Seismic analysis of reinforced concrete buildings with participating masonry infills

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

doi:10.1590/S1983-41952021000300015

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Revista IBRACON de Estruturas e Materiais

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

Seismic analysis of reinforced concrete buildings with participating masonry infills

Análise sísmica de edifícios de concreto armado com alvenarias participantes

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

In this paper, seismic analyses are performed of a reinforced concrete frame building with participating masonry walls are carried out. The spectral method of the Brazilian code – ABNT 15421:2006 – was used to obtain the lateral seismic loads. The equivalent diagonal-strut model was employed to simulate the axial stiffness of the masonry walls in the frames, according to different formulations founded in literature. The main purpose is to evaluate the differences implemented by the different formulations for the equivalent strut on the seismic response. This paper also aims at comparing results obtained when the masonry stiffness is not considered under seismic loads. The results obtained are analyzed with the purpose of providing contributions for structural engineers in the design of framed structure buildings with participating masonry walls subjected to seismic loads.

Keywords:
participating masonry, infilled frames, dynamic analysis; structural analysis

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