Seismic Analysis Options for Steel Truss Bridges

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ing a comprehensive seismicanalysis and computing capaci-ty-demand ratios for variouscomponents of the bridge.Unfortunately, it is difficult tostandardize the seismic analysisand evaluation procedure for

truss bridges due to their varietyin size, shape and form. Manypracticing engineers today arefaced with the question of select-ing an appropriate method for aseismic analysis and evaluationof truss bridges. What follows isa summary, based on a review of literature and the author’s expe-rience, of various options avail-able for seismic evaluation, com-puter modeling and dynamicanalysis.

SEISMIC E VALUATION

Seismic evaluation can be per-formed at three different levels.Usually, the owner of the bridgespecifies the level of seismicevaluation required.

Level 1 is a simple screening using flowcharts based on bridgecharacteristics previously knownto be vulnerable to seismic activ-ity. It is not necessary to performcomputer modeling or calcula-

tions at this level. “SeismicDesign and Retrofit Manual forHighway Bridges,” published bythe FHWA, outlines this proce-dure. This procedure can be usedto quickly screen several “regu-lar” bridges as defined in

AASHTO Standard Spec-ifications (section 4.2, Division I-

A).Level 2 evaluation is a

schematic assessment. Simpleand approximate models are

used to evaluate the applied seis-mic demand against the capacity

By Sanjay Mehta, Ph.D., P.E.

TRU SS BRI DG ES H AVE L ONG

BEEN A POPULAR DESIGN

OPTION and come in a wide variety of si zes, shapes andforms—from a simple span trussof less than 100’ to a cantilever

truss with a total length of thou-sands of feet. However, many of

Modern Steel Construction / March 1999

these bridges were not designedfor seismic loads as now specifiedin the current AASHTO provi-sions. As a result, many publictransportation agencies are nowconsidering seismic retrofit as acomponent of major rehabilita-tion projects.

The extent of seismic retro-fitting is determined by perform-

SEISMIC ANALYSIS OPTIONS

FOR STEEL TRUSS BRIDGES

Seismic retrofitting is becoming increasingly commonduring major rehabilitation contracts



of the component. The resultsare conservative for “regular”structures. However, for “irregu-lar” structures with unusualgeometry, abrupt changes instiffness, framing action betweendifferent components, varying

soil conditions and foundations,this assessment may not be con-servative. Many engineers usethis approach as a first step inseismic evaluation of trussbridges.

Level 3 evaluation is an in-depth seismic evaluation. This isusually employed for bridgesthat cannot be conservativelyassessed by a Level 2 evaluationand for bridges that serve as

very critical links in the trans-

portation system. Global andlocal 3-D finite element modelsare developed to compute theseismic demand. Foundationsare modeled considering soil-structure interaction. A site spe-cific response spectrum may bedeveloped for seismic input incase of a very important bridge.

COMPUTER MODELS

Computer models are neces-sary for Level 2 and Level 3 seis-

mic evaluations. For trussbridges, three different types of computer models have been usedin engineering practice:1. Equivalent Beam Model;2. Truss Action Model; and3. Finite Element Model.

Al l are considered as threedimensional models and requirea structural analysis program.

Equivalent Beam Model. Thetruss system consisting of truss

members, laterals and swaymembers is represented as an“equivalent beam” in this type of model. The properties of an“equivalent beam” are computedbased on the geometry and crosssectional area of the truss mem-bers. This equivalent is thenlocated at the centroid of thecross section of the truss super-structure. This is an approxi-mate modeling method for trussbridges based on the assumption

that the superstructure is verystiff and its exact modeling is not

critical in seismic vulnerabilityassessment.

An advantage of this methodis that it is easy to develop thistype of model and results of theseismic analysis can be quicklyinterpreted. The method is very

accurate for girder and shortspan truss bridges because thesuperstructure of such bridges isstiff and the first mode in bothlongitudinal and transversedirection can characterize thedynamic behavior of the bridgewith accuracy.

However, the results are notstrictly valid with long spantruss bridges, which tend to beflexible. Furthermore, it is neces-sary to evaluate the capacity of

critical truss members such assway bracing over piers andshear locks at expansion joints.Since the superstructure is mod-eled as a line element, it is diffi-cult—if not impossible—to com-pute forces in the critical trussmembers. An effective retrofitscheme for reducing the seismicdemand is to permit limitedyielding of truss members. Thisretrofit scheme cannot be evalu-ated unless truss members are

explicitly modeled.

