges, whichincreases the torsional efficiency of tubgirders and avoids excessive bendingloads in web stiffeners.

2. Analysis Torsional moments induced by dead loadsand construction loads will result in braceforces in lateral bracing members. Theseforces can be derived from the St.-Venantshear flow at the girder crosssections,assuming the horizontal truss acts as animaginary plate.

Lateral brace members, transverse strutsin internal diaphragms, and top flangesform a geometrically stable horizontaltruss. It is therefore possible to take axialforces representing the top flangecomponent of girder bending momentsand calculate member forces in the lateral

bracing due to box girder bending. Designequations have been developed toevaluate this component of force fordifferent truss types (18).

Vertical loads on the top flanges also inducebrace forces due to web slope. However,the majority of these forces are resisteddirectly by the lateral struts. Thus, the totalforces in lateral bracing members areessentially the sum of torsional and bendingcomponents. Because bending forces are afunction of member size, trial truss membersizes have to be assumed before the forcecalculation. External diaphragms alsocontribute load to the bracing system. If a3-D FEA program is available, total forcescan be obtained directly from the analysis.

3. Member Size Selection andConnection Detailing

Once forces are determined, bracemembers can be designed as beamcolumns. Depending on theconnection details, bending momentsresulting from any eccentricity mustbe considered. The effective lengthfactor (k) used in design of bracemembers should reflect endconnection conditions

It is suggested tokeep the plane ofthe top flangelateral bracingreasonably closeto the plane of thetop flanges...

DIA

PHR

AG

MS A

ND

BR

AC

ING

25

MISCELLANEOUS DETAILS AND ISSUES

MISC

ELLAN

EOU

SD

ETAILS

AN

DISSU

ES

26

FLANGE-TO-WEB WELDS AND SHEARSTUDSFlange-to-web welds are designed in asimilar manner as for plate girders, but thereare additional loading effects exclusive to tubgirders that must be addressed. The shearcontributing to longitudinal load in the weld(calculated as VQ/I) should include bothvertical shear (resolved to account for webslope) and shear due to torsion. In addition,the effects of transverse loading on the weldbecause of web slope and lateral bracingloads should be included. Shear studs aredesigned in a similar manner as for plategirders, but there are additional loadingeffects exclusive to tub girders that must beaddressed. The shear contributinglongitudinal load in the studs (calculated asVQ/I) should include both vertical shear(resolved to account for web slope) andshear due to torsion. Shear studs must beprovided along the total girder length toensure that the slab is acting as the fourthside of a box girder.

BEARINGSAn important decision to make aboutbearings is how many to use: one or two persupport. As with most decisions, the choicesoffered each have pros and cons. Thenumber of bearings per support can changefrom support to support, allowing designersto optimize the design.

Using two bearings allows girder torsionbe directly removed through the forcecouple provided by the bearings, and

reduces reaction demand on the bearings.Two-bearing systems work well with radialsupports, but are impractical with supportsskewed more than a few degrees, wheretub girder and/or diaphragm stiffness workagainst uniform bearing contact duringvarious stages of girder erection and slabconstruction. One way to try to ensureproper contact in two-bearing systems isto build the structure on temporarysupports and then grout the bearings inplace prior to shoring removal.

Using one bearing per support optimizescontact between girder and bearing. One-bearing systems also are more forgiving ofconstruction tolerances and, for skewedsupports, one-bearing systems aredemonstrably better than two-bearingsystems. The drawback to one-bearingsystems is that stiff cross frames ordiaphragms between girders are required toresolve girder torsion into the bearings.Fabricating and erecting these stiff elementsis demanding, and bearing installation can bedifficult with very wide bottom flanges.

What type of bearing to employ is asimportant as deciding how many bearingsper support will be used. Steel-reinforcedneoprene and pot bearings are the mostcommonly encountered bearings with tubgirders, although disc bearings areoccasionally used. Steel-reinforcedneoprene bearings generally cost less thanpot bearings in smaller sizes, are forgiving ofconstruction tolerances, and are easily

The effects oftransverse loadingon the weldbecause of webslope and lateralbracing loadsshould beincluded...

MISC

ELLAN

EOU

SD

ETAILS

AN

DISSU

ES

27

The decision touse an empiricaldeck design withtub girders mustnot be takenlightly...

