The required steps, process, diagrams, and$/$or unknowns are specified below.

The continuous beam with an internal hinge at node $2$ is carrying loads as shown in Fig. $1.$ The nodal numbers, element numbers, and the global coordinates are indicated in Fig. $1.$ It's required that a three$-$element model must be used for the analysis. Also, both Cases $1$ and $2$ of the ondensed element stiffness matrices must be applied. By means of the structural finite element method to:

$($a$)$ Compute the equivalent nodal loads.

$(10$ points$)$

$($b$)$ Draw a diagram of the continuous beam carrying the equivalent loads $($magnitudes and directions must be clearly indicated on the diagram$).$

$(4$ points$)$

$($c$)$ Determine the global element stiffness matrices, $\frac{?}{\text{b}\text{a}\text{r}}(k),$ for each element.

$(9$ points$)$

$($d$)$ Solve the unknown nodal displacements.

$(15$ points$)$

$($e$)$ Compute the element forces in element $(1).$

$(5$ points$)$

Take $E=200$GPa and $I=400{10}^{6}m{m}^4$ for entire beam.

$=1$

$\frac{642}{L}$

Exam #$1$

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