Punching Shear Calculator

Punching is the column pushing through the slab. The failure surface is a cone starting 2d out from the column face, so the critical perimeter is u1 = 2(a + b) + 4πd for a rectangular column — not the column perimeter, and not 4(a + b + 2d). The resistance is vRd,c = 0.12 k (100 rho fck)^(1/3), where k handles the size effect (thicker slabs have lower unit strength, falling from a cap of 2.0, which a 200 mm slab just reaches), rho is the tension reinforcement ratio capped at 2%, and fck is concrete strength, which enters as a cube root. There is also a floor: vRd,c must not be taken below vmin = 0.035 k^1.5 sqrt(fck). At very low reinforcement the expression falls under that, vmin governs, and skipping the check under-predicts capacity by about a fifth. A point often missed: without shear reinforcement, going from C30 to C50 raises the resistance only about 18% because of that cube root. To gain real capacity, increase the slab depth or add a drop panel or links. Above 100% utilisation, shear reinforcement is mandatory, the resistance becomes 0.75 vRd,c u1 d plus the contribution of the links, and the check must be repeated on a perimeter at 1.5d — adding links without rechecking the outer ring just moves the failure outside them. Flat slabs also carry unbalanced moment from the column, and edge and corner columns are the critical cases.