Punching Shear Slab Calculator

Punching shear is the two-way shear failure in which a column pushes a truncated cone of concrete straight through a flat slab. It is checked on a critical perimeter b0 drawn at half the effective depth from the column face, giving b0 equal to 2 times the quantity c1 plus d, plus 2 times the quantity c2 plus d for a rectangular interior column. ACI 318 sets the nominal stress as the smallest of three expressions in SI units: a baseline 0.33 times the square root of fc, a term of 0.17 times one plus two over beta that penalizes elongated columns, and a term of 0.083 times the quantity alpha-s times d over b0 plus two that penalizes very long perimeters relative to depth. The alpha-s constant is 40 for interior columns, 30 for edge columns, and 20 for corner columns. A strength reduction factor of 0.75 converts nominal to design capacity. Effective depth dominates: capacity scales with both b0 and d, while concrete strength enters only as a square root, so doubling fc from 30 to 60 MPa gains just 41 percent. This tool assumes d equals the slab thickness minus 40 mm and treats the connection as an interior column with concentric load. Several real effects are excluded. Unbalanced moment transfer at edge and corner columns forces part of the moment across the critical section as eccentric shear, which routinely governs perimeter connections. ACI 318-19 also introduced a size effect factor that reduces capacity for slabs with effective depth beyond about 250 mm.

The failure mode was documented long before it had a formula. Arthur Newell Talbot, testing reinforced concrete footings at the University of Illinois around 1913, reported specimens in which the column drove a truncated pyramid of concrete through the slab rather than failing in bending, and he recognized it as a distinct problem needing its own check. Flat slab construction was spreading rapidly at the time, driven by C. A. P. Turner and others, which made the question commercially urgent as well as academically interesting. Systematic testing came in the 1950s and early 1960s, largely at the Portland Cement Association laboratories, where Eivind Hognestad, Richard Elstner, and Johannes Moe accumulated the slab-column test data that still anchors the provisions. Moe published his influential report on the shear strength of slabs around columns in 1961. The joint ACI-ASCE Committee 326 report on shear and diagonal tension, issued in 1962, consolidated this work and established the conventions still in use: a critical section at d/2 from the column face and a nominal strength proportional to the square root of concrete strength. The aspect ratio and perimeter-to-depth terms were added in later editions as tests showed the single baseline equation was unconservative for elongated columns and large perimeters. The stakes were underscored by the 1981 collapse of the Harbour Cay Condominium in Cocoa Beach, Florida, a flat plate failure that killed eleven workers and drew federal scrutiny to slab effective depth.