GATE 2022 CE (CE2) – Question 54
Sixteen piles form a 4×4 grid, spacing s=3 m, diameter d=1 m, embedment 20 m, each capacity 1000 kN. Given $\eta_g=1-\frac{\theta}{90}\frac{(n-1)m+(m-1)n}{mn}$, $\theta=\tan^{-1}(d/s)$ in degrees, find group capacity (nearest kN).
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Correct answer: 11084
Explanation
The square group has m=n=4. The bracket in the supplied efficiency formula is $[3(4)+3(4)]/16=1.5$, and $\theta=\tan^{-1}(1/3)=18.43495^\circ$.
Thus $\eta_g=1-18.43495/60=0.6927509$. Group capacity is $16(1000)\eta_g=11084.015$ kN, rounded to **11084 kN**.