$2\mathrm{.}2$ Two $230mm90mm$ standard channels are laced together to form a column $10$ m long$-$with built$-$in ends.

$2\mathrm{.}2\mathrm{.}1$ If $lo{x}_x=l_{yy}$ for the cross section, calculate the dimension $"$b$".$

$(5)$

$2\mathrm{.}2\mathrm{.}2$ Calculate the crippling load for this column according to both Euler and Rankine theories. Assume $E=200$GPa, Yield stress $=260$MPa and $"$a$"$ for pinned ends $=\frac{1}{7500}$

$(7)$

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