Simple Stress and Strain MCQ with answer and solution

Concept

G and E are linked by Poisson's ratio. Poisson's ratio μ is normally between 0 and 0.5.

Formula

E = 2G(1 + μ), so G = E / [2(1 + μ)]

Step-by-step solution

1. Use the relation E = 2G(1 + μ), so G = E / [2(1 + μ)]. 2. For normal engineering materials, 0 ≤ μ ≤ 0.5. 3. When μ = 0: G = E/2 (maximum value). 4. When μ = 0.5: G = E/(2 × 1.5) = E/3 (minimum value). 5. So G lies between E/3 and E/2.

Explanation

G depends on E and Poisson's ratio. Poisson's ratio is between 0 and 0.5 for common materials, so G is between E/3 and E/2. A higher Poisson's ratio gives a smaller G.

Why the other options are wrong

A: G cannot be zero, and the range misses E/3 to E/2. B: G is never below E/3 for 0 ≤ μ ≤ 0.5. C: G = E/2 is the upper limit, not the lower limit.

Shortcut

Put μ = 0 and μ = 0.5 in G = E/[2(1+μ)] to get the two limits.

Common mistake

Using the K-E relation, or swapping the limits (μ = 0.5 gives the smaller G).