$2\mathrm{.}31$ The stepped shaft A$-$B$-$C shown in Sketch $a$ is loaded with the forces $P_1$ and$/$or $P_2.$ Note that $P_1$ gives a tensile stress $$ in B$-$C and $\frac{}{4}$ in A$-$B and that $P_2$ gives a bending stress $$ at B and $1\mathrm{.}5$ at A $.$ What is the critical section

$($a$)$ If only $P_1$ is applied?

$($b$)$ If only $P_2$ is applied?

$($c$)$ If both $P_1$ and $P_2$ are applied?

Sketch a$,$ used in Problems $2\mathrm{.}31$ and $2\mathrm{.}32.$

$2\mathrm{.}32$ The stepped shaft in Sketch a has loads $P_1$ and $P_2.$ Find the load classification if $P_1\text{'}$s variation is sinusoidal and $P_2$ is the load from a weight

$($a$)$ If only $P_1$ is applied

$($b$)$ If only $P_2$ is applied

$($c$)$ If both $P_1$ and $P_2$ are applied