Punching shear in footings per ACI 318-19

Q: What is the critical section for punching shear in a footing?

Per ACI 318-19 Section 22.6.4.1, the critical section is located at d/2 from the face of the column or loaded area, where d is the average effective depth of both reinforcement layers (Section 22.6.2.1). For a square interior column of side c on a footing, the critical perimeter is bo = 4(c + d).

Q: Does the ACI 318-19 size effect factor apply to footings?

No. Per ACI 318-19 Section 13.2.6.2, the size effect factor lambda_s is taken as 1.0 for footings. This exemption recognizes that footing behavior under punching is better-constrained than flat slabs: the soil provides distributed upward reaction, and punching failure cracks in footings are steeper than in slabs.

Two-way (punching) shear is the tendency of the column to punch through the footing slab. ACI 318-19 evaluates it on a closed perimeter at d/2 from the column face (Section 22.6.4.1). Three concrete shear-strength equations from Table 22.6.5.2 apply; the smallest governs. This page covers punching shear for isolated footings under concentric loading. Eccentric moment transfer (γ_v / J_c per Section 8.4.4.2) is a separate analysis not covered here.

Applicable clauses

Clause	Requirement
§22.6.4.1	Critical section at d/2 from the face of the column or loaded area.
§22.6.2.1	d = average effective depth of both reinforcement layers.
Table 22.6.5.2	Three v_c equations; the smallest governs (see below).
§22.6.5.3	α_s = 40 (interior), 30 (edge), 20 (corner).
§22.6.3.1	√f'_c capped at 100 psi for two-way shear.
§13.2.6.2	λ_s = 1.0 for footings (size effect exemption).
Table 21.2.1	φ = 0.75 for shear.

Critical section geometry

The critical section is a closed perimeter located d/2 from the face of the column, where d is the average effective depth:

d = \frac{d_1 + d_2}{2}

d₁ = h − cover − d_b/2 (effective depth to the bottom reinforcement layer)
d₂ = h − cover − d_b − d_b/2 (effective depth to the top layer, same bar size)

For a square interior column of side c_col, the critical perimeter and enclosed area are:

b_o = 4\,(c_{col} + d)

A_{crit} = (c_{col} + d)^2

For edge and corner columns the perimeter is truncated at the footing edge, and α_s changes (see the lookup table below). calcnote handles all three column positions automatically.

The three v_c equations (Table 22.6.5.2)

ACI 318-19 provides three concrete shear-strength equations. The governing value is the smallest of the three:

(a) General two-way shear:

v_{c,a} = 4\,\lambda_s\,\lambda\,\sqrt{f'_c}

(b) Column aspect ratio (β = long side / short side of column):

v_{c,b} = \left(2 + \frac{4}{\beta}\right)\lambda_s\,\lambda\,\sqrt{f'_c}

v_{c,c} = \left(2 + \frac{\alpha_s\,d}{b_o}\right)\lambda_s\,\lambda\,\sqrt{f'_c}

The governing capacity is:

v_c = \min(v_{c,a},\; v_{c,b},\; v_{c,c})

Equation (a) is the general cap. Equation (b) accounts for elongated columns where stress concentrates at the short sides. Equation (c) prevents the formula from becoming unconservative for very large perimeters relative to the slab depth. For square interior columns on typical footings, equation (a) almost always governs.

α_s by column position

Column position	α_s	When it applies
Interior	40	Column surrounded by footing on all four sides.
Edge	30	One face of column at or near the footing edge.
Corner	20	Two adjacent faces at or near the footing edge.

Footing-specific provisions

λ_s = 1.0 (Section 13.2.6.2): The size effect factor λ_s is taken as 1.0 for footings. This exemption recognizes that footing behavior under punching is better-constrained than flat slabs: the soil provides distributed upward reaction, and punching failure cracks in footings are steeper than in slabs.

√f'_c cap (Section 22.6.3.1): For two-way shear, √f'_c shall not exceed 100 psi. This limits the benefit of high-strength concrete in punching calculations. With f'_c = 10,000 psi, √f'_c = 100 psi exactly; concrete above 10,000 psi yields no additional punching capacity.

