GATE 2017 CE (CE2) – Question 54
Four 5000 kN point loads act at corners A, B, C, D of a 4 m × 4 m square as shown. By Boussinesq theory, vertical stress increment 5 m below centre M, to one decimal place, is ______ kPa.
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Correct answer: 187.0 to 192.0
Explanation
Each load is at radial distance $r=\sqrt{2^2+2^2}=\sqrt8$ m. Sum four Boussinesq contributions: $$\Delta\sigma_z=\frac{4(3)(5000)}{2\pi(5^2)[1+8/25]^{5/2}}=190.808\ \mathrm{kPa}.$$ Rounded answer: 190.8 kPa.