$(60$ points$)$ The crank in the figure below is dimensioned and loaded as shown

a$)$ Calculate the i$)$ axial force, ii$)$ shear force, iii$)$ bending moment, and iv$)$ torque acting on points A and $D$ at the fixed wall $x-$section

b$)$ Calculate the i$)$ axial stress, ii$)$ transverse shear stress, iii$)$ bending stress, and iv$)$ torsional stress and at points A and $D$

c$)$ at Point A only: Calculate principal stresses ${}_1$&${}_2,$ max shear stresses ${}_1$&${}_2$ and the angle of the principal plane. No need to draw the stress element.

Ignore transverse shear stress in principal stress calculations

Area of circle $=\frac{d^2}{4}$

$I_y=I_z=\frac{d^4}{64}$

$J_x=\frac{d^4}{32}$

Axial Stress $=$P$/$A

Bending Stress $=M\frac{c}{\text{I}}$

Torsional Stress $=$ Tr$/$

Transverse Shear Stress $=4\frac{V}{3}A$

${}_1,{}_2=\frac{{}_x+{}_y}{2}+-\sqrt[\phantom{2}]{(\frac{{}_x-{}_y}{2}{)}^2+{}_{xy}^2}$

${}_1,{}_2=+-\sqrt[\phantom{2}]{(\frac{{}_x-{}_y}{2}{)}^2+{}_{xy}^2}$

$tan2{}_p=\frac{2{}_{xy}}{{}_x-{}_y}$