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Ann-Kathrin Dannwerth, B.Sc.

2026-07-22

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Punching

IBC 2021 / ACI 318-19 (LRFD): Punching Shear Design

Design Purpose

The punching shear design checks whether the shear force acting on the column does not exceed the load capacity of the foundation plate in the area of the basic control perimeter.
The design is performed at the perimeter section, located at a distance of d/2 from the loaded surface.

Punching Shear Resistance

According to ACI 318, the punching shear resistance for plates without shear reinforcement is determined as the smallest value among three failure criteria (ACI 22.6.5.2):

\begin{matrix} v_{c, a} = 4 \cdot λ_{s} \cdot λ \cdot \min (\sqrt{{f^{'}}_{c}}; \sqrt{{f^{'}}_{c, \lim}}) \\ v_{c, b} = (2 + \frac{4}{β}) \cdot λ_{s} \cdot λ \cdot \min (\sqrt{{f^{'}}_{c}}; \sqrt{{f^{'}}_{c, \lim}}) \\ v_{c, c} = (2 + α_{s} \cdot \frac{d}{b_{0}}) \cdot λ_{s} \cdot λ \cdot \min (\sqrt{{f^{'}}_{c}}; \sqrt{{f^{'}}_{c, \lim}}) \\ v_{c} = \min (v_{c, a}; v_{c, b}; v_{c, c}) \\ λ_{s} = \min (\sqrt{\frac{2}{1 + 0.1 \cdot d}}; 1) \\ β = \frac{\max (b, h)}{\min (b, h)} \end{matrix}

λ	Modification factor for lightweight concrete (= 1.0 for normal concrete)
α_s	Location factor (40 for inner column, 30 for edge column, 20 for corner column)
d₀	Length of the perimeter section [in]

Punching Shear Resistance

The design resistance is given by φ · v_c, where φ = 0.75 (strength reduction factor for shear and torsion, ACI 21.2).

Punching Shear Stress

The existing punching shear stress consists of the basic stress component resulting from the shear force at the basic control perimeter, as well as the stress components resulting from the moment transfer (asymmetric shear stress distribution):

\begin{matrix} v_{u} = v_{uv} - \frac{γ_{v, 1} \cdot M_{sc, 1, sl} \cdot e_{1}}{J_{1}} + \frac{γ_{v, 2} \cdot M_{sc, 2, sl} \cdot e_{2}}{J_{2}} \\ v_{uv} = \frac{V_{u, res}}{b_{0} \cdot d} \\ γ_{v, 1}, γ_{v, 2} = 1 - γ_{f, 1 / 2} \end{matrix}

V_u,res	Governing shear force within the basic control perimeter (support force minus the soil pressure component within the perimeter section)
M_sc,1, M_sc,2	Calculated plate moment in the 1st/2nd direction
e₁, e₂	Distance from the center of mass of the perimeter section to the point of maximum stress
J₁, J₂	Moment of inertia for bending of the basic control perimeter

Existing Punching Shear Stress

Design / Design Ratio

η = \frac{| v_{u} |}{φ \cdot v_{c}} \leq 1.0

Design Condition and Design Ratio – Punching

Software Configuration

The material properties are taken from the assigned concrete and reinforcement materials. The geometry of the basic control perimeter (b₀, location relative to the edge/corner/internal column) is automatically determined from the foundation and column dimensions. The shear force and the moment components are determined from the governing load combinations.

Parent Chapter

Internal Stability – Reinforced Concrete Design