Punching shear in flat slabs by strut and tie model

Silva, Ricardo José Carvalho; Oliveira, Dênio Ramam Carvalho de; Albuquerque, Nívea Gabriela Benevides de; Gomes, Thiago Andrade; Nzambi, Aaron Kadima Lukanu Lwa

doi:10.1590/S1983-41952021000500006

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Revista IBRACON de Estruturas e Materiais

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ORIGINAL ARTICLE • Rev. IBRACON Estrut. Mater. 14 (5) • 2021 • https://doi.org/10.1590/S1983-41952021000500006 copy

Punching shear in flat slabs by strut and tie model

Punção em lajes lisas via modelo de bielas e tirantes

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract

Research on behavior of flat slabs under punching shear, performed by Kinnunen, Regan and Muttoni influenced the main design recommendations. Meanwhile, studies about strut and tie model developed by Schlaich for beams, deep beams and corbels also influenced these design codes. This work aimed to adapt the strut and tie model for the punching shear resistance analysis in flat slabs. The punching shear resistance of 30 flat slabs verified through strut and tie model was compared to the one designed following Brazilian, American and European codes recommendation. Subsequently, this same model was validated by comparing the test results of 32 flat slabs. The strut and tie model results, when compared with the test results, showed a better average than those from codes, and the modified strut and tie model can become an alternative for punching shear strength prediction.

Keywords:
flat slab; punching shear; strut and tie model

Slabs	f_c	c	Codes	STM	A_{s, Total}	Codes	STM	ρ_l
	f_c	c	c+6d	c+1.5d	A_{s, Total}	A_{s, Prop}	A_{s, Prop}	ρ_l
	(MPa)	(mm)	(mm)	(mm)	(mm²)	(mm²)	(mm²)	(%)
A1	30	150	1110	390	2107.20	1053.60	370.18	0.59
A2					2307.20	1153.60	405.32	0.65
A3					2507.20	1253.60	440.45	0.71
A4					2707.20	1353.60	475.59	0.76
A5					2907.20	1453.60	510.72	0.82
A6					3107.20	1553.60	545.86	0.87
A7					3307.20	1653.60	580.99	0.93
A8					3507.20	1753.60	616.13	0.99
A9					3707.20	1853.60	651.26	1.04
A10					3907.20	1953.60	686.40	1.10
B1	30	150	1080	390	3907.20	1953.60	686.40	1.10
B2	32
B3	34
B4	36
B5	38
B6	40
B7	42
B8	44
B9	46
B10	48
C1	30	120	1080	360	3907.20	1900.80	633.60	1.10
C2		125	1085	365		1909.60	642.40
C3		130	1090	370		1918.40	651.20
C4		135	1095	375		1927.20	660.00
C5		140	1100	380		1936.00	668.80
C6		145	1105	385		1944.80	677.60
C7		150	1110	390		1953.60	686.40
C8		155	1115	395		1962.40	695.20
C9		160	1120	400		1971.20	704.00
C10		165	1125	405		1980.00	712.80

Slabs	V_STM	V_STM/V_ACI	V_STM/V_EC	V_STM/V_NBR
Slabs	(kN)	V_STM/V_ACI	V_STM/V_EC	V_STM/V_NBR
Varying ρ_l between 0.59% and 1.10%
A1	314.2	0.88	0.80	0.76
A2	338.2	0.94	0.84	0.79
A3	361.2	1.01	0.87	0.82
A4	383.2	1.07	0.90	0.85
A5	404.2	1.13	0.92	0.87
A6	424.1	1.18	0.95	0.90
A7	443.1	1.24	0.97	0.92
A8	461.1	1.29	0.99	0.94
A9	478.0	1.33	1.01	0.95
A10	489.9	1.37	1.02	0.96
Average		1.14	0.93	0.87
Standard Deviation		0.14	0.06	0.06
Coefficient of variation (%)		12.09	6.57	6.57
Varying f_c between 30 MPa and 48 MPa
B1	489.9	1.37	1.02	0.96
B2	506.0	1.37	1.03	0.97
B3	516.6	1.35	1.03	0.97
B4	526.0	1.34	1.03	0.97
B5	534.5	1.32	1.02	0.97
B6	542.1	1.31	1.02	0.96
B7	548.9	1.29	1.02	0.96
B8	555.2	1.28	1.01	0.96
B9	560.9	1.26	1.01	0.95
B10	566.1	1.25	1.00	0.95
Average		1.31	1.02	0.96
Standard Deviation		0.04	0.01	0.01
Coefficient of variation (%)		2.71	0.66	0.66
Varying c between 120 mm and 165 mm
C1	338.6	1.05	0.74	0.69
C2	364.8	1.11	0.79	0.74
C3	390.6	1.16	0.84	0.79
C4	415.9	1.22	0.88	0.83
C5	440.9	1.27	0.93	0.88
C6	465.6	1.32	0.97	0.92
C7	489.9	1.37	1.02	0.96
C8	504.1	1.38	1.04	0.98
C9	514.2	1.39	1.05	0.99
C10	524.1	1.39	1.06	1.00
Average		1.27	0.93	0.88
Standard Deviation		0.11	0.10	0.09
Coefficient of variation (%)		8.35	10.42	10.42

