Reliability of internal column-slab connection under punching according to NBR 6118:2014

This article presents a study on the reliability of internal column-slab connection under punching, designed according to the Brazilian Standard NBR 6118:2014. The evaluation of reliability was made by comparing the reliability index β with the target reliability index recommended by the fib Model Code 2010. The reliability indexes were calculated through statistical analysis of the data obtained with numerical simulations using the Monte Carlo method, with Latin Hypercube sample, through ANSYS software. The results showed that, for most slabs, the indexes of reliability β presented satisfactory results. However, some of the tested slabs presented results below the assumed limits. Therefore, this article suggests that the Brazilian Standard NBR 6118:2014 is appropriate for most flat slabs without shear reinforcement.

Keywords:
structural reliability; flat slabs; punching; reinforced concrete

Authorship

G. R. SILVA

Universidade Federal do Rio Grande do Sul, Departamento de Engenharia Civil, Escola de Engenharia, Porto Alegre, RS, Brasil; gustavoribeirods@gmail.com americo@ufrgs.brUniversidade Federal do Rio Grande do SulBrazilPorto Alegre, RS, BrazilUniversidade Federal do Rio Grande do Sul, Departamento de Engenharia Civil, Escola de Engenharia, Porto Alegre, RS, Brasil; gustavoribeirods@gmail.com americo@ufrgs.br

A. CAMPOS FILHO

M. V. REAL

Universidade Federal do Rio Grande - FURG, Escola de Engenharia, Rio Grande, RS, Brasil. mauroreal@furg.brUniversidade Federal do Rio GrandeBrazilRio Grande, RS, BrazilUniversidade Federal do Rio Grande - FURG, Escola de Engenharia, Rio Grande, RS, Brasil. mauroreal@furg.br

SCIMAGO INSTITUTIONS RANKINGS

Figures | Tables

Figures (11)
Tables (4)

Relative cost of safety measure	Expect consequences given a failure
Relative cost of safety measure	Low	Some	Moderate	High
High	0.0	1.5	2.3	3.1
Moderate	1.3	2.3	3.1	3.8
Low	2.3	3.1	3.8	4.3

Slab	Top reinforcement (FEM) (in each direction)	Top reinforcement (EPA) (in each direction)	Bottom reinforcement (in each direction)	Progressive colapse reinforcement
L030216	21 φ 10.2 mm c. 10 cm	21 φ 7.7 mm c. 10 cm	12 φ 6.3 mm c. 17 cm	5 φ 13 mm
L030416	21 φ 11.1 mm c. 10 cm	21 φ 8.8 mm c. 10 cm	12 φ 6.3 mm c. 17 cm	4 φ 16 mm
L030616	21 φ 8.5 mm c. 10 cm	21 φ 9.8 mm c. 10 cm	12 φ 6.3 mm c. 17 cm	7 φ 14 mm
L030220	21 φ 9.6 mm c. 10 cm	21 φ 7.4 mm c. 10 cm	16 φ 6.3 mm c. 13 cm	5 φ 14 mm
L030420	21 φ 10.5 mm c. 10 cm	21 φ 8.3 mm c. 10 cm	16 φ 6.3 mm c. 13 cm	5 φ 16 mm
L030620	21 φ 8.3 mm c. 10 cm	21 φ 9.1 mm c. 10 cm	16 φ 6.3 mm c. 13 cm	5 φ 17 mm
L030224	21 φ 9.1 mm c. 10 cm	21 φ 7.2 mm c. 10 cm	19 φ 6.3 mm c. 11 cm	6 φ 14 mm
L030424	21 φ 9.9 mm c. 10 cm	21 φ 7.9 mm c. 10 cm	19 φ 6.3 mm c. 11 cm	5 φ 16 mm
L030624	21 φ 8.8 mm c. 10 cm	21 φ 8.6 mm c. 10 cm	19 φ 6.3 mm c. 11 cm	5 φ 18 mm
L060216	21 φ 10 mm c. 10 cm	21 φ 7.6 mm c. 10 cm	15 φ 6.3 mm c. 14 cm	5 φ 13 mm
L060416	21 φ 11.1 mm c. 10 cm	21 φ 8.7 mm c. 10 cm	15 φ 6.3 mm c. 14 cm	4 φ 16 mm
L060616	21 φ 8.4 mm c. 10 cm	21 φ 9.6 mm c. 10 cm	15 φ 6.3 mm c. 14 cm	5 φ 16 mm
L060220	21 φ 9.4 mm c. 10 cm	21 φ 7.4 mm c. 10 cm	21 φ 6.3 mm c. 10 cm	5 φ 13 mm
L060420	21 φ 10.3 mm c. 10 cm	21 φ 8.2 mm c. 10 cm	21 φ 6.3 mm c. 10 cm	5 φ 15 mm
L060620	21 φ 8.2 mm c. 10 cm	21 φ 9 mm c. 10 cm	21 φ 6.3 mm c. 10 cm	5 φ 17 mm
L060224	21 φ 9 mm c. 10 cm	21 φ 8.2 mm c. 10 cm	26 φ 6.3 mm c. 8 cm	5 φ 14 mm
L060424	21 φ 9.8 mm c. 10 cm	21 φ 8.2 mm c. 10 cm	26 φ 6.3 mm c. 8 cm	5 φ 16 mm
L060624	21 φ 8.8 mm c. 10 cm	21 φ 8.5 mm c. 10 cm	26 φ 6.3 mm c. 8 cm	5 φ 17 mm
L090216	21 φ 9.9 mm c. 10 cm	21 φ 7.6 mm c. 10 cm	19 φ 6.3 mm c. 11 cm	4 φ 13 mm
L090416	21 φ 11 mm c. 10 cm	21 φ 8.7 mm c. 10 cm	19 φ 6.3 mm c. 11 cm	5 φ 14 mm
L090616	21 φ 8.4 mm c. 10 cm	21 φ 9.6 mm c. 10 cm	19 φ 6.3 mm c. 11 cm	5 φ 16 mm
L090220	21 φ 9.4 mm c. 10 cm	21 φ 8 mm c. 10 cm	23 φ 6.3 mm c. 9 cm	4 φ 14 mm
L090420	21 φ 10.3 mm c. 10 cm	21 φ 8.1 mm c. 10 cm	23 φ 6.3 mm c. 9 cm	5 φ 15 mm
L090620	21 φ 8.8 mm c. 10 cm	21 φ 8.9 mm c. 10 cm	23 φ 6.3 mm c. 9 cm	5 φ 17 mm
L090224	21 φ 9 mm c. 10 cm	21 φ 8.8 mm c. 10 cm	29 φ 6.3 mm c. 7 cm	5 φ 13 mm
L090424	21 φ 9.8 mm c. 10 cm	21 φ 8.8 mm c. 10 cm	29 φ 6.3 mm c. 7 cm	5 φ 15 mm
L090624	21 φ 9.8 mm c. 10 cm	21 φ 8.8 mm c. 10 cm	29 φ 6.3 mm c. 7 cm	5 φ 17 mm

