Assignment $4$

Problem

In the figure shown, shaft A$,$ made of AISI $1020$ hot$-$rolled steel $(S_{ut}=36k$ and $S_y=30k),$ is welded to a fixed support and is subjected to loading by equal and opposite forces $F$ via shaft $B$ and to an axial force $2F.$

The theoretical stress$-$concentration factors for the $(\frac{1}{8}in)$ radius fillet are $3\mathrm{.}0$ and $1\mathrm{.}6$ for the axial and torsional loading, respectively.

The length of shaft A from the fixed support to the connection at shaft $B$ is $2$ ft and its diameter is $7/8$ in$.$ The load $F$ cycles from $150$ to $500$ lbf $.$

For shaft $A,$ find the factor of safety for infinite life using the Goodman fatigue failure criterion. If infinite life is not predicted estimate the number of cycles at failure. Check for yielding.