Análise sísmica de edifícios de concreto armado com alvenarias participantes

Alva, Gerson Moacyr Sisniegas; Rigão, Alessandro Onofre; Kaminski Junior, João; Pinheiro, Marco Antônio Silva

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ORIGINAL ARTICLE • Rev. IBRACON Estrut. Mater. 14 (3) • 2021 • https://doi.org/10.1590/S1983-41952021000300015 copiar

Análise sísmica de edifícios de concreto armado com alvenarias participantes

Autoria SCIMAGO INSTITUTIONS RANKINGS

RESUMO

Neste trabalho são realizadas análises sísmicas em edifício de concreto armado com sistema estrutural de pórticos preenchidos com alvenarias participantes. Para a determinação das forças sísmicas, utiliza-se o método espectral da ABNT NBR 15421:2006. Para a simulação da rigidez axial das alvenarias nos pórticos emprega-se o modelo de diagonal equivalente, segundo diversas expressões encontradas na literatura. O principal objetivo é avaliar as diferenças entre essas expressões da literatura para a diagonal equivalente na resposta sísmica. Outro objetivo é de comparar resultados ao se desconsiderar a rigidez das alvenarias sob a ação sísmica. Os resultados são comentados e fornecem contribuições a engenheiros estruturais para o projeto de estruturas aporticadas de edifícios com alvenarias participantes submetidos a ações sísmicas.

Palavras-chave:
alvenarias participantes; pórticos preenchidos; análise dinâmica; análise estrutural

Authors	Expression
Mainstone [54]	$a = 0.175 {(λ_{H})}^{- 0,4} D$
Hendry [55]	$a = \frac{\sqrt{α_{p}^{2} + α_{v}^{2}}}{2}$	$α_{v} = \frac{π}{λ_{p}} \leq l$		$α_{p} = \frac{π}{2 λ_{p}} \leq h$
Liauw and Kwan [56]	$a = \frac{0.95 s e n (2 θ)}{2 \sqrt{λ_{H}}} D$
Decanini and Fantin [57]: cracked	$λ_{H} \leq 7.85$		$a = (0.010 + \frac{0.707}{λ_{H}}) D$
Decanini and Fantin [57]: cracked	$λ_{H} > 7.85$		$a = (0.040 + \frac{0.470}{λ_{H}}) D$
Paulay and Priestley [58]	$a = \frac{D}{4}$
Durrani and Luo [53]	$a = γ s e n (2 θ) D$
	$γ = 0.32 \sqrt{s e n (2 θ)} {(\frac{H^{4} E t}{m E_{p} I_{p} h})}^{- 0.1}$
	$m = 6 (\frac{1 + 6 E_{V} I_{V} H}{π E_{P} I_{P} L})$
Chrysostomou and Asteris [59]	$a = 0.27 {(λ_{H})}^{- 0.4} D$

Authors	Equivalent strut width (cm)		Lateral stiffness (S.B.)
(EQUIVALENT STRUT WIDTH)	Equivalent strut width (cm)		(N/m)
	Stories	Stories	Stories	Stories
	1-2	3-12	1-2	3-12
Without infill walls	-	-	0.9506 x 10⁸	0.7610 x 10⁸
CSA S304 [⁶6 Canadian Standards Association, Design of Masonry Structures, S304-14, 2014.]	151.17	151.17	2.184 x 10⁸	1.994 x 10⁸
Mainstone [⁵⁴54 R. Mainstone, Supplementary Note on the Stiffness and Strengths of Infilled Frames. Garston: Building Research Station, 1974.]	78.25	76.52	1.589 x 10⁸	1.385 x 10⁸
Durrani and Luo [⁵³53 A. Durrani and Y. Luo, “Seismic retrofit of flat-slab buildings with masonry infills,” in Proc. NCEER Workshop on Seismic Response Mas. Infills, Buffalo, N.Y., 1994, pp. 1–8.]	101.52	99.28	1.779 x 10⁸	1.571 x 10⁸
Liauw and Kwan [⁵⁶56 T. Liauw and K. Kwan, "Nonlinear behavior of non-integral infilled frames," Comp. and Struct., vol. 18, no. 3, pp. 551–560, 1984, http://dx.doi.org/10.1016/0045-7949(84)90070-1. http://dx.doi.org/10.1016/0045-7949(84)9... ]	143.50	139.56	2.121 x 10⁸	1.889 x 10⁸
Decanini and Fantin [⁵⁷57 L. Decanini and G. Fantin, “Modelos simplificados de la mampostería incluida en porticos: caracteristicas de rigidez y resistencia lateral en estado limite,” in J. Argentinas Ing. Estructural, vol. 2, Buenos Aires, Argentina, 1986, pp. 817–836.]	207.06	196.16	2.640 x 10⁸	2.361 x 10⁸
Paulay and Priestley [⁵⁸58 T. Paulay and M. Priestley, Seismic Design of Reinforced Concrete and Masonry Buildings. New York: Wiley, 1992. http://dx.doi.org/10.1002/9780470172841. http://dx.doi.org/10.1002/9780470172841... ]	151.17	151.17	2.184 x 10⁸	1.994 x 10⁸
Chrysostomou and Asteris [⁵⁹59 C. Chrysostomou and P. Asteris, "On the in-plane properties and capacities of infilled frames," Eng. Struct., vol. 41, pp. 385–402, 2012, http://dx.doi.org/10.1016/j.engstruct.2012.03.057. http://dx.doi.org/10.1016/j.engstruct.20... ]	120.73	118.06	1.936 x 10⁸	1.724 x 10⁸