MISC

ELLAN

EOU

SD

ETAILS

AN

DISSU

ES

28

inspected. However, steel-reinforcedneoprene bearings usually have lessreaction capacity than pot or disc bearings.The upper reaction limit with neoprenebearings is about 1,000 kips (22); withreactions much greater than this, pot or discbearings become a more practical choice.Note that pot bearings also have a lower limiton reactions (22) and may not be anappropriate choice when low reactionsare expected.

Girder translation is readily accommodatedwith steel-reinforced neoprene bearings. Incases where the amount of translationcreates tall, unstable pads, a stainlesssteel/polytetrafluoroethylene (PTFE) slidingsurface can be introduced. Pot bearingsalways need a stainless steel/PTFE slidingsurface to accommodate translations.

Regardless what type is selected, designersshould ensure bearings can be replaced withlimited jacking.

Both the current AASHTO StandardSpecifications for Highway Bridges (7) andAASHTO LRFD Bridge Design Specifications(9) include general formulas for designingreinforced neoprene bearings. For specificguidance on designing steel-reinforcedneoprene bearings for tub girders, see thearticle “Elastomeric Bearings for SteelTrapezoidal Box Girder Bridges” (23). For anoverview of most bearing types used withsteel bridges, see the National Steel BridgeAlliance’s (NSBA’s) “Steel Bridge BearingSelection and Design Guide” (22).

BRIDGE DECKSConcrete deck slabs on most tub girders arecast in place with extensive use of stay-in-place metal deck forms. If designers elect touse the empirical design method in theAASHTO LRFD Bridge DesignSpecifications (9), Section 9.7.2 for thebridge deck, intermediate diaphragmsbetween tub girders are required at 25-footmaximum spacing. Such diaphragmspartially negate the reasons to use tubgirders in the first place. In lieu of thisrequirement, the LRFD Specifications,Section 9.7.2.4 (9), permits designers toinvestigate if additional slab reinforcementover the girder webs is necessary fortransverse slab bending between girders. Abridge deck could be modeled with both tubgirders and I-shaped girders to ascertaindifferences in transverse deck bendingmoments. The moment difference between thetwo girder systems could be accommodatedwith supplemental reinforcement.

The decision to use an empirical deckdesign with tub girders must not be takenlightly. Designers should carefully weightheir perceived advantages against theirmany limitations.

FIELD SPLICESJust as with plate girders, tub girders usuallyneed field splices to facilitate girdertransportation and erection. Maximumallowable shipping lengths of about 120 feetare common throughout much of the U.S.,but some states are more restrictive.Designers must be cognizant ofoversize/overweight permit requirementsimposed by the state the bridge is located in.Sometimes the fabricator is not in the samestate as the bridge and designers do notknow which fabricator will be building andshipping the girders, adding a level ofuncertainty in locating field splices forshipping purposes.

Overall girder width of tub girders (includingsweep for curved girders) should beconsidered for shipping purposes. Thoughnot likely, shipping costs of very wide girders

Figure 17: Steel-reinforced neoprenebearings are a simple, low-maintenancebearing option.

(in excess of 14 feet) can outweigh costs ofadding additional field splices. In rare cases,tub girders are so wide they must havelongitudinal field splices in bottom flanges.

Weight can be another consideration inlocating field splices. Tub girders areheavier than plate girders and weight canbecome excessive for economicalshipping and erection. When determiningfield splice location, consultation withseveral regional fabricators familiar withtub girders is recommended. For fieldsplices provided only for transportationissues, designers should be clear in theirplans that these splices can be completedprior to final girder erection.

As with plate girders, field splices can bebolted or welded. Welded field splices withtub girders are difficult – even for highlytrained welders experienced with fieldwelding bridge girder splices – and timeconsuming. The longer time required tocomplete welded splices can result in highcosts from traffic control if the splice is overtraffic. Fitup tolerances prior to welding arein some ways more restrictive than withbolted connections. Bolted field splicespredominate throughout much of the UnitedStates for tub girders. Although not asaesthetically appealing as welded splices,they are quicker to complete with lessskilled labor. The current AASHTO GuideSpecifications for Horizontally Curved SteelGirder Highway Bridges (5) has acomprehensive example to guide designersthrough the bolted splice design.

However, some erectors maintain thatwelded splices are more forgiving with regardto fit-up tolerances, given skilled welders.Some owners suggest welded splices maybe more durable, due to observed corrosionin some bolted splices. The decision to usewelded field splices should be undertakenwith care and full consideration of all issues.

