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Frontiers of Structural and Civil Engineering

Front. Struct. Civ. Eng.    2018, Vol. 12 Issue (1) : 3-15
Estimation of relations among hysteretic response measures and design parameters for RC rectangular shear walls
Department of Civil and Environmental Engineering, School of Engineering, Shiraz University, Shiraz, Fars 71348-51156, Iran
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Seismic design of RC structures requires estimation of structural member behavioral measures as functions of design parameters. In this study, the relations among cyclic behavioral measures and design parameters have been investigated for rectangular RC shear walls using numerical simulations calibrated based on the published laboratory tests. The OpenSEES numerical simulations modeling of plastic hinge hysteretic behavior of RC shear walls and estimation of empirical relations among wall hysteretic indices and design parameters are presented. The principal design parameters considered were wall dimensions, axial force, reinforcement ratios, and end-element design parameters. The estimated hysteretic response measures are wall effective stiffness, yield and ultimate curvatures, plastic moment capacity, yield and ultimate displacements, flexural shear capacity, and dissipated energy. Using results of numerous analyses, the empirical relations among wall cyclic behavioral measures and design parameters are developed and their accuracy is investigated.

Keywords RC wall hysteretic measures      RC wall design parameters      empirical relations      numerical simulations      RC rectangular wall plastic hinge     
Corresponding Authors: A. ARAB   
Online First Date: 26 September 2017    Issue Date: 08 March 2018
 Cite this article:   
A. ARAB,Ma. R. BANAN,Mo. R. BANAN, et al. Estimation of relations among hysteretic response measures and design parameters for RC rectangular shear walls[J]. Front. Struct. Civ. Eng., 2018, 12(1): 3-15.
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Fig.1  Error definition for the modeled hysteretic curves
Fig.2  Pilakoutas and Elnashai’s test specimen [16]
Fig.3  Comparison between the test by Pilakoutas and Elnashai and the numerical modeling results [16]
behavioral measureerror (%)
maximum lateral strength1.6
effective stiffness6.7
dissipated energy7.5
Tab.1  Calibration errors [16]
Fig.4  Details of the wall tested by Oesterle et al. [15]
Fig.5  Comparison between experimental and modeling results (Oerestle et al. [15])
behavioral measureerror (%)
maximum lateral strength2.3
effective stiffness4.6
dissipated energy3.7
Tab.2  Erros of modelling(Oesterle et al. [16])
test indexestimated errorspecimen design parameter
lw(mm)hw(mm)tw(mm)fc(MPa)fy(MPa)ρh(%)ρv(%)ρmin?(%)maximum lateral strengtheffective stiffnessdissipated energy
Tab.3  Verification of the models
design parametersvariation
wall length (Lw)2000–7000 mm
wall thickness (tw)300–800 mm
end element length ratio (LeL)0.1–0.2
end element thickness ratio (TeL)0.1–0.2
aspect ratio (hD)3–9
longitudinal rebar ratio (ρl)1%–4%
transverse rebar ratio (ρt)0.3%– 1%
minimum rebar ratio (ρt)0.25%–1%
axial force (PP0)4%–40%
loading patternuniform
Tab.4  Design parameters of database
Fig.6  Wall design parameters definition and the loading pattern
Fig.7  Results for typical hysteresis curve
Fig.8  Effect of axial load ratio and end element thickness on yield curvature
Fig.9  The effect of axial load ratio and end element rebar ratio on effective stiffeness
Tab.5  Constant design parameters in investigating the effect of design parameters on yield curvatu
Tab.6  Constant design parameters in investigating the effect of design parameters on effective stiffness
behavioral measureparameterdefinition
yield curvatureϕycurvature when first rebar reach yield strain
ultimate curvatureϕucurvature when rupture criteria reach
effective stiffness(EIEIg)yield moment divided by yield curvature
member effective stiffnessKeffyield base shear divided by yield displacement
plastic momentMpmoment corresponding to idealized elastic-plastic curve
yield displacementΔydisplacement when first rebar reach yield strain
ultimate base shearVubase shear when rupture criteria reach
ultimate momentMumoment when rupture criteria reach
ultimate displacementΔudisplacement when rupture criteria reach
back bone energyBD. Energyenergy under idealized curve
dissipated energyD. Energyarea under hysteresis curve
equivalent momentMe0.8ρ1Lw
Tab.7  Behavioral measures definition
Tab.8  Insignificant parameters
Fig.10  Comparison between empirical data and OpenSEES results
behavioral measurecorrelationR.M.S
minimum yield curvature0.880.004
maximum yield curvature0.660.012
minimum ultimate curvature0.510.035
maximum ultimate curvature0.610.024
minimum effective stiffness0.920.011
maximum effective stiffness0.940.009
minimum effective member stiffness0.990.012
maximum effective member stiffness0.990.013
minimum plastic moment0.970.014
maximum plastic moment0.970.009
yield displacement0.920.011
yield moment0.980.011
ultimate displacement0.970.009
ultimate base shear0.980.017
ultimate moment0.960.017
back bone dissipated energy0.930.110
dissipated energy0.930.110
Tab.9  Correlation of derived formula
Fig.11  Details of the wall tested by Aaleti [23]
Fig.12  Experimental and numerical hystresis behavior of the wall reported by Aaleti [23]
design parametermagnitude
lw2286 mm
tw152.4 mm
Tab.10  Design parameters for the wall tested by Aaleti [23]
Fig.13  Effect of wall end element thickness ratio on the ductility damage index
Fig.14  Effect of wall end element transverse rebar ratio on the ductility damage index
Fig.15  Effect of wall end element longitudinal rebar ratio on the ductility damage index
Fig.16  Effect of wall end element length ratio on the ductility damage index
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