$($Maximum $20$ points$)$ Answer any five of the following with examples, wherever appropriate:

$($a$)(4$ points$)$ What is the difference between strain energy and complementary strain encrgy? When are they equal?

$($b$)(1$ points$)$ What is the difference between static indeterminacy and kinematic indeterminacy?

$($c$)(4$ points$)$ Show that the cross$-$flexibility coefficients $f_{ab}$ and $f_{ba}$ are equal.

$($d$)(4$ points$)$ Consider that an external force $P$ acts on a body slowly and then remains constant. If the deflection is $,$ under what conditions is the work done: $($i$)W=0\mathrm{.}5P$ and $($ii$)W=P.$

$($e$)(4$ points$)$ Explain the principle of superposition. Why is it valid for linear systems only?

$($f$)(4$ points$)$ In the context of force method of analysis, what is a primary structure?