Authors	Shear Building			Plane Frame
(EQUIVALENT STRUT WIDTH)	1st mode	2nd mode	3rd mode	1st mode	2nd mode	3rd mode
Without infill walls	0.745	2.214	3.630	0.580	1.762	3.042
CSA S304 [⁶6 Canadian Standards Association, Design of Masonry Structures, S304-14, 2014.]	1.183	3.525	5.728	1.138	3.600	6.832
Mainstone [⁵⁴54 R. Mainstone, Supplementary Note on the Stiffness and Strengths of Infilled Frames. Garston: Building Research Station, 1974.]	0.993	2.956	4.855	0.960	2.958	5.938
Durrani and Luo [⁵³53 A. Durrani and Y. Luo, “Seismic retrofit of flat-slab buildings with masonry infills,” in Proc. NCEER Workshop on Seismic Response Mas. Infills, Buffalo, N.Y., 1994, pp. 1–8.]	1.052	3.138	5.164	1.026	3.185	5.892
Liauw and Kwan [⁵⁶56 T. Liauw and K. Kwan, "Nonlinear behavior of non-integral infilled frames," Comp. and Struct., vol. 18, no. 3, pp. 551–560, 1984, http://dx.doi.org/10.1016/0045-7949(84)90070-1. http://dx.doi.org/10.1016/0045-7949(84)9... ]	1.156	3.442	5.657	1.117	3.521	6.645
Decanini and Fantin [⁵⁷57 L. Decanini and G. Fantin, “Modelos simplificados de la mampostería incluida en porticos: caracteristicas de rigidez y resistencia lateral en estado limite,” in J. Argentinas Ing. Estructural, vol. 2, Buenos Aires, Argentina, 1986, pp. 817–836.]	1.292	3.846	6.322	1.212	3.910	7.536
Paulay and Priestley [⁵⁸58 T. Paulay and M. Priestley, Seismic Design of Reinforced Concrete and Masonry Buildings. New York: Wiley, 1992. http://dx.doi.org/10.1002/9780470172841. http://dx.doi.org/10.1002/9780470172841... ]	1.183	3.525	5.728	1.138	3.600	6.832
Chrysostomou and Asteris [⁵⁹59 C. Chrysostomou and P. Asteris, "On the in-plane properties and capacities of infilled frames," Eng. Struct., vol. 41, pp. 385–402, 2012, http://dx.doi.org/10.1016/j.engstruct.2012.03.057. http://dx.doi.org/10.1016/j.engstruct.20... ]	1.104	3.289	5.405	1.072	3.350	6.258

