QUESTION $3$

$(7\mathrm{.}50-8\mathrm{.}05$ p$.$m$.)$

Determine the diameter of the six bars to be provided as the longitudinal reinforcement in

a short column with the cross$-$section shown in the figure below for $P_u=1000kN$ and $e=$

$18mm.$ Consider M$25$ grade concrete and Fe$415$ steel. The column has an unsupported

length of $3m.$ It may be assumed to bend only along the longer dimension.

Consider the cross$-$section with the bar diameter determined above and find the

maximum possible value of $P_u,$ when it is applied concentrically $($i$.$e$.,$ with no possibility

of bending moment and shear in the column$)$ and the maximum strain permitted is $0\mathrm{.}0025$

$($instead of $0\mathrm{.}002)$ at collapse.