Question $3(20$ marks$)$

A light is hanged on pin jointed frame $($PJF$)$ at point C$.|$The PJF consists of truss element

as shown in Figure $3.$ All the members of PJF are made of sections of aluminium pipes

$(E=70$GPa$)$ cross$-$sectional area of $1000m{m}^2.$ Knowing that the light weighs $5kg.$

$($a$)$ Calculate the reaction at A and $B$

$($b$)$ Find force carried by each members of PJF in terms vertical force $P$ and virtual

force $Q$ and

$($c$)$ Calculate the vertical and horizontal deflection at $C.$