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NON-LINEAR BAHAVIOR ANALYSIS OF T-BEAM BRIDGE GIRDER AT DIFFERENT SPAN LEVELS

Shirish Hanmant Kadam1, P. J. Salunke2

1PG Student, Dept. of Civil Engineering, Mahatma Gandhi Mission’s College of Engineering and Technology (MGMCET), Kamothe, Navi Mumbai, Maharashtra, India

2Head of Department, Dept. of Civil Engineering, Mahatma Gandhi Mission's College of Engineering and Technology (MGMCET), Kamothe, Navi Mumbai, Maharashtra, India

Abstract – The non-linear behavior of reinforced concrete T-Beam bridge girders plays a critical role in the accurate assessment of their load-carrying capacity and failure mechanisms. This studyinvestigatesthenon-linearresponseof T-Beam bridge girders under different live loads condition specified in the Indian Road Congress (IRC) codes,particularly the class AA tracked vehicle and Class 70R wheeled loadings. Through finite element modeling and non-linear static analysis, the structural response is evaluated in terms of moment-curvature relationships, crack propagation, stress redistribution and ultimate capacity. Emphasis is placed on material and geometric non-linearity to simulate realistic structural behavior under service and ultimate loads. The analysis provides insight intotheinfluenceofloadingstypeson the failure modes and performance of bridgegirders,aidingin enhanced design and safety evaluation procedures.

Key Words: Non-linearanalysis,T-beambridgegirder,IRC ClassAATrackedLoadings,IRCClass70RWheeledLoadings, Crackpropagation,Loadredistribution.

1.INTRODUCTION

T-Beam bridge girders are commonly adopted superstructuretypeinreinforcedconcretebridgedesigndue totheirstructuralefficiency,constructabilityandeconomic feasibility. These beams are characterized by monolithic integrationofslabandbeamsresultinginimprovedstiffness andstrength.However,traditionallinearanalysismethods oftenfailtocapturethetruebehaviorofsuchsystemsunder extremeloadingsorfailureconditions.Thus,thenon-linear behaviour analysis of T-beam bridge girders has become essential for accurate prediction of structural response, particularly in the context of ultimate strength, crack propagation,plastichingeformation,andfailuremodes.

Non-linear analysis incorporates both material and geometricnonlinearity,whicharecrucialforunderstanding the inelastic behaviour of reinforced concrete under high stress or deformation. In practice, concrete exhibits nonlinearstress-straincharacteristicsbeyonditsproportional limit,especiallyundercompressionandtension,whilesteel reinforcement behaves plastically after yielding. These complexinteractionsbetweenconcreteandsteel,aswellas the redistribution of internal forces, demand robust non-

linearmodellingtechniques.Bridgedesignandanalysisin India are governed by the Indian Roads Congress (IRC) loadingstandards.Amongthese,theIRCClassAATracked Vehicle Loading and Class 70R Wheeled Loading are the mostcriticalforevaluatingtheperformanceofhighway

1.2 IMPORTANCE OF ANALYSIS

Nonlinear behavior analysis plays a crucial role in assessingthestructuralresponseofT-beambridgegirders, especiallywhensubjectedtocomplexloadingconditionsat varyingspanlevels.T-beamgirders,widelyusedinbridge construction for their composite behavior and structural efficiency,exhibitsignificantnonlinearcharacteristicsunder load,includingcracking,plasticdeformations,andstiffness degradation. These effects are more pronounced at longer spanswhereflexuralandsheardemandsincrease.Atshorter spans, local failures and early cracking are the dominant concerns, necessitating detailed nonlinear modeling to capture the true behavior and ensure safety and serviceabilityunderoperationalandextremeevents.

