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

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

Given     Cast steel, machined:s_{u}= 120 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 Strength s^{\prime }_{n} .

Step 1: The ultimate tensile strength is given to bes_{u} = 120 ksi.

Step 2: Surfaces are machined.

Step 3: From Figure 5_8.s_{n} = 44 ksi

Step 4: Material factor for cast steel:C_{m} = 0.80

Step 5: Type-of-stress factor for bending:C_{st}= 1.00

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

Step 7: Size factor for rectangular section: First use Equation 5_8  0.0766D^{2}_{c} =0.05hb

D_{c}=0.808\sqrt{hb} 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_9, C_{s}= 0.85.

Step 8: Use Equation 5_4 s_{n}^{\prime}=s_{n}\left(C_{m}\right)\left(C_{s}\right)\left(C_{R}\right)\left(C_{s}\right) to compute the estimated actual endurance strength.s_{n}^{\prime}=s_{n}\left(C_{m}\right)\left(C_{s s}\right)\left(C_{R}\right)\left(C_{s}\right)=44 \mathrm{ksi}(0.80)(1.00)(0.81)(0.85)=24.2 \mathrm{ksi}