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A bar of steel has the minimum properties Se = 276 MPa, Sy = 413 MPa, and Sut = 551 MPa.
The bar is subjected to a steady torsional stress of 103 MPa and an alternating bending stress of 172 MPa. Find the factor of safety guarding against a static failure, and either the factor of safety guarding against a fatigue failure or the expected life of the part. For the fatigue analysis use:

(a) Modified Goodman criterion.

(b) Gerber criterion.

(c) ASME-elliptic criterion.

(a) Modified Goodman criterion.

(b) Gerber criterion.

(c) ASME-elliptic criterion.

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