Proposal for estimating the punching shear load-carrying capacity of steel fibers reinforced concrete flat slabs

Dantas, Lucas Guedes; Oliveira, Leonardo Henrique Borges de; Santos, Antônio Carlos dos; Trautwein, Leandro Mouta

doi:10.1590/S1983-41952023000500009

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Revista IBRACON de Estruturas e Materiais

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ORIGINAL ARTICLE • Rev. IBRACON Estrut. Mater. 16 (5) • 2023 • https://doi.org/10.1590/S1983-41952023000500009 copy

Proposal for estimating the punching shear load-carrying capacity of steel fibers reinforced concrete flat slabs

Proposta para estimativa de capacidade de carga na punção de lajes lisas de concreto armado reforçado com fibras de aço

Authorship SCIMAGO INSTITUTIONS RANKINGS

abstract:

This paper proposes an adjusted function for estimating the punching shear load-carrying capacity of concrete flat slabs without shear reinforcement according to the Brazilian standard code. The Adjusted function considers the influence of the steel fiber content. Data from 68 steel fiber reinforced concrete slabs (SFRC slabs) were used, simulating the connection of flat slabs with square section columns. These slabs were obtained from a study conducted by 14 different researchers. The parameters used for the adjusted function were the fiber content and the compressive strength of the concrete. The adjusted function was obtained by curve-fitting. The result from the adjusted function shows a relation in the order of 1.3 between the experimental rupture load and the calculated load, a value close to that already obtained by the normative text when the calculation is for conventional concrete. This shows that the proposal presented here keeps the same level of security with a confidence index of 96% in comparison with other authors’ models presented in this study.

Keywords:
load-carrying capacity; steel fiber reinforced concrete; SFRC; punching shear; flat slabs

Author	Tests	Author	Tests
Narayanan and Darwish [⁴4 R. Narayanan and I. Y. S. Darwish, "Punching shear tests on steel-fibre-reinforced micro-concrete slabs," Mag. Concr. Res., vol. 39, no. 138, pp. 42-50, 1987, http://dx.doi.org/10.1680/macr.1987.39.138.42. http://dx.doi.org/10.1680/macr.1987.39.1... ]	12	Musse [¹⁹19 T. H. Musse, "Punção em lajes cogumelos - fibras de aço e armadura de cisalhamento", M.S. thesis, Univ. Fed. Goiás, Goiânia, GO, Brasil, 2004.]	2
Theodorakopoulos and Swamy [¹³13 D. D. Theodorakopoulos and N. Swamy, "Contribution of steel fibers to the strength characteristics of lightweight concrete slab-column connections falling in punching shear," ACI Struct. J., vol. 90, no. 4, pp. 342-355, 1993, http://dx.doi.org/10.14359/3957. http://dx.doi.org/10.14359/3957... ]	20	De Hanai and and Holanda [²⁰20 J. B. De Hanai and K. M. A. Holanda, "Similarities between punching and shear strength of steel fiber reinforced concrete (SFRC) slabs and beams," Rev. IBRACON Estrut. Mater., vol. 1, no. 1, pp. 1-16, 2008.]	8
