$2\mathrm{.}2-4$ A steel cable with a nominal diameter of $25$ mm $($see Table $2-1)$ is used in a construction yard to lift a bridge section weighing $38$ kN $,$ as shown in the figure. The cable has an effective modulus of elasticity $\backslash ($ E$=140\backslash )$ GPa.

$($a$)$ If the cable is $14$ m long, how much will it stretch when the load is picked up$?$

$($b$)$ If the cable is rated for a maximum load of $70$ kN $,$ what is the factor of safety with respect to failure of the cable?

PROBLEM $2\mathrm{.}2-4$