Three-dimensional modelling of wall-beam interaction in structural masonry buildings

Lopes, Anna Christinna Secundo; Nascimento Neto, Joel Araújo do; Medeiros, Klaus André de Sousa; Maciel, Daniel Nelson

doi:10.1590/S1983-41952020000400014

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ORIGINAL ARTICLE • Rev. IBRACON Estrut. Mater. 13 (4) • 2020 • https://doi.org/10.1590/S1983-41952020000400014 copy

Three-dimensional modelling of wall-beam interaction in structural masonry buildings

Modelagem tridimensional da interação parede-viga em edifícios de alvenaria estrutural

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT:

Wall-beam interaction (wall-beam system) is a phenomenon that requires further investigation in order to be consistently incorporated into structural building analysis. Researchers such as Wood, Rosenhaupt, Burhouse, Stafford Smith, Navaratnarajah, Davies, Riddington and Armed conducted tests on specimens to develop simplified analysis models, emphasizing the behavior of walls without openings under one span beams. The present study performed computational analysis using an specific equivalent frame model in order to study the behavior of the wall-beam system in more complex wall and beam arrangements. The examples considered the linear elastic behavior of materials and consisted of assessing stress distribution and displacements on support beams, in addition to stresses at the bottom of the walls, for panels in a real structural masonry building. Two- and three-dimensional analyses were used and the results showed the importance of three-dimensional analysis of wall interconnections. The effects of eccentricity between the vertical plane of the wall and horizontal support beam axis were also evaluated, showing the strong influence of twisting moments in support beam design.

Keywords:
structural masonry; wall-beam composite behavior; computational modeling; equivalent frame; wall-beam eccentricity

Material	Specific weight ϒ (kN/m³)	Modulus of elasticity (MPa)
Material	Specific weight ϒ (kN/m³)	Longitudinal	Transverse
Beam concrete	25	23800	9917
Grouted masonry	22	16320	8160
Ungrouted masonry	14	9600	4800

Models	Modulus of elasticity (MPa)			Element thickness (cm)
	Grouted Masonry	Ungrouted masonry		Element thickness (cm)
	Grouted Masonry	Longitudinal	Transverse	Grouted	Ungrouted
Reference	16320	9600	4800	28	14
1	9600	9600	4800	1.7x14	14
2	16320	9600	4800	14	14
3	16320	19200	9600	14	7

Model	Normal stress (MPa) – Maximum values
Model	Region C1	∆_2D	∆_3D	Region C2	∆_2D	∆_3D	Region C2	∆_2D	∆_3D
2D	7.03	-	-	3.28	-	-	3.36	-	-
3D	8.77	25%	-	5.18	58%	-	5.33	59%	-
3DW	10.52	50%	20%	6.17	88%	19%	7.13	112%	34%
Model	Shear stress (MPa) – Maximum values
Model	Region C1	∆_2D	∆_3D	Region C2	∆_2D	∆_3D	Region C2	∆_2D	∆_3D
2D	0.60	-	-	0.40	-	-	0.16	-	-
3D	0.47	-22%	-	0.40	0%	-	0.11	-31%	-
3DW	0.51	-15%	9%	0.40	0%	0%	0.17	6%	55%

Model	Axial force (kN)			Shear force (kN)			Bending moment (kN∙m)			Displacements (cm)
Model	Maximum	∆_2D	∆_3D	Maximum	∆_2D	∆_3D	Maximum	∆_2D	∆_3D	Maximum	∆_2D	∆_3D
2D	57.83	-	-	396.68	-	-	183.50	-	-	0.11	-	-
3D	65.89	14%	-	467.57	18%	-	194.70	6%	-	0.16	45%	-
3DW	85.69	48%	30%	519.26	31%	11%	228.09	24%	17%	0.17	55%	6%

Modelo	Normal stress (MPa) – Maximum values
Modelo	Region C1	∆_2D	∆_3D	Região C14	∆_2D	∆_3D	Região C20	∆_2D		∆_3D
2D	5.97	-	-	5.91	-	-	3.56		-	-
3D	8.77	47%	-	11.14	88%	-	6.64		87%	-
3DW	10.52	76%	20%	10.82	83%	-3%	6.54		84%	-2%
Modelo	Shear stress (MPa) – Maximum values
Modelo	Region C1	∆_2D	∆_3D	Região C14	∆_2D	∆_3D	Região C20	∆_2D		∆_3D
2D	0.46	-	-	0.91	-	-	0.07		-	-
3D	0.44	-4%	-	1.43	57%	-	0.06		-14%	-
3DW	0.42	-9%	-5%	1.42	56%	-1%	0.08		14%	33%

Model	Axial force (kN)			Shear force (kN)			Bending moment (kN∙m)			Displacements (cm)
Model	Maximum	∆_2D	∆_3D	Maximum	∆_2D	∆_3D	Maximum	∆_2D	∆_3D	Maximum	∆_2D	∆_3D
2D	69.97	-	-	380.73	-	-	182.94	-	-	0.12	-	-
3D	98.80	41%	-	577.77	52%	-	255.12	39%	-	0.21	72%	-
3DW	98.67	41%	0%	571.62	50%	-1%	252.70	38%	-1%	0.20	71%	-1%

