Problem $(3)$

$(20$ marks$)$

$($a$)$ The figure shows a shaft mounted in bearings at A and D and having pulleys at B and C $.$ The

forces shown acting on the pulley surfaces represent the belt tensions. The shaft is to be made

of AISI $1035$ CD steel. Using an appropriate non$-$conservative failure theory with a design factor

of $2,$ determine the minimum shaft diameter to avoid yielding.

$($b$)$ By modern standards, the shaft design of Prob. $($a$)$ is poor because it is so long. Suppose it is

redesigned by halving the length dimensions. Using the same material and design factor as in

Prob. $($a$),$ find the new shaft diameter.