While painted faying surfaces may be moredurable, allowing painted faying surfaces cancreate confusion, since two types of paint areusually encountered with tub girders. Exteriorpaint system primers are usually differentfrom interior paint. Designers must be clearon which, if any, paint is allowed in boltedfaying surfaces and what slip coefficient thedesign is based on.

DETAILINGFor detailing guidelines, the reader isdirected to www.steelbridge.org, theAASHTO/NSBA Steel Bridge Collaboration’sWeb site. One of the Collaboration’sdocuments is helpful in outlining detailingrequirements specific to tub girders: G1.4,“Design Details Sample Drawings,” which iscurrently (May 2003) in draft form; a finalversion should be available in the near future.

Also, Appendix B of this book containsguidance on detailing steel tub girders,including a set of suggested details. Thesedetails have been reviewed by a wide rangeof engineers, detailers, fabricators anderectors, and represent the best consensuson good detailing practice for steel tubgirders. Of course, each tub girder is unique

Figure 18 (nearright): Boltedfield splices aregenerallyquicker tocomplete thanwelded splices,but may provemore prone tocorrosion.

MISC

ELLAN

EOU

SD

ETAILS

AN

DISSU

ES

29

Placing wire meshover any copes orclips in end platesand bottom flangedrain holes aretwo moresuggested detailspeculiar to tubgirders...

MISC

ELLAN

EOU

SD

ETAILS

AN

DISSU

ES

30

and may have design or detailingrequirements which differ from thesesuggested details, but these detailsrepresent a broadly applicable set of“recommended practices.”

This Web site also offers two more goodreferences in detailing tub girders: the TexasSteel Quality Council’s “Preferred Practicesfor Steel Bridge Design, Fabrication, andErection” (16) and Mid-Atlantic StatesStructural Committee for Economic

Fabrication (SCEF) Standards (24). Someimportant detailing issues bear repeating:

• Both webs should be equal in heightand the girders should be rotatedabout the point defined by theintersection of the girder’s centerlineand the top of the webs.

• Bottom flanges must extend at least1½ inches beyond web centerlinesfor welding purposes.

• Provide details consistent with futureinspection needs, such asadequately proportioned accessholes, light access doors, electricalservice along the girders, andpainting interiors a light color.

• Connection details for external crossframe or diaphragm details must beprepared in consideration of thetremendous lateral and torsionalstiffness of tub girders. Tub girderscannot be manipulated as easily asplate girders during erection.

Placing wire mesh over any copes or clips inend plates and bottom flange drain holes aretwo more suggested details peculiar to tubgirders. Wire mesh, which prevents girderinteriors from becoming wildlife habitat,should be 10 gage to withstand welding andblasting and have a tight weave, about ½inch by ½ inch. Suggested bottom flangedrain holes are 1 ½ inches in diameter andspaced along the bottom flange’s low sideevery 50 feet. Holes should be placed 4inches away from the web plate. Place a ½inch bead of adhesive caulk to direct water tothe drain hole. These holes will mitigaterainwater buildup in tub girders prior to deckplacement and provide helpful ventilation forthe life of the girder. See Fig. 22 forsuggested drain hole details.

MATERIAL SELECTIONTub girders offer excellent opportunities to useHigh Performance Steel (HPS) A709 GradeHPS- 70W. Like its use in plate girders, HPSwill be most economical in hybrid applications.Negative and positive moment tension flanges

Figure 19: Cost versus benefit: Full shop fit-up was required on this tub girder project tohelp ensure erection would go smoothly.Requiring full bridge assembly in the shopmay avoid some fit-up problems in the field,but can be quite costly. Designers areadvised to explore all consequences of theirdecisions.

Figure 20: Steel tub girders, top flanges andstiffeners are typically assembled as a sub-unit upside down, then flipped over andwelded to the bottom flange.

MISC

ELLAN

EOU

SD

ETAILS

AN

DISSU

ES

31

show the greatest potential in utilizing HPS.Recent studies such as found in Reference 28discuss this in more detail. It should be notedthat the current AASHTO Guide Specificationsfor Horizontally Curved Steel Girder HighwayBridges (5) does not provide for hybrid girders,due to lack of related research. However,upcoming revisions to the AASHTO “LRFDBridge Design Specifications” (see Reference26) do include provisions for hybrid girders.

