Question $3.$ Force vector for a linearly distributed load $(20$ pts$)$

Compute work$-$equivalent nodal forces for a linearly distributed load applied to the two$-$node bar element shown above. The distributed load is given by

$q=q_i(1-\frac{x-x_i}{L})+q_j\frac{x-x_i}{L}$

where $q_i$ and $q_j$ are the values of the distributed load at the end nodes, $x$ is the coordinate indicated above and $L$ is the length of the element. To receive full credit, use finite element shape functions and the expression for the virtual work of distributed load $q.$