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?
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AThe 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
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BThe bending tensile stress at midspan is less than the permissible stress in steel
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CThe average bearing pressure under the footing is less than one-third of the soil’s safe bearing capacity
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DNone of these
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E—
Answer
Correct 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
Explanation
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