Problem $01$

The non$-$prismatic beam shown below is drawn in terms of $3$ nodes along the span. Determine the stiffness matrix of a single element in terms of node $1$ and $3$ by using the direct stiffness matrix and assuming the end unit displacement or rotation as a prescribed displacement. Hint: solve for the reactions at nodes $1$ and $3$ as the stiffness coefficients for the entire single element.

$1$

$2$

$0\mathrm{.}5$ El

$3$