$4-74.$ A $6-ft-$long steam pipe is made of $A-36$ steel with ${}_Y=40$ksi. It is connected directly to two turbines A and $B$ as shown. The pipe has an outer diameter of $4in.$ and a wall thickness of $0\mathrm{.}25in.$ The connection was made when $T_1=70F.$ If the turbines' points of attachment are assumed to have a stiffness of $k=80({10}^3)ki\frac{p}{i}n.,$ determine the force the pipe exerts on the turbines when the steam and thus the pipe reach a temperature of $T_2=275F.$

Probs. $4-\frac{73}{74}$