Theapplicationofnonlinearanalysisallowsengineersto simulate real-world loading scenarios and predict performance beyond elastic limits. For example, studies involving dynamic or seismic loading on bridge girders

Fig.1:T-BeamBridgeGirders

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056

Volume: 12 Issue: 05 | May 2025 www.irjet.net p-ISSN: 2395-0072

demonstrate that the inclusion of geometric and material nonlinearityimprovestheaccuracyofstressredistribution predictions, particularly in continuous or skewed spans. Nonlinear finite element methods (FEM) enable the evaluationofcriticalparameterssuchasmoment-curvature relationships,ultimateloadcapacity,andfailuremodes(e.g., flexural vs. shear failure). These insights are essential for optimizing reinforcement design, improving ductility, and enhancing the resilience of T-beam bridges to progressive collapseoroverloadscenarios.

Atvariousspanlevels,nonlinearbehavioranalysissupports tailoreddesigninterventions.Shorttomedium-spangirders benefit from detailed nonlinear stress-strain modeling to control early cracking and increase load capacity without overdesigning the structure. For long-span girders, nonlinearity becomes essential for understanding large deformation behaviors and post-yield redistribution, includingarchingandcatenaryactions.Researchershavealso applied nonlinear dynamic analysis techniques to model collapsemechanismstriggeredbycolumnremovalorseismic excitations, highlighting how span length directly affects structuralrobustness.Assuch,nonlinearanalysisisnotonly vitalfordesignvalidationbutalsoforretrofittingexistingTbeam bridges under varying span conditions and loading environments.

1.3 APPLICATION

The non-linear behavior analysis of T-beam bridge girdersplaysacriticalroleinunderstandingthestructural performance and safety of bridges under various loading conditions.Thisformofanalysisaccountsformaterialnonlinearity (such as concrete cracking and steel yielding), geometricnon-linearity(largedeformations),andboundary condition variations. Applications of such analysis across differentspanlevelsinclude:

1.Non-linearanalysishelpsidentifycrackingpatternsand theonsetofplastichinges,whicharecrucialforevaluating serviceabilityanddurability.

 At medium spans (e.g., 15–25 meters), Non-linear simulationshelpassesscombinedshear-flexuralfailure mechanisms and evaluate the effectiveness of web reinforcement, particularly in earthquake-prone regions.

 Forlongspans(30metersandabove),Non-linearfinite element models (using tools such as DIANA or ABAQUS)cansimulateprogressivecollapsepotential, load redistribution post-local failure, and residual strength.

2.Non-linear dynamic analysishelpstraceload paths and activationofsecondarymechanismslikecatenaryorarching action.

3. At different span levels, the stiffness of connections betweenT-beamsanddeckslabsorcrossgirdersaffectsthe overall structural response. Studies like those by Pavel Korenkovetal.(2024)highlightthoseflexibleconnections lead to significant force redistribution due to joint compliance,whichiseffectivelycapturedusingnon-linear modeling

4.Non-lineartimehistoryanalysishelpsevaluatetheimpact ofdynamicseismicloadsandidentifycollapse-pronespans. Structural irregularities and asymmetries amplify these effects.

5.Non-linearanalysisinformsretrofitting needs suchas external prestressing, fiber-reinforced polymer (FRP) wrapping, or jacketing for different spans. It aids in quantifying post-retrofit performance gains and residual strengthunderrepeatedloading

2. LITERATURE REVIEW

R. Shreedhar & Spurti Namadapur, (2012) studiedthat astraightspanT-beamextensionwasanalyzedbyutilizing I.R.C.determinationsandloading(deadloadandliveload)as a one-dimensional structure. Finite Element analysis of a three-dimensional structure was done using Staad pro programming.BothmodelsweresubjectedtoI.R.C.Loadings to convey most outrageous bending moment. The results werebrokendownanditwasfoundthattheresultsgotfrom thelimitedcomponentmodelarelesserthantheresultsgot fromonedimensionalexamination,whichsuggeststhatthe results got from I.R.C. loadings are traditionalist and FEM givespracticaldesign.

