Question

The ratio of shear stress to the shear strain is called

• A. Young's modulus
• B. Section modulus
• C. Modulus of rigidity
• D. Bulk modulus

Hint:

Elastic Moduli Formulas:
MODULUS OF RIGIDITY ($G$) = $\frac{\text{Shear Stress}}{\text{Shear Strain}}$.
Young's Modulus ($E$) = $\frac{\text{Normal Stress}}{\text{Normal Strain}}$.
Bulk Modulus ($K$) = $\frac{\text{Volumetric Stress}}{\text{Volumetric Strain}}$.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Elastic constitutive equations: the Modulus of Rigidity (Shear Modulus, $G$) is defined as the ratio of shear stress ($ au$) to shear strain ($\gamma$) within the elastic limit.
Key Formula or Approach:
\[ \mathbf{Modulus \text{ } of \text{ } Rigidity \text{ } (G)} = \frac{\text{Shear Stress } (\tau)}{\text{Shear Strain } (\gamma)} \quad [\text{SI Unit: Pascal (Pa) / N/m}^2] \]

Step 2: Detailed Explanation:
In solid mechanics and elasticity theory:
1. Modulus of Rigidity (Shear Modulus, $G$ or $C$) (C): Defined by Hooke's law in shear as the direct ratio of shear stress ($\tau$) to shear strain ($\gamma$) within the proportional elastic limit:
\[ G = \frac{\tau}{\gamma} \]
2. Young's Modulus of Elasticity ($E$): Ratio of normal (tensile/compressive) stress ($\sigma$) to normal longitudinal strain ($\epsilon$), $E = \frac{\sigma}{\epsilon}$.
3. Bulk Modulus ($K$): Ratio of volumetric (hydrostatic) stress to volumetric strain, $K = \frac{-dp}{dV/V}$.
4. Section Modulus ($Z$): Geometric property of a beam cross-section, $Z = I/y_{\max}$.

Step 3: Final Answer:
Therefore, the ratio of shear stress to shear strain is called Modulus of rigidity, corresponding to option (C).