Shaaban and Gesund [¹⁴14 A. M. Shaaban and H. Gesund, "Punching shear strength of steel fiber reinforced concrete flat plates," ACI Struct. J., vol. 91, no. 3, pp. 406-414, 1994, http://dx.doi.org/10.14359/4145. http://dx.doi.org/10.14359/4145... ]	12	Cheng and Parra-Montesinos [²¹21 M. Y. Cheng and G. J. Parra-Montesinos, "Evaluation of steel fiber reinforcement for punching shear resistance in slab-column connections—Part I: monotonically increased load," ACI Struct. J., vol. 107, no. 1, pp. 101-109, 2010, https://doi.org/10.14359/51663394 https://doi.org/10.14359/51663394... ]	10
Harajli et al. [¹⁵15 M. H. Harajli, D. Maalouf, and H. Khatib, "Effect of fibers on the punching shear strength of slab-column connections," Cement Concr. Compos., vol. 17, no. 2, pp. 161-170, 1995, http://dx.doi.org/10.1016/0958-9465(94)00031-S. http://dx.doi.org/10.1016/0958-9465(94)0... ]	10	Nguyen-Minh et al. [²²22 L. Nguyen-Minh, M. Rovnak, and T. Tran-Quoc, "Punching shear capacity of interior SFRC Slab-Column connections," J. Struct. Eng., vol. 138, no. 5, pp. 613-624, 2012, http://dx.doi.org/10.1061/(ASCE)ST.1943-541X.0000497. http://dx.doi.org/10.1061/(ASCE)ST.1943-... ]	12
Vargas [¹⁶16 E. N. Z. Vargas, "Punção em lajes-cogumelo de concreto de alta resistência reforçado com fibras de aço. Dissertação, Esc. Eng. São Carlos, Univ. São Paulo, São Carlos, SP, Brasil, 1997.]	6	Gouveia et al. [²³23 N. D. Gouveia, N. A. G. Fernandes, D. M. V. Faria, A. M. P. Ramos, and V. J. G. Lucio, "SFRC flat slabs punching behaviour - Experimental research," Compos., Part B Eng., vol. 63, no. 1, pp. 161-171, 2014, http://dx.doi.org/10.1016/j.compositesb.2014.04.005. http://dx.doi.org/10.1016/j.compositesb.... ]	6
Azevedo [¹⁷17 A. P. Azevedo, "Resistência e ductilidade das ligações laje-pilar em lajes-cogumelo de concreto de alta resistência armado com fibras de aço e armadura transversal de pinos," M.S. thesis, Eng. Estrut., Esc. Eng. São Carlos, Univ. São Paulo, São Carlos, SP, Brasil, 1999.]	6	Barros et al. [⁵5 J. A. O. Barros, B. N. Moraes Neto, G. S. S. A. Melo, and C. M. V. Frazão, "Assessment of the effectiveness of steel fibre reinforcement for the punching resistance of flat slabs by experimental research and design approach," Compos., Part B Eng., vol. 8, no. 1, pp. 8-25, 2015, http://dx.doi.org/10.1016/j.compositesb.2015.03.050. http://dx.doi.org/10.1016/j.compositesb.... ]	8
McHarg et al. [¹⁸18 P. J. McHarg, W. D. Cook, D. Mitchell, and Y. S. Yoon, "Benefits of concentrated slab reinforcement and steel fibers on performance of slab-column connections," ACI Struct. J., vol. 97, no. 2, pp. 225-234, 2000, http://dx.doi.org/http://dx.doi.org. https://doi.org/http://dx.doi.orghttps:/... ]	4	Alves [⁶6 V. S. S. Alves, "Avaliação do efeito de punção em lajes lisas de concreto com fibras com a variação do índice de retangularidade," M.S. thesis, Fac. Eng. Civ., Univ. Fed. Uberlândia, Uberlândia, MG, Brasil, 2017.]	3

