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

doi:10.1007/s11709-017-0418-6

Frontiers of Structural and Civil Engineering

2018, Vol. 12

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

本期目录

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.

Key words： RC wall hysteretic measures RC wall design parameters empirical relations numerical simulations RC rectangular wall plastic hinge

收稿日期: 2016-05-07 出版日期: 2018-03-08

Corresponding Author(s): A. ARAB

引用本文:

. [J]. Frontiers of Structural and Civil Engineering, 2018, 12(1): 3-15.
A. ARAB, Ma. R. BANAN, Mo. R. BANAN, S. FARHADI. Estimation of relations among hysteretic response measures and design parameters for RC rectangular shear walls. Front. Struct. Civ. Eng., 2018, 12(1): 3-15.

链接本文:

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

Fig.1

Fig.2

Fig.3

Tab.1

Fig.4

Fig.5

Tab.2

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

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

Fig.6

Fig.7

Fig.8

Fig.9

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

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

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

	$ϕ y$	$ϕ u$	$(E I E I g)$	$K$	$M p$	$Δ y$	$M y$	$V u$	$M u$	$Δ u$	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

Fig.10

Tab.9

Fig.11

Fig.12

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

Fig.13

Fig.14

Fig.15

Fig.16

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