A $50100mm$ rectangular timber strut with fixed ends is used to support an axial compressive load. Determine: $($a$)$ the minimum length at which the Euler's formula can be applied and $($b$)$ the safe load the strut can carry with a factor of safety of $2,$ for a length of $2\mathrm{.}5$ m $.$ The stress at proportional limit and modulus of elasticity are ${}_p=1=30$MPa and $E=10$GPa, respectively.

$[$Ans$.L=1\mathrm{.}66m$ and $P=32\mathrm{.}9kV]$