The figure shows a column supporting a floor. Assuming the column length is $18ft,$ and the column is a W$1482$ formed from grade $50$ steel, determine the critical buckling load and average compressive stress.

W $14$ x $82$ steel properties

$A=24i{n}^2,I_x=881i{n}^2,I_x=148i{n}^2,E=29000$ksi

$F_y=50$ksi,$r_y=2\mathrm{.}48in$

$P_{cr}={}^{2}E\frac{\text{I}}{L^2}$

${}_{cr}=$

a$)P_{cr}=712$kips,${}_{cr}=76\mathrm{.}1$ksi

b$)P_{cr}=512$kips,${}_{cr}=56\mathrm{.}1$ksi

c$)P_{cr}=612$kips,${}_{cr}=66\mathrm{.}1$ksi

Solution: