Project ForgeA linear elastic structure under plane stress condition is subjected to two sets of loading, I and II. Loading I is uniaxial tension σ along the x-axis (σxx=σ, σyy=0, τxy=0). Loading II is the same uniaxial tension σ but applied along a direction rotated 45° from the x-axis. If these two sets of loading are applied simultaneously, then the net normal component of stress σxx is ________.
- 3σ/2
- Bσ(1+1/√2)
- Cσ/2
- Dσ(1−1/√2)
Explanation
By superposition, total σxx = (σxx from loading I) + (σxx from loading II). Loading I directly contributes σxx=σ. For loading II, a uniaxial stress σ applied at angle θ=45° from x transforms to σxx=σcos²θ in the original x-y frame; with θ=45°, cos²45°=1/2, so loading II contributes σ/2. Total σxx = σ+σ/2 = 3σ/2.
Source: GATE ME 2022 Session 2 (ME-2) (2022)
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