The W$200$x$22,$ A$-36-$steel column is fixed at

its base. Its top is constrained to rotate about

the y$$y axis and free to move along the y$$y

axis. Also, the column is braced along the x$$x

axis at its mid$-$height. Determine the

allowable eccentric force P that can be

applied without causing the column either to

buckle or yield. Use against buckling F$.$O$.$S$.=$

$2\mathrm{.}0$ and F$.$O$.$S$.=1\mathrm{.}5$ against yielding.

For W$250$x$58$ Section

A$=28600$ mm$2$

Ix $=20$x$106$ mm$4$

$,$ rx $=83\mathrm{.}6$ mm

e $=100$ mm $,$ Iy $=1\mathrm{.}42$x$106$ mm$4$

$,$ ry $=22\mathrm{.}3$ mm

d $=200$ mm$,$ bf $=102$ mm $,$ E $=200$ GPa