Simple Stress and Strain MCQ with answer and solution

Concept

Triaxial stress state volumetric strain calculation

Formula

ε_v = [(σ_x + σ_y + σ_z) / E] × (1 - 2·ν)

Step-by-step solution

1. In 3D elasticity, volumetric strain under triaxial normal stresses is ε_v = (σ_x + σ_y + σ_z) × (1 - 2·ν) / E. 2. Sum of normal stresses = 100 + 100 + 300 = 500 MPa. 3. Given E = 200 GPa = 200,000 MPa and ν = 0.3. 4. ε_v = [500 × (1 - 2 × 0.3)] / 200000 = (500 × 0.4) / 200000 = 200 / 200000 = 0.001. Answer: B

Explanation

Under a 3D triaxial state of stress, volumetric strain is given by ε_v = [(σ_x + σ_y + σ_z) / E] × (1 - 2·ν). With σ_x = 100 MPa, σ_y = 100 MPa, σ_z = 300 MPa (sum = 500 MPa), E = 200,000 MPa, and ν = 0.3: ε_v = (500 / 200000) × (1 - 0.6) = 0.0025 × 0.4 = 0.001.

Why the other options are wrong

A) 0.0005 corresponds to taking ν = 0.4. C) 0.0015 corresponds to omitting one of the normal stress components. D) 0.002 corresponds to taking ν = 0.1.

Shortcut

Volumetric strain = (Sum of stresses / E) × (1 - 2·ν) = (500 / 200000) × 0.4 = 0.001.

Common mistake

Forgetting the factor (1 - 2·ν) and calculating simply sum(σ) / E = 0.0025.