Question $3$

$15$ marks

A column section is formed by connecting two $1256513\mathrm{.}42k\frac{g}{m}$ taper flange channel sections together as shown. Take the elastic modulus for steel $=200$GPa.

$($a$)$ Calculate the Second Moment of Area of the built$-$up channel section, about both the X $-$ and Y $-$axis.

$($b$)$ Calculate the Euler buckling load for the column if the column is $8$ m long assuming it is treated as a braced member rigidly fixed top and bottom.

$($c$)$ Calculate the crushing $($yielding$)$ load, for a load acting along the longitudinal axis passing through the centroid, if the yield strength of the steel is taken to be $400$ MPa $.$ Comment on the validity of the Euler load calculated above.