A solid pipe is being loaded by a wrench with a force shown in the schematic. The dimensions are also

provided. The Pipe has a diameter of $90$ mm $.$

$(1$ points$)$ Determine the location vector of point $D$ with respect to point $A^{\text{'}}$ which is at the centerline

of the pipe and directly underneath point $A.($Point $D$ is on the $y$ axis$)$

$(1$ points$)$ Estimate the moment generated due to the applied force using the location vector $r_{\frac{D}{A^{\text{'}}}}.$

$(1$ points$)$ Write down the $3$D stress component $($you do not need to compute the components, only

use unknown variables$)$ in matrix form. Under which assumption the problem dimension could be

reduced from $3$D down to $2$D for the element $A?$ Write the reduced dimension stress components.

$[$Pay close attention to the component indices$]$

$(1$ points$)$ Draw the stress element for A and show all the stress component directions in the

schematic.

$(3$ points$)$ Calculate all the stress elements and construct the stress state for element A$.$ You can

assume the normal stress component along the $y$ direction $({}_{yy}$~~$0)$ as zero.

$(3$ points$)$ Estimate the principal stresses, max shear, and principal plane for the estimated stress

state.

hat$(F)=10$hat$()-25$hat$()-600$hat$(k)N$