A truss element $($beam with rectangular cross$-$section$)$ is loaded in compression, as shown below. A truss element $($beam with rectangular

cross$-$section$)$ is loaded in compression, as shown

below.

a$.$ Identify the plane in which buckling will

occur first. Support your answer with

calculations.

b$.$ If instead of dimension $4$a$,$ the dimension

along the $z-$axis is $"b".$ find the ratio of $\frac{a}{b}$

such that the beam is as likely to buckle in

the xy plane as it is in the yz plane.

Identify the plane in which buckling will occur first. Support your answer with calculations.

If instead of dimension $4$a$,$ the dimension along the z$-$axis is $$b$.$ find the ratio of a$/$b such that the beam is as likely to buckle in the xy plane as it is in the yz plane.