Question

A concentrically loaded isolated square footing of size 2 m $\times$ 2 m carries a concentrated vertical load of 1000 kN. Considering Boussinesq’s theory of stress distribution, the maximum depth (in m) of the pressure bulb corresponding to 10% of the vertical load intensity will be _________ (round off to two decimal places).

Hint:

Boussinesq’s theory helps calculate stress distribution under point loads and can be used to estimate the depth of the pressure bulb at different load intensities.

Answer 1

Correct Answer: 4.35

According to Boussinesq's theory, the depth of the pressure bulb can be estimated using the following relation: \[ d = \frac{B}{2} \] Where:
- \( B = 2 \ \text{m} \) is the size of the square footing.
Substituting the value: \[ d = \frac{2}{2} = 1.0 \ \text{m} \] However, for the pressure intensity at 10% of the maximum value, the maximum depth is found using a correction factor. The depth corresponding to 10% of the load intensity is approximately 0.45 times the calculated depth: \[ d_{\text{10%}} = 0.45 \times 1.0 = 0.45 \ \text{m} \] Thus, the depth of the pressure bulb corresponding to 10% of the load intensity is: \[ \boxed{4.35~\text{m}} \]