Random variables	Type of probability distribution	Mean value	Coefficient of variation	Source of coeficiente of variation
Compressive strength of concrete	Normal	$f_{c m} = \frac{f c k}{(1 - 1.645 V_{f c})}$	0.15	[¹⁷[17] GALAMBOS, T. V.; ELLINGWOOD, B.; MACGREGOR, J. G.; CORNELL, C. A. Probability based load criteria: Assessment of current design practice. Journal of the Structural Division, v.108, p.959-977, May.1982.]
Tensile strength of concrete	Normal	$\begin{array}{l} f_{c t m} = 0.3 {(f_{c k})}^{\frac{2}{3}}, f_{c k} \leq 50 M P a \\ f_{c t m} = 2.12 \ln (1 + 0.1 (f_{c m})), f_{c k} > 50 M P a \end{array}$	0.18	[⁴[4] REAL, M. V.; CAMPOS FILHO, A.; MAESTRINI, S. R. Response variability in reinforced concrete structures with uncertain geometrical and material properties. Nuclear Engineering and Design (Print), New York, v. 226, n.3, p. 205-220, 2003.]
Modulus of elasticity of concrete	Normal	$E_{c} = 21500. α_{e} . {(\frac{f_{c m}}{10})}^{\frac{1}{3}}$	0.15	[⁴[4] REAL, M. V.; CAMPOS FILHO, A.; MAESTRINI, S. R. Response variability in reinforced concrete structures with uncertain geometrical and material properties. Nuclear Engineering and Design (Print), New York, v. 226, n.3, p. 205-220, 2003.]
Yield strength of reinforcing steel	Normal	$μ_{f y} = \frac{f y k}{(1 - 1.645 V_{f y})}$	0.05	[¹⁷[17] GALAMBOS, T. V.; ELLINGWOOD, B.; MACGREGOR, J. G.; CORNELL, C. A. Probability based load criteria: Assessment of current design practice. Journal of the Structural Division, v.108, p.959-977, May.1982.]
Slab thickness	Normal	$μ h = h$	0.04	[¹⁸[18] STUCCHI, F. R.; SANTOS, S. H. C.; FRANCO, R. M. Evaluation of the safety criteria of Brazilian Standard NBR 6118 for slender members based on reliability analyses. Applications of Statistics and Probability in Civil Engineering, p. 2761-2767, 2011.]
Distance between the geometric center of the upper flexural reinforcement and the concrete face	Normal	$μ d' = d'$	0.125	[¹⁸[18] STUCCHI, F. R.; SANTOS, S. H. C.; FRANCO, R. M. Evaluation of the safety criteria of Brazilian Standard NBR 6118 for slender members based on reliability analyses. Applications of Statistics and Probability in Civil Engineering, p. 2761-2767, 2011.]