Rajamoori Arun Kumar, (2014) studiesthatBending momentandshearforceforPSCT-BeamGirderarelesser thenRCCT-Beamgirderbridge.TheuseofPSC(Prestressed Concrete)T-beamgirdersallowsdesignerstooptforlighter sectionscomparedtoRCC(ReinforcedCementConcrete)Tbeam girders for a 24-meter span. This is because PSC Tbeams offer a higher moment of resistance than RCC Tbeamsoverthesamespan.Additionally,theconcretecost associatedwithPSCT-beamgirdersislowerthanthatofRCC T-beamgirders.

Pallvi rai, (2016) studies that to shield connect from blastloading,thereisneedtoconsiderblastloadingatthe periodofdesignofstructure.Forexistingstructures,eithera retrofitting system can be implemented or the impact resistance capacity can be enhanced throughout the structure.ThefindingsindicatethatatypicalT-beambridge is likely to fail under the impact load generated by an explosionequivalentto226.8kgofexplosivesplacedabove orbelowthedeck.However,partsofthebridgemayremain intactdependingontheimpactlocation specifically,ifthe blast occurs near a support section. In cases where the impactisclosetothesupport,someofthepropsatvarious spansmayremainunaffected.Fromthisanalysis,itcanbe

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056

Volume: 12 Issue: 05 | May 2025 www.irjet.net p-ISSN: 2395-0072

concluded that a standard T-beam bridge with reinforced components and piers is generally not capable of withstandingsuchhigh-magnitudeimpactloads.

Sandesh Upadhayaya, (2016) Researchindicatesthat the performance of T-beam deck slabs can be further enhanced by applying pre-tensioning or post-tensioning techniques. These prestressing methods are easier to implement in T-beam configurations, and calculating the necessary jacking force is relatively straightforward. This configuration provides a practical solution for addressing suchrequirementswithgreaterefficiency.

Shreyali S. Pratapwar (2023) studiesthattheanalysis ofaT-beambridgewithadeckslabusingIRCloadingsand STAAD Pro V8i revealed the distribution of loads on structuralmembers,themax.bendingmoment,shearforce, anddeflectionfordifferentspans.Bridgedesigniscrucialfor safetyandeconomy,andcompliancewithIRCandIRScodes ismandatoryinIndia.Variousstudiesandcomparisonshave been conducted to enhance bridge construction technologies,leadingtotheselectionofappropriatebridge typesbasedonfactorssuchaseconomy,safety,stability,and aesthetics. Innovations in bridge construction technology haveprovidedmultipleoptionsforanalyzinganddesigning bridges, ensuring their structural integrity while meeting functional requirements.Theresearchpaperexploredthe dynamic behavior ofT-beambridgedecksunderdifferent loading conditions, demonstrating the importance of efficientdesignmethodsandaccurateanalysisforoptimal bridge performance. Advances in bridge engineering have resultedinthedevelopmentofsuitablesectionsforbridges ofvaryingspans,suchasT-beamandboxgirders,enabling cost-effective and safe bridge construction practices to supportthegrowingtransportationinfrastructureneedsofa developingnation.

Abhinav Kumar, (2020) studiesthatrecentprojectsaim to alleviate traffic congestion in cities by constructing advanced transit systems, including curved bridges with varying curvatures. To reduce costs and ensure safety, researchers have developed a reusable formwork called multi-tasking formwork for precast prestressed concrete (PSC)curvedgirders. Resultsindicatedthebridge'ssafety andserviceability,withahigherloadcapacityandallowable deflectionthandesignstandards.FEMsimulationsand 23 full-scale experiments further demonstrated the effectivenessofthemulti-taskingformworkincreatingcostefficientandstableprecastPSCcurvedgirderbridges.

