Influence of shear walls on the structural behavior of a multi-storey concrete building according to Brazilian Technical Code ABNT NBR 15421:2006

Seruti, Carlos Alexandre; Lima, Eduardo Fernandes; Lima, Silvio de Souza; Santos, Sergio Hampshire de Carvalho

doi:10.1590/S1983-41952023000500004

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Revista IBRACON de Estruturas e Materiais

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ORIGINAL ARTICLE • Rev. IBRACON Estrut. Mater. 16 (5) • 2023 • https://doi.org/10.1590/S1983-41952023000500004 copy

Influence of shear walls on the structural behavior of a multi-storey concrete building according to Brazilian Technical Code ABNT NBR 15421:2006

Influência de pilares-parede no comportamento estrutural de um edifício de múltiplos pavimentos de concreto de acordo com a norma técnica brasileira ABNT NBR 15421:2006

Authorship SCIMAGO INSTITUTIONS RANKINGS

abstract:

This paper presents a comparative study of the influence of shear walls on the behavior of a multi-storey concrete building when subjected to seismic actions. Two structures with different earthquake-resistant systems were evaluated. One is composed of concrete frames with usual detailing in both directions (x and y), and the other one is formed by a dual system, composed of frames and shear walls with usual detailing. The Equivalent Lateral Force procedure and the Modal Response Spectrum analysis presented by the Brazilian Technical Code ABNT NBR 15421:2006 were considered. The dual system building presented a greater stiffness with the shear walls arranged parallel to direction y. In the x direction, the responses are equivalent in both buildings. The horizontal forces obtained by the Equivalent Lateral Force method at the base of the buildings were greater than the Modal Response Spectrum method.

Keywords:
seismic analysis; equivalent lateral force procedure; modal response spectrum analysis

Elements and properties	Values
Columns section	(60 x 60) cm²
Beams section	(30 x 60) cm²
Slabs thickness	20 cm
Walls thickness	30 cm
Floor height	3.0 m
Concrete compression strength (f_ck)	30 MPa
Concrete specific weight	25 kN/m³
Concrete modulus of elasticity	30000 MPa
Poisson coefficient	0.20

Parameters	Direction x	Direction y
1st period of structure (T) - obtained computationally:	0.88 s	0.92 s
Period limitation coefficient (C_up) - Table 10*:	1.5	1.5
Period coefficients: C_T:	0.0466	0.0466
x:	0.9	0.9
Height of the structure above the base (h_n):	36 m	36 m
Approximate natural period of the structure (T_a): C_T · h_n^x	1.17 s	1.17 s
C_T · h_n^x · C_up > T	1.78 s	1.78 s
Use importance factor (I) - Table 4*:	1.0	1.0
Response modification coefficient (R) - Table 6*:	3.0	3.0
I / R ratio:	0.3333	0.3333
Design characteristic acceleration (a_g): 0.15 g (Zone 4) - Table 1*:	1.47 m/s²	1.47 m/s²
Seismic amplification factor for the period of 0.0 s (C_a) - Table 3*:	1.5	1.5
Spectral acceleration for the period of 0.0 s (a_gs0): C_a · a_g	2.21 m/s²	2.21 m/s²
Seismic amplification factor for the period of 1.0 s (C_v) - Table 3*:	2.2	2.2
Spectral acceleration for the period of 1.0 s (a_gs1): C_v · a_g	3.23 m/s²	3.23 m/s²
Seismic response coefficient (C_s): 2.5 I a_gs0 / (g R)	0.19	0.19
Maximum seismic response coefficient (C_s): I a_gs1 / (g R T)	0.13	0.12
Distribution exponent (k) for 0.5 s < T < 2.5 s: (T + 1.5) / 2	1.19	1.21
Amplification coefficient of the displacements (C_d) - Table 6^*:	2.5	2.5
C_d / R ratio:	0.8333	0.8333

Storey	w_x [kN]	Direction x			Direction y
Storey	w_x [kN]	C_vx	F_x [kN]	M_ta,x [kN·m]	C_vy	F_y [kN]	M_ta,y [kN·m]
1st	2058.09	0.0086	26.08	15.65	0.0083	24.10	19.28
2nd	2058.09	0.0198	59.58	35.75	0.0193	55.76	44.61
3rd	2058.09	0.0320	96.61	57.96	0.0315	91.09	72.87
4th	2058.09	0.0451	136.12	81.67	0.0446	129.03	103.22
5th	2058.09	0.0589	177.60	106.56	0.0584	169.03	135.23
6th	2058.09	0.0732	220.71	132.42	0.0728	210.77	168.62
7th	2058.09	0.0880	265.22	159.13	0.0878	254.01	203.20
8th	2058.09	0.1031	310.98	186.59	0.1031	298.56	238.85
9th	2058.09	0.1187	357.85	214.71	0.1190	344.31	275.45
10th	2058.09	0.1346	405.74	243.44	0.1351	391.14	312.91
11th	2058.09	0.1507	454.55	272.73	0.1517	438.97	351.17
Roof	2058.09	0.1672	504.22	302.53	0.1685	487.72	390.18
Σ (Base)	24697.07	1.0	3015.28		1.0	2894.48

