$($a$)$ The aluminium rod shown below $($Fig$.1$i$)$ will be used as part of the support mechanism in a footbridge over the river Thames. The aluminium rod has a varying circular cross section $($Fig $1$i$)$ and will be subjected to an axial tensile load of $12$ kN$.$ Assume that the load is being applied uniformly through both cross sections. A portion of the stress$-$strain diagramo Determine and justify whether the rod is strained elastically or plastically.

o Determine the approximate elongation of the rod when the load is applied.