GATE 2023 CE (CE2) – Question 58
A square footing is to be designed to carry a column load of 500 kN which is resting on a soil stratum having the following average properties: bulk unit weight = 19 kN/m$^3$; angle of internal friction = 0° and cohesion = 25 kPa. Considering the depth of the footing as 1 m and adopting Meyerhof’s bearing capacity theory with a factor of safety of 3, the width of the footing (in m) is ______ (round off to one decimal place). [Assume the applicable shape and depth factor values as unity; ground water level at greater depth.]
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Correct answer: 3.0 to 3.5
Explanation
For $\phi=0$, Meyerhof gives $N_c=\pi+2=5.14$, $N_q=1$, and $N_\gamma=0$. Net ultimate capacity is $25(5.14)=128.5$ kPa. With safety factor 3 the net safe pressure is 42.83 kPa. Size the area for the column load using this net pressure: $B=\sqrt{500/42.83}=3.42$ m, or 3.4 m. Adding overburden to the safe pressure while retaining the unreduced column pressure gave the former undersized footing.
Official GATE 2023 answer key: https://gate2026.iitg.ac.in/doc/download/Answer_keys2023/CE2_ANS_GATE2023.pdf