Storey	Direction x				Direction y
Storey	δ_xe [cm]	δ_x [cm]	Δ_x [cm]	θ_x [× 10^-4]	δ_ye [cm]	δ_y [cm]	Δ_y[cm]	θ_y [× 10^-4]
1st	0.25	0.64	0.64	85.19	0.25	0.64	0.64	88.80
2nd	0.69	1.72	1.08	66.91	0.70	1.74	1.10	71.00
3rd	1.15	2.88	1.16	44.38	1.17	2.94	1.20	47.60
4th	1.62	4.04	1.16	30.87	1.66	4.14	1.20	33.37
5th	2.07	5.16	1.12	22.37	2.13	5.32	1.18	24.34
6th	2.49	6.23	1.07	16.58	2.58	6.45	1.13	18.16
7th	2.89	7.23	1.00	12.40	3.00	7.50	1.06	13.66
8th	3.25	8.13	0.90	9.22	3.39	8.47	0.96	10.24
9th	3.57	8.91	0.79	6.73	3.73	9.32	0.85	7.55
10th	3.83	9.57	0.65	4.73	4.01	10.03	0.72	5.38
11th	4.03	10.07	0.50	3.09	4.24	10.60	0.56	3.61
Roof	4.17	10.41	0.35	1.79	4.40	11.01	0.41	2.19

Storey	Direction x			Direction y
Storey	δ_xe [cm]	δ_x [cm]	Δ_x [cm]	δ_ye [cm]	δ_y [cm]	Δ_y[cm]
1st	0.63	0.52	0.52	0.63	0.52	0.52
2nd	1.68	1.40	0.88	1.70	1.42	0.89
3rd	2.80	2.34	0.93	2.85	2.37	0.96
4th	3.90	3.25	0.91	3.98	3.32	0.94
5th	4.94	4.12	0.87	5.07	4.22	0.91
6th	5.92	4.93	0.81	6.09	5.07	0.85
7th	6.80	5.67	0.74	7.02	5.85	0.78
8th	7.59	6.33	0.66	7.87	6.55	0.70
9th	8.26	6.89	0.56	8.59	7.16	0.61
10th	8.81	7.34	0.46	9.20	7.66	0.50
11th	9.22	7.68	0.34	9.66	8.05	0.39
Roof	9.50	7.92	0.23	10.00	8.33	0.28

Parameters	Direction x	Direction y
1st period of structure (T) - obtained computationally:	0.92 s	0.65 s
Period limitation coefficient (C_up) - Table 10^* * See ABNT NBR 15421 [3]. :	1.5	1.5
Period coefficients: C_T:	0.0466	0.0488
x:	0.9	0.75
Height of the structure above the base (h_n):	36 m	36 m
Approximate natural period of the structure (T_a): C_T · h_n^x	1.17 s	0.72 s
C_T · h_n^x · C_up > T	1.78 s	1.08 s
Use importance factor (I) - Table 4*:	1.0	1.0
Response modification coefficient (R) - Table 6*:	3.0	4.5
I / R ratio:	0.3333	0.2222
Design characteristic acceleration (a_g): 0.15 g (Zone 4) - Table 1*:	1.47 m/s²	1.47 m/s²
Seismic amplification factor for the period of 0.0 s (C_a) - Table 3*:	1.5	1.5
Spectral acceleration for the period of 0.0 s (a_gs0): C_a · a_g	2.21 m/s²	2.21 m/s²
Seismic amplification factor for the period of 1.0 s (C_v) - Table 3*:	2.2	2.2
Spectral acceleration for the period of 1.0 s (a_gs1): C_v · a_g	3.23 m/s²	3.23 m/s²
Seismic response coefficient (C_s): 2.5 I a_gs0 / (g R)	0.19	0.13
Maximum seismic response coefficient (C_s): I a_gs1 / (g R T)	0.12	0.11
Distribution exponent (k) for 0.5 s < T < 2.5 s: (T + 1.5) / 2	1.21	1.08
Amplification coefficient of the displacements (C_d) - Table 6*:	2.5	4.0
C_d / R ratio:	0.8333	0.8889

