Project ForgeStrength of Materials
Stress & Strain
GATE 2016
Expert
The state of plane stress at a point, (σxx, σyy, τxy), is equivalent in another (45°-rotated) coordinate system to a pure shear state with shear stress p on all faces (with zero normal stress). The components (σxx, σyy, τxy) in the original system are given by
- A(p/√2, -p/√2, 0)
- (0, 0, p)
- C(p, -p, p/√2)
- D(0, 0, p/√2)
Explanation
A pure-shear state on faces rotated 45° from the principal/original axes corresponds to (σxx, σyy, τxy) = (0, 0, p) in the original coordinate system — a classic stress-transformation identity (equal and opposite normal stresses at 45° become pure shear, and vice versa).
Source: GATE ME 2016 Set-3 (2016)
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