Example. A rod of 0.5in^2 is subjected to static mean tensile load of 10 kips. What fatigue stress amplitude sigma _(a) will produce failure after 10^6 cycles? Assume sigma _(n)=32ksi,sigma _(n)=60ksi Goodman (sigma _(a))/(S_(e))+(sigma _(m))/(sigma _(uts))=1 sigma _(m)=(F_(m))/(A)=(10)/(0.5)=20 sigma _(a)=S_(e)-(S_(e))/(sigma _(u))(sigma _(m)) =32-(32)/(60)20=21.3ksithusF_(A)=21.3ksi

To solve this problem, we need to use the Goodman criterion for fatigue stress amplitude.Given information:- Cross-sectional area of the rod: - Static mean tensile load: - Yield strength: - Ultimate tensile strength: - Number of cycles: Step 1: Calculate the mean stress, , using the formula: Step 2: Use the Goodman criterion to calculate the fatigue stress amplitude, : where is the yield strength and is the ultimate tensile strength.Substituting the values: Therefore, the fatigue stress amplitude, , that will produce failure after cycles is 21.3ksi.