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Punching shear resistance - A23.3-2014
v1.0 (20240507)
2026-04-09

Input data

Concrete properties

f'c = ksi Concrete resistance
(31 MPa)
φc =   Concrete resistance coefficient
8.4.2 Factored concrete strength
The factored concrete compressive strengths used in checking ultimate limit states shall be taken as φcf'c. The factored concrete tensile strengths used in checking ultimate limit states are given in terms of φc√f'c, where φc = 0.65, except as specified in Clause 16.1.3.

16.1.3
For elements produced in manufacturing plants prequalified in accordance with CSA A23.4, the concrete material resistance factor, φc, specified in Clause 8.4.2 of this Standard may be taken as 0.70.

source : CSA A23.3 (2014) Design of concrete structures 8.4.2 [1]
λ =   Concrete density factor
8.6.5 Modification factors for concrete density
The effect of low-density aggregates on tensile strength and other related properties shall be accounted for by the factor λ, where
a)λ = 1.00 for normal density concrete;
b)λ = 0.85 for structural semi-low-density conrete in which all the fine aggregate is natural sand; and
c)λ = 0.75 for structural low-density concrete in which none of the fine aggregate is natural sand.

Linear interpolation may be applied based on the fraction of natural sand in the mix.

source : CSA A23.3 (2014) Design of concrete structures 8.6.5 [1]

Geometric data

Pos = Position where punching is checked in slab
 
αs = 4   Factor to take position of reaction into account
13.3.4.1.b) [1]
d = in Rebar lever in tension
 
a = in Short side of the column, concentrated load, or reaction area
 
b = in Long side of the column, concentrated load, or reaction area
 
βc = 1   Ratio of long side to short side of reaction area
b / a
bo = in Perimeter of critical section for shear

Calculations

Factored shear stress resistance, smallest of :

vc,1 = 0.2993   Factored shear stress resistance a)
13.3.4.1.a) eq. 13.5 [1]
  • (1 + 2 / βc) 0.19 λ φc √f'c
  • (1 + 2/1 0.19 · 1 · 0.65 · (31 MPa)0.5 = 2.06 MPa
vc,2 = 0.4936   Factored shear stress resistance b)
13.3.4.1.b) eq. 13.6 [1]
  • (αsd / bo + 0.19) λ φc √f'c
  • (4 · 6 in / 32 in + 0.19) · 1 · 0.65 · (31 MPa)0.5 = 3.4 MPa
vc,3 = 0.1995   Factored shear stress resistance c)
13.3.4.1.c) eq. 13.7 [1]
  • 0.38 λ φc √f'c
  • 0.38 · 1 · 0.65 · (31 MPa)0.5 = 1.38 MPa

Final factored resistance

F1 = 1   Correction factor if √f'c > 8 MPa
13.3.4.2
The value of √f'c used to calculate vc in Equations 13.5 to 13.7 and 13.10 shall not exceed 8 MPa
source : CSA A23.3 (2014) Design of concrete structures 13.3.4.2 [1]
  • min(√f'c, 8) / √f'c
  • min(8 MPa, 5.57 MPa) / 5.57 MPa
F2 = 1   Correction factor if d > 300 mm
13.3.4.3
If the effective depth, d, used in two-way shear calculations exceed 300 mm, the value of vc obtained from Equations 13.5 to 13.7 shall be multiplied by 1300/(1000+d).
source : CSA A23.3 (2014) Design of concrete structures 13.3.4.3 [1]
  • 1300 / (1000 + max(d, 300))
  • 1300 mm / [1000 mm + max(300 mm, 152 mm)]
vr = 0.1995 ksi Final factored resistance
F1 F2 min(vc,1, vc,2, vc,3)
  • F1 F2 min(vc,1, vc,2, vc,3)
  • 1 · 1 · min(0.2993 ksi, 0.4936 ksi, 0.1995 ksi)
Pr = 38.31 kip Punching resistance
vr bo d [1]
  • vr bo d
  • 0.1995 ksi · 32 in · 6 in