GATE 2026 MN – Question 43

Geomechanics and Ground Control · Geomechanics · 2 marks · Multiple choice

The flat-jack slots P,Q,R on the gallery wall measure σP,σQ,σR. Slot R is at45° as drawn, σP>σQ and σR=0. Find wall shear stress with the displayed sign convention.

$(\sigma_P+\sigma_Q)/2$
$(\sigma_P-\sigma_Q)/2$
$-(\sigma_P+\sigma_Q)/2$
$-(\sigma_P-\sigma_Q)/2$

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Correct answer: (A) $(\sigma_P+\sigma_Q)/2$

Explanation

The orthogonal slots give the two normal stresses. Stress transformation to the45° slot, with the orientation drawn, gives σR=(σP+σQ)/2−τxy. Since σR=0, τxy=(σP+σQ)/2, A. The half-difference would describe maximum shear only when the original stresses were principal, which is not stated.

GATE 2026 MN – Question 43

Explanation

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