For a circular column of 200 mm radius, a circular footing of radius 1.25 m is provided. If the depth of footing is 600 mm and factored earth pressure is qu, the design two-way shear will be

Concept:

To calculate the design two-way shear (punching shear) for a circular column and footing, we use the formula based on the areas of the column and the footing.

\( \text{Design Punching Shear} = q_0 \pi (R^2 - r_0^2) \)

Given Data:

• Radius of the circular column, $r_0 = 200 \, \text{mm} = 0.2 \, \text{m}$
• Radius of the circular footing, $R = 1.25 \, \text{m}$
• Depth of the footing, $d = 600 \, \text{mm} = 0.6 \, \text{m}$
• Factored earth pressure, $q_u$

Calculation:

1. Substitute the given values into the formula:

\( \text{Design Punching Shear} = q_u \pi (1.25^2 - 0.2^2) \)

2. Calculate the squared values:

\( 1.25^2 = 1.5625 \) and \( 0.2^2 = 0.04 \)

3. Substitute these values back into the formula:

\( \text{Design Punching Shear} = q_u \pi (1.5625 - 0.04) \)

\( \text{Design Punching Shear} = q_u \pi (1.5225) \)

The design two-way shear is approximately $1.5225 \pi q_u$ .