GATE 2022 CE (CE2) – Question 32
A concentrically loaded isolated square footing of size 2 m × 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)
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Correct answer: 4.35 to 4.39
Explanation
The footing pressure is $q=1000/(2\times2)=250$ kPa, so the 10% bulb corresponds to 25 kPa. For the stated concentrated-load Boussinesq approximation, maximum depth occurs directly below the load.
Use $\sigma_z=3P/(2\pi z^2)$: $z=\sqrt{3000/(50\pi)}=4.37019$ m. **Answer: 4.37 m**.