$1$ The pin$-$jointed structure ABC is loaded as shown in Fig. $8\mathrm{.}18.$ The members AB and BC

are subjected to compressive axial force and considered as a long column. The structure

is made of steel pipe with $50$ mm outside diameter and $5$ mm thickness. E$=200$GPa.

Determine

$($a$)$ the slenderness ratio of AB and BC $.$

$($b$)$ the permissible load W $,$ which can be supported by the structure without buckling.

Assume that buckling can only occur in the plane of structure ABC and a factor of

safety of $2\mathrm{.}5.$

Answers: $($a$)195,177,($b$)7\mathrm{.}68$ kN