$(25$ points$)$: A machine component made from AISI $1040$ steel $,$

$E=200$GPa,

$u=0\mathrm{.}29,G=80$GPa has been fabricated as a circular bar $,$

$A=176\mathrm{.}7m{m}^2,I=2485\mathrm{.}0m{m}^4,J=4970\mathrm{.}1m{m}^4)$ of length $a=100mm,$ welded to a

plate of length $r=200mm.$ When in use, the base is fixed and the component is loaded

as shown with a force of $F=F_x$hat$(i)+F_z$hat$(k)=500$hat$(i)+600$hat$(k)N$ at the end of the plate $($point $B).$

a$.(8$ pts$)$: What is the shear stress due to any torsional loads in the beam at the fixed

end $($location $A)?$

b$.(8$ pts$)$: What is the magnitude of the stress due to any axial or bending loads in the

beam at the fixed end $($location $A)?$

c$.(9$ pts$)$: If the answer to part $\text{'}$a$\text{'}$ was $250$ MPa and the answer to part $\text{'}$ b $\text{'}$ was $400$ MPa

$($NOTE: these are not the correct values for the loads given!$),$ will the beam yield

at that location? Quantitatively justify your answer.