In addition to HPS, A709 Grades 50 or 50Ware the next steel of choice for tub girders. It is

hard to justify using Grade 36 steel foreconomics; Grade 100 steels will likely seeeconomical applications in bridges withunusually long span lengths.

As with all steel bridges, weathering steel isthe material of choice unless site conditionsor aesthetic requirements preclude its use. Tooptimize weathering steel aesthetics,fabricators should be required to perform anSSPC-SP 10 level blast cleaning of fasciaweb surfaces (and bottom flanges and otherwebs if they will be visible to the public) priorto shipping girders. It is easier–and thereforeless costly–to do this at the fabricator’s shopthan in the field.

PAINTING Considerations for painting the exteriors oftub girders are the same as for plate girders.Tub girder interiors should always be coated.Without owner direction towards a specificcoating and preparation, girder interiorsshould receive a light brush blast and bepainted with a white or light colored paintcapable of telegraphing cracks (which aidsbridge inspection). Specified interior paintshould be tolerant of minimal surfacepreparation. In most cases, interior paint isprovided not for corrosion protection but forgirder inspection. As such, localized paintfailure can be tolerated. Specifying stringentrequirements for tub girder interior paints andsurface preparation must not be taken lightly,because they will add significant costs toprojects. Note that the painted interiorsurfaces do not necessarily need to includethe top flange lateral bracing members.

Figure 22: Suggested details for drain holesin tub girder bottom flanges.

Figure 21 (nearright): Tub girderinterior surfacesshould alwaysbe coated with awhite or lightcolored paint.

PRACTICAL EXAMPLES

PRA

CTIC

AL

EXA

MPLES

32

IH 35/US 290 INTERCHANGE, AUSTIN,TEXASTub girders were selected for all the directconnection structures in the IH 35/US 290interchange in Austin. Approach spansused precast, prestressed concrete TexasU-beams; the longer span and/or curvedportions used steel tub girders.

TxDOT funded two research projectsrelated to steel tub girders prior to theconstruction of this interchange. Oneproject, under the direction of Karl Frank,Ph.D., covered the measurement of forcesin tub girders at different stages ofconstruction. The other project dealt withsimplifying costly details associated withtub girders and was directed by JosephYura, Ph.D. An interesting finding fromthese projects was that lateral braceforces arising from slab placement weresensitive to where concrete pours wereinitiated and their subsequent direction. Toillustrate: if an end span pour began closeto midspan and progressed toward thespan end, maximum lateral brace forceswere close to calculated values. If endspan pours began at the span’s end andprogressed into the span, maximumlateral brace forces were significantly lessthan predicted. This phenomenon wasattributed to the stiffness gain rate of

freshly placed concrete. Steel-reinforced neoprene bearings wereemployed throughout the interchange.One bearing per support was used in allcases. The screening instrument inreference (22) indicated that pot bearingswere the best choice, since maximumreactions were over 1,000 kips; however,the designers elected to use neoprenebearings based on cost, ease ofmanufacturing and long-term maintenance.See Figs. 17 and 23 for the simplicity of anexpansion bearing at the end of an 880-foot continuous girder unit. Fixed bearingswere detailed with anchor boltspenetrating through the bearings andgirder bottom flange. This turned out to bea poor detail, due to the reality of constructiontolerances, and accommodations had to bemade in several instances where anchorbolts did not align with their respective holes.

VARIOUS TXDOT HOUSTON DISTRICTPROJECTS, HOUSTON, TEXASWithin the last 10 years, TxDOT’s HoustonDistrict completed or has underconstruction dozens of steel tub girderbridges, totaling more than 110 millionpounds of steel. About half of theseprojects were designed directly by TxDOTHouston District engineers. There issimply no substitute for steel structureswhen roadway geometry is complex,spans are unbalanced, and speed ofconstruction is important.

In the Houston area, tub girders areselected primarily for aesthetic reasons,despite the cost premium. Steel I-girderbridges range in cost from $70 to $80 persquare foot of deck area, while steel tubgirders range in cost from $90 to $105 persquare foot of deck area. The reasons forthis approximately 25 percent costpremium for tub girders are complex andmany, but several have been identified asthe primary causes. Fabrication anderection costs are higher because theindividual pieces are larger than forcomparable I-girder bridges. Unbalancedspans are common in steel units these

An interestingfinding from theseprojects was thatlateral braceforces arisingfrom slabplacement weresensitive to whereconcrete pourswere initiated andtheir subsequentdirection...

