All the beam cross$-$sections below have the same area, A$.$ The area moment of inertia for each crosssection is labelled below.

A

B

C

D

E

Choose the best shape to minimize deformation and explain the reason:

A$.$ If loads are primarily in one direction that only bends the beam in the $x-y$ plane.

B$.$ If the loads are in two directions that can either bend the beam in the $x-y$ plane or the $x-z$ plane.

C$.$ If a torsional load is applied along the $x-$axis. $[$Hint: think of which moment of inertia would be applicable and how can you make an educated guess$]$