Effects of Staircase on the Seismic Behavior of RC Moment Frame Buildings

NOORIFARD, Azadeh; TABESHPOUR, Mohammad Reza

doi:10.21307/acee-2018-058

Figures & Tables

A chart for effects of staircase on seismic behavior of structure and variables studied in defined groups

Architectural plan of southern building with a width of 6 meter and staircase at corner

Architectural plan of southern building with a width of 10 meter and staircase at corner

Architectural plan of northern building with a width of 10 meter and staircase at the middle of length

Model of southern building with a width of 6 meter and staircase slabs

Drift ratio of southern building with a width of 6 meter in X direction

Drift ratio of southern building with a width of 6 meter in Y direction

K-shaped bracing performance of staircase attached to the structure

Southern building with a width of 10 meter; (a) All frames with the same dimension, (b) Frame with shorter length on the landing, (c) Both frames of staircase with shorter length

Northern building with a width of 10 meter; (a) All frames with the same dimension, (b) Frame with shorter length on the landing, (c) Both frames of staircase with shorter length

Southern building with a width of 6 meter; (a) Main moment frame, (b) Hinge connections on the side of staircase, (c) Extra column on the opposite side of the staircase, (d) Columns with larger cross section on the opposite side of the staircase

Shear distribution under seismic force along Y direction (ton): (Left side) Model without stair case, (Right side) Model with staircase

Moment distribution under seismic force along Y direction (ton.m): (Left side) Model without stair case, (Right side) Model with staircase

Shear distribution under seismic force along X direction (ton): (Left side) Model without stair case, (Right side) Model with staircase

Moment distribution under seismic force along X direction (ton.m): (Left side) Model without stair case, (Right side) Model with staircase

Staircase isolated from master structure

Concrete and rebar properties

Mass per unit volume kg/m³	Modulus of Elasticity N/mm²	Poisson’s Ratio-	f’_c Concrete compressive Strength N/mm²	f_y Bending Reinforcement Yield Stress N/mm²	f_ys Shear Reinforcement Yield Stress N/mm²
2500	24516	0.15	24.5	392	392

Ratio of the maximum relative story drift to the average relative story drift in story 3 of southern building with a width of 10 meter and staircase at the corner

	EQX	EQXP	EQXN	EQY	EQYP	EQYN
(a) Bare frame	1.00	1.11	1.07	1.02	1.06	1.02
(b) Bare frame with slabs of stair	1.14	1.06	1.24	1.15	1.09	1.18
(c) Infilled frame	1.12	1.06	1.18	1.00	1.02	1.10
(d) Infilled frame with slabs of stair	1.19	1.12	1.25	1.12	1.05	1.21

Eccentricity of northern building with a width of 10 meter and staircase at the middle of length

	Story 1		Story 2		Story 3		Story 4		Story 5
	%ex	%ey	%ex	%ey	%ex	%ey	%ex	%ey	%ex	%ey
(a) Bare frame	2.12	1.23	0.96	3.99	2.54	2.81	3.49	2.02	5.62	2.50
(b) Bare frame with slabs of stair	-1.86	-0.21	-6.00	2.87	-6.97	1.83	-7.82	1.09	-8.07	1.43
(c) Infilled frame	2.36	3.28	1.59	7.73	2.95	8.11	3.67	8.47	5.71	10.22
(d) Infilled frame with slabs of stair	0.15	2.01	-1.87	6.67	-1.06	7.08	-0.59	7.45	1.21	9.14

Ratio of the maximum relative story drift to the average relative story drift in story 3 of southern building with a width of 6 meter and staircase at the corner

	EQX	EQXP	EQXN	EQY	EQYP	EQYN
(a) Bare frame	1.03	1.12	1.05	1.01	1.02	1.04
(b) Bare frame with slabs of stair	1.43	1.33	1.52	1.12	1.20	1.10
(c) Infilled frame	1.07	1.12	1.01	1.04	1.04	1.08
(d) Infilled frame with slabs of stair	1.20	1.14	1.25	1.05	1.15	1.00

Eccentricity of southern building with a width of 10 meter and staircase at the corner

	Story 1		Story 2		Story 3		Story 4		Story 5
	%ex	%ey	%ex	%ey	%ex	%ey	%ex	%ey	%ex	%ey
(a) Bare frame	4.26	6.61	2.65	6.50	2.32	5.58	1.88	5.01	-1.46	2.28
(b) Bare frame with slabs of stair	10.70	11.64	13.24	12.40	15.63	12.62	17.38	12.92	17.27	11.12
(c) Infilled frame	4.03	9.49	2.51	11.47	4.52	12.57	6.19	13.48	6.02	12.48
(d) Infilled frame with slabs of stair	7.52	13.47	7.41	15.65	9.66	16.93	11.37	17.83	11.19	16.67

Period and mode shape of southern building with a width of 10 meter and staircase at the corner

	Mode 1				Mode 2				Mode 3
	Period (s)	Dir.	UX	UY	Period (s)	Dir.	UX	UY	Period (s)	Dir.	UX	UY
(a) Bare frame	1.01	X	73.76	0.00	0.97	Y	0.01	73.43	0.82	T	0.19	1.04
(b) Bare frame with slabs of stair	0.92	X	61.95	3.17	0.83	Y	8.78	57.92	0.69	T	4.47	15.91
(c) Infilled frame	0.89	X	74.93	0.00	0.62	T	1.36	3.37	0.59	Y	0.05	77.04
(d) Infilled frame with slabs of stair	0.84	X	71.22	0.08	0.59	T	4.24	26.98	0.53	Y	1.22	53.69

