Analysis of the equivalent strut width expressions for modeling masonry infilled frames

Queiroz, Luiz Flávio de; Alva, Gerson Moacyr Sisniegas

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Artigos • Matéria (Rio J.) 26 (03) • 2021 • https://doi.org/10.1590/S1517-707620210003.13022 copy

Analysis of the equivalent strut width expressions for modeling masonry infilled frames

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

The focus of this paper is to evaluate the effects of considering masonry infill walls as resistant elements in concrete structures. Recommendations of the recently updated Brazilian code for the design of structural masonry - ABNT NBR 16868-1 - were included in the analysis of this paper. Expressions presented in the literature and in Brazilian code were used to determine the equivalent diagonal width. Two-dimensional models with the aid of the Finite Element Method (FEM) were used to determine the equivalent diagonal width allowing the comparison with analytical expressions from the literature. The differences were also analyzed in terms of lateral displacements of a multistory reinforced concrete building with concrete masonry infill walls. The simulations were carried out using ANSYS and FTOOL programs. Significant differences between the values of the equivalent diagonal width obtained by the expressions from the literature were observed in all the single-story single-bay frames. Such differences had influence on the lateral displacements of the single-story frames and the multistory building. For the cases analyzed, the expression proposed by Mainstone was the one that led to the best results in comparison to MEF simulations.

Keywords
Participating masonry; Structural analysis; Infill frames

AUTORES	EXPRESSÕES ANALÍTICAS
MAINSTONE [¹⁷17 MAINSTONE, R.J. “Supplementary note on the stiffness and strengths of infilled frames”, Building Research Station, Garston, UK, 1974.]	$w = 0, 175 \cdot {(λ_{H})}^{- 0, 4} \cdot D$
HENDRY [¹⁸18 HENDRY, A.W. Structural Brickwork, London, MacMillan, 1981.]	$w = \frac{\sqrt{α_{p}^{2} + α_{v}^{2}}}{2} α_{v} = \frac{π}{λ_{v}} \leq l α_{p} = \frac{π}{2 \cdot λ_{p}} \leq h$
LIAUW e KWAN [¹⁹19 LIAUW, T.C., KWAN, K.H. “Nonlinear behavior of non-integral infilled frames”. Computers and Structures, v. 18, n. 3, pp. 551-560, 1984.]	$w = \frac{0, 95 \cdot sen (2 θ)}{2 \cdot \sqrt{λ_{H}}} \cdot D$
DECANINI e FANTIN [²⁰20 DECANINI, L.D., FANTIN, G.E. “Modelos simplificados de la mampostería incluida en porticos. Caracteristicas de rigidez y resistencia lateral en estado limite”, In: Jornadas Argentinas de Ingeniería Estructural, v. 2, pp. 817-836, Buenos Aires, 1986.]: NÃO FISSURADO-1	$\begin{array}{cc} λ_{H} \leq 7, 85 & λ_{H} > 7, 85 \\ w = (0, 085 + \frac{0, 748}{λ_{H}}) \cdot D & w = (0, 130 + \frac{0, 393}{λ_{H}}) \cdot D \end{array}$
DECANINI e FANTIN [²⁰20 DECANINI, L.D., FANTIN, G.E. “Modelos simplificados de la mampostería incluida en porticos. Caracteristicas de rigidez y resistencia lateral en estado limite”, In: Jornadas Argentinas de Ingeniería Estructural, v. 2, pp. 817-836, Buenos Aires, 1986.]: FISSURADO-2	$\begin{array}{cc} λ_{H} \leq 7, 85 & λ_{H} > 7, 85 \\ w = (0, 010 + \frac{0, 707}{λ_{H}}) \cdot D & w = (0, 040 + \frac{0, 470}{λ_{H}}) \cdot D \end{array}$
PAULAY e PRIESTLEY [²¹21 PAULAY, T., PRIESTLEY, M.J.N. “Seismic design of reinforced concrete and masonry buildings”, New York, Wiley, 1992.]	$w = \frac{D}{4}$
DURRANI e LUO [²²22 DURRANI, A.J., LUO, Y.H. “Seismic retrofit of flat-slab buildings with masonry infills”, Proceedings from the NCEER Workshop on Seismic Response of Masonry Infills, National Center for Engineering Earthquake, Buffalo, N.Y., 1994.]	$\begin{matrix} w = γ \cdot sen (2 θ) \cdot D \\ γ = 0, 32 \sqrt{sen (2 θ)} \cdot {(\frac{H^{4} \cdot E \cdot t}{m \cdot E_{p} \cdot I_{p} \cdot h})}^{- 0, 1} \\ m = 6 \cdot (\frac{1 + 6 \cdot E_{v} \cdot I_{v} \cdot H}{π \cdot E_{P} \cdot I_{P} \cdot L}) \end{matrix}$
CHRYSOSTOMOU e ASTERIS [⁶6 CHRYSOSTOMOU, C.Z., ASTERIS, P.G. “On the in-plane properties and capacities of infilled frames”, Engineering Structures, v. 41, pp. 385-402, Aug. 2012.]	$w = 0, 27 \cdot {(λ_{H})}^{- 0, 4} \cdot D$
CSA S304 [²³23 CANADIAN STARDARDS ASSOCIATION. S304 – Design of masonry structures. CSA. Ontario. 2014.] ABNT NBR 16868-1 [¹1 ASSOCIAÇÃO BRASILEIRA DE NORMAS TÉCNICAS (ABNT). NBR 16868-1. Alvenaria estrutural – Parte 1: Projeto. Rio de Janeiro, 2020.]	w = menor valor entre HENDRY [¹⁸18 HENDRY, A.W. Structural Brickwork, London, MacMillan, 1981.] e D/4
$λ_{H} = λ_{p} \cdot H λ_{p} = \sqrt{\frac{E \cdot t \cdot sen (2 θ)}{4 \cdot E_{p} \cdot I_{p} \cdot h}} λ_{v} = \sqrt{\frac{E \cdot t \cdot sen (2 θ)}{4 \cdot E_{v} \cdot I_{v} \cdot l}}$

