Principal Stresses and Strains MCQ with answer and solution

Concept

Maximum shear stress in plane stress

Formula

τmax = √(((σx - σy) / 2)² + τxy²)

Step-by-step solution

1. The maximum shear stress in plane stress is calculated using τ_max = √(((σx - σy) / 2)² + τxy²). 2. Substitute σx = 60 MPa, σy = 20 MPa, and τxy = 10 MPa into the formula. 3. τ_max = √(((60 - 20) / 2)² + 10²) = √(20² + 10²) = √(500) ≈ 22.36 MPa. Answer: D

Explanation

The maximum shear stress in a plane stress state is calculated using the formula √(((σx - σy)/2)² + τxy²). Substituting the given values yields √(20² + 10²), which equals approximately 22.36 MPa. Therefore, option D is correct.

Why the other options are wrong

A) 10 MPa corresponds only to the given shear stress component τxy rather than the combined maximum shear stress. B) 15 MPa fails to properly combine the normal stress difference with the shear stress in Mohr's circle radius calculation. C) 20 MPa represents only half the normal stress difference rather than the total radius of Mohr's circle.

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