Two-Way Slab Punching Shear at a Column (ACI 318-19 22.6)
The limit state that sets flat-plate thickness and footing depth.
Example
You enter
- Column dimension c1 (in) 20
- Column dimension c2 (in) 20
- Effective slab depth d (in) 6
- Concrete strength f'c (psi) 4000
- Column position (alpha_s) interior
- Lightweight factor lambda 1
You get
- Critical perimeter bo (at d/2) 104 in
- Concrete shear stress vc 253 psi
- Design capacity phi Vc 118.4 kip
Details, formula, and sources
The column punches a truncated cone through the slab on the critical perimeter d/2 from its face. The stress is the least of 4, (2 + 4/beta), and (2 + alpha_s d/bo) times lambda sqrt(f'c) (alpha_s 40/30/20 interior/edge/corner), and phi Vc = 0.75 vc bo d. An interior 20 in column on a d = 6 in slab holds 118.4 kip; grow the column to 36 in and the large-column term takes over - the case a drop panel fixes. No moment transfer or shear reinforcement. A design aid, not the engineer of record's stamped design.
bo = 2(c1 + d) + 2(c2 + d); beta = max(c1,c2)/min(c1,c2); vc = min(4, 2 + 4/beta, 2 + alpha_s d/bo) x lambda sqrt(f'c); phi Vc = 0.75 vc bo d. (alpha_s = 40/30/20 interior/edge/corner)
The ACI 318-19 Table 22.6.5.2 two-way (punching) shear stress (least of the three terms) on the 22.6.4.1 critical section at d/2 from the column face, with alpha_s = 40/30/20 and phi = 0.75, by name.
ACI 318 is readable free through the ACI online reading room at concrete.org; Table 22.6.5.2 and the 22.6.4.1 critical-section definition are in the published code.
Estimate. AHJ and licensed professional govern.
Field names used by the API: c1_in, c2_in, d_in, fc_psi, position, lambda, bo_in, vc_psi, phi_vc_kip
- Critical section the perimeter bo at d/2 from the column faces; capacity phi vc bo dACI 318-19 22.6.4.1
- Three-term least 4, 2 + 4/beta, and 2 + alpha_s d/bo, each x lambda sqrt(f'c); the least governsACI 318-19 Table 22.6.5.2
- Position constant alpha_s = 40 interior, 30 edge, 20 cornerACI 318-19 22.6.5.3