When a body is subjected to biaxial stress i.e. direct stresses (σ_x) and (σ_y) in two mutually perpendicular planes accompanied by a simple shear stress (τ_xy), then minimum normal stress is

Question

A. (σ_x + σ_y)/2 + (1/2) × √[(σ_x - σ_y)² + 4 τ²_xy]

B. (σ_x + σ_y)/2 - (1/2) × √[(σ_x - σ_y)² + 4 τ²_xy]

C. (σ_x - σ_y)/2 + (1/2) × √[(σ_x + σ_y)² + 4 τ²_xy]

D. (σ_x - σ_y)/2 - (1/2) × √[(σ_x + σ_y)² + 4 τ²_xy]

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Accepted Answer

B. (σ_x + σ_y)/2 - (1/2) × √[(σ_x - σ_y)² + 4 τ²_xy]

When a body is subjected to biaxial stress i.e. direct stresses (σx) and (σy) in two mutually perpendicular planes accompanied by a simple shear stress (τxy), then minimum normal stress is