P

A

B

$1800$ mm

H

D

$600$ mm

$1200$ mm

$2.$ Two concentrated forces, each having a magnitude of P$,$ are acting on a walkway supported by a truss,

as illustrated. The truss is pinned at A and F$.$

$($a$)$ Find the forces in members AB$,$ CH$,$ CG and GH of the truss, in terms of P;

$($b$)$ Members AB$,$ CG and CH are to be constructed from Grade $6061-$T$4$ aluminium with a yield stress of

$110$ MPa and must all have the same solid square cross$-$section. Assuming that P $=18$ kN$,$ determine the

dimension of the cross$-$section, a$,$ given that the material is available in $5$ mm increments and the load

factor for axiai tension is $1\mathrm{.}6$;

$($c$)$ Knowing that the modulus of elasticity for aluminium is $70,000$ MPa, determine the elongation of

member CH$,$ as designed.

P

$900$ mm $900$ mm $900$ mm

C

E

G

F $2.$ Two concentrated forces, each having a magnitude of P $,$ are acting on a walkway supported by a truss, as illustrated. The truss is pinned at $\backslash ($ A $\backslash )$ and $\backslash ($ F $\backslash ).$

$($a$)$ Find the forces in members $\backslash ($ A B$,$ C H$,$ C G $\backslash )$ and $\backslash ($ G H $\backslash )$ of the truss, in terms of P ;

$($b$)$ Members $\backslash ($ A B$,$ C G $\backslash )$ and $\backslash ($ C H $\backslash )$ are to be constructed from Grade $\backslash (6061-\backslash$mathrm$\{$T$\}4\backslash )$ aluminium with a yield stress of $110$ MPa and must all have the same solid square cross$-$section. Assuming that $\backslash (\backslash$mathrm$\{$P$\}=18\backslash$mathrm$\{$kN$\}\backslash ),$ determine the dimension of the cross$-$section, $\backslash ($ a $\backslash ),$ given that the material is available in $5$ mm increments and the load factor for axial tension is $1\mathrm{.}6$ ;

$($c$)$ Knowing that the modulus of elasticity for aluminium is $\backslash (70,000\backslash$mathrm$\{$MPa$\}\backslash ),$ determine the elongation of member CH $,$ as designed.