A steel bar undergoes cyclic loading such that \sigma _{max}= 60 \ kpsi \ and \ \sigma _{min}= −20 \ kpsi. \ For \ the \ material \ , \ S_{ut}= 80 \ kpsi, \ S_y= 65 \ kpsi,
a fully corrected endurance limit of S_e=40 \ kpsi, \ and \ f = 0.9.
Estimate the number of cycles to a fatigue failure using:
(a) Modified Goodman criterion.
(b) Gerber criterion.