$1.$ A simply supported timber beam has a span of $6m$ long and carries a uniformly distributed load of $25K\frac{N}{m}$ over its entire span. This load already includes an allowance for beam weight. The timber is $80\%$ stress grade Apitong. The allowable deflection is $\frac{1}{240}$ of the span. The properties of the Apitong are given.

$E=7\mathrm{.}31{10}^3$Mpa

$F_b=16\mathrm{.}5$Mpa

$F_v=1\mathrm{.}73$Mpa

i$.$ Which of the following gives the smallest dimension of the beam such that the allowable bending stress is not exceeded.

a$.220mm440mm$

b$.150mm300mm$

c$.250mm500mm$

d$.200mm400mm$

$2.$ Determine the slendemess ratio of the given column. Supports are pinned $($rotation free, translation fixed$)$ The unbraced lengths lu and their corresponding depths with respect to the plane of bending.

$l_{u1}=4\mathrm{.}5m$;$d1=350mm(0\mathrm{.}35m)$

$l_{u2}=2\mathrm{.}5m$;$d2=300mm(0\mathrm{.}30m)$

Determine the Column Stability Factor, $Cp$ for the same column given the following conditions:

Species: Molave, visually graded $(84\%$ exceeded$)$

For long$-$term usc $(10$yrs$)$

Under service conditions,

Moisture Content $<19\%$

Temperature $50C$

Incising was used