Concrete strength (MPa)	Parameter
20~30	k₂₀
30~40	k₃₀
40~50	k₄₀
50~60	k₅₀
60~70	k₆₀
70~80	k₇₀
80~90	k₈₀

f_c	Number of slabs	k	R_e,m
(MPa)	Number of slabs	k	X	S	CV
20~30	10	0.248	1.118	0.171	15.32
30~40	15	0.132	1.262	0.167	13.21
40~50	23	0.208	1.305	0.201	15.39
50~60	13	0.319	1.11	0.082	7.37
60~70	4	0.548	1.031	0.027	2.61
70~80	2	0.615	1.019	0.026	2.6
80~90	1	0.218	1	-	-
Total	68	-	1.199	0.187	15.59

Compressive Strength (f_c)	Parameter	Value
20~30	k₂₀	0.248
30~40	k₃₀	0.132
40~50	k₄₀	0.208
50~60	k₅₀	0.319
60~70	k₆₀	0.548
70~80	k₇₀	0.615
80~90	k₈₀	0.218

Model	$R_{e, m}$ (Mean)	$R_{e, m}$ (Standard Deviation)	$R_{e, m}$ (Variation Coefficient)	Confidence Indicator
Proposed Model	1.29	0.23	18%	96%
Narayanan and Darwish [⁴4 R. Narayanan and I. Y. S. Darwish, "Punching shear tests on steel-fibre-reinforced micro-concrete slabs," Mag. Concr. Res., vol. 39, no. 138, pp. 42-50, 1987, http://dx.doi.org/10.1680/macr.1987.39.138.42. http://dx.doi.org/10.1680/macr.1987.39.1... ]	1.59	0.76	48%	74%
Harajli et al. [¹⁵15 M. H. Harajli, D. Maalouf, and H. Khatib, "Effect of fibers on the punching shear strength of slab-column connections," Cement Concr. Compos., vol. 17, no. 2, pp. 161-170, 1995, http://dx.doi.org/10.1016/0958-9465(94)00031-S. http://dx.doi.org/10.1016/0958-9465(94)0... ]	1.50	0.65	44%	74%
De Hanai and Holanda [²⁰20 J. B. De Hanai and K. M. A. Holanda, "Similarities between punching and shear strength of steel fiber reinforced concrete (SFRC) slabs and beams," Rev. IBRACON Estrut. Mater., vol. 1, no. 1, pp. 1-16, 2008.]	1.50	0.60	40%	77%
Higashiyama et al. [¹¹11 H. Higashiyama, A. Ota, and M. Mizukoshi, "Design equation for punching shear capacity of SFRC slabs," Int. J. Concr. Struct. Mater., vol. 5, no. 1, pp. 35-42, Jun 2011.]	1.49	0.56	37%	72%

Slab	L	h	d	a	$ρ$	$v_{f}$	$f_{c}$	$P_{e x p}$
Slab	(mm)	(mm)	(mm)	(mm)	$ρ$	(%)	(MPa)	(kN)
L1-50-1	1800	130	99	250	0.016	0.64	42.01	469
L1-50-2	1800	130	99	250	0.016	0.64	42.01	469
L2-50	1800	130	98	250	0.016	0.64	42.01	513
L3-50	1800	130	99	250	0.016	0.64	42.01	455

Identification	$C M O D$	Opening	$F_{R, i}$	$f_{R, i}$
Identification	$C M O D$	(mm)	(kN)	(MPa)
C40/50-1	$C M O D_{1}$	0.5	13.24	4.24
	$C M O D_{2}$	1.5	12.89	4.12
	$C M O D_{3}$	2.5	12.67	4.06
	$C M O D_{4}$	3.5	11.05	3.54
C40/50-2	$C M O D_{1}$	0.5	12.83	4.10
	$C M O D_{2}$	1.5	13.21	4.23
	$C M O D_{3}$	2.5	11.79	3.77
	$C M O D_{4}$	3.5	11.90	3.81

Slab	d	$ρ$	$f_{c}$	$f_{R 3}$	$f_{F t u, k}$	$τ_{R d 1}$	$μ$	$V_{c}$	$V_{R d, f}$	$V_{R d, A B N T}$
Slab	(mm)	$ρ$	(MPa)	(MPa)	(MPa)	(MPa)	(mm)	(kN)	(kN)	(kN)
L1-50-1	99	0.016	42	4.06	1.35	1.77	2244.07	393.66	300.32	693.98
L1-50-2	99	0.016	42	3.77	1.26	1.77	2244.07	393.66	279.32	672.98
L2-50	98	0.016	42	4.06	1.35	1.77	2231.50	393.66	295.62	684.28
L3-50	99	0.016	42	3.77	1.26	1.77	2231.50	393.66	274.95	663.61

Slab	D	$ρ$	$f_{c}$	$v_{f}$	$V_{c}$	$k$	$V_{R d, P r o p}$
Slab	(mm)	$ρ$	(MPa)	(%)	(kN)	$k$	(kN)
L1-50-1	99	0.016	42	0.64	393.66	0.208	442.86
L1-50-2	99	0.016	42	0.64	393.66	0.208	442.86
L2-50	98	0.016	42	0.64	393.66	0.208	437.23
L3-50	99	0.016	42	0.64	393.66	0.208	437.23

Slab	$V_{R d, A B N T}$	$V_{R d, P r o p}$	$V_{e x p}$	$\frac{V_{R d, A B N T}}{V_{R d, P r o p}}$	$\frac{V_{e x p}}{V_{R d, A B N T}}$	$\frac{V_{e x p}}{V_{R d, P r o p}}$
Slab	(kN)	(kN)	(kN)	$\frac{V_{R d, A B N T}}{V_{R d, P r o p}}$	$\frac{V_{e x p}}{V_{R d, A B N T}}$	$\frac{V_{e x p}}{V_{R d, P r o p}}$
L1-50-1	693.98	442.86	469	1.57	0.68	1.06
L1-50-2	672.98	442.86	469	1.52	0.70	1.06
L2-50	684.28	437.23	513	1.57	0.75	1.17
L3-50	663.61	437.23	455	1.52	0.69	1.04

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[1] Corresponding author: Leonardo Henrique Borges de Oliveira. E-mail: leonardo.oliveira@ufersa.edu.br