Truss Action Model. Manyexisting truss bridges have beendesigned based on “pure trussaction”. That is, only memberaxial forces are considered in thedesign. Moments resulting fromthe rigidity of riveted truss jointsare neglected. A computer modelwith this assumption can bedeveloped for seismic analysis.Unlike the Equivalent Beam

Model, all truss members aremodeled explicitly. Space trussmembers with only axial stiff-ness are used to model eachtruss member.

Most of the informationrequired to develop the 3-D mod-els is available from contractdrawings of existing bridges.This results in significant sav-ings in time and cost becausecomputation of section propertiesand other related can be avoided.

However, while reasonable fordead load and live load analysis,

this model may not be appropri-ate for seismic analysis. Seismicforces act in longitudinal, trans-

verse and vertical (not consid-ered in AASHTO at this time)directions. It becomes necessaryto consider the flexural stiffness

of truss members because signif-icant amounts of seismic energyare absorbed due to the ductilityof truss members. The endresults do not justify even thereduced efforts required to buildthis type of model.

Finite Element Model. As inthe Truss Action Model, all trussmembers are explicitly modeledin this approach. Usually spaceframe members with bending,

shear and axial stiffnesses areused for modeling truss membersand other components of thebridge. This model can be usedfor multi-mode response spec-trum analysis, nonlinear timehistory analysis and push-overanalysis.

An advantage of this system isthat it permits the accurate rep-resentation of the superstructure(truss) stiffness, which is animportant dynamic characteris-

tic of long-span truss bridges. Itis possible to evaluate axialforces and bending moments incritical truss members with rea-sonable accuracy. Recentresearch has found that forcedemand on bearings and sub-structure will be significantlyreduced if truss members andconnections have sufficient duc-tility after yielding. Of course, itis necessary to perform nonlin-ear analysis to check the ductili-

ty if elastic seismic force demandexceeds the capacity of trussmembers. Nonlinear analysis isrequired in such cases to com-pute: limit state displacementsand rotations of truss joints toensure serviceability of a bridgeafter an earthquake and reducedearthquake demands on sub-structure. Furthermore, effectsof a local failure of truss mem-bers, such as buckling of swayframe members, fracture of ten-

sion members, etc., can be evalu-ated before designing expensive



strengthening schemes.Performance of various retro-fitting schemes can also be eval-uated using such models andcomparisons can be made withthe original structure. The cur-rent engineering practice is to

adopt this approach for computermodeling.

One disadvantage, however, isthat substantial effort isrequired to develop this type of model. Usually trusses aredesigned as axial force membersand only the cross sectional areais published on design drawings.Thus, it becomes necessary tocompute the moment of inertia of truss members before developing this type of model. Further, all

critical superstructure details—such as expansion joints, shearlocks, truss-floorbeam connec-tions, etc.—should be modeledfor correct estimate of forces. Italso becomes difficult to performnonlinear analysis using suchlarge models. (Nonlinear analy-sis will be required only if mem-bers are stressed well beyond theyield strength.) Usually, localmodels of truss end sway framesand substructure are developed

to perform nonlinear analysisbased on results of this largefinite element model. This fur-ther increases cost and timerequired to complete the project.

COMPARISON

To date, very little publishedinformation is available regard-ing what type of models shouldbe used in seismic assessment.Particularly, it is difficult to dif-ferentiate between using the

Truss Action Model and theFinite Element Model.Therefore, a study was per-formed to compare the Truss

Action Model wi th the Fini teElement Model.

Two bridges on the New YorkThruway were selected for thispurpose: the 4,025’-long NorthGrand Island Bridge over theNiagara River and the 640’-long Normanskill Bridge. The FiniteElement Models for these

bridges were developed byLichtenstein Engineering during

Modern Steel Construction / March 1999

a Level III seismic evaluationproject. These models were thenconverted into the Truss ActionModels. A multi-mode responsespectrum analysis was per-formed and seismic demands incritical truss members were com-

puted. Particularly, dead loadand seismic forces in verticalmembers and bottom chordmembers at piers were comput-ed. A seismic evaluation in termsof capacity/demand (C/D) ratiowas performed. A C/D ratio of less than 1 indicates that thecomponent does not have enoughstrength to resist the seismicforces and vice versa.

