Consider the pin$-$ended truss shown below with two vertical point loads P and Q$.$ Based on this loading the greatest tension and compression forces in members BC and GF respectively are as follows;

FBC $=95$ kN $($T$)$ and FGF $=100$ kN $($C$)$

$($i$)$ Member BC is to be designed as a steel square hollow section. Based on applying a strength factor of safety $($FOS$)$ of $2\mathrm{.}2,$ which minimum weight member in the Table below would you choose for this section? What will be the actual FOS of your chosen member? ANS: FOS $=2\mathrm{.}24$ Member $65$x$65$x$2\mathrm{.}5$ SHS

$($ii$)$ Based on your section choice in part a$)$ what is the change in length of this member based on the unfactored axial load experienced? Provide your answer in units of mm$.$ ANS: Change in length $=3\mathrm{.}12$ mm

$($i$)$ Member GF is to be a custom made steel circular hollow section of outer diameter $110$mm$.$ Based on applying a strength factor of safety of $2\mathrm{.}2$ again, what is the minimum required thickness for this section based on a strength limit state design. ANS: t$\_$min $=3\mathrm{.}785$ mm

$($ii$)$ Based on the section chosen in part $($b$)($i$)$ above at what member length will the failure mode change from buckling to yielding? Draw the axial compression failure curve showing this value. ANS: L$=2\mathrm{.}82$ m

Assume the following values for the Material Properties: Young$$s modulus E $=200,000$ MPa and Yield strength $=350$MPa