Modelo	Normal stress (MPa) – Maximum values
Modelo	Region C7	∆_2D	∆_3D	Region C8	∆_2D	∆_3D
2D	2.43	-	-	2.43	-	-
3D	5.75	137%	-	5.75	137%	-
3DW	6.40	163%	11%	6.40	163%	11%
Modelo	Shear stress (MPa) – Maximum values
Modelo	Region C7	∆_2D	∆_3D	Region C8	∆_2D	∆_3D
2D	0.29	-	-	0.29	-	-
3D	0.19	-34%	-	0.19	-34%	-
3DW	0.22	-24%	16%	0.22	-24%	16%

Model	Axial force (kN)			Shear force (kN)			Negative bending moment (kN.m)			Displacements (cm)
Model	Maximum	∆_2D	∆_3D	Maximum	∆_2D	∆_3D	Maximum	∆_2D	∆_3D	Maximum	∆_2D	∆_3D
2D	43.16	-	-	175.65	-	-	61.18	-	-	0.05	-	-
3D	-45.11	105%	-	373.63	113%	-	124.89	104%	-	0.11	120%	-
3DW	-94.02	218%	108%	388.91	121%	4%	132.41	116%	6%	0.12	140%	9%

Model	Normal stress (MPa) – Maximum values
Model	Region C18	∆_2D	∆_3D	Region C7	∆_2D	∆_3D
2D	11.4	-	-	11.17	-	-
3D	5.44	-52%	-	5.75	-49%	-
3DW	5.57	-51%	2%	6.40	-43%	11%
Model	Shear stress (MPa) – Maximum values
Model	Region C18	∆_2D	∆_3D	Region C7	∆_2D	∆_3D
2D	1.07	-	-	1.00	-	-
3D	0.70	-35%	-	0.71	-29%	-
3DW	0.70	-35%	0%	0.77	-23%	8%

Model	Axial force (kN)			Shear force (kN)			Bending moment (kN.m)			Displacements (cm)
Model	Maximum	∆_2D	∆_3D	Maximum	∆_2D	∆_3D	Maximum	∆_2D	∆_3D	Maximum	∆_2D	∆_3D
2D	187.04	-	-	555.46	-	-	318.63	-	-	0.23	-	-
3D	214.56	15%	-	505.54	-9%	-	270.67	-15%	-	0.28	22%	-
3DW	216.23	16%	1%	525.97	-5%	4%	277.63	-13%	3%	0.28	22%	0%

WALL/ BEAM (section)	MODEL	MAXIMUM TWISTING MOMENT (kN∙m)		VARIATION
WALL/ BEAM (section)	MODEL	Disregarding eccentricity (1)	Considering eccentricity (2)	∆_(2)-(1)	∆_3D-2D
W1/B1 (35x80)	2D	--	38.39	--	--
	3D	13.91	51.09	267%	33%
	3DW	14.23	53.94	279%	40%
W30/B29 (35x80)	2D	--	25.83	--	--
	3D	8.78	35.90	309%	39%
	3DW	14.31	41.36	189%	60%
W3/B3 (30x80)	2D	--	12.48	--	--
	3D	48.94	60.29	23%	383%
	3DW	54.38	65.70	21%	426%
W41/B40 (35x80)	2D	--	63.06	--	--
	3D	2.02	56.33	2689%	-11%
	3DW	2.12	56.43	2562%	-11%

Wall/ Beam (section)	Model	Non-eccentric loading			Eccentric loading
		Long. Reinf. (flexo-tensile + torsion)	Trans. Reinf. (shear force + torsion)		Long. Reinf. (flexo-tensile + torsion)	Trans. Reinf. (shear force + torsion)
		As (cm²)	Strut colapse	As (cm²)	As (cm²)	Strut colapse	As (cm²)
W1/B1 (35x80)	2D	8.07	No	11.67	15.38	No	14.85
	3D	11.24	No	16.14	18.00	Yes	--
	3DW	12.81	No	18.58	19.56	Yes	--
W30/B29 (35x80)	2D	8.05	No	10.92	12.97	No	13.06
	3D	13.13	No	20.87	18.27	No	22.49
	3DW	14.08	No	21.04	19.20	Yes	--
W3/B3 (30x80)	2D	3.60	No	2.32	5.41	No	3.58
	3D	16.40	Yes	--	18.69	Yes	--
	3DW	17.95	Yes	--	20.10	Yes	--
W41/B40 (35x80)	2D	14.52	No	19.10	26.53	Yes	--
	3D	12.58	No	16.93	22.65	Yes	--
	3DW	12.96	No	17.89	22.86	Yes	--

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E-mail: arlene@ibracon.org.br

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[1] Corresponding author: Anna Christinna Secundo Lopes. E-mail: annasecundolopes@gmail.com