Calculate the critical load Per for a W 250 x 89 steel colum

Calculate the critical load Per for a W 250 x 89 steel column (see figure) having length L =10m. and E=200 GPa under the following conditions: (a) The column buckles by bending about its strong axis (axis 1-1), and the column buckles by bending about its weak axis (axis 2-2). In both cases, assume that the column has pinned ends.

Solution

Pcr= ^2 EI / 4l^2

E = 200 GPa = 200 x10^9 N/m2

L = 10 mm

Case (1)

I = Ixx

Pcr =  ^2 EIxx / 4l^2

Pcr = ^2 x 200 x10^9 x Ixx / (4 x 10 x 10)

Pcr = 5 x10^9 x ^2 x Ixx

Case (2)

I = Iyy

Pcr =  ^2 EIyy / 4l^2

Pcr = ^2 x 200 x10^9 x Iyy / (4 x 10 x 10)

Pcr = 5 x10^9 x ^2 x Iyy