Estimation of relations among hysteretic response measures and design parameters for RC rectangular shear walls

doi:10.1007/s11709-017-0418-6

Front. Struct. Civ. Eng.

2018, Vol. 12

Issue (1) : 3-15 https://doi.org/10.1007/s11709-017-0418-6

RESEARCH ARTICLE

Estimation of relations among hysteretic response measures and design parameters for RC rectangular shear walls

A. ARAB(

), Ma. R. BANAN, Mo. R. BANAN, S. FARHADI

Department of Civil and Environmental Engineering, School of Engineering, Shiraz University, Shiraz, Fars 71348-51156, Iran

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Abstract

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 Author(s): 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.

URL:

https://academic.hep.com.cn/fsce/EN/10.1007/s11709-017-0418-6
https://academic.hep.com.cn/fsce/EN/Y2018/V12/I1/3

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]

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])

Tab.2 Erros of modelling(Oesterle et al. [16])

test index		estimated error								specimen design parameter
test index		$l w (mm)$	$h w (mm)$	$t w (mm)$	$f c (MPa)$	$f y (MPa)$	$ρ h (%)$	$ρ v (%)$	$ρ min ? (%)$	maximum lateral strength	effective stiffness	dissipated energy
Wallace (2004)	RW-2	1220	3.88	102	43.0	426	0.04	----	0.002	3.6	3.6	3.6
Oesterle (1976)	B1	2320	4500	98	52.0	473	1.11	0.31	0.290	2.3	4.6	3.7
	B3	2320	4500	98	47.0	475	1.11	0.31	0.290	7.2	5.2	3.5
	B4	2320	4500	98	45.0	508	1.11	0.31	0.290	5.4	5.3	3.7
	B5	2320	4500	98	45.0	477	3.67	0.63	0.290	2.3	4.1	2.4
Elnashai (1993)	RW4	600	1200	60	36.9	550	0.39	0.50	6.860	6.5	8.1	6.2
	RW5	600	1200	60	31.8	550	0.31	0.59	12.750	4.1	2.3	4.1
	RW6	600	1200	60	38.6	550	0.31	0.50	6.860	8.6	2.1	8.8
	RW7	600	1200	60	32.0	550	0.39	0.59	12.750	2.2	2.0	9.6
	RW8	600	1200	60	45.8	550	0.28	0.50	7.140	1.7	6.7	5.1
	RW9	600	1200	60	38.9	550	0.56	0.50	7.140	2.3	7.2	4.8
Riva (2006)	full scale	2800	15500	----	34.3	414	----	----	----	1.6	6.7	7.5

Tab.3 Verification of the models

design parameters	variation
wall length $(L w)$	2000–7000 mm
wall thickness $(t w)$	300–800 mm
end element length ratio $(L e L)$	0.1–0.2
end element thickness ratio $(T e L)$	0.1–0.2
aspect ratio $(h D)$	3–9
longitudinal rebar ratio $(ρ l)$	1%–4%
transverse rebar ratio $(ρ t)$	0.3%– 1%
minimum rebar ratio $(ρ t)$	0.25%–1%
axial force $(P P 0)$	4%–40%
loading pattern	uniform
loading pattern	triangular

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

parameter	$t w$	$L w$	$A . R$	$E L$	$ρ 1$	$ρ h$	$ρ m i n$
Value	300	4000	3	0.1	0.04	0.003	0.0025

Tab.5 Constant design parameters in investigating the effect of design parameters on yield curvatu

parameter	$t w$	$L w$	$A . R$	$E L$	$E t$	$ρ h$	$ρ m i n$
value	300	4000	3	0.1	0.075	0.003	0.0025

Tab.6 Constant design parameters in investigating the effect of design parameters on effective stiffness

behavioral measure	parameter	definition
yield curvature	$ϕ y$	curvature when first rebar reach yield strain
ultimate curvature	$ϕ u$	curvature when rupture criteria reach
effective stiffness	$(E I E I g)$	yield moment divided by yield curvature
member effective stiffness	$K e f f$	yield base shear divided by yield displacement
plastic moment	$M p$	moment corresponding to idealized elastic-plastic curve
yield displacement	$Δ y$	displacement when first rebar reach yield strain
ultimate base shear	$V u$	base shear when rupture criteria reach
ultimate moment	$M u$	moment when rupture criteria reach
ultimate displacement	$Δ u$	displacement when rupture criteria reach
back bone energy	BD. Energy	energy under idealized curve
dissipated energy	D. Energy	area under hysteresis curve
equivalent moment	$M e$	$0.8 ρ 1 L w$

Tab.7 Behavioral measures definition

	$ϕ y$	$ϕ u$	$(E I E I g)$	$K$	$M p$	$Δ y$	$M y$	$V u$	$M u$	$Δ u$	BD.Energy*	D.Energy**
Insignificant	$E L$	$A . R$	$E t$	$ρ h$	$ρ h$	$E L$	$A . R$	$ρ h$	$A . R$	$E L$	$ρ min ?$	$ρ min ?$
parameters	A.R	$E L$	$ρ h$	$ρ min ?$	$ρ min ?$	$ρ l$	$ρ h$	$ρ min ?$	$ρ h$	$ρ l$
	$ρ l$	$ρ l$	$ρ min ?$			$ρ h$	$ρ min ?$		$ρ min ?$	$ρ min ?$
	$ρ h$	$ρ h$				$ρ min ?$
	$ρ min ?$

Tab.8 Insignificant parameters

Fig.10 Comparison between empirical data and OpenSEES results

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 parameter	magnitude
$l w$	2286 mm
$t w$	152.4 mm
$(L e L)$	0.077
$(T e L)$	0.066
$(h D)$	2.820
$(ρ l)$	0.0567%
$(ρ t)$	0.0081%
$(ρ min)$	0.0080%
$(P P 0)$	0.005

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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