Combined footing depth governed by punching shear: Based on punching shear considerations under column A, the overall depth of a combined footing should be chosen so that which condition is satisfied?

Introduction / Context:
Combined footings support two or more columns and are designed for bending, one-way shear, and two-way (punching) shear. Of these, punching shear near a column can govern the required thickness, especially under high concentrated loads.

Given Data / Assumptions:

• Combined footing supporting at least one column A.
• Critical section for punching shear taken around the column.
• Allowable shear stress of concrete considered without shear reinforcement (unless provided).

Concept / Approach:
The critical perimeter for punching is typically located at a distance d/2 from the loaded area (column face) all around. The design condition is: V_u / (b_0 * d) ≤ τ_c,allowable, where V_u is factored shear, b_0 is critical perimeter length, and d is effective depth. Satisfying this often controls the overall depth.

Step-by-Step Solution:
Determine column load and footing reaction near the column.Compute V_u at the critical section located d/2 from the column face.Choose depth so that V_u / (b_0 * d) ≤ τ_c,allowable; increase overall depth if needed.

Verification / Alternative check:
After meeting punching, check one-way shear along a line at distance d from column face, and bending moments along the footing length. Adjust bar sizes and layout accordingly.

Why Other Options Are Wrong:
Bending stress limit (option b) controls steel area, not necessarily overall depth.Average soil pressure (option c) relates to sizing and proportioning plan area, not thickness.None of these: The punching criterion is the standard depth-governing check.

Common Pitfalls:

• Using the wrong punching perimeter location (not at d/2).
• Ignoring load eccentricity and column moments that increase V_u.

Final Answer:
The nominal punching shear stress at the critical perimeter located at a distance d/2 from the column face does not exceed the allowable shear stress of concrete