Period and mode shape of southern building with a width of 6 meter and staircase at the corner

	Mode 1				Mode 2				Mode 3
	Period (s)	Dir.	UX	UY	Period (s)	Dir.	UX	UY	Period (s)	Dir.	UX	UY
(a) Bare frame	0.90	X	69.45	0.00	0.74	Y	0.03	68.82	0.70	T	1.15	1.04
(b) Bare frame with slabs of stair	0.75	X	46.33	1.73	0.59	Y	14.37	47.47	0.52	T	12.26	24.05
(c) Infilled frame	0.75	X	72.73	0.00	0.48	T	0.84	0.72	0.42	Y	0.00	78.42
(d) Infilled frame with slabs of stair	0.60	X	69.86	0.01	0.43	T	4.44	5.72	0.38	Y	0.32	72.76

Eccentricity of southern building with a width of 6 meter and staircase at the corner

	Story 1		Story 2		Story 3		Story 4		Story 5
	%ex	%ey	%ex	%ey	%ex	%ey	%ex	%ey	%ex	%ey
(a) Bare frame	-0.33	4.11	-0.48	3.42	-0.15	2.65	-0.33	0.69	0.68	-2.56
(b) Bare frame with slabs of stair	-7.05	13.96	-12.17	18.51	-13.03	19.89	-13.98	19.94	-14.09	18.70
(c) Infilled frame	-0.37	-0.08	-0.44	-0.04	-0.07	-1.22	0.51	-2.87	2.17	-5.76
(d) Infilled frame with slabs of stair	-4.35	9.58	-6.84	13.87	-6.57	14.71	-5.78	14.18	-3.89	12.24

Period and mode shape of northern building with a width of 10 meter and staircase at the middle of length

	Mode 1				Mode 2				Mode 3
	Period (s)	Dir.	UX	UY	Period (s)	Dir.	UX	UY	Period (s)	Dir.	UX	UY
(a) Bare frame	1.00	X	73.01	0.14	0.90	Y	0.37	68.61	0.79	T	1.03	3.39
(b) Bare frame with slabs of stair	0.87	X	73.39	0.03	0.81	Y	0.83	50.39	0.74	T	1.04	23.82
(c) Infilled frame	0.76	X	72.82	0.05	0.57	Y	1.29	63.40	0.53	T	3.28	15.78
(d) Infilled frame with slabs of stair	0.71	X	72.25	0.00	0.53	Y	0.30	74.46	0.52	T	4.53	5.22

Ratio of the maximum relative story drift to the average relative story drift in story 2 of northern building with a width of 10 meter and staircase at the middle of length

	EQX	EQXP	EQXN	EQY	EQYP	EQYN
All frames the same	1.07	1.04	1.19	1.03	1.02	1.08
One different frame	1.08	1.21	1.03	1.01	1.01	1.06
Two different frames	1.07	1.03	1.19	1.00	1.04	1.04

Ratio of the maximum relative story drift to the average relative story drift in story 3 of northern building with a width of 10 meter and staircase at the middle of length

	EQX	EQXP	EQXN	EQY	EQYP	EQYN
(a) Bare frame	1.05	1.08	1.18	1.05	1.00	1.09
(b) Bare frame with slabs of stair	1.03	1.12	1.18	1.09	1.13	1.03
(c) Infilled frame	1.17	1.08	1.29	1.07	0.98	1.16
(d) Infilled frame with slabs of stair	1.18	1.08	1.27	0.98	1.05	1.07

Period and mode shape of southern building with a width of 6 meter

	Mode 1				Mode 2				Mode 3
	Period (s)	Dir.	UX	UY	Period (s)	Dir.	UX	UY	Period (s)	Dir.	UX	UY
Bare frame	0.90	X	69.45	0.00	0.74	Y	0.03	68.82	0.70	T	1.15	1.04
Frame with staircase slabs	0.75	X	46.33	1.73	0.59	Y	14.37	47.47	0.52	T	12.26	24.05
Frame with stringer beams	0.93	X	71.58	0.05	0.72	T	0.29	14.12	0.62	Y	0.00	58.87

Effects of Staircase on the Seismic Behavior of RC Moment Frame Buildings

Figures & Tables

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Concrete and rebar properties

Ratio of the maximum relative story drift to the average relative story drift in story 3 of southern building with a width of 10 meter and staircase at the corner

Eccentricity of northern building with a width of 10 meter and staircase at the middle of length

Ratio of the maximum relative story drift to the average relative story drift in story 3 of southern building with a width of 6 meter and staircase at the corner

Eccentricity of southern building with a width of 10 meter and staircase at the corner

Period and mode shape of southern building with a width of 10 meter and staircase at the corner

Period and mode shape of southern building with a width of 6 meter and staircase at the corner

Eccentricity of southern building with a width of 6 meter and staircase at the corner

Period and mode shape of northern building with a width of 10 meter and staircase at the middle of length

Ratio of the maximum relative story drift to the average relative story drift in story 2 of northern building with a width of 10 meter and staircase at the middle of length

Ratio of the maximum relative story drift to the average relative story drift in story 3 of northern building with a width of 10 meter and staircase at the middle of length

Period and mode shape of southern building with a width of 6 meter

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