# Performance Modeling Strategies for Modern Reinforced Concrete Bridge Columns

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Performance Modeling Strategies for Modern Reinforced Concrete Bridge Columns Michael P Berry Marc O Eberhard University of Washington Project funded by the Pacific Earthquake Engineering Research Center PEER UW PEER Structural Performance 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 Research Develop 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 damage Advanced Modeling Strategies DistributedPlasticity LumpedPlasticity F Elastic Portion of Beam A EI eff Force Based Fiber Force Based Fiber Element Beam Column Beam Column Element Flexure Flexure Fiber Section at each integration point with Aggregated Elastic Shear Zero Length Section Bond Slip Lp to Plastic Hinge Cross Section Modeling Cross Section Modeling Components Concrete Material Model Reinforcing Steel Material Model Cross Section Discretization Strategy Concrete Material Model Popovic s Curve with Mander et al Constants and Added Tension Component Concrete04 Reinforcing Steel Material Models 1 5 1 5 Es b 1 fy f y 1 0 5 0 5 Bilinear Measured 0 0 0 05 0 1 s Giufre Menegotto Pinto Steel02 0 15 Measured Kunnath 0 0 0 05 0 1 s Mohle and Kunnath ReinforcingSteel 0 15 Section Fiber Discretization Objective Use as few fibers as possible to eliminate the effects of discretization 8 x 10 5 7 M5 Longitudinal Steel Fibers Cover Concrete Fibers Core Concrete Fibers Moment KN mm 6 y M10 Ratio y Ratio 5 4 y Ratio 3 2 1 0 0 Radial Unilateral 1 2 1 mm 3 4 x 10 4 Cross Section Fiber Discretization Uniform 220 Fibers Confined ncr 10 t c n 20 Unconfined r u n 1 nut 20 Reduced Fiber Discretization Uniform 220 Fibers Nonuniform Strategies Cross Section Fiber Discretization Uniform 220 Fibers Reduced 140 Fibers r 2 Confined r c n 10 t c n 20 Unconfined Confined Unconfined r u r u n rfine 5 n 1 t u ntfine 20 nut 20 n 1 n 20 r ncoarse 2 t ncoarse 10 Modeling with DistributedPlasticity Element Model Components Force Based Fiber Beam Column Element Flexure Flexure Model Force Based Beam Column Fiber Section at each integration point with Aggregated Elastic Shear nonlinearBeamColumn Fiber section Popovics Curve Mander constants Giufre Menegotto Pinto b Number of Integration Points Np Anchorage Slip Model zeroLengthSection Fiber section Reinforcement tensile stressdeformation response from Lehman et al 1998 bond model Effective depth in compression dcomp Zero Length Section Bond Slip Shear Model section Aggregator Elastic Shear Model Optimization Objective Determine model parameters such that the error between measured and calculated global and local responses are minimized n E push F F max F n 1 meas meas calc 2 2 2 n Estrain max n 1 meas meas calc 2 Model Evaluation Optimized Model Strain Hardening Ratio b 0 01 Number of Integration Points Np 5 Bond Strength Ratio 0 875 Bond Compression Depth dcomp 1 2 N A Depth at 0 002 comp strain Shear Stiffness 0 4 Etotal mean cov 14 89 E push 6 73 S R 0 D 2 Estrain 7 78 M R K meas K calc D 2 D Estrain 14 4 M meas 4 M calc 4 S R M R 1 02 15 1 03 8 Modeling with LumpedPlasticity Element Lumped Plasticity Model Hinge Model Formulation Elastic Portion of Beam A EI eff 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 Lp Lp Fiber Section assigned to Plastic Hinge Section Stiffness Calibration Stiffness Ratio Stats EI eff gcalc Ec I g calc sec EI sec mean cov 1 00 19 1 00 16 Plastic Hinge Length Calibration Cyclic Response Cyclic Material Response Cyclic response of the fiber column model depends on the cyclic response of the material models Reinforcing Steel Confined and Unconfined Concrete Giufre Menegotto Pinto with Bauschinger Effect Steel02 Karsan and Jirsa with Added Tension Component Concrete04 Current Methodologies Do not account for cyclic degradation steel Do not account for imperfect crack closure Evaluation of Response Lumped Plasticity DistributedPlasticity Ef orce Ef orce 16 13 6 63 44 71 15 66 6 47 46 05 mean min max Lehman No 415 300 200 Force KN 100 0 100 200 300 15 Measured OpenSees 10 5 0 y 5 10 15 Kunnath and Mohle Steel Material Model Cyclic degradation according to Coffin and Manson Fatigue Model parameters Ductility Constant Cf Strength Reduction Constant Cd Preliminary Study with Kunnath Steel Model Ductility Constant Cf 0 4 Strength Reduction Constant Cd 0 4 Giufre MenegottoPinto Kunnath and Mohle E f orce E f orce 16 13 6 63 44 71 11 98 5 15 29 45 mean min max Lehman No 415 300 200 200 100 100 Force KN Force KN Lehman No 415 300 0 100 100 200 300 15 0 200 Measured OpenSees 10 5 0 y 5 10 Giufre Menegotto Pinto with Bauschinger Effect 15 300 15 Measured OpenSees 10 5 0 5 10 y Kunnath and Mohle 2006 15 Continuing Work Imperfect Crack Closure Prediction of Flexural Damage Drift Ratio Equations Distributed Plasticity Modeling Strategy Lumped Plasticity Modeling Strategy Key Statistics Fragility Curves Design Recommendations Evaluation of Modeling Strategies for Complex Loading Bridge Bent Purdue 2006 Unidirectional and Bi directional Shake Table Hachem 2003 Thank you