GATE_AE_2027_MOCK_01_Q65 GATE 2027 Aerospace Engineering All-India Master Mock 01 (Foundation & Standard Core Calibration) NAT · 2 Marks
Aerospace Structures • Aerospace Materials & Fatigue • Damage Tolerance & Non-Destructive Testing

A wide aerospace fuselage panel has a through-thickness central crack of length $2a = 16\text{ mm}$ (half-crack $a = 8\text{ mm} = 0.008\text{ m}$). The panel is subjected to uniform tensile stress $\sigma = 250\text{ MPa}$. Taking the geometric correction factor $Y = 1.0$, what is the stress intensity factor $K_I$ in $\text{MPa}\sqrt{\text{m}}$? (Take $\pi \approx 3.1416$, round to two decimal places).

Answer Key:
39.63

Step-by-Step Verified Solution

### Solution: Stress intensity factor: $K_I = Y \sigma \sqrt{\pi a} = 1.0 \times 250 \times \sqrt{3.1416 \times 0.008} = 250 \times \sqrt{0.025133} = 250 \times 0.15853 = 39.633\text{ MPa}\sqrt{\text{m}}$. Correct: 39.63 (range 39.0 to 40.2).
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