The C/D ratios were signifi-cantly different for the two mod-

els. For instance, the C/D ratioover Pier 1S is 0.83 from theFinite Element Model as com-pared to 1.13 from the Truss

Action Model—a di fference of 36%. Reactions (base shear) atthe base of piers were also com-pared. The reactions from thetwo models differed by less than5% for the Normanskill Bridge.For the North Grand IslandBridge, however, the maximumdifference in reaction was 15-

20% with the Finite ElementModel generally giving higherreaction compared to the Truss

Action Model.It was thus concluded that the

Finite Element Model is moreappropriate for seismic evalua-tion because it accounts for bothaxial and bending stresses intruss members.

METHODS FOR

SEISMIC A NALYSIS

Single Mode ResponseSpectrum Analysis. Thismethod is discussed in the

AASHT O St andard Spec-ifications and is used for “regularbridges”. According to AASHTO,regular bridges do not haveabrupt changes in mass, stiff-ness or geometry along its spanand have no large differences inthese parameters between adja-cent supports. This method isbased on the assumption that

the first mode in longitudinaland transverse directions can

accurately characterize thedynamic behavior of the bridge.This method is very useful forgirder bridges in conjunctionwith an “equivalent beammodel.”

The advantage of the system

is its ease of use. For simplespan structures, calculations canbe performed manually to avoidthe use of expensive computerprograms. However, this methodshould not be used for irregularbridges such as long span truss-es with varying cross section andexpansion points. The methodassumes that dynamic responseis characterized by the firstmode of vibration, which maynot always be the case for long

span truss bridges.

Multi Mode ResponseSpectrum Analysis. This is therecommended AASHTO proce-dure for “irregular bridges.”

According to AASH TOSpecifications, bridges that can-not be classified as regular areconsidered irregular. Thismethod should be employedwhen several vibration modesare required to characterize the

dynamic behavior of the bridge. AASHTO is silent about the“regular” or “irregular” nature of truss bridges. Current engineer-ing practice uses this method forseismic analysis of truss bridges.Push-over analysis and nonlin-ear time-history analysis alsohave been used for the seismicretrofit of major truss bridges.

This method accounts for thefact that many modes of vibra-tion will be required to charac-

terize the dynamic behavior of alarge and irregular bridge.Computations can be easily per-formed on a personal computerusing a structural analysis pro-gram such as GTSTRUDL,

ADINA, ANSYS or any such pro-gram with capabilities to per-form multi-mode spectral analy-sis. This method serves as astarting point for a very criticalbridge that requires push-overanalysis or nonlinear time-histo-

ry analysis.


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Computer modeling is an

essential part of this analysis,however. Modeling techniqueshave not been standardized todate and substantial engineering

judgement is required to developappropriate models. The methodis not valid if member stressesand forces exceed yield strengthor elastic buckling stress. This isa distinct possibility for themany truss bridges that werenot designed based on currentseismic performance criteria.

Member forces, from different vibration modes, are combined in

a predetermined way to obtain

the total seismic forces in mem-bers. This method of mode com-bination could result in conserv-ative force estimates that are notalways desirable for retrofit pro-

jects—particularly in SPC B cat-egory where earthquakes are notfrequent.

Push-Over (Non-LinearStatic) Analysis. The push-overanalysis is a static nonlinearanalysis that can be used to esti-

mate the dynamic demandsimposed on a structure by earth-

quake ground motions. A prede-

termined lateral load patternthat approximately representsthe seismic forces generated dur-ing an earthquake is applied tothe structure. The structure isthen “pushed over” (by applying displacement) to the level of deformation expected during theearthquake while maintaining the applied load pattern.Nonlinearities in form of mem-ber yielding, buckling, plastichinge rotations, etc., are intro-

duced in the analysis to accountfor the possibility that members



will be stressed well beyond the

elastic limit during an earth-quake. Usually, push-over analy-sis is performed before (or in lieuof) nonlinear time-history analy-sis.

Push-over analysis clearlyidentifies redundant load pathsin the structure and actual later-al load capacity of the structuralsystem. It is more realistic ascompared to response spectrumanalysis when the structure isstressed beyond its elastic limit.

For structures with short periodsof vibration (stiff structures)whose response is governed byfirst mode, the push-over deflec-tion profiles correlate well withdeflected profiles of the structureduring an earthquake.

