A pin$-$jointed structure is supported and loaded as shown in Figure $1.$ The structure is

constructed from tubular aluminium bars of hollow circular cross$-$section whose

external diameter is $50mm$ and whose wall thickness is $5mm.$ The Young's modulus

for the material is $73$GPa.

$($a$).$ Perform a test to show that this structure is statically determinate.

$($b$).$ Determine the reaction forces at points A and $C.$

$($c$).$ Determine the axial force in any $5$ bars, noting whether each bar is in tension or

compression.

$($d$).$ Calculate the effective slenderness ratio of bar $CD$ and hence determine if

the Euler buckling formula is valid for this bar.

$($e$).$ Use the Euler buckling formula to determine whether or not buckling will

occur in bar $CD.$