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 _(u)=60ksi.

To solve this problem, we need to use the fatigue strength reduction equation, which is commonly used in engineering to estimate the fatigue strength of a material under cyclic loading.Given information:- Cross-sectional area of the rod: - Static mean tensile load: - Number of cycles to failure: The fatigue stress amplitude can be calculated using the following equation: Where:- is the yield strength of the material (given as 32 ksi)- is the mean stress level (given as 60 ksi)- is the number of cycles to failure (given as )Substituting the given values, we get: Simplifying the equation, we get: Therefore, the fatigue stress amplitude that will produce failure after cycles is approximately 31.99997 ksi.