PRA

CTIC

AL

EXA

MPLES

33

PRACTICAL EXAMPLES

Figure 23: The simplicity of steel-reinforcedneoprene bearings illustrated in an expansionbearing at the end of an 880-foot continuoustub girder unit

days, but web depth is maintainedthroughout, so efficiency is sacrificed foraesthetic reasons. Another source ofinefficiency is that tub girder spacingrequirements force the designer to useone or more webs than is required for acomparable I-girder superstructure.Essentially, tub girder superstructures cantend to weigh more than equivalentI-girder superstructures due to additionalconservatism on the part of engineers,since design and analysis proceduresare much less well defined for tubgirders than I-girders.

Nearly all the field problems encounteredto date can be traced to fundamentalengineering errors not unique to tub girderdesign. Over the last 10 years, the fullrange of analysis tools has been used todesign tub girder bridges in the Houstonarea. Many problems have occurredduring construction, especially whengeneral-purpose analysis programs wereused or when the superstructure wasdesigned as individual girders andinteraction with adjacent girders was notproperly accounted for. Incorrect modelingof boundary conditions has also resultedin field problems especially with bearingsand uplift at the support. Recent bridgesdesigned with commercially availablesoftware, based on grid analysis, haveperformed well. Problems with secondarymembers have occurred but the frequency

has diminished as more emphasis hasbeen placed on accounting for sequenceof loading and connection eccentricity.For example, intermediate externaldiaphragms are installed after the girdershave deflected under self weight. Thisincreases forces in the top lateral bracesystem and has resulted in bowing ofbraces during construction. While notperfect, grid analysis programs haveproven to be a reliable and efficient designtool for tub girder systems.

US 75 UNDERPASS AT CHURCHILL WAY,DALLAS, TEXASThe US 75 Underpass at Churchill Way isa three-span continuous tangent steel tubgirder bridge (138.91 feet – 132.63 feet –100 feet), built on a 34 degree skew. Thisbridge might be described as a goodexample of several things to try to avoid insteel tub girder bridges.

First, the span arrangement is far fromideal, both in terms of its lack of good spanbalance and in the relative shortness ofthe spans. The span arrangement wasdictated by existing site conditions,including the locations of abutmentprovisions in an existing retaining wall andexisting lane configurations of the eight-lane expressway, frontage roads andramps below the bridge. To blend thebridge’s appearance with the strongexisting aesthetic theme of the US 75expressway, it was desired to provide asmooth soffit superstructure, thuseliminating steel I-girders as an option.Lane closure limitations and the givenspan lengths eliminated precast and cast-in-place concrete options, leaving steeltub girders as the most viablesuperstructure type.

Next, the 34-degree skew noticeablycomplicated the design and detailing ofthis bridge, as might be expected. A 3-DFEA analysis was performed (using theproprietary BSDI3-D System) to ensureskew effects were adequately quantified.The designers chose to use paired,

Nearly all thefield problemsencountered todate can be tracedto fundamentalengineering errorsnot unique to tubgirder design...

PRA

CTIC

AL

EXA

MPLES

34

Figure 24: Some of the 110 million pounds oftub girder steel designed in the TxDOTHouston District.

staggered, right (non-skewed) pierdiaphragms to simplify detailing anderection. At the end diaphragms, therewas not much choice but to detail thediaphragms on the 34-degree skew; thedesigners consulted a steel detailing shopand a local fabricator during the designprocess to solicit input on preferred detailsfor the skewed end diaphragms.

To simplify and streamline erection (a keyproject criterion was minimizing theduration of lane closures on theexpressway below), the designers choseto omit any external intermediatediaphragms. As would be expected, thisresulted in higher top flange lateralbracing loads, but the benefit of simpler,quicker erection was deemed of greatervalue. The designers also denoted two ofthe four field splices as “optional,” so thata properly equipped contractor could erectfewer, larger field sections and avoidsome lane closures (and the associated“lane rental” costs stipulated in theconstruction contract).

Figure 25 (nearright): Framingplan for US 75Underpass atChurchill Way;right diaphragmsused at interiorpiers to simplifydetailing for thisbridge, which isbuilt on a 34-degree skew.

