A $45-$mm$-$diameter solid steel shaft supports loads $P_A=1\mathrm{.}8kN$ and $P_C=3\mathrm{.}1kN$ as shown. Assume that $L_1=125mm,L_2=260mm,$ and $L_3=190mm.$ The bearing at $B$ can be idealized as a roller support, and the bearing at $D$ can be idealized as a pin support. Determine the magnitude of

$($a$)$ the maximum horizontal shear stress in the shaft.

$($b$)$ the maximum tension bending stress in the shaft.

Answers:

$($a$){}_{\text{m}\text{a}\text{x}}=$ MPa

$($b$){}_{\text{m}\text{a}\text{x}}=$ MPaA $45-$mm$-$diameter solid steel shaft supports loads $P_A=1\mathrm{.}8kN$ and $P_C=3\mathrm{.}1kN$ as shown. Assume that $L_1=125mm,L_2=260mm,$ and $L_3=190mm.$ The bearing at $B$ can be idealized as a roller support, and the bearing at $D$ can be idealized as a pin support. Determine the magnitude of

$($a$)$ the maximum horizontal shear stress in the shaft.

$($b$)$ the maximum tension bending stress in the shaft.

Answers:

$($a$){}_{\text{m}\text{a}\text{x}}=$ MPa

$($b$){}_{\text{m}\text{a}\text{x}}=$ MPa