Figure $7$: Elbow beam with vertical load at tip

$($i$)$ The line marked $d$ is a plane parallel to the wall where the beam enters the wall. Section the

beam OD at plane $d.$ Draw a Free Body Diagram showing the internal shear forces and moments

on this face. You should draw the portion of beam which contains the external force of $250$ N $.$

$($ii$)$ On the plane $d,$ calculate the different stresses on the face. Make a neat sketch showing the

distribution of the various stresses, including the directions.

$($iii$)$ Consider the magnitude of the shear stresses due to applied shear forces, compared to shear

stresses arising due to applied torque. Which of these is most meaningful in sizing the beam?

Could you demonstrate this analytically for a beam of circular section?

$($iv$)$ Identify the point$($s$)$ on plane $d$ where the beam is most highly stressed. At this point, find the

maximum and minimum principal stresses, as well as the maximum shear stress. You may use a

graphical version of Mohr's circle or the analytical equations.

$($v$)$ Assume this beam is made from low carbon steel $($AISI $1020)$ which has an elastic modulus

$E_y=200$GPa, yield strength $S_y=300$MPa and Ultimate Tensile Strength $S_{\text{U}\text{T}\text{S}}=450$MPa.

Using the Maximum Shear Stress Theory of Failure for permanent deformation, what is the

factor of safey at this location?

Q$7($vi$)$: ${}_{\text{M}\text{a}\text{x}}=53$MPa;${}_1=91$MPa

Q$7($vii$)$; Factor of safety on yield ~~$2\mathrm{.}8$

Please solve asap, answering every question step by step with expalnations and diagrams