A solid shaft $($can be treated as a beam on two rollers$)$ with an outside

diameter of $20\mathrm{.}0$mm is subjected to the loads on the pulleys as shown in

figure. The yield strength of the steel is $350\mathrm{.}0$MPa.

$($a$)$ calculate the reactions at A and D$,$

$($b$)$ calculate the individual stress components in locations H and K and

superimpose into the combined plane stress. Show the combined

stress states on two separate plane stress elements: one for location H

and one for location K$,$

$($c$)$ calculate principal stresses for location H and for location K$,$

$($d$)$ determine the factors of safety at locations H and K predicted by the maximum$-$shear$-$stress theory. According to the

MSST does the shaft fail in location $($s$)$ H and$/$or K$?$

$($e$)$ determine the factors of safety at locations H and K predicted by the maximum$-$distortion$-$energy theory. According to

the MDET does the shaft fail in location $($s$)$ H and$/$or K$?$

$($f$)$ on a one common or two separate diagrams draw the stress envelopes $($failure diagrams$)$ for both theories indicating all

stress values as well as all the load lines