Two-Way Slab Punching Shear at a Column (ACI 318-19 22.6)
The limit state that sets flat-plate thickness and footing depth: 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.
Formula and source
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.
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