A built$-$up column with two channels $[2$ ISMC$350]$ back$-$to$-$back of length $10$m to carry an axial factored load of $1450$ kN$.$ The column is restrained in position but not in direction at both ends. Provide single lacing system with bolted connections. Assume steel of grade Fe $410$ and bolts of grade $4\mathrm{.}6$ and $20$ mm dia. Check the following

$($i$)$ Check the capacity of the column

$($ii$)$ Determine the suitable spacing b$/$w the components and show in the diagram.

$($iii$)$ Force in the lacing members. Assuming inclination of lacing bar is $450$

$($iv$)$ Check for failure of main component

$($v$)$ Determine the minimum size of lacing required as per IS code

$($vi$)$ if $60$ISF$14$ is used a lacing member, check for slenderness ratio and determine its compressive strength.