(Solved): 5. In the figure shown, shaft \( A \), made of AISI 1020 hot-rolled steel, is welded to a fixed sup ...

5. 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 \( F \) applied as shown to shaft \( B \). A theoretical stress concentration factor \( K_{s} \) of \( 1.6 \) is induced in the shaft by the \( \frac{1}{8} \) in weld fillet at the wall. Ignore stress concentrations at the intersection of shafts \( A \) and \( B \). Shaft \( A \) is \( 2 \mathrm{ft} \) long from the fixed support to the connection at shaft \( B \). The load \( F \) cycles between \( 150 \mathrm{lb} \) to \( 500 \mathrm{lb} \). a) For shaft \( A \), find the factor of safety for infinite life using the modified Goodman criterion. b) Repeat a) using the Gerber criterion.