$4$Two $2007525\mathrm{.}3$ channels, back to back, as shown below, act as column of length $5m$

with pinned ends. Yield stress $=250$MPa,$E=210$GPa.

$($a$)$ Use the formula with a buckling load of $100kN$ and calculate the maximum value of

the clear spacing a between the channels. $(35mm)$

$($b$)$ Use the Perry$-$Robertson formula given below to calculate the safe load the column

can carry. Take the load factor $=1\mathrm{.}7$ and $a=120mm$

$K.f_a=\frac{f_y+(1+n)f_e}{2}=[(\frac{f_y+(1+n)f_e}{2}{)}^2-f_y{f}_e{]}^{0\mathrm{.}5}$

$(771\mathrm{.}9kN)$