Question 5.2: Estimate the actual endurance strength of AISI 1050 cold-dra...

Objective     Compute the estimated actual endurance strength of the shaft material.

Given       AISI 1050 cold-drawn steel, machined. Size of section: D =1.75 in.Type of stress: Reversed, repeated bending.

Analysis     Use the Procedure for Estimating Actual Endurance Strength.s^{\prime }_{n}

Step 1: The ultimate tensile strength:S_{u} = 100 ksi from Appendix 3.

Step 2: Diameter is machined.

Step 3: From Figure 5_8, S_{n} = 38 ksi

Step 4: Material factor for wrought steel:C_{m}= 1.0

Step 5: Type-of-stress factor for reversed bending:C_{s1}= 1.0

Step 6: Specify a desired reliability of 0.99. Then C_{R} = 0.81 (Design decision)

Step 7: Size factor for circular section with D = 1.75 in.From Figure 5-9, C_{s} = 0.83.

Step 8: Use Equation 5_4 to compute the estimated actual endurance strength s_{n}^{\prime}=s_{n}\left(C_{m}\right)\left(C_{s t}\right)\left(C_{R}\right)\left(C_{s}\right)=38 \mathrm{ksi}(1.0)(1.0)(0.81)(0.83)=25.5 \mathrm{ksi}

Comments     This is the level of stress that would be expected to produce fatigue failure in a rotating shaft due to the action of reversed bending. It accounts for the basic endurance strength of the wrought AISI 1050 cold-drawn material, the effect of the machined surface, the size of the section, and the desired reliability.