Abrar Ahmed, (2017) studies that the comparison betweenthe'T-beamgirder'and'boxgirder'wasconducted to determine the most suitable section for bridges of differentspansbyanalysing,designing,andcostcomparison. The study aimed to identify the suitable section for spans exceeding 25 meters, using prestressed concrete sections duetotheircost-effectiveness.Theanalysiswasdoneusing theCSIBridgesoftware,validatedmanually,anddeveloped

in Excel sheets following the working stress method and Courbonne’s theory. The results showed that the IRC 70R vehiclehadthemaximumeffectonthesections,leadingto theconclusionthatT-beamgirdersaresuitableforspansup to 30 meters, while box girders are more economical for higher spans. The study also indicated that the software resultswereacceptableandcouldbeusedforsubstructure design. The findings suggest that the selection of the appropriatesectionforrespectivespanscanbedetermined based on the obtained results, with T beam girders recommendedforsmallerspansandboxgirdersforlonger spans,especiallybeyond30meters.

Praful NK, (2015) studies in view of this review Courbonne’s method gives the normal outcome with deference BM values in the longitudinal girder when contrasted with Guyon Massenet technique. While Guyon Massenet’sstrategybelittlestheBMvalueswhencontrasted andCourbonne’smethod.TheStaadprofessionaloutcome nearlycoordinateswiththequalitiesgottenbyCourbonne’s technique for class AA followed vehicle. For class AA Followed vehicle the Staad professional outcome is decreased by (0.01%) when contrasted with Courbonne’s technique and increment in result contrasted with Guyon masonedstrategyby(34.22%)forBowingMoment.Forclass AA Followed vehicle the Staad star result is lessened by (33.73%)whencontrastedwithCourbonne’sstrategyand increment in result contrasted with Guyon-Massenet techniqueby(26.93%)forShearConstrain.

Akanksha Yadav, (2024) analysed the simply supportedRCCT-framegirderbridgewasperformedunder standard IRC loading, and results were compared across different models for various spans using STAAD. pro software.Fourdifferentspanlengths(20 m,30 m,40 m,and 50 m) were analysed to assess performance across both short and long spans. Additionally, the effect of girder thickness for the 20 m span was examined using four differentthicknesses(0.22 m,0.24 m,0.26 m,and0.28 m). Themethodologyinvolvedanalysingasingle-span,two-lane RCCslabT-framebridgedeckundervariousdeadandlive loadconditions.Thisincludedbothstaticanddynamicload analysis, resulting in a detailed study of maximum deformation, stress, and moments influenced by girder thicknessandspanlength.

Anushia K Ajay, (2017) revealed that construction costsdecreasedasthelength-to-depth(l/d)ratioincreased, up to a certain limit defined as the optimum l/d ratio. An optimal l/d ratio of 14 was identified. Additionally, slab thickness was found to influence stress intensity, with a range between 170 mm and 200 mm providing the most efficientperformance.TheanalysiswascarriedoutusingVB 6.0 software A bridge is a structure constructed over obstaclestofacilitatepassagewithoutobstructingwhatlies beneath. It may support a railway, roadway, pipeline, or canaloverfeaturessuchasriversorvalleys.Inthiscontext, theT-beambridge,suitableforspansrangingfrom10to25

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056

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meters, was studied due to its T-shaped configuration formed by casting girders and deck slabs together researcher examined the performance of T-beam bridges underIRCClassAAtrackedloadingbyvaryingparameters suchasspanlength,concretegrade,deckslabthickness,and girderdepth

3. CONCLUSION OF LITARETURE REVIEW

Afterreviewingtheresearchpapersmentionedabove,the followingissummaryoftheliteraturereview.

▪ The selection between T-beam and box girder designs depends on project-specific requirements, such as span length,cost,andload-carryingcapacity.

▪Thestudyemphasizestheneedforfiniteelementanalysis (FEA) in the design process, especially for evaluating the real-world performance of RC T-beams under different loadingconditions.

▪ Pre-stressed T-beams provide superior flexural performancecomparedtoconventionalRCT-beams.▪The study finds that T-beam bridges perform well under dead loads but require more reinforcement when subjected to dynamicloads.