Computing V_u (demand)

The factored shear demand at the critical section equals the total factored column load minus the upward soil reaction acting within the critical perimeter:

V_u = P_u - q_u \cdot A_{crit}

q_u = P_u / (L × B) for concentric loading (uniform factored soil pressure).
A_crit = (c_col + d)² for a square interior column.

The soil reaction inside the critical section pushes up against the punching cone, so it offloads the critical section. Omitting this deduction is conservative but can lead to unnecessarily thick footings.

Punching shear vs one-way shear

For typical isolated footings with centered square columns, punching shear is the more critical check. One-way shear tends to govern for long rectangular footings, large columns relative to the footing width, or wall footings (which have no punching check because the loaded area extends the full wall width and no closed perimeter forms). calcnote checks both automatically and reports the governing case.

Worked example: interior column

Input	Value
f'_c	4,000 psi
λ	1.0 (normal-weight)
Column	16 × 16 in, interior
Footing	7 ft × 7 ft × 20 in thick
Reinforcement	#8 bars both ways, 3 in cover
P_u	150 kips (concentric)

Step 1: Effective depth

d₁ = 20 − 3 − 0.5 = 16.5 in
d₂ = 20 − 3 − 1.0 − 0.5 = 15.5 in
d = (16.5 + 15.5) / 2 = 16.0 in

Step 2: Critical perimeter

b_o = 4 × (16 + 16) = 128 in
A_crit = (16 + 16)² = 1,024 in²

Step 3: Demand

q_u = 150,000 / (84 × 84) = 21.26 psi
V_u = 150,000 − 21.26 × 1,024 = 128,230 lb

Step 4: Capacity

√f'_c = 63.25 psi (< 100; no cap)
λ_s = 1.0 (footing), β = 16/16 = 1.0, α_s = 40 (interior)
v_c,a = 4 × 1.0 × 1.0 × 63.25 = 253.0 psi
v_c,b = (2 + 4/1.0) × 63.25 = 379.5 psi
v_c,c = (2 + 40 × 16/128) × 63.25 = 442.8 psi
v_c = min(253.0, 379.5, 442.8) = 253.0 psi (equation a governs)

Step 5: Check

φV_c = 0.75 × 253.0 × 128 × 16 = 388,608 lb = 388.6 kips
V_u = 128.2 kips < 388.6 kips → OK (DCR = 0.33)

For a square column, β = 1 makes equation (b) = 6√f'_c, which never governs over (a) = 4√f'_c. On typical footings (column dimension well under 4d), equation (a) also governs over (c). For very large columns on thin footings (c_col > 4d), equation (c) can drop below (a) and control. Rectangular columns with β > 2 are where equation (b) begins to control.

Frequently asked questions

What is the critical section for punching shear in a footing?

Per ACI 318-19 §22.6.4.1, the critical section is located at d/2 from the face of the column or loaded area, where d is the average effective depth of both reinforcement layers (§22.6.2.1). For a square interior column of side c on a footing, the critical perimeter is b_o = 4(c + d).

How do you calculate punching shear demand V_u for a footing?

The factored shear demand at the critical section equals the total factored column load minus the upward soil reaction acting within the critical perimeter: V_u = P_u − q_u × A_crit. For concentric loading, q_u = P_u / (L × B) and A_crit is the area enclosed by the critical section (for example, (c + d)² for a square interior column).

Does the ACI 318-19 size effect factor apply to footings?

No. Per §13.2.6.2, the size effect factor λ_s is taken as 1.0 for footings. This exemption recognizes that footing behavior under punching is better-constrained than flat slabs: the soil provides distributed upward reaction, and punching failure cracks in footings are steeper than in slabs.

When does punching shear govern over one-way shear in a footing?

Sources

ACI 318-19: §22.6.4.1 (critical section), §22.6.2.1 (average d), Table 22.6.5.2 (three v_c equations), §22.6.5.3 (α_s), §22.6.3.1 (√f'_c cap), §13.2.6.2 (λ_s = 1.0 for footings), Table 21.2.1 (φ = 0.75).