Question $5$

$($a$)$ A $1\mathrm{.}5$ m long column has a circular cross$-$section of $5$ cm diameter. One of the ends of the column is fixed in position and the other end is free.

$($i$)$ Using a sketch, describe the effective length of the column.

$($ii$)$ Calculate the buckling load of the column using the Rankine formula, given yield stress $=560\frac{N}{m}{m}^2$ and Rankine's constant $=\frac{\text{a}\text{n}\text{d}}{?}$

$[6+6$ marks$]$

$($b$)$ A cantilever $2$ metres long is of rectangular section $100$ mm wide and $200$ mm deep. It carries a uniformly distributed load of $2k\frac{N}{m}$ over a length of $1\mathrm{.}25$ m from the fixed end.

Young's modulus is $10G\frac{N}{m^2}.$

Calculate the deflection at the free end.

$[13$ marks$]$

END OF QUESTION PAPER