A cyclic stress with a mean stress σm = 200 MPa is applied to a steel with a fully reversed fatigue limit σw = 300 MPa and a tensile strength σB = 800 MPa. Using the modified Goodman relation σa = σw(1 − σm/σB), which value is closest to the stress amplitude corresponding to the fatigue limit?

Answer: B. About 225 MPa

σm/σB = 200/800 = 0.25, so σa = 300×(1 − 0.25) = 225 MPa. A tensile mean stress acts to open cracks, so the allowable stress amplitude is smaller than the fully reversed value (σm = 0). The modified Goodman diagram is a conservative guide that joins σw on the vertical axis and σB on the horizontal axis with a straight line. About 281 MPa is the value from the parabolic Gerber relation, which squares the mean stress ratio, 300×(1 − 0.25²), and is a less conservative estimate than Goodman. About 100 MPa divides by σw instead of σB. A compressive mean stress often works in favor of fatigue resistance, but designs usually do not take credit for that effect.