Punching Shear Design

What is punching Shear?

Punching shear arises when a concentrated load is applied to a small area of a slab or, most commonly, the reaction of a column against a slab. The resulting stresses are verified along defined control perimeters around the loaded area.

International Design Codes

ACI 318-19 : Punching Shear Design per ACI 318-19 with ideCAD

TSC 2018 : Punching Shear Stress at Critical Section (7.11.8) (8.3.1) TS500 Puching Shear Design Conditions

Notation in ACI 318-19

A_g = gross area of the concrete section, in²
A_s = area of non-prestressed longitudinal tension reinforcement, in²
b_o = perimeter of critical section for two-way shear in slabs and footings.
b_slab = effective slab width, in.
b₁ = dimension of the critical section b_o measured in the direction of the span for which moments are determined.
b₂ = dimension of the critical section b_o measured in the direction perpendicular to b₁, in.
d = distance from extreme compression fiber to centroid of longitudinal tension reinforcement, in.
E_c = modulus of elasticity of concrete, psi
E_s = modulus of elasticity of reinforcement, psi
√f_c‘ = square root of specified compressive strength of concrete, psi
f_c^' = specified compressive strength of concrete, psi
f_y = specified yield strength for non-prestressed reinforcement, psi
J_c = property of assumed critical section analogous to the polar moment of inertia
M_sc = factored slab moment that is resisted by the column at a joint, in.-lb
v_c = stress corresponding to nominal two-way shear strength provided by concrete, psi
v_uv = factored shear stress on the slab critical section for two-way action, from the controlling load combination, without moment transfer, psi
α_s = constant used to calculate V_c in slabs and footings
ϕ = strength reduction factor
λ = modification factor to reflect the reduced mechanical properties of lightweight concrete relative to normalweight concrete of the same compressive strength
λ_s = factor used to modify shear strength based on the effects of member depth, commonly referred to as the size effect factor
ε_t = net tensile strain in an extreme layer of longitudinal tension reinforcement at nominal strength, excluding strains due to effective prestress, creep, shrinkage, and temperature
ε_ty = value of net tensile strain in the extreme layer of longitudinal tension reinforcement used to define a compression-controlled section
γ_f = factor used to determine the fraction of M_sc transferred by slab flexure at slab-column connections
γ_v = factor used to determine the fraction of M_sc transferred by the eccentricity of shear at slab-column connections