PRA

CTIC

AL

EXA

MPLES

35

CONCLUSION

CO

NC

LUSIO

N

36

Steel tub girders are often an excellentchoice for modern highway bridgesuperstructures. They offer advantagesover other superstructure types in termsof span range, stiffness, and durability –particularly in curved bridge applications.In addition, steel tub girders have distinctaesthetic advantages, due to their clean,simple appearance.

However, the layout, design, detailing,fabrication and erection of steel tub girderbridges is in many ways different and oftenmore complicated than for steel plategirder bridges. Designers are advised tounderstand and evaluate all these issuesvery early in the design process.

Designers should also realize that in manycases, there are no hard and fast rulesassociated with these issues. Each tubgirder project is unique and a solution thatworked on one bridge might notnecessarily work on another. Instead, it isimperative that the designer of a tub girderbridge explore all options on a case-by-case basis, often in consultation with localfabricators and/or erectors.

A full understanding and carefulconsideration of all these issues will result ina more successful tub girder bridge project.

Designers shouldalso realize that inmany cases, thereare no hard andfast rulesassociated withthese issues...

CO

NC

LUSIO

N

37

REFERENCES & APPENDICES

REFER

ENC

ES & A

PPEND

ICES

38

1. Hedefine, A., Swindlehurst, J., and Sen, M., “Section 12, Beam and Girder Bridges”,Structural Steel Designer’s Handbook, (Brockenbrough, R.L, and Merritt, F.S.,Editors), 3rd Edition, 1999, McGraw Hill, Inc. Current edition can be ordered fromMcGraw-Hill publishers, www.mcgraw-hill.com, or call 1-877-833-5524.

2. Hall, D. H., “Why Steel Box Girders?” Modern Steel Construction, April 1997.Reprint may be downloaded from the website of the National Steel BridgeAlliance, www.aisc.org, click on the National Steel Bridge Alliance button, thenclick on “Bridge Crossing Articles.”

3. Poellot, W.N., “Section 21, Curved Steel Box Girder Bridges,” StructuralEngineering Handbook, (Gaylord, E.H, Gaylord, C.N., and Stallmeyer, J.E.,Editors), 4th Edition, 1997, McGraw-Hill, Inc. Current edition can be orderedfrom McGraw-Hill publishers, www.mcgraw-hill.com, or call 1-877-833- 5524.

4. AISC Marketing, Inc., Highway Structures Design Handbook, ADUSS 88-8535,1981. This book has long been out of print. The NSBA offers a modern version(see references 15 and 21), but its examples for steel tub girders lack some ofthe introductory text of the older version; this older version can sometimes befound in office libraries or in the personal collections of experienced engineers.

5. American Association of State Highway Transportation Officials (AASHTO),Guide Specifications for Horizontally Curved Steel Girder Highway Bridges,GHC-4, 2003. Current edition can be ordered from AASHTO, www.aashto.org(click on “Bookstore”), or call 1-800-231-3475.

6. Kase, R.A., “Twelve Commandments for Economic Steel Box Girders,” ModernSteel Construction, August 1997. Reprint may be downloaded from the Web siteof the National Steel Bridge Alliance, www.aisc.org, click on the National SteelBridge Alliance button, then click on “Bridge Crossing Articles.”

7. American Association of State Highway Transportation Officials (AASHTO),Standard Specifications for Highway Bridges, 17th Edition, HB-17, 2002. Currentedition can be ordered from AASHTO, www.aashto.org (click on “Bookstore”), orcall 1-800-231-3475.

8. Mattock, A.H., “Development of Design Criteria for Composite Box GirderBridges,” Development in Bridge Design and Construction, Crosby Lockwood &Sons, London, England, 1971.

9. American Association of State Highway Transportation Officials (AASHTO),LRFD Bridge Design Specifications, 3rd Edition, LRFD-3, 2004. Current editioncan be ordered from AASHTO, www.aashto.org (click on “Bookstore”), or call 1-800-231-3475.

10. Samaan, M., Sennah, K., and Kennedy, J.B., “Distribution of Wheel Loads onContinuous Steel Spread- Box Girder Bridges,” ASCE Journal of BridgeEngineering, Vol. 7, No. 3, May-June 2002, pp. 175-183. Copies may beobtained by contacting ASCE (www.asce.org, or call 1-800-548-2723) or canusually be found in local university libraries.

