Question 5.3: Estimate the actual endurance limit of cast steel having an ...

Objective: Compute the estimated actual endurance limit of the bar material.

Given: Cast steel, machined: s_{u}=120 \mathrm{ksi}.
Size of section: b=1.50 in., h=2.00 in rectangular
Type of stress: Repeated, reversed bending.
Analysis: Use the Procedure for Estimating Actual Endurance Limit, s_{n}^{\prime}.
Step 1: The ultimate tensile strength is given to be s_{u}=120 \mathrm{ksi}.
Step 2: Surfaces are machined.
Step 3: From Figure 5-11, s_{n}=44 ksi.
Step 4: Material factor for cast steel: C_{m}=0.80.
Step 5: Type-of-stress factor for bending: C_{\text {st }}=1.00.
Step 6: Specify a desired reliability of 0.99. Then C_{R}=0.81 (Design decision).
Step 7: Size factor for rectangular section: First use Equation (5-25) (D_{e}=0.808 \sqrt{h b}) to determine the equivalent diameter,
D_{e}=0.808 \sqrt{h b}=0.808 \sqrt{(2.00 \mathrm{in})(1.50 \mathrm{in})}=1.40 \mathrm{in}
Then from Figure 5-12, C_{s}=0.85.
Step 8: Use Equation (5-21) (s_{n}^{\prime}=s_{n}\left(C_{m}\right)\left(C_{s t}\right)\left(C_{R}\right)\left(C_{s}\right)), to compute the estimated actual endurance limit.
s_{n}^{\prime}=s_{n}\left(C_{m}\right)\left(C_{s t}\right)\left(C_{R}\right)\left(C_{s}\right)=44 \mathrm{ksi}(0.80)(1.00)(0.81)(0.85)=24.2 \mathrm{ksi}