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Performance Modeling Strategies for Modern Reinforced Concrete Bridge Columns

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Performance Modeling Strategies Performance Modeling Strategies for Modern Reinforced Concrete for Modern Reinforced Concrete Bridge ColumnsBridge ColumnsMichael P. BerryMarc O. EberhardUniversity of WashingtonProject funded by the Pacific Earthquake Engineering Research Center (PEER)Pacific Earthquake Engineering Research Center (PEER)UWUW--PEER Structural PEER Structural Performance DatabasePerformance Database• Nearly 500 Columns– spiral or circular hoop-reinforced columns (~180)– rectangular reinforced columns (~300)• Column geometry, material properties, reinforcing details, loading• Digital Force-Displacement Histories• Observations of column damage• http://nisee.berkeley.edu/spd• User’s Manual (Berry and Eberhard, 2004)Objective of ResearchObjective of ResearchDevelop, calibrate, and evaluate column modeling strategies that are capable of accurately modeling bridge column behavior under seismic loading.–Global deformations–Local deformations (strains and rotations)–Progression of damageAdvanced Modeling StrategiesAdvanced Modeling StrategiesFForce-Based Fiber Beam Column Element (Flexure)Lumped-PlasticityForce-Based Fiber Beam Column Element (Flexure)Fiber Section at each integration point with Aggregated Elastic ShearZero Length Section (Bond Slip)Elastic Portion of Beam(A, EI )to Plastic HingeeffLpDistributed-PlasticityCrossCross--Section ModelingSection ModelingCrossCross--Section Modeling ComponentsSection Modeling Components• Concrete Material Model• Reinforcing Steel Material Model• Cross-Section Discretization StrategyConcrete Material ModelConcrete Material ModelPopovic’s Curve with Mander et. al. Constants and Added Tension Component (Concrete04)Reinforcing Steel Material ModelsReinforcing Steel Material ModelsGiufre-Menegotto-Pinto(Steel02)0 0.05 0.1 0.1500.511.5σσσσ/fyεεεεsBilinearMeasuredEs * b0 0.05 0.1 0.1500.511.5εεεεsσσσσ/fy,MeasuredKunnathMohle and Kunnath(ReinforcingSteel)Section Fiber Section Fiber DiscretizationDiscretization• Objective: Use as few fibers as possible to eliminate the effects of discretizationCover-Concrete FibersCore-Concrete FibersLongitudinal Steel Fibers0 1 2 3 4x 10-4012345678x 105φφφφ (1/mm)Moment (KN-mm)RadialUnilateralφy RatioM5 εy RatioM10 εy RatioCrossCross--Section Fiber Section Fiber DiscretizationDiscretizationUniform (220 Fibers)1020rctcnn==120rutunn==ConfinedUnconfinedReduced Fiber Reduced Fiber DiscretizationDiscretizationUniform (220 Fibers)Nonuniform StrategiesCrossCross--Section Fiber Section Fiber DiscretizationDiscretization520210rfinetfinercoarsetcoarsennnn====120rutunn==ConfinedUnconfinedUniform (220 Fibers)Reduced (140 Fibers)1020rctcnn==120rutunn==ConfinedUnconfinedr/2Modeling with DistributedModeling with Distributed--Plasticity ElementPlasticity ElementModel ComponentsModel ComponentsForce-Based Fiber Beam Column Element (Flexure)Fiber Section at each integration point with Aggregated Elastic ShearZero Length Section (Bond Slip)• Flexure Model (Force-Based Beam-Column)– nonlinearBeamColumn– Fiber section– Popovics Curve (Mander constants)– Giufre-Menegotto-Pinto (b)– Number of Integration Points (Np)• Anchorage-Slip Model– zeroLengthSection– Fiber section– Reinforcement tensile stress-deformation response from Lehman et. al. (1998) bond model (λ)– Effective depth in compression (dcomp)• Shear Model– section Aggregator– Elastic Shear (γ)Model OptimizationModel Optimization• Objective: Determine model parameters such that the error between measured and calculated global and local responses are minimized.( )( )( )212maxnmeas calcpushmeasF FEF n−=∑( )( )( )212maxnmeas calcstrainmeasEnε εε−=∑Model EvaluationModel Evaluation. .meascalcKS RK=_ 4%_ 4%. .meascalcMM RM=mean 14.89 6.73 7.78 14.4 1.02 1.03cov (%) – – – – 15 8totalEpushE(0 / 2)DstrainE−( / 2 )D DstrainE−. .S R. .M ROptimized Model:• Strain Hardening Ratio, b = 0.01• Number of Integration Points, Np= 5• Bond-Strength Ratio, λ = 0.875• Bond-Compression Depth, • dcomp=1/2 N.A. Depth at 0.002 comp strain• Shear Stiffness γ = 0.4Modeling with LumpedModeling with Lumped--Plasticity ElementPlasticity ElementLumpedLumped--Plasticity ModelPlasticity ModelFiber Section assigned to Plastic HingeElastic Portion of Beam(A, EI )Lpeff• Hinge Model Formulation:– beamwithHinges3– Force Based Beam Column Element with Integration Scheme Proposed by Scott and Fenves, 2006.– Fiber Section• Elastic Section Properties– Elastic Area, A – Effective Section Stiffness, EIeff• Calculated Plastic-Hinge Length– LpSection Stiffness CalibrationSection Stiffness Calibrationmean 1.00 1.00cov (%) 19 16Stiffness Ratio StatseffEI=sec seccalcEIαcalcg c gE IαPlasticPlastic--Hinge Length CalibrationHinge Length CalibrationCyclic ResponseCyclic ResponseCyclic Material ResponseCyclic Material Response• Cyclic response of the fiber-column model depends on the cyclic response of the material models.• Current Methodologies– Do not account for cyclic degradation steel– Do not account for imperfect crack closureGiufre-Menegotto-Pinto (with Bauschinger Effect)Steel02Reinforcing Steel Confined and Unconfined ConcreteKarsan and Jirsa with Added Tension Component Concrete04Evaluation of ResponseEvaluation of ResponseLumped-PlasticityDistributed-PlasticityEf orce (%) Ef orce (%)mean 16.13 15.66min 6.63 6.47max 44.71 46.05-15 -10 -5 0 5 10 15-300-200-1000100200300∆∆∆∆/∆∆∆∆yForce (KN)Lehman No.415 MeasuredOpenSeesKunnathKunnathand and MohleMohleSteel Material ModelSteel Material Model• Cyclic degradation according to Coffin and Manson Fatigue.• Model parameters:– Ductility Constant, Cf– Strength Reduction Constant, CdPreliminary Study with Preliminary Study with KunnathKunnathSteel Steel ModelModel• Ductility Constant, Cf=0.4• Strength Reduction Constant, Cd=0.4-15 -10 -5 0 5 10 15-300-200-1000100200300∆∆∆∆/∆∆∆∆yForce (KN)Lehman No.415 MeasuredOpenSees-15 -10 -5 0 5 10 15-300-200-1000100200300∆∆∆∆/∆∆∆∆yForce (KN)Lehman No.415 MeasuredOpenSeesGiufre-Menegotto-Pinto (with BauschingerEffect)Kunnath and Mohle (2006)Giufre-Menegotto-PintoKunnath and MohleEf orce (%) Ef orce (%)mean 16.13 11.98min 6.63 5.15max 44.71 29.45Continuing WorkContinuing WorkImperfect Crack Closure•Drift Ratio Equations•Distributed-Plasticity Modeling Strategy•Lumped-Plasticity Modeling


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