Exercise $2($Equilibrium$,$ Stress and Material Properties$)$

A simply supported pin$-$jointed warren truss that is subjected to external loads is shown in Figure $2$ below. All triangular segments have the same dimensions.

$($a$)$ Determine the support reactions at A and G

$($b$)$ Using the method of sections, find the internal axial forces in members BD and CE$.$ State whether they are in compression or tension.

$($c$)$ Using the method of joints, find the internal axial forces in ALL other members. State whether they are in compression or tension. Tabulate your results.

$($d$)$ Following allowable stress design principles, determine the minimum suitable cross$-$sectional dimensions that can be used for all truss members, assuming that the same square cross$-$section is to be used for all members. The ultimate strength of the truss material is $\backslash (\backslash$sigma$\_\{$u$\}=490\backslash$mathrm$\{$MPa$\}\backslash ),$ its modulus of elasticity can be taken as $\backslash ($ E$=200\backslash$mathrm$\{$GPa$\}\backslash )$ and its Poisson's ratio is $\backslash ($ v$=0\mathrm{.}3\backslash ).$ Apply a factor of safety of F$.$S$.\backslash (=2\backslash ).$

$($e$)$ Based on the material properties given in part $($d$),$ what type of material is this likely to be$?$