However, special analysissoftware with nonlinear capabili-ties is required to perform thisanalysis. Also, it is often difficultto determine the appropriate lat-eral load pattern required for

push-over analysis. Particularlyfor irregular bridges when

response cannot be characterizedby the first mode of vibration,push-over analysis looses itsaccuracy when applied to anentire bridge. Usually push-overanalyses in such in such casesare performed on a component

basis and results are related tothe global model of the bridge.Thus, either response spectrumor time history analysis may berequired in addition to push-overanalysis in case of irregularbridges.

Nonlinear Time-History Analysis. Time-history analysisis by far the most comprehensivemethod for seismic analysis. Theearthquake record in the form of

time vs. acceleration is input atthe base of the structure. Theresponse of the structure is com-puted at ever second (or evenless) for the entire duration of anearthquake. This method differsfrom response spectrum analysisbecause the effect of “time” isconsidered. That is, stresses anddeformation in the structure atan instant are considered as aninitial boundary condition forcomputation of stresses in the

next step. Furthermore, nonlin-earities a that commonly occurduring an earthquake can beincluded in the time-historyanalysis. Such nonlinearitiescannot be easily incorporated inresponse spectrum analysis.

Unlike the response spectrummethod, nonlinear time-historyanalysis does not assume a spe-cific method for mode combina-tion. Hence, results are realisticand not conservative.

Furthermore, this method isequivalent to getting 100% massparticipation using responsespectrum analysis. Full massparticipation is necessary to gen-erate correct earthquake forces.Usually, only 90-95% participa-tion is obtained in response spec-trum analysis. All types of non-linearities can be accounted forin this analysis. This could be

very important when se ismicretrofit involves energy dissipa-

tion using yielding of membersor plastic hinge rotation.

However, this method is veryexpensive and time consuming toperform. Large amounts of infor-mation are generated.Furthermore, input earthquakeis never known with certainty.Hence, three to five different his-

tories are used, further increas-ing the cost. Resources are usu-ally not available to perform fullnonlinear time-history analysisof large bridges. Also, specialanalysis software with nonlinearmaterial models and hysteresismodels is required to performnonlinear time-history analysis.

SUMMARY

Computer models and meth-ods for seismic analysis should

be selected based on the com-plexity, size and functionalimportance of the truss bridge.Some guidelines include: The equivalent beam model,

in conjunction with single-mode response spectrumanalysis, can be accuratelyused for short span trussbridges with constant crosssection.

• However, this choice of options will not be suitable for

a large truss bridge with sus-pended spans and varying truss cross section. The analy-sis methods in such casesshould consider the ultimateseismic retrofit objective.

• Multi-mode spectral methodin conjunction with the finiteelement model may be appro-priate in regions of low tomoderate seismicity for such abridge. This is because thebridge can be retrofitted to

remain within the elastic limitwith little additional cost tothe ongoing rehab projects.

• Push-over analysis or nonlin-ear time-history analysisshould be performed when thebridge members are expectedto be stressed well beyond theyield limit during an earth-quake.

• Use of seismic isolationdevices also require specialmodeling and analysis consid-

eration.

Selected Sources

“Seismic Design and Retrofit Manual forHighway Bridges,” FHWA, Report:FHWA-IP-87-6, May 1987

“Ductil ity of the Bay Bridge in theTransverse Direction,” A. Astaneh-Asl,

S.W. Cho, and D. Modjtahedi, Proceedingsof the Third Annual Seismic ResearchWorkshop, Caltrans, Sacramento, CA

“Behavior of Steel Structures in SeismicAreas,” A. Astaneh-Asl, Proceedings of theInternational Workshop organized by theEuropean Convention for ConstructionalSteelwork, Published in 1995 by E&FNSpon, 2-6 Boundary Road, London SE18HN

“Nonlinear Seismic Analysis of CarquinezStrait Bridges,” T.A. Ballard, A. Krimotat, RMutobe, and S. Treyger, Computers andStructures, Vol 64, No. 5/6, pp. 1041-1052,

1997

“Standard Specifications for HighwayBridges,” AASHTO, 1992, Division 1-ASeismic Design

“Nonlinear Static Push-Over Analysis—Why, When, and How?” R. Scott Lawson,Vicki Vance, and Helmut Krawinkler,Proceedings of the Fifth U.S. NationalConference on Earthquake Engineering,University of California, Richmond, CA94804-4698



Sanjay Mehta, Ph.D., P.E., isa project engineer with the NewYork City office of Lichtenstein

Engineer ing Associates, P.C. ,Consulting Engineers.

Seismic Analysis Options for Steel Truss Bridges

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