Shear modulus of elasticity is the ratio of:
Try it first: pick an option, then read the explanation.
Correct answer: D. shear stress and shear strain
Asked in SSC JE 23/09/2019 (Evening)
Detailed Explanation
Each kind of stress has its own modulus. Normal stress uses E; shear stress uses the modulus of rigidity G (also written N or C).
\[ G = \frac{\tau}{\gamma} \qquad E = 2G(1 + \mu) \]
Why “shear stress and shear strain” Is Correct
The shear modulus is the ratio of shear stress to shear strain within the elastic limit — option (d).
| Relation | Formula |
|---|---|
| Young's modulus and rigidity | E = 2G(1 + μ) |
| Young's modulus and bulk modulus | E = 3K(1 − 2μ) |
| All three moduli | E = 9KG/(3K + G) |
| Poisson's ratio | μ = (3K − 2G)/(6K + 2G) |
Only two elastic constants are independent for a homogeneous, isotropic, linearly elastic material.
Why the Other Options Are Wrong
- A. tensile stress and strain: Tensile stress ÷ strain is Young's modulus.
- B. compressive stress and strain: Compressive stress ÷ strain is also Young's modulus.
- C. bending stress and strain: Bending stress is a normal stress, related through E.
Key Point
G = τ/γ; for steel G ≈ 80 GPa.
Key Concepts for Students
- Shear strain γ is an angle change in radians.
- G governs torsion of shafts.
- G ≈ 0.4E for μ ≈ 0.25.
Practice more: this is question 19 in Stress and Strain MCQs – Part 2. Try the whole set and check every answer instantly.