Question $1$

$11\mathrm{.}3-19$ The roof over a concourse at an airport is supported by the use of pretensioned cables. At a typical joint in the roof structure, a strut $AB$ is

compressed by the action of tensile forces $F$ in a cable that makes an angle $=75$ with the strut $($see figure and photo$).$ The strut is a circular tube of steel $(E=200$GPa $)$ with outer diameter $d_2=60mm$ and inner diameter $d_1=50mm.$ The strut is $1\mathrm{.}75$ m long and is assumed to be pin$-$connected at both ends.

Using a factor of safety $n=2\mathrm{.}5$ with respect to the critical load, determine the allowable force $F$ in the cable.