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Punching Shear Force on a Footing

Mediumfootingpunching-shearequilibrium
A centered 400 mm square column applies a factored load Pu = 900 kN to a square footing with effective depth d = 200 mm. The footing extends well beyond the critical perimeter. The uniform net factored upward soil pressure is 100 kPa (footing weight and overburden already removed from it), balancing the column load; no moment is transferred. The critical square lies d/2 from every column face. What is the punching-shear demand Vu across that perimeter?
  1. A900 kN
  2. B884 kN
  3. C864 kN
  4. D836 kN
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Answer: C. 864 kN

Equation: Vu = Pu − qu,net·Ainside. Inputs: critical side = c + d = 0.4 + 0.2 = 0.6 m, Ainside = 0.36 m². Substitution: upward force inside = 100(0.36) = 36 kN; Vu = 900 − 36 = 864 kN. Wrong: 900 kN ignores the soil pressure inside the perimeter; 884 kN subtracts pressure over only the column area (0.16 m²); 836 kN uses a side of c + 2d = 0.8 m (perimeter d from the face).
kN
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