estion $1(25$ marks$)$

A simply supported pin$-$jointed warren truss that is subjected to external loads

is shown in Figure Q$1.$ All triangular segments have the same dimensions.

$($a$)$ Determine the support reactions at A and G $(5$ marks$)$

$($b$)$ Using the method of sections, find the internal axial forces in members BD

and CE$.$ State whether they are in compression or tension. $(7$ marks$)$

$($c$)$ Using the method of joints, find the internal axial forces in members AB$,$ AC$,$

EG and FG$.$ State whether they are in compression or tension. $(6$ marks$)$

$($d$)$ Following the allowable stress design method and answers from Q$1($b$)$ and

Q$1($c$),$ determine the minimum suitable cross$-$sectional dimension that can

be used for all truss members, assuming that the same circular cross$-$

section is to be used for all members. The ultimate strength of the truss

material is u $=410$ MPa, its modulus of elasticity can be taken as E $=200$

GPa and its Poisson$$s ratio is $=0\mathrm{.}3.$ Apply a factor of safety of F$.$S$.=2$