About Punching Shear Calculator (ACI 318)
The punching shear calculator checks two-way (punching) shear in a flat concrete slab at a rectangular supporting column following ACI 318. It builds the critical control perimeter b0 located d/2 from the column face, where d is the effective slab depth, for interior, edge, and corner column positions.
It evaluates the three ACI limits on the concrete two-way shear stress vc, takes the governing (least) value, and compares the factored demand stress vu = Vu / (b0 d) against the design capacity phi*vc using the shear reduction factor phi = 0.75. Inputs use SI units (MPa, mm, N), and the tool reports the punching capacity and the utilisation ratio.
How It Works
- Select the column position (interior, edge, or corner), which sets the perimeter geometry and the constant alphaS (40, 30, or 20).
- Enter the concrete strength fc (MPa), column dimensions c1 and c2 (mm), the effective depth d (mm), and the factored shear Vu (N).
- The calculator forms the control perimeter b0 at d/2 from the face and computes the three vc limits, taking the smallest as the governing concrete capacity.
- It computes the demand stress vu = Vu / (b0 d) and checks it against phi*vc with phi = 0.75, reporting the capacity phi*vc*b0*d and the utilisation ratio.
Worked Example
An interior 400 x 400 mm column supports a flat slab with effective depth d = 200 mm and concrete fc = 30 MPa, carrying a factored punching shear Vu = 400 kN. The control perimeter is b0 = 2(400+200) + 2(400+200) = 2400 mm. With beta = 1, the governing vc is the aspect limit 0.33*sqrt(30) = 1.808 MPa, so phi*vc = 0.75*1.808 = 1.356 MPa and the capacity is 1.356 * 2400 * 200 = 650,694 N (651 kN). The demand vu = 400,000 / (2400*200) = 0.833 MPa, giving a utilisation of 0.833/1.356 = 0.61, so the slab is adequate.
Formulas
- Control perimeter b0 at d/2
interior: b0 = 2(c1+d) + 2(c2+d) | edge: b0 = 2(c1+d/2) + (c2+d) | corner: b0 = (c1+d/2) + (c2+d/2)- Concrete two-way shear stress limits (SI, ACI 318)
vc = min[ 0.33*L*sqrt(fc), 0.17*(1 + 2/beta)*L*sqrt(fc), 0.083*(2 + alphaS*d/b0)*L*sqrt(fc) ]- Design strength check
vu = Vu / (b0 * d) <= phi * vc, phi = 0.75- Punching capacity and utilisation
phi*Vc = phi * vc * b0 * d ; utilisation = vu / (phi * vc)
Standards & References
- ACI 318 Building Code Requirements for Structural Concrete
- ACI 318-19 Table 22.6.5.2 (two-way shear)
Frequently Asked Questions
Where is the critical punching shear perimeter located?
ACI 318 places the critical section at a distance d/2 from the face of the column, where d is the effective slab depth. The control perimeter b0 wraps around the column at this offset, with reduced sides for edge and corner columns.
Why are there three different limits on vc?
ACI 318 limits the concrete two-way shear stress by the least of three expressions: a baseline 0.33*sqrt(fc), a reduction for elongated columns through the aspect ratio beta, and a reduction for large perimeters relative to depth through alphaS*d/b0. The smallest value governs.
What is phi and why is it 0.75?
Phi is the strength reduction factor that converts nominal capacity into design capacity. For shear, ACI 318 uses phi = 0.75, so the slab is adequate when the factored demand stress vu does not exceed phi*vc.
Does this calculator include shear reinforcement or moment transfer?
No. It checks the concrete punching capacity for concentric shear only. Unbalanced moment transfer increases the peak stress through a gamma_v factor, and shear studs or stirrups raise the capacity; both require a more detailed analysis.