A structural beam is subjected to different loading

conditions in service. The beam is constructed from a

steel alloy that has limited material testing data

available. The manufacturer provides the following

minimum fully$-$corrected endurance strength, yield

strength and ultimate tensile strength respectively: $276$

MPa,$413$MPa, and $551$ MPa $.$ For the following loading

conditions, calculate the safety margin on first$-$cycle

failure, fatigue failure and estimate the fatigue life using

the Goodman, Gerber and ASME Elliptic failure criteria:

LC$1-$ Steady torsional stress of $103$ MPa and alternating

bending stress of $172$ MPa

LC$2-$ steady torsional stress of $103$ MPa, an alternating

torsional stress of $69$ MPa and an alternating bending

stress of $83$ MPa $.$