Problem $4$:

For the three$-$node bar element shown below: $($a$)$ derive the N$\_(1)$ shape function, $($b$)$ find the k$\_(11)$

stiffness coefficient, and $($c$)$ discuss the differences in terms of modeling performance between a

two$-$node and a three$-$node bar element. Let E and A be constant along the element.

Note: The three nodes are part of a single element.