Study on reliability of punching shear of flat slabs without shear reinforcement according to NBR6118

The frequent use of flat slabs in building constructions highlights the importance of improving the study of slab-column joints, particularly regarding the verification of the ultimate limit state of punching shear, given the complexity of this phenomenon. This article applies concepts of the Theory of Reliability in order to evaluate the safety of the formulation established by NBR6118: 2014 standard to check punching shear in flat slabs with centered columns. Twelve probabilistic model analysis for C and C' equations were developed, considering the influence that the variation of the slab thickness, the 𝑓_𝑐𝑘 and the shear force eccentricity have on reliability index 𝛽 and failure rate 𝑃_𝑓. Results indicated that formulation of C boundary is reasonably safe, although C'boundary revealed 𝛽 index below expectations.

Keywords:
punching shear; flat slab; reliability; reinforced concrete

Authorship

M. L. CARVALHO

São Paulo State University, Department of Structural and Foundation Engineering, Polytechnic School, São Paulo, SP, Brazil mth.carvalho@hotmail.com.br, carolina_rs@outlook.com.br, frstucchi@uol.com.brSão Paulo State UniversityBrazilSão Paulo, SP, BrazilSão Paulo State University, Department of Structural and Foundation Engineering, Polytechnic School, São Paulo, SP, Brazil mth.carvalho@hotmail.com.br, carolina_rs@outlook.com.br, frstucchi@uol.com.br

C. R. SILVA

F. R. STUCCHI

SCIMAGO INSTITUTIONS RANKINGS

Figures | Tables | Formulas

Figures (12)
Tables (5)
Formulas (24)

Relative cost of safety measure	Ultimate Limit State
	Expected consequences given a failure
	Low	Some	Moderate	High
High	β=0	β=1,5	β=2,3	β=3,1
Moderate	β=1,3	β=2,3	β=3,1	β=3,8
Low	β=2,3	β=3,1	β=3,8	β=4,3

Random variables	Type of probability distribution	Characteristic value	Average value	Coefficient of variation (%)	Source of coefficient of variation
Calculation model - perimeter C	Normal	0,27	0,27	11	[13]
Calculation model - perimeter C'	Normal	0,13	0,18	11	[13]
Compressive strength of concrete (fck)	Normal	fck	fcm=fck/(1-1,645CV)	15	[12]
Tensile strength of concrete (fctk)	Normal	fctk	${(f_{c m})}^{\frac{1}{3}}$	20	[12]
Diameter Column (φ, a, b)	Normal	Design value		4	[12]
Slab thickness (h)	Normal	Design value		4	[12]
Distance between the CG of the upper flexural reinforcement and the concrete face (d')	Normal	Design value		12,5	Value adopted by the authors
Load eccentricity (e, e_x, e_y)	Normal	Design value		10	[13]
Coefficient K	Normal	Design value			[13]
Mean reinforcement ratio for longitudinal reinforcement (𝜌)	Normal	Design value		5	[12]
Permanent loading (G)	Normal	Sgk	Sgm =1,05 Sgk	10	[14]
Variable loading (Q)	Gumbel type 1	Sqk	Sqm =0,934 Sqk	20	[14]

Considered data - Circular Column
h(cm)	16
d'(cm)	3,5
ρ(%)	0,5
Ø(cm)	50
f_ck(MPa)	35
e(cm)	10

Considered data - Rectangular Column
h(cm)	16
d'(cm)	3,5
ρ(%)	0,5
a(cm)- parallel to the𝑥 axis	40
b(cm) parallel to the𝑦axis	30
f_ck(MPa)	35
e_x(cm)	8
e_y(cm)	6

Combinations of actions
Permanent (g)	Variable (q)	Values of (δ)
30%	70%	0,3
50%	50%	0,5
70%	30%	0,7