Question 7.6: Cumulative Fatigue Damage of a Machine Bracket A steel brack...
Cumulative Fatigue Damage of a Machine Bracket
A steel bracket of a machine is subjected to a reversed bending stress of S_{1} for n_{1} cycles, S_{2} for n_{2} cycles, and S_{3} for n_{3} cycles. Determine whether failure will occur.
Given: S_{1} = 420 MPa, S_{2} = 350 MPa, S_{3} = 280 MPa
n_{1} = 5,000 cycles, n_{2} = 20,000 cycles, n_{3} = 30,000 cycles.
Design Decisions: The bracket has a machined surface and Bhn = 200. Miner’s cumulative damage rule is used.
The appropriate limiting number of cycles corresponding, respectively, to the preceding stress values is, from Figure 7.18,
N_{1} = 12,000 cycles, N_{2} = 50,000 cycles, N_{3} = 280,000 cycles
Applying Equation 7.36,
\frac{n_1}{N_1}+\frac{n_2}{N_2}+\cdots=1 (7.36)
\frac{5,000}{12,000}+\frac{20,000}{50,000}+\frac{30,000}{280,000}=0.924
Comment: Since 0.924 < 1, the member is safe.
