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10 Years of International Cooperation: FTI, Nippon Keidanren and TUSIIT Commemorative Publication, 2002The comparison of load-deflection relations betweennon pre-cracked and inclined pre-cracked beams areshown in Fig. 6. As shown in the figure, the loadingcapacity and stiffness of damaged beam weredecreased compared with the non pre-cracked one. Thefailure crack pattern of damaged beam is shown in Fig.7. The new diagonal crack was not formed. Instead,pre-crack itself was active from the beginning andtotally governed the beam behavior. This explainedwhy the inclined pre-crack accelerated the formation offailure.Most engineers have primarily used linear finiteelement analysis for the design of new structures. Butvery few employ non-linear finite element analysis as atool to evaluate the existing structures. However, asthe need to obtain information of existing structures isincreasing, the use of non-linear finite element willbecome more and more. At the present time, theJapanese design code [5] has endorsed the use of nonlinearfinite element analysis for evaluation of RCstructures damaged in the previous earthquakes.This paper presents a non-linear finite element analysisto evaluate the pre-cracked reinforced concretemembers. The intention is to show the possibility ofthis tool to simulate the behavior of pre-crackedreinforced concrete members tested in the experiments.The capabilities of non-linear finite element analysiswill be demonstrated through the correct prediction offailure mode, load-deformation response and capacityof the RC members with sufficient accuracy.4. Finite Element Analysis of Pre-CrackedBeam4.1 Beams with Vertical Pre-cracksPre-cracked condition (First shear)Shear failure (second shear)Fig. 7 Failure crack pattern of inclined pre-cracked beam.3. Finite Element Analysis as a Tool toEvaluate the Cracked StructuresThe finite element analysis is the numerical methodthat solves a set of governing partial differentialequation using computers [2, 3]. Recently, it has beenincreasingly used to analyze structures withcomplicated shape, load and boundary conditions.There are two major types of finite element analysis forstructural analysis: linear analysis and non-linearanalysis. In the linear finite element analysis, theconstitutive models or material models are linear. As aresult, it cannot deal with plasticity of reinforcementand fracture of concrete. On the other hand, the nonlinearfinite element analysis employs the non-linearconstitutive models [4]. Hence it can trace the loaddeformationresponse of structures throughout theloading history as well as the failure mode.It was shown in the previous section that the behaviorof pre-cracked beams significantly differ from the nonpre-cracked one. The capacity may decrease orincrease compared with the un-cracked beam. It wasclear that the conventional knowledge applicable toperfect un-cracked concrete could not be used toexplain the behavior of pre-cracked beam. In thissection, the non-linear finite element analysis is used tosimulate the behavior of pre-cracked reinforcedconcrete beams tested in the previous section [6].The finite element mesh of the pre-cracked beam isshown in Fig. 8. Discrete joint elements are used torepresent vertical pre-cracks. Due to the symmetry ofthe problem, the analysis of half-beam is sufficient.The load-displacement relationship under shear loadingRC Smeared elementsDiscrete joint element450750Unit:mm(a) Finite element meshFig. 8 FEM mesh of beam with vertical pre-cracks.Load(kN)25020015010050Non pre-cracked beamExperimentAnalysis00 5 10 15 20Center span deflection(mm)Fig. 9 Prediction of load-deflection by FEM.4
10 Years of International Cooperation: FTI, Nippon Keidanren and TUSIIT Commemorative Publication, 2002Pre-crack zonePre-crack zone(a) Z-crackMain failure crackFig. 12 Comparison of numerical and experimentalcrack patterns.Load(kN)(b) Failure crackFig. 10 Comparison of experimental andnumerical crack patterns.120100806040200AnalysisExperiment0 1 2 3 4 5Center span deflection(mm)Fig. 11 Comparison of analytical and experimental loaddeflectionof beam with inclined pre-cracks.is shown in Fig. 9. It is seen that the FEM can predictthe load-deflection relation with sufficient accuracy.The comparison of crack pattern is shown in Fig. 10.The experimental crack pattern and the failure processare well captured by the finite element analysis.4.2 Beams with Inclined Pre-CracksThe comparison of experimental and numerical loaddisplacementrelationship for beam is shown in Fig. 11.Good agreement is obtained. Similar to the experiment,analysis predicts a reduction in shear capacity.Numerical crack pattern (Fig. 12) closely follows theexperiment. Similar to the experiment, the analysispredicts no new diagonal crack. Instead, it predicts theactivation of pre-crack, which brings failure to thebeam. It is seen that the non-linear finite elementanalysis can reliably trace load-deflection response,crack pattern and failure mode of the pre-crackedbeam.5. Recommendations for Future Researchand DevelopmentsThe finite element method with the nonlinearconstitutive models was demonstrated to be capable ofsimulating the behavior of damaged existing reinforcedconcrete member. This paper showed just onecapability of the method to deal with reinforcedconcrete members with cracking damages. There areother damages that need to be considered; for example,corrosion of reinforcing steels, chemical attack,carbonation and so on. The author believes that most ofall these damages can be simulated by the nonlinearfinite element method. The research is currentlyconducted to include the effect of these damages byemploying the constitutive (material) models fordamaged concrete and reinforcing steel. This is anadvanced step beyond the nonlinear constitutivemodels for perfect undamaged materials [4] and linearconstitutive models mostly used by engineersnowadays [2]. This method would be greatly valuablefor the engineers to decide the destiny of theirdeteriorated structures.6. ConclusionsThis paper presented a non-linear finite elementanalysis as a tool to evaluate the reinforced concretestructures with cracking damages. This tool isnecessary to understand the behavior of damaged RCmembers. The information will be useful for theappropriate measure against deteriorated structures. Incontrast to using linear finite element analysis for thedesign of new structures, the finite element analysiswith non-linear constitutive models can be used for theevaluation of existing structures. Here, the author hasdemonstrated the capability of this tool by simulatingthe experiment of pre-cracked in computer. It wasfound that the finite element method could reasonablycapture the behavior of pre-cracked members.5
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