A rectangular base plate is fixed at each of its four corners by

a $20$ mm diameter bolt and nut as shown in the Figure below. The

plate rests on washers of $22$ mm internal diameter and $50$ mm

external diameter. Copper washers which are placed between the nut

and the plate are of $22$ mm internal diameter and $44$ mm external

diameter. If the base plate carries a load of $120$ kN $($including

self$-$weight, which is equally distributed on the four corners$),($a$)$

calculate the stress, in ksi, on the lower washers before the nuts

are tightened. $($b$)$ What could be the stress, in ksi, in the upper

and lower washers, when the nuts are tightened so as to produce a

tension of $5$ kN on each bolt? $($c$)$ With the resulting stress in $($b$),$

determine the factors of safety of the bolt and the washers based

on the yield point. The bolt and nut are made of C$1035,$ as rolled,

steel, and the washers are made aluminum alloy $2014-$T$6$ Two solid shafts of different materials are rigidly fastened together and attached to rigid

supports $3$ m apart shown in Fig$\mathrm{.}3.$ The aluminium segment is $2$ m long and $7\mathrm{.}5$ cm in diameter

$G_{Al}=28$GPa. The steel segment is $1$ m long and has a diameter of $5cm{G}_s=84$GPa. The

torque $T=1kN-m$ is applied at the junction of the two segments. Compute the maximum

shearing stress developed in the assembly.