REFER

ENC

ES

39

REFERENCES

11. American Association of State Highway Transportation Officials (AASHTO),Guide Specifications for Horizontally Curved Highway Bridges, GHC-3, 1993with Interim Revisions through 1995. This is the previous version of thisspecification, but it may still be available from AASHTO, check at AASHTO,www.aashto.org (click on “Bookstore”), or call 1-800-231-3475.

12. Richardson, Gordon, and Associates (presently the Pittsburgh, Pennsylvania,office of HDR), “Curved Girder Workshop Lecture Notes,” prepared underContract No. DOT-FH-11-8815, Federal Highway Administration, 1976. Thisdocument has long been out of print and may be difficult to locate.

13. Tung, D.H.H, and Fountain, R.S., “Approximate Torsional Analysis of Curved BoxGirders by the M/R Method,” AISC Engineering Journal, Vol. 7, No. 3, July 1970.Reprint may be downloaded from AISC’s Web site at www.aisc.org. Click on theEngineering Journal button, then click on “Downloadable PDFs.”

14. American Iron and Steel Institute, “Four LRFD Design Examples of SteelHighway Bridges,” Vol. II, Chapters 1A and 1B, Highway Structures DesignHandbook, 1996. Available from the National Steel Bridge Alliance,www.aisc.org, click on the “Bookstore” button.

15. American Iron and Steel Institute and National Steel Bridge Alliance, “Four LFDDesign Examples of Steel Highway Bridges,” Vol. II, Chapter 2B, HighwayStructures Design Handbook, 1999. Available from the National Steel BridgeAlliance, www.aisc.org, click on the “Bookstore” button.

16. Texas Steel Quality Council, Preferred Practices for Steel Bridge Design,Fabrication, and Erection, November 2000. Current edition can be downloadedfrom http://www.steelbridge.org, click on “Regional Groups” and find thedocument link in the Texas Quality Council section.

17. Wolchuk, R., and Mayrbaurl, R.M., “Proposed Design Specifications for SteelBox Girder Bridges,” Report No. FHWA-TS-80-205, Federal HighwayAdministration, January 1980. Copies can be purchased by contacting theNational Technical Information Service at 1-800-553-6847.

18. Fan, Z., and Helwig, T.A., “Behavior of Steel Box Girders with Top FlangeBracing,” ASCE Journal of Structural Engineering, Vol. 125, No. 8, August, 1999,pp 829-837. Copies may be obtained by contacting ASCE (www.asce.org, or call1-800-548-2723) or can usually be found in local university libraries.

19. Heins, C.P., and Hall, D.H., Designer’s Guide to Steel Box Girder Bridges,Booklet No. 3500, February, 1981, Bethlehem Steel. This guide has long beenout of print. Copies may be obtained by directly contacting the National SteelBridge Alliance technical staff (not the NBSA publications department).

20. United States Steel, Steel / Composite Box-Girder Bridges–A ConstructionManual, ADUSS 88-7493- 01, December 1978. This guide has long been out ofprint. Copies may be obtained by directly contacting the National Steel BridgeAlliance technical staff (not the NBSA publications department).

REFER

ENC

ES

40

21. Fan, Z., and Helwig, T.A., “Distortional Loads and Brace Forces in Steel BoxGirders,” ASCE Journal of Structural Engineering, Vol. 128, No. 6, June, 2002,pp 710-718. Copies may be obtained by contacting ASCE (www.asce.org, or call1-800-548-2723) or can usually be found in local university libraries.

22. American Iron and Steel Institute and National Steel Bridge Alliance, “SteelBridge Bearing Selection and Design Guide,” Vol. II, Chapter 4, HighwayStructures Design Handbook, 1996. Available from the National Steel BridgeAlliance, www.aisc.org, click on the “Bookstore” button.

23. Bradberry, T.E., Cotham, J.C., and Medlock, R.D., “Elastomeric Bearings forSteel Trapezoidal Box Girder Bridges,” Proceedings of the ASCE Texas SectionMeeting, Waco, TX, October 2-5, 2002. Copies can be downloaded from theTxDOT Bridge Division website, www.dot.state.tx.us/brg, click on DivisionPublications.

24. Mid-Atlantic States Structural Committee for Economic Fabrication (SCEF)Standards, available on line at www.steelbridge.org, click on the “more” where itsays “Mid-Atlantic States Structural Committee for Economic Fabrication (SCEF)Standards - more” on the home page.

