Problem $6-20$

A bar ot steel has the minimum properties $S_e=40k,S_y=60k,$ and $S_{ut}=80k.$ The bar is subjected to a steady torsional stress of $15$ kpsi and an alternating bending stress of $25$ kpsi $.$ 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$)$ Goodman criterion.

$($b$)$ Gerber criterion.

$($c$)$ Morrow criterion.

$6-23$ Repeat Problem $6-20$ but with an alternating torsional stress of $30$ kpsi $.$

$6-56$ In the figure shown, shaft $A,$ made of AISI $1020$ hot$-$rolled steel, is welded to a fixed support and is subjected to loading by equal and opposite forces $F$ via shaft $B.$ A theoretical stress$-$concentration factor $K_{ts}$ of $1\mathrm{.}6$ is induced in the shaft by the $\frac{1}{8}-$in weld fillet. The length of shaft A from the fixed support to the connection at shaft $B$ is $2$ ft $.$ The load $F$ cycles from $150$ to $500$ lbf $.$

$($a$)$ For shaft A $,$ find the factor of safety for infinite life using the Goodman fatigue failure criterion.

$($b$)$ Repeat part $($a$)$ using the Gerber fatigue failure criterion.