BDA $21302/20903$

Q$1$ A column of length $L$ can be constructed by gluing together three identical planks in each of the arrangements shown in Figure Q$1.$ The column is pin$-$supported at both ends. Assume that arrangement $\text{'}a\text{'}$ and arrangement $\text{'}b\text{'}$ differ in the orientation of the planks, which affects the moment of inertia.

$($a$)$ Using Euler's critical load formula, calculate the critical load Pcr $,$ for arrangement $\text{'}b\text{'}$

$(18$ marks$)$

$($b$)$ Determine the ratio of the critical load

$(7$ marks$)$

arrangement a

arrangement b