GATE CE 2026 Set 2 — Question 17
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Structural Engineering → Torsion, Stress Transformation & Columns → Principal Stresses & Planes
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Question
Which one of the following stress conditions represents the state of pure shear stress?
Correct answer
(A) [figure]
Solution
A state of pure shear stress is characterized by a stress condition where the principal stresses are equal in magnitude but opposite in sign, i.e., . This results in a Mohr's circle centered at the origin of the - plane.In option (A), the element is subjected to a normal tensile stress of 40 units in the x-direction () and a normal compressive stress of 40 units in the y-direction (), with no shear stress on these planes (). The principal stresses are thus and . Since , this represents a state of pure shear stress.Other options represent different states:
- (B) represents hydrostatic tension ().
- (C) represents a general state of stress with both normal and shear components.
- (D) represents a state of hydrostatic tension (or compression depending on arrow direction).
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