Slabs	f_c	f_y	E_s	c	d	h	ρ_l	V_u	V_STM / V_u	V_ACI / V_u	V_EC / V_u	V_NBR / V_u
Slabs	MPa	MPa	GPa	mm	mm	mm	%	(kN)	V_STM / V_u	V_ACI / V_u	V_EC / V_u	V_NBR / V_u
Regan
I/2	23.4	500	200	200	77	100	1.20	176.0	1.26	0.77	0.85	1.10
I/4	32.3	500	200	200	77	100	0.90	194.0	0.98	0.82	0.78	1.01
I/6	21.9	480	200	200	79	100	0.80	165.0	0.98	0.83	0.80	1.04
I/7	30.4	480	200	200	79	100	0.80	186.0	0.92	0.86	0.79	1.03
II/1	34.9	530	200	250	200	250	1.00	825.0	1.14	0.85	1.00	1.00
II/2	33.3	485	200	160	128	160	1.00	390.0	0.91	0.72	0.85	0.96
II/3	34.3	485	200	160	128	160	1.00	365.0	0.98	0.78	0.92	1.04
II/4	33.3	480	200	80	64	80	1.00	117.0	0.75	0.60	0.71	0.99
II/5	34.3	480	200	80	64	80	1.00	105.0	0.84	0.68	0.80	1.11
II/6	36.2	480	200	80	64	80	1.00	105.0	0.85	0.70	0.82	1.13
III/1	23.2	494	200	150	95	120	0.80	197.0	0.90	0.75	0.82	1.01
III/3	37.8	494	200	150	95	120	0.80	214.0	0.90	0.88	0.89	1.09
III/5	26.8	464	200	150	93	120	1.50	214.0	1.19	0.72	0.95	1.17
III/6	42.6	464	200	150	93	120	1.50	248.0	1.23	0.79	0.95	1.18
V/1	34.3	628	200	54	118	150	0.80	170.0	0.50	0.92	1.28	1.47
V/2	32.2	628	200	170	118	150	0.80	280.0	1.19	0.91	0.97	1.12
V/3	32.4	628	200	110	118	150	0.80	265.0	0.98	0.76	0.91	1.05
V/4	36.2	628	200	102	118	150	0.80	285.0	0.90	0.72	0.87	1.00
Marzouk & Hussein
NS1	42.0	490	200	150	95	120	1.50	320.0	1.02	0.62	0.76	0.93
Moe
S1-60	23.3	399	179	254	114	152	1.10	389.0	0.89	0.69	0.76	0.89
S1-70	24.5	483	171	254	114	152	1.10	393.0	1.03	0.70	0.77	0.89
S5-60	22.2	399	179	203	114	152	1.10	343.0	0.86	0.66	0.78	0.91
S5-70	23.0	483	171	203	114	152	1.10	378.0	0.90	0.61	0.72	0.83
H1	26.1	328	195	254	114	152	1.10	372.0	0.81	0.76	0.83	0.96
M1A	20.8	481	195	305	114	152	1.50	433.0	1.03	0.66	0.79	0.92
Elster & Hognestad
A-1b	25.2	332	200	254	118	152	1.20	365.0	0.94	0.80	0.91	1.04
A-1c	29.0	332	200	254	118	152	1.20	356.0	0.98	0.88	0.97	1.12
A-1d	36.6	332	200	254	118	152	1.20	351.0	1.03	1.00	1.07	1.23
A-1e	20.3	332	200	254	118	152	1.20	356.0	0.92	0.73	0.86	0.99
A-7b	27.9	321	200	254	114	152	2.50	512.0	1.09	0.57	0.81	0.94
A-4	26.1	332	200	356	118	152	1.20	400.0	1.08	0.94	0.97	1.12
B-9	43.9	341	200	254	114	152	2.00	505.0	1.11	0.73	0.88	1.03
Average									0.97	0.76	0.87	1.04
Standard Deviation									0.11	0.08	0.09	0.09
Coefficient of variation (%)									11.51	11.09	9.83	8.44

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[1] Corresponding author: Ricardo José Carvalho Silva. E-mail: ricardo.carvalho222@gmail.com