Authors	Shear Building	Plane Frame
(EQUIVALENT STRUT WIDTH)	T (s)	T (s)
Without infill walls	1.342	1.724
CSA S304 [⁶6 Canadian Standards Association, Design of Masonry Structures, S304-14, 2014.]	0.845	0.879
Mainstone [⁵⁴54 R. Mainstone, Supplementary Note on the Stiffness and Strengths of Infilled Frames. Garston: Building Research Station, 1974.]	1.001	1.042
Durrani and Luo [⁵³53 A. Durrani and Y. Luo, “Seismic retrofit of flat-slab buildings with masonry infills,” in Proc. NCEER Workshop on Seismic Response Mas. Infills, Buffalo, N.Y., 1994, pp. 1–8.]	0.951	0.975
Liauw and Kwan [⁵⁶56 T. Liauw and K. Kwan, "Nonlinear behavior of non-integral infilled frames," Comp. and Struct., vol. 18, no. 3, pp. 551–560, 1984, http://dx.doi.org/10.1016/0045-7949(84)90070-1. http://dx.doi.org/10.1016/0045-7949(84)9... ]	0.865	0.895
Decanini and Fantin [⁵⁷57 L. Decanini and G. Fantin, “Modelos simplificados de la mampostería incluida en porticos: caracteristicas de rigidez y resistencia lateral en estado limite,” in J. Argentinas Ing. Estructural, vol. 2, Buenos Aires, Argentina, 1986, pp. 817–836.]	0.774	0.825
Paulay and Priestley [⁵⁸58 T. Paulay and M. Priestley, Seismic Design of Reinforced Concrete and Masonry Buildings. New York: Wiley, 1992. http://dx.doi.org/10.1002/9780470172841. http://dx.doi.org/10.1002/9780470172841... ]	0.845	0.879
Chrysostomou and Asteris [⁵⁹59 C. Chrysostomou and P. Asteris, "On the in-plane properties and capacities of infilled frames," Eng. Struct., vol. 41, pp. 385–402, 2012, http://dx.doi.org/10.1016/j.engstruct.2012.03.057. http://dx.doi.org/10.1016/j.engstruct.20... ]	0.906	0.933

Floor	Without infill walls	CSA S304 [⁶6 Canadian Standards Association, Design of Masonry Structures, S304-14, 2014.]	Mainstone [⁵⁴54 R. Mainstone, Supplementary Note on the Stiffness and Strengths of Infilled Frames. Garston: Building Research Station, 1974.]	Durrani and Luo [⁵³53 A. Durrani and Y. Luo, “Seismic retrofit of flat-slab buildings with masonry infills,” in Proc. NCEER Workshop on Seismic Response Mas. Infills, Buffalo, N.Y., 1994, pp. 1–8.]	Liauw and Kwan [⁵⁶56 T. Liauw and K. Kwan, "Nonlinear behavior of non-integral infilled frames," Comp. and Struct., vol. 18, no. 3, pp. 551–560, 1984, http://dx.doi.org/10.1016/0045-7949(84)90070-1. http://dx.doi.org/10.1016/0045-7949(84)9... ]	Decanini and Fantin [⁵⁷57 L. Decanini and G. Fantin, “Modelos simplificados de la mampostería incluida en porticos: caracteristicas de rigidez y resistencia lateral en estado limite,” in J. Argentinas Ing. Estructural, vol. 2, Buenos Aires, Argentina, 1986, pp. 817–836.]	Chrysostomou and Asteris [⁵⁹59 C. Chrysostomou and P. Asteris, "On the in-plane properties and capacities of infilled frames," Eng. Struct., vol. 41, pp. 385–402, 2012, http://dx.doi.org/10.1016/j.engstruct.2012.03.057. http://dx.doi.org/10.1016/j.engstruct.20... ]
12	60.23	79.80	70.84	73.47	78.59	85.36	76.05
11	51.12	73.40	63.43	66.39	71.99	79.25	69.25
10	42.25	66.25	55.76	58.93	64.71	72.19	61.88
9	35.51	59.99	49.47	52.76	58.42	65.79	55.62
8	30.26	54.21	44.00	47.25	52.68	59.73	49.97
7	26.50	48.75	39.31	42.34	47.32	53.82	44.83
6	23.87	43.45	35.12	37.81	42.17	47.89	39.98
5	21.99	38.15	31.16	33.44	37.04	41.81	35.22
4	20.15	32.47	27.02	28.82	31.55	35.26	30.15
3	17.61	26.12	22.21	23.55	25.38	28.00	24.41
2	13.40	18.66	16.14	16.70	18.07	19.64	17.50
1	8.32	10.38	9.32	9.53	10.11	10.77	9.87
Base	0	0	0	0	0	0	0

