$1.$ The shaft shown in Figure $\backslash (4-7\backslash )$ is supported by two bearings and carries two V$-$belt sheaves. The tensions in the belts exert horizontal forces on the shaft, tending to bend it in the $\backslash ($ x$-$z $\backslash )$ plane. Sheave B exerts a clockwise torque on the shaft when viewed toward the origin of the coordinate system along the x $-$axis. Sheave C exerts an equal but opposite torque on the shaft. For the loading condition shown, determine the principal stresses and the maximum shear stress on element K on the front surface of the shaft $($on the positive z side$)$ just to the right of sheave B$.(15$ points$)$

$1.$ Follow the general procedure for analyzing combined stresses given in this section.

$2.$ Use the procedure for constructing the $2$D Mohr's circle in this section.

$3.$ Can you extend this example to cover Tresca Tresca Stress and von Mises Stress?

Where,

$\backslash ($ A B $\backslash )$ and $\backslash ($ B C $15\backslash$mathrm$\{$~cm$\}\backslash )$ and $\backslash ($ C D $10\backslash$mathrm$\{$~cm$\}\backslash )$

Shaft Diameter $5$cm

Torque $100$ Nm

Ra $200$ Kgd

Rb $230$ Kgf

Rc $150$ Kgf

Rd $220$ Kgf plane with reactions at bearings