GATE_AE_2027_MOCK_02_Q65
GATE 2027 Aerospace Engineering All-India Master Mock 02 (Compressible Aerodynamics & High-Speed Propulsion)
NAT · 2 Marks
Aerospace Structures • Aerospace Materials & Fatigue • S-N Curves, Miner's Rule & Stress Concentrations
An aircraft titanium bulkhead experiences fatigue loading in two sequential blocks: Block 1: 20000 cycles at a stress level where fatigue life is $N_1 = 50000$ cycles. Block 2: cycles applied until failure at a stress level where fatigue life is $N_2 = 25000$ cycles. According to Miner's Rule ($\sum n_i/N_i = 1$), how many cycles can be sustained in Block 2 before failure occurs?
Answer Key:
15000
Step-by-Step Verified Solution
### Solution: Damage from Block 1: $D_1 = \frac{n_1}{N_1} = \frac{20000}{50000} = 0.40$. Remaining allowable damage: $D_2 = 1.0 - 0.40 = 0.60$. Allowable cycles in Block 2: $n_2 = D_2 \times N_2 = 0.60 \times 25000 = 15000\text{ cycles}$. Correct: 15000.