Available calculation tools - CSA A23.3

Unidirectional slab
2014
Punching shear resistance
2014

Modifications history

v0.2 (20240507)

The usage factors were multiplied by a factor of a 100 when calculation was loaded from the permalink, however the usage factor in the summary table was correct.

v0.1 (20240412)

Translation in English completed

v0.0 (20231204)

First beta version

Disclaimers and others

0.x Versions (beta): The Calculations tools in version 0.x are still in development and should be used with caution. No in-depth quality-control have been done on those versions. Don't hesitate to participate in the Quality Assurance process and report any bug or error you find.

By using Isocel.ca and information derived from this Service, you have agreed to the Terms of Service.

This information must be read and used in conjunction with the CAN/CSA-A23.3-14 Design of Concrete Structures Standard and the Cement Association of Canada (CAC) Concrete Design Handbook (CDH), 4th edition. In the case of discrepancies, the CAN/CSA-A23.3-14 Standard and the CAC CDH, 4th ed. shall govern.

Unidirectional slab - A23.3-2014

v0.2 (20240507)

Project

N^o

Prepared by

Client

Verified by

Subject

Date 2026-02-06

Summary table

	Effort	Max allowed	Units	Usage factor (%)	Comments
Flexion	0	44.38	kN·m	0
Shear	0	241.9	kN	0

Material properties

Concrete

φ_c =			Resistance factor	8.4.2 ?8.4.2 Factored concrete strength The factored concrete compressive strengths used in checking ultimate limit states shall be taken as φ_cf'_c. The factored concrete tensile strengths used in checking ultimate limit states are given in terms of φ_c(f'_c)^0.5, where φ_c = 0.65, except as specified in Clause 16.1.3.
f'_c =		MPa	Compression resistance
γ_c =		kg/m³	Density
E_c =	25 794	MPa	Modulus of elasticity	8.6.2.2, eq. 8.1
λ_c =			Concrete density factor	8.6.5
f_r =	3.286	MPa	Modulus of rupture	8.6.4
a_g =		mm	Specified nominal maximum size of coarse aggregate

Reinforcing steel

φ_s =	0.85		Resistance factor	8.4.3
f_y =		MPa	Yield strength
E_s =		MPa	Modulus of elasticity
ε_y =	2 x10^-3		Déformation élastique	f_y / E_s
Epoxy ?			Traitement des barres d'armature
n =	7.754		Steel to concrete transformation ratio	E_s / E_c
w_max =		mm	Maximal allowable crack's opening
z_max =	25 000	kN/m	Quantity limiting distribution of flexural reinforcement	10.6.1

Section properties

Geometry

h =		mm	Slab depth
b =		mm	Considered width of slab
Ig =	677.7 x10⁶	mm⁴	Gross inertia - uncracked	bh³ / 12

Bending reinforcement

		Bottom face		Top face
		1st bed	2nd bed	1st bed	2nd bed
e	(mm)					c/c space between rebars
Rebar						Designation
d_b	(mm)	16	0	16	0	Real diameter
A_b	(mm²)	200	0	200	0	Area of one rebar
s_min	(mm)	30	30	30	30	Min. net spacing
s_ver	(mm)					Vert. net spacing
cover	(mm)					Concrete cover

Shear reinforcement

Rebar =			Designation
d_b =	11.3	mm	Real diameter
A_{vb =}	100	mm²	Area of one rebar
n_bv =			Number of strands, 0 if no reinforcement
s =		mm	Horizontal net space between rebars
A_{v =}	0	mm²	area of shear reinforcement within the distance s
A_{v,min =}	-1	mm²	Minimal area of rebar in shear	11.2.8.2, eq. 11.1

Loading at verification points

M_f,b =	kN·m	Factored bending moment	Bending
N_f,b =	kN	Factored axial load	Bending
V_f,v =	kN	Factored shear load	Shear
N_f,v =	kN	Factored axial load	Shear
M_f,v =	kN·m	Factored bending moment	Shear

Bending resistance

Reinforcement

	Bottom face		Top face
	(1) 1st bed	(2) 2nd bed	(3) 2nd bed	(4) 1st bed
d_i (mm)	167	n.a.	n.a.	33	Lever arm of each bed
A_s,i (mm²)	800	n.a.	n.a.	800	Reinf. area for each bed
ε_s,i	18.18 x10^-3	n.a.	n.a.	784.7 x10^-6	Strain of reinforcement
f_s,i (MPa)	400	n.a.	n.a.	156.9	Stress in reinforcement
F_s,i (kN)	272	n.a.	n.a.	106.7	Force in reinforcement

Equivalent compression block

α₁ =	0.805		Stress/resistance factor	10.1.7, eq. 10.1
β₁ =	0.895		Depth factor a/c	10.1.7, eq. 10.2
c =	26.96	mm	Neutral axis position	0.0035 d₁ / (0,0035 + ε_s,1) ≤ h
a =	24.13	mm	Compression block depth	c β₁
C_c =	-378.7	kN	Compression force in concrete	α₁ φ_c f'_c (ab - A'_s)
N_res =	0	kN	Resulting axial load	∑ F_s,i - C_c
M_{r,final =}	44.38	kN·m	Resistance in bending with axial loading	11.2.8.2, eq. 11.1
M_f / M_{r =}	0	%	Usage factor	10.5.1.3

Shear resistance

d_v =	150.3	mm	Effective shear depth	2.3
V_{r, max} =	732.7	kN	Maximal shear resistance	11.3.3, eq. 11.5

Simplified method

s_ze =	150.3	mm	Equivalent crack spacing parameter	11.3.6.3, eq. 11.10
β =	0.21			11.3.6.2(a), 11.3.6.3(b) & (c)
V_c =	112.4	kN	Shear resistance of concrete	11.3.4, eq. 11.6

General method

M_f =	0	kN·m		11.3.6.4(a)
ε_x =	0		Longitudinal strain at mid-depth	11.3.6.4(a)
s_ze =	150.3	mm	Equivalent crack spacing parameter	11.3.6.4
β =	0.4521			11.3.6.4, eq. 11.11
V_c =	241.9	kN	Shear resistance of concrete	11.3.4, eq. 11.6

Final Resistance

V_c =	241.9	kN	Shear resistance of concrete
θ =	29	^o	Angle of inclination	11.3.6.4, eq. 11.12
V_s =	0	kN	Shear resistance of steel	11.3.5.1, eq. 11.7
V_r =	241.9	kN	Final shear resistance of slab	11.3.3, eq. 11.5
V_f / V_r =	0	%	Usage factor