MODELO	f_bk (MPa)	f_a (MPa)	f_pk (MPa)	E_a (MPa)	COESÃO (MPa)	DIMENSÕES DO PILAR (cm)	FORÇA APLICADA (kN)
L = 4,5 m (Viga 20 cm x 40 cm)
B4V40P40	4,0	4,0	3,2	2,6×10³	0,150	20×40	162,90
B4V40P60	4,0	4,0	3,2	2,6×10³	0,150	20×60	238,50
B4V40P80	4,0	4,0	3,2	2,6×10³	0,150	20×80	292,95
B4V40P100	4,0	4,0	3,2	2,6×10³	0,150	20×100	344,70
B8V40P40	8,0	6,0	6,0	4,8×10³	0,150	20×40	162,90
B8V40P60	8,0	6,0	6,0	4,8×10³	0,150	20×60	238,50
B8V40P80	8,0	6,0	6,0	4,8×10³	0,150	20×80	292,95
B8V40P100	8,0	6,0	6,0	4,8×10³	0,150	20×100	344,70
B12V40P40	12,0	8,0	8,4	6,7×10³	0,345	20×40	162,90
B12V40P60	12,0	8,0	8,4	6,7×10³	0,345	20×60	238,50
B12V40P80	12,0	8,0	8,4	6,7×10³	0,345	20×80	292,95
B12V40P100	12,0	8,0	8,4	6,7×10³	0,345	20×100	344,70
B16V40P40	16,0	12,0	10,4	8,3×10³	0,345	20×40	162,90
B16V40P60	16,0	12,0	10,4	8,3×10³	0,345	20×60	238,50
B16V40P80	16,0	12,0	10,4	8,3×10³	0,345	20×80	292,95
B16V40P100	16,0	12,0	10,4	8,3×10³	0,345	20×100	344,70
L = 6,0 m (Viga 20 cm x 50 cm)
B4V50P40	4,0	4,0	3,2	2,6×10³	0,150	20×40	203,85
B4V50P60	4,0	4,0	3,2	2,6×10³	0,150	20×60	308,70
B4V50P80	4,0	4,0	3,2	2,6×10³	0,150	20×80	374,85
B4V50P100	4,0	4,0	3,2	2,6×10³	0,150	20×100	428,40
B8V50P40	8,0	6,0	6,0	4,8×10³	0,150	20×40	203,85
B8V50P60	8,0	6,0	6,0	4,8×10³	0,150	20×60	308,70
B8V50P80	8,0	6,0	6,0	4,8×10³	0,150	20×80	374,85
B8V50P100	8,0	6,0	6,0	4,8×10³	0,150	20×100	428,40
B12V50P40	12,0	8,0	8,4	6,7×10³	0,345	20×40	203,85
B12V50P60	12,0	8,0	8,4	6,7×10³	0,345	20×60	308,70
B12V50P80	12,0	8,0	8,4	6,7×10³	0,345	20×80	374,85
B12V50P100	12,0	8,0	8,4	6,7×10³	0,345	20×100	428,40
B16V50P40	16,0	12,0	10,4	8,3×10³	0,345	20×40	203,85
B16V50P60	16,0	12,0	10,4	8,3×10³	0,345	20×60	308,70
B16V50P80	16,0	12,0	10,4	8,3×10³	0,345	20×80	374,85
B16V50P100	16,0	12,0	10,4	8,3×10³	0,345	20×100	428,40
L = 7,5 m (Viga 20 cm x 60 cm)
B4V60P40	4,0	4,0	3,2	2,6×10³	0,150	20×40	246,15
B4V60P60	4,0	4,0	3,2	2,6×10³	0,150	20×60	386,55
B4V60P80	4,0	4,0	3,2	2,6×10³	0,150	20×80	472,05
B4V60P100	4,0	4,0	3,2	2,6×10³	0,150	20×100	534,60
B8V60P40	8,0	6,0	6,0	4,8×10³	0,150	20×40	246,15
B8V60P60	8,0	6,0	6,0	4,8×10³	0,150	20×60	386,55
B8V60P80	8,0	6,0	6,0	4,8×10³	0,150	20×80	472,05
B8V60P100	8,0	6,0	6,0	4,8×10³	0,150	20×100	534,60
B12V60P40	12,0	8,0	8,4	6,7×10³	0,345	20×40	246,15
B12V60P60	12,0	8,0	8,4	6,7×10³	0,345	20×60	386,55
B12V60P80	12,0	8,0	8,4	6,7×10³	0,345	20×80	472,05
B12V60P100	12,0	8,0	8,4	6,7×10³	0,345	20×100	534,60
B16V60P40	16,0	12,0	10,4	8,3×10³	0,345	20×40	246,15
B16V60P60	16,0	12,0	10,4	8,3×10³	0,345	20×60	386,55
B16V60P80	16,0	12,0	10,4	8,3×10³	0,345	20×80	472,05
B16V60P100	16,0	12,0	10,4	8,3×10³	0,345	20×100	534,60

