GATE CE 2020 Set 1 — Question 17
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Structural Engineering → Torsion, Stress Transformation & Columns → Principal Stresses & Planes
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Question
In a two-dimensional stress analysis, the state of stress at a point isThe necessary and sufficient condition for existence of the state of pure shear at the point , is
Correct answer
(C) σₓₓ + σ_(yy) = 0
Solution
For a state of pure shear at a point, the normal stresses on the principal planes must be equal in magnitude and opposite in sign, i.e., , which implies . In a two-dimensional stress state, the sum of the normal stresses is an invariant:For pure shear, the center of Mohr's circle must coincide with the origin . The coordinates of the center are given by:Setting the x-coordinate of the center to zero:Thus, the correct condition is .
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