25. Yura, J. A., Helwig, T. A., Herman, R. H., and Williamson, E.; "Trapezoidal BoxGirders - State of the Art", Research Report 0-4307-1, Report for TexasDepartment of Transportation, anticipated publication date: May 2005. Contactthe University of Texas at Austin, Department of Civil, Architectural, andEnvironmental Engineering (http://www.ce.utexas.edu/) or the University ofHouston, Department of Civil and Environmental Engineering(http://www.egr.uh.edu/CIVE/).

26. American Association of State Highway Transportation Officials (AASHTO), LRFDBridge Design Specifications, 2005 Interim Revisions to the 3rd Edition,anticipated publication date: May 2005. Contact AASHTO, www.aashto.org(click on "Bookstore"), or call 1-800-231-3475.

27. Fry, G. T., Bailey, B. M., Farr, J. L., Elliot, J. E., and Keating, P. B.; "Behavior andDesign of Dapped Steel Plate Girders", Research Report 0-2102-1, Report forTexas Department of Transportation, anticipated publication date: May 2005.Contact Texas A&M University, Department of Civil Engineering(http://www.civil.tamu.edu).

28. Horton, R., Power, E., Azizinamini, A. and Krupicka, G., “High PerformanceSteel Cost Comparison Study - Box Girder,” Conference Proceedings, 2004FHWA Steel Bridge Conference, San Antonio, Texas, Dec. 2004.

REFER

ENC

ES

41

A.1 AISC SIMONThis DOS-based line girder program with tub girder design features is available fromAISC (www.aisc.org, type “SIMON” into the search box, or call 312-670-2400).

A.2 VARIOUS TANGENT I-GIRDER PROGRAMS STLBRIDGE is a Windows-based program available from Bridgesoft, Ltd.(www.bridgesoftinc.com or call 402-449-1581). It is one of many tangent I-girder designprograms (both new and old, commercially sold and “in-house” developed programs)commonly available to bridge designers. Designers can use these programs to developpreliminary shear and moment diagrams and/or flange stresses. However, theseprograms are limited to I-shaped members (plate girders and rolled beams) and thus donot provide the ability to directly design all pieces of a tub girder. Generally, one half ofthe tub girder is input as the cross-section, and web slope is ignored.

A.3 DESCUS IIDESCUS II is a commercially sold program (www.opti-mate.com). DESCUS II is a DOS-based program (now with a Windows interface) that performs a grid analysis for curvedtub girder design in accordance with AASHTO ASD or LFD (currently only per theprevious edition of the AASHTO Guide Specifications for Curved Steel Girder HighwayBridges) specifications.

A.4 MDXMDX is a commercially sold program (www.mdxsoftware.com or call 573-446-3221).MDX is a Windowsbased program that performs a grid analysis and curved tub girderdesign in accordance with the AASHTO ASD, LFD (currently only per the previous editionof the AASHTO Guide Specifications for Curved Steel Girder Highway Bridges), andLRFD specifications.

A.5 BSDI3-D SYSTEMThe BSDI3D System is a design service (BSDI Ltd., call 610-282-2888) that provides3-D FEA of plate or tub girders, including code checking in accordance with the AASHTOASD and LFD specifications. Forces are calculated for all members modeled, but codechecks are only provided for webs and flanges. A

PPEND

IX A

42

APPENDIX A - COMPUTER DESIGN TOOLS

Appendix B consists of example steel tub girder detail drawings. These details representa starting point that shows preferred detailing practice for cost-effective fabrication.These details do not reflect any specific actual design conditions. All components of anytub girder bridge require careful analysis that may require deviation from preferreddetailing practices for economical fabrication.

These details are based on similar details published by the AASHTO/NSBA Steel BridgeCollaboration, Task Group 1.4, in their document “Steel Bridge Design Detail Guidelines,”which is available at http://www.steelbridge.org.

APPEN

DIX

B

43

APPENDIX B - EXAMPLE DESIGN DETAILS

APPEN

DIX

B

44

APPEN

DIX

B

45

APPEN

DIX

B

46

APPEN

DIX

B

47

APPEN

DIX

B

48

APPEN

DIX

B

49

APPEN

DIX

B

50

APPEN

DIX

B

51