Storey	w_x [kN]	Direction x			Direction y
Storey	w_x [kN]	C_vx	F_x [kN]	M_ta,x [kN·m]	C_vy	F_y [kN]	M_ta,y [kN·m]
1st	2238.00	0.0083	26.81	16.09	0.0110	33.34	26.67
2nd	2238.00	0.0193	62.00	37.20	0.0232	70.24	56.19
3rd	2238.00	0.0315	101.24	60.75	0.0358	108.61	86.89
4th	2238.00	0.0446	143.38	86.03	0.0488	147.97	118.38
5th	2238.00	0.0584	187.80	112.68	0.0621	188.08	150.47
6th	2238.00	0.0728	234.14	140.48	0.0755	228.81	183.05
7th	2238.00	0.0878	282.12	169.27	0.0891	270.05	216.04
8th	2238.00	0.1031	331.57	198.94	0.1029	311.73	249.39
9th	2238.00	0.1189	382.34	229.40	0.1168	353.81	283.05
10th	2238.00	0.1351	434.30	260.58	0.1308	396.24	316.99
11th	2238.00	0.1516	487.37	292.42	0.1449	438.99	351.19
Roof	2238.00	0.1684	541.46	324.84	0.1591	482.04	385.63
Σ (Base)	26856.00	1.0	3214.54		1.0	3029.91

Storey	Direction x				Direction y
Storey	*δ_xe* [cm]**	δ_x [cm]	Δ_x [cm]	θ_x [× 10^-4]	*δ_ye* [cm]**	δ_y [cm]	Δ_y[cm]	θ_y [× 10^-4]
1st	0.26	0.66	0.66	88.11	0.06	0.26	0.26	23.13
2nd	0.72	1.79	1.13	70.39	0.20	0.79	0.53	21.88
3rd	1.21	3.01	1.23	46.99	0.38	1.50	0.71	18.28
4th	1.70	4.24	1.22	32.75	0.59	2.34	0.84	15.03
5th	2.17	5.43	1.19	23.74	0.81	3.25	0.91	12.27
6th	2.62	6.56	1.13	17.60	1.05	4.20	0.95	9.98
7th	3.05	7.61	1.05	13.15	1.29	5.15	0.95	8.09
8th	3.43	8.57	0.95	9.78	1.52	6.08	0.93	6.53
9th	3.76	9.40	0.83	7.14	1.74	6.96	0.89	5.25
10th	4.04	10.09	0.69	5.01	1.95	7.80	0.84	4.21
11th	4.25	10.62	0.53	3.29	2.15	8.58	0.78	3.37
Roof	4.40	10.99	0.37	1.92	2.33	9.31	0.73	2.64

Storey	Direction x			Direction y
Storey	*δ_xe* [cm]**	δ_x [cm]	Δ_x [cm]	*δ_ye* [cm]**	δ_y [cm]	Δ_y[cm]
1st	0.64	0.53	0.53	0.21	0.19	0.19
2nd	1.73	1.44	0.91	0.65	0.58	0.39
3rd	2.89	2.41	0.97	1.23	1.10	0.52
4th	4.03	3.36	0.95	1.92	1.71	0.61
5th	5.11	4.26	0.90	2.67	2.37	0.66
6th	6.12	5.10	0.84	3.44	3.06	0.69
7th	7.05	5.87	0.77	4.22	3.75	0.69
8th	7.86	6.55	0.68	4.98	4.43	0.68
9th	8.56	7.13	0.58	5.71	5.07	0.64
10th	9.12	7.60	0.47	6.39	5.68	0.61
11th	9.55	7.96	0.35	7.03	6.25	0.57
Roof	9.84	8.20	0.24	7.62	6.77	0.52

	Direction x				Direction y
	ELF		Spectral		ELF		Spectral
	Hx [kN]	δx [cm]	Htx [kN]	δtx [cm]	Hy [kN]	δy [cm]	Hty [kN]	δty [cm]
	3198	10.41	2486	7.92	2988	11.01	2384	8.33
	3360	10.99	2615	8.20	3509	9.31	2224	6.77
Difference [%]	+ 5.1	+ 5.6	+ 5.2	+ 3.5	+ 17.4	- 15.4	- 6.7	- 18.7

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[1] Corresponding author: Carlos Alexandre Seruti. E-mail: carlosseruti@gmail.com