MODELO	DESLOCAMENTO (mm)	MODELO	DESLOCAMENTO (mm)	MODELO	DESLOCAMENTO (mm)
B4V40P40	2,66	B4V50P40	3,41	B4V60P40	4,35
B4V40P60	3,21	B4V50P60	4,36	B4V60P60	5,60
B4V40P80	3,55	B4V50P80	4,76	B4V60P80	6,15
B4V40P100	3,76	B4V50P100	4,92	B4V60P100	6,43
B8V40P40	1,95	B8V50P40	2,32	B8V60P40	3,21
B8V40P60	2,34	B8V50P60	3,16	B8V60P60	3,74
B8V40P80	2,65	B8V50P80	3,46	B8V60P80	4,18
B8V40P100	2,67	B8V50P100	3,60	B8V60P100	4,43
B12V40P40	1,70	B12V50P40	2,11	B12V60P40	2,66
B12V40P60	1,99	B12V50P60	2,72	B12V60P60	3,29
B12V40P80	2,30	B12V50P80	2,97	B12V60P80	3,59
B12V40P100	2,40	B12V50P100	3,09	B12V60P100	3,74
B16V40P40	1,65	B16V50P40	2,04	B16V60P40	2,54
B16V40P60	1,85	B16V50P60	2,40	B16V60P60	2,95
B16V40P80	2,02	B16V50P80	2,63	B16V60P80	3,23
B16V40P100	2,14	B16V50P100	2,74	B16V60P100	3,37

EXPRESSÃO	LARGURA (cm)
MAINSTONE [¹⁷17 MAINSTONE, R.J. “Supplementary note on the stiffness and strengths of infilled frames”, Building Research Station, Garston, UK, 1974.]	74,08
HENDRY [¹⁸18 HENDRY, A.W. Structural Brickwork, London, MacMillan, 1981.]	225,98
LIAUW e KWAN [¹⁹19 LIAUW, T.C., KWAN, K.H. “Nonlinear behavior of non-integral infilled frames”. Computers and Structures, v. 18, n. 3, pp. 551-560, 1984.]	137,53
DECANINI e FANTIN [²⁰20 DECANINI, L.D., FANTIN, G.E. “Modelos simplificados de la mampostería incluida en porticos. Caracteristicas de rigidez y resistencia lateral en estado limite”, In: Jornadas Argentinas de Ingeniería Estructural, v. 2, pp. 817-836, Buenos Aires, 1986.]	179,68
PAULAY e PRIESTLEY [²¹21 PAULAY, T., PRIESTLEY, M.J.N. “Seismic design of reinforced concrete and masonry buildings”, New York, Wiley, 1992.]	152,18
DURRANI e LUO [²²22 DURRANI, A.J., LUO, Y.H. “Seismic retrofit of flat-slab buildings with masonry infills”, Proceedings from the NCEER Workshop on Seismic Response of Masonry Infills, National Center for Engineering Earthquake, Buffalo, N.Y., 1994.]	93,00
CHRYSOSTOMOU e ASTERIS [⁶6 CHRYSOSTOMOU, C.Z., ASTERIS, P.G. “On the in-plane properties and capacities of infilled frames”, Engineering Structures, v. 41, pp. 385-402, Aug. 2012.]	114,30
CSA 304 [²³23 CANADIAN STARDARDS ASSOCIATION. S304 – Design of masonry structures. CSA. Ontario. 2014.] e ABNT NBR 16868-1 [¹1 ASSOCIAÇÃO BRASILEIRA DE NORMAS TÉCNICAS (ABNT). NBR 16868-1. Alvenaria estrutural – Parte 1: Projeto. Rio de Janeiro, 2020. ]	152,18

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[1] Autor Responsável: Gerson Moacyr Sisniegas Alva