Q1: If qis the punching shear resistance per unit area a, is the side of a square footing for a column of side b, carrying a weight W including the weight of the footing, the depth (D) of the footing from punching shear consideration, is

ANS:B -

To determine the depth (D) of the footing required to resist punching shear, we need to consider the punching shear resistance per unit area (q) and the weight (W) carried by the column, including the weight of the footing. We'll assume that the column is centrally located on the square footing with a side length of b. The punching shear resistance (V) of the footing can be calculated as the product of the punching shear resistance per unit area (q) and the area of the footing in contact with the column. Since the footing is square with side length b, the area in contact with the column is b×b=b^2. Therefore, the punching shear resistance (V) is given by: V=q×b^2 To ensure the footing is adequate to resist punching shear, the punching shear resistance should be greater than or equal to the applied load (W). Mathematically, this can be expressed as: q×b^2≥W To find the depth (D) of the footing, we need to consider the shear stress (τ) acting on the critical section. The critical section for punching shear is typically assumed to be located at a distance of d/2 from the face of the column, where d is the depth of the footing. The shear stress (τ) at the critical section can be calculated using the formula: τ=​V/Ac​ Where:

• Ac​ is the critical section area, which is equal to b×d for a square footing.

Now, we equate the shear stress to the punching shear resistance per unit area (q) to solve for the depth (D): V/Ac​=q q×b^2/b×d ​=q d=q×b/q×b^2​ d=b Therefore, the depth (D) of the footing from punching shear consideration is equal to the side length of the square footing (b). This means that the depth of the footing should be equal to its side length to adequately resist punching shear.