Punching Shear Calculator
This punching shear calculator checks two-way (punching) shear in a reinforced concrete flat slab at a column per ACI 318-19. It locates the critical section d/2 from the column face, computes the critical perimeter bo, evaluates the three code equations for the concrete shear stress vc, and reports the design strength φVc against your factored load. The result includes the demand-to-capacity ratio and a stud-rail recommendation when reinforcement is needed.
Formula
vc = min(4, 2 + 4/β, 2 + αs·d/bo) · λ·√f′c ; φVc = 0.75 · vc · bo · d / 1000
- bo
- Critical perimeter at d/2 from the column face (inches)
- β
- Ratio of long to short column side dimension
- αs
- Column-location factor: 40 interior, 30 edge, 20 corner
- d
- Slab effective depth (inches)
- f′c
- Specified concrete compressive strength (psi); λ = 1.0 for normal-weight concrete
How it works
- Select the column position (interior, edge, or corner), which sets both the critical perimeter geometry and the αs factor (40, 30, or 20).
- Enter the column width and depth, the slab effective depth d, and the concrete strength f′c in psi. The critical perimeter is built at d/2 from each loaded face.
- Enter the factored shear load Vu in kips. The tool computes vc as the minimum of the three ACI equations, the design strength φVc with φ = 0.75, the demand-capacity ratio, and whether shear reinforcement (stud rails) is required.
Worked example
An interior 24 in × 24 in column supports a 10-inch slab with effective depth 8.5 in, f′c = 4000 psi, and a factored load Vu = 100 kips.
- Critical perimeter bo = 2·((24 + 8.5) + (24 + 8.5)) = 2·(32.5 + 32.5) = 130 in.
- β = 24/24 = 1, so the three vc values are 4√4000, (2 + 4/1)√4000, and (2 + 40·8.5/130)√4000.
- These equal 253.0, 379.5, and 291.0 psi; vc = min = 252.98 psi (governed by the 4√f′c equation).
- φVc = 0.75 × 252.98 × 130 × 8.5 / 1000 = 209.66 kips; DCR = 100 / 209.66 = 0.477.
bo = 130 in, vc ≈ 252.98 psi, φVc ≈ 209.66 kips, and DCR ≈ 0.477 — the slab is adequate with no stud rails required.
Frequently asked questions
- Where is the critical section for punching shear?
- ACI 318 places the critical section at a distance d/2 from the face of the column, where d is the slab effective depth. The perimeter of this section, bo, depends on whether the column is interior, edge, or corner.
- Why are there three equations for vc?
- ACI 318-19 limits the two-way shear stress with three expressions that account for the slab depth, the column aspect ratio β, and the perimeter-to-depth ratio. The governing concrete capacity is the smallest of the three.
- What happens when the demand-capacity ratio exceeds 1.0?
- When DCR is above 1.0 the concrete alone cannot carry the punching load, so the tool recommends shear reinforcement such as stud rails. Headed shear studs raise the allowable shear and let the slab carry more load without thickening.
- Does this calculator include unbalanced moment transfer?
- The core check covers direct punching shear. Unbalanced moment increases the peak shear stress on one face of the critical section and should be added separately for edge and corner columns where moment transfer is significant.