Punching Shear Slab Calculator
Estimate punching shear slab for your project with our free calculator. Get accurate material quantities, costs, and specifications.
Formula
vc = min(0.33*sqrt(fc), 0.17*(1+2/beta)*sqrt(fc), 0.083*(alpha_s*d/b0+2)*sqrt(fc))
The punching shear capacity per ACI 318 is the minimum of three equations. The first is the basic two-way shear stress, the second accounts for rectangular column aspect ratio (beta), and the third considers the critical perimeter to depth ratio. The design capacity phi*Vc uses a strength reduction factor of 0.75.
Worked Examples
Example 1: Interior Column Punching Shear Check
Problem: Check punching shear for a 400x400 mm column supporting a 250 mm slab with fc = 30 MPa and Vu = 500 kN.
Solution: d = 250 - 40 = 210 mm\nb0 = 2(400+210) + 2(400+210) = 2440 mm\nvc = 0.33*sqrt(30) = 1.807 MPa\nphi*Vc = 0.75 * 1.807 * 2440 * 210 / 1000 = 694.1 kN
Result: phi*Vc = 694.1 kN > 500 kN, slab is adequate (72% utilized)
Example 2: Rectangular Column with High Aspect Ratio
Problem: Check punching shear for a 200x600 mm column, 300 mm slab, fc = 35 MPa, Vu = 800 kN.
Solution: d = 260 mm, b0 = 2(200+260) + 2(600+260) = 2640 mm\nbeta = 600/200 = 3.0\nvc2 = 0.17*(1+2/3)*sqrt(35) = 1.676 MPa (governs)\nphi*Vc = 0.75 * 1.676 * 2640 * 260 / 1000 = 862.7 kN
Result: phi*Vc = 862.7 kN > 800 kN, slab is adequate (93% utilized)
Frequently Asked Questions
What is punching shear in flat slabs?
Punching shear is a failure mode where a concentrated load, typically from a column, punches through a flat slab along a truncated cone or pyramid shape. It occurs around the perimeter of the column at a critical section located at a distance d/2 from the column face, where d is the effective depth of the slab. This type of failure is sudden and brittle, making it one of the most critical checks in flat slab design.
How is the critical perimeter calculated for punching shear?
The critical perimeter b0 is measured at a distance of d/2 from the face of the column, where d is the effective depth of the slab. For a rectangular column of dimensions c1 by c2, the critical perimeter is b0 = 2(c1 + d) + 2(c2 + d). For circular columns, it forms a circle with diameter equal to the column diameter plus d. Edge and corner columns have reduced perimeters since part of the critical section extends beyond the slab edge.
What factors affect punching shear capacity according to ACI 318?
ACI 318 considers three factors that limit punching shear capacity: the basic two-way shear stress of 0.33*sqrt(fc), the column aspect ratio (beta) which reduces capacity for elongated columns, and the alpha-s factor which accounts for the ratio of critical perimeter to effective depth. The governing capacity is the minimum of these three checks. Concrete compressive strength, slab thickness, and column dimensions are the primary variables.
When is punching shear reinforcement required?
Punching shear reinforcement is required when the factored shear demand Vu exceeds the design shear capacity phi*Vc. Common reinforcement options include shear studs (stud rails), stirrup cages, and drop panels or column capitals that increase the effective slab depth locally. Shear studs are the most common modern solution as they can increase the punching shear capacity by up to 50-75% compared to the unreinforced slab capacity.
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