Question $4(24$ marks$)$

A steel column of length $8$ m is fixed at the bottom and pinned at the top. As shown in Figure $4($a$),$ the column supports two loads of $300$ kN and $500$ kN with the respective eccentricities of $80$ mm and $120$ mm $($on opposite sides$)$ from the $x$ axis of column cross section. It is fully braced against buckling about the $y$ axis. Let Young's modulus be $200$ GPa $.$ The geometric properties for the section shown in Figure $4($b$)$ are as follows:

$A=12,000m{m}^2$;$,I_x=110\mathrm{.}4{10}^{6}m{m}^4$;$,I_y=26\mathrm{.}8{10}^{6}m{m}^4$

$($a$)$ Determine the maximum horizontal deflection of the column.

$(8$ marks$)$

$($b$)$ Determine the maximum compressive stress in the column.

$(10$ marks$)$

$($c$)$ Determine the maximum tensile stress, if any, in the column.

$(6$ marks$)$

$($Hint: First combine the two applied loads by determining the resultant and its line of action.$)$

Figure $4($a$)$ Column $($not to scale$)$

$300kN,500kN$

Thickness $=20mm$ for web and flanges

Figure $4($b$)$ Section C$-$C $($not to scale$)$

End of Paper