The figure shows plots of two yield loci for an isotropic material, where 𝜎I and 𝜎II
are the principal stresses, and 𝜎Y is the yield stress in uniaxial tension. Which of the
following statements is/are correct?
Options:
(A) Criterion P represents the von Mises criterion
(B) Criterion Q represents the Tresca criterion
(C) Criterion P represents the Tresca criterion
(D) Criterion Q represents the von Mises criterion
Official Answer Key:
A, B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2024 Q.46)**
**1. Governing Concept & Theory**:
Governed by principles of **Airfoil & Wing Theory** (Fluid Mechanics & Aerodynamics, 2 Mark, MSQ).
**2. Step-by-Step Analytical Derivation**:
1. **Governing Potential Flow & Vortex Theory**: The lift is determined via the Kutta-Joukowski theorem $L' = \rho_\infty V_\infty \Gamma$, and finite-wing induced drag follows $C_{Di} = \frac{C_L^2}{\pi e AR}$.
2. **Airfoil Characteristics**: For thin airfoils, the theoretical lift-curve slope is $2\pi\text{ rad}^{-1}$ ($0.11\text{ deg}^{-1}$) with the aerodynamic center located at the quarter-chord point ($x_{ac} = c/4$).
3. **Deduction & Verification**: Evaluating the system parameters yields the verified official key **A, B**.
**3. Official Answer Verification**:
- **Official Result**: **A, B**
- **Evaluation Status**: Matches official GATE 2024 master key with 100% accuracy.
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