A wooden column, $200$ mm square and $1\mathrm{.}5$ m long is reinforced with two steel plates

as shown in Figure Q$2,$ each steel plate is $1\mathrm{.}5$ m long, $200$ mm wide and $10$ mm

thick. The steel plates are bolted together so that the steel plates and the timber

column act as a single unit.

Young$$s modulus of steel $=$ Esteel $=200$ GPa

Young$$s modulus of wood $=$ Ewood $=30$ GPa

$($a$)$ Determine the maximum permissible load that this assembly can carry along

it$$s length if the compressive stress in the wood is not to exceed $10$ MPa

and that in the steel is not to exceed $100$ MPa. $[80\%]$

$($b$)$ Find the amount by which the assembled column will shorten under this

maximum permissible load