Expression	Total shear force (kN)
Without infill walls	351.20
CSA 304 [⁶6 Canadian Standards Association, Design of Masonry Structures, S304-14, 2014.]	551.61
Mainstone [⁵⁴54 R. Mainstone, Supplementary Note on the Stiffness and Strengths of Infilled Frames. Garston: Building Research Station, 1974.]	463.77
Durrani and Luo [⁵³53 A. Durrani and Y. Luo, “Seismic retrofit of flat-slab buildings with masonry infills,” in Proc. NCEER Workshop on Seismic Response Mas. Infills, Buffalo, N.Y., 1994, pp. 1–8.]	490.98
Liauw and Kwan [⁵⁶56 T. Liauw and K. Kwan, "Nonlinear behavior of non-integral infilled frames," Comp. and Struct., vol. 18, no. 3, pp. 551–560, 1984, http://dx.doi.org/10.1016/0045-7949(84)90070-1. http://dx.doi.org/10.1016/0045-7949(84)9... ]	538.01
Decanini and Fantin [⁵⁷57 L. Decanini and G. Fantin, “Modelos simplificados de la mampostería incluida en porticos: caracteristicas de rigidez y resistencia lateral en estado limite,” in J. Argentinas Ing. Estructural, vol. 2, Buenos Aires, Argentina, 1986, pp. 817–836.]	599.51
Paulay and Priestley [⁵⁸58 T. Paulay and M. Priestley, Seismic Design of Reinforced Concrete and Masonry Buildings. New York: Wiley, 1992. http://dx.doi.org/10.1002/9780470172841. http://dx.doi.org/10.1002/9780470172841... ]	551.61
Chrysostomou and Asteris [⁵⁹59 C. Chrysostomou and P. Asteris, "On the in-plane properties and capacities of infilled frames," Eng. Struct., vol. 41, pp. 385–402, 2012, http://dx.doi.org/10.1016/j.engstruct.2012.03.057. http://dx.doi.org/10.1016/j.engstruct.20... ]	514.74

Expression	N(kN)	a (cm)	σ (MPa)
CSA S304 [⁶6 Canadian Standards Association, Design of Masonry Structures, S304-14, 2014.]	214.46	151.17	0.747
Mainstone [⁵⁴54 R. Mainstone, Supplementary Note on the Stiffness and Strengths of Infilled Frames. Garston: Building Research Station, 1974.]	195.37	76.52	1.344
Durrani and Luo [⁵³53 A. Durrani and Y. Luo, “Seismic retrofit of flat-slab buildings with masonry infills,” in Proc. NCEER Workshop on Seismic Response Mas. Infills, Buffalo, N.Y., 1994, pp. 1–8.]	159.53	99.28	0.846
Liauw and Kwan [⁵⁶56 T. Liauw and K. Kwan, "Nonlinear behavior of non-integral infilled frames," Comp. and Struct., vol. 18, no. 3, pp. 551–560, 1984, http://dx.doi.org/10.1016/0045-7949(84)90070-1. http://dx.doi.org/10.1016/0045-7949(84)9... ]	203.91	139.56	0.769
Decanini and Fantin [⁵⁷57 L. Decanini and G. Fantin, “Modelos simplificados de la mampostería incluida en porticos: caracteristicas de rigidez y resistencia lateral en estado limite,” in J. Argentinas Ing. Estructural, vol. 2, Buenos Aires, Argentina, 1986, pp. 817–836.]	250.58	196.16	0.672
Paulay and Priestley [⁵⁸58 T. Paulay and M. Priestley, Seismic Design of Reinforced Concrete and Masonry Buildings. New York: Wiley, 1992. http://dx.doi.org/10.1002/9780470172841. http://dx.doi.org/10.1002/9780470172841... ]	214.46	151.17	0.747
Chrysostomou and Asteris [⁵⁹59 C. Chrysostomou and P. Asteris, "On the in-plane properties and capacities of infilled frames," Eng. Struct., vol. 41, pp. 385–402, 2012, http://dx.doi.org/10.1016/j.engstruct.2012.03.057. http://dx.doi.org/10.1016/j.engstruct.20... ]	184.40	118.06	0.822

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[1] Corresponding author: Gerson Moacyr Sisniegas Alva. E-mail: alva_gerson@yahoo.com.br