$4.$i$)$ Draw an approximate curve for column capacity vs slenderness ratio. On the same plot, draw Euler's curve for elastic column buckling. Label and explain the regions for yielding, inelastic buckling and elastic buckling. Discuss reasons due to which inelastic buckling occurs before critical elastic buckling capacity is reached $[3]$

$4.$ii$)$ Are the columns shown in Figure $4($a$)$ and $($b$)$ expected to buckle first about $x-x$ axis or $y-y$ axis? Note that $($a$)$ is a single channel section, and $($b$)$ is a built$-$up column with two channel sections. Justify your answers with calculations as needed. $($Hint $-$ Column cross section properties are provided in Question $1)[3]$

$($a$)$

Figure $4$

$4.$iii$)$ Determine the factored ultimate load $P$ that can be supported by the bearing$-$type bolted connections shown in Figure $5($a$)$ and $5($b$).$ Assume plates to be E$350$ material, bolt ultimate strength as $400$MPa and bolt diameter as $16mm.$ Assume that bolt threads are not in the shear plane$($s$).[4]$

Figure $5$

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$.$pleease do this question within $1\mathrm{.}30$ hours as soon as possible much neeedd please