▪ T-beams, however, are more economical and easier to constructforshorterspans,makingthemsuitableforsmallscaleprojects.

▪ Courbonne’s Theory provides a reasonable approximationforloaddistributioninTbeambridges,but itslimitationsbecomeevidentincurvedorskewbridges.

▪T-beamsarelessefficientunderseismicconditions,while box girders demonstrate better structural integrity and vibrationresistance.

▪Theparametricstudyconcludesthatvariousfactors,such as span length, girder spacing, and deck thickness, play a significantroleintheoverallbehaviorofT-beambridges.

4. GAPS IN LITERATURE REVIEW

▪TheeffectofcurvatureonthestructuralperformanceofTbeamgirdersisnotexploredindepth.

▪ The study does not focus on dynamic load conditions, whichcansignificantlyinfluencethenon-linearperformance ofT-beams.

▪ The study does not consider the impact of curvature, whichiscrucialfornon-linearanalysisingirders.

▪ There is no analysis of how concrete’s non-linear properties (e.g., cracking) affect the overall structural behavior.

▪ This study is based on the linear design of a specific bridge, without exploring nonlinear effects or behavior under dynamic conditions like earthquakes or heavy vehicularloads.

REFERENCES

1. R.Shreedhar&SpurtiNamadapur(2012)“Analysisof T-beam Bridge Using Finite Element Method”InternationalJournalofEngineeringandInnovative Technology (IJEIT) Volume 2, Issue 3, September 2012

2. Raja mooriArunKumar&B.VamsiKrishna (2014) “DesignofPre-StressedConcreteT-BeamBridges”International Journal of Bridge Engineering (IJBE), Vol.2,No.3,(2014),pp.01-14

3. PallaviRai&RajneeshKumar(2016)“AnalysisofTBeamBridgeSubjectedtoBlastLoadingusingFEMSPH Coupling” - Journal of Civil Engineering and Environmental Technology Volume 3, Issue 3, January-March,2016

4. Sandesh Upadhayaya & F. Sahaya Sachin (2016) “A Comparative Study of T-Beam Bridges for Varrying SpanLengths”-InternationalJournalofResearchin Engineering and Technology (IJRET) eISSN: 23191163,pISSN:2321-7308

5. Shreyali S. Pratapwar & Kirti Padmawar (2023) “A ReviewPaperonAnalysisOfT-BeamAlongwithDeck Slab” - International Journal of Engineering and Innovative Technology (IJEIT) Volume 11, Issue 6 June2023

6. AbhinavKumar&NiteshKushwaha(2020)“AReview StudyonAnalysisofConcreteT-BeamGirderBridge” -InternationalJournalofTrendinScientificResearch and Development (IJTSRD) Volume 4, Issue 6, September-October2020

7. Abrar Ahmed & Prof. R.B. Lokhande (2017) “ComparativeAnalysisandDesignofT-BeamandBox Girders” - International Research Journal of Engineering and Technology (IRJET) Volume: 04, Issue:07,July-2017

8. PrafulNK&BalasoHanumant(2015)“Comparative Analysis of T-Beam Bridge by Rational Method and Staad Pro” - International Journal of Engineering Sciences & Research Technology ISSN: 2277-9655, June,2015

9. AkankshaYadav&VijayK.Shukla(2024)“Analysisof RCC-T Frame Girder Bridge under IRC Loading i.e ClassAAand70R”-InternationalResearchJournalof EngineeringandTechnology(IRJET)Volume9,Issue 6,June2024

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Volume: 12 Issue: 05 | May 2025 www.irjet.net p-ISSN: 2395-0072

10.Anushia K. Ajay & Asha U. Rao (2017) “Parametric StudyOnT-BeamBridge”-InternationalJournalofCivil EngineeringandTechnology(IJCIET)Volume8,Issue6, June2017