For the next beam, solve subsection $a,b,c,d$ and e$.$ Give the numerical results as a

function of El $($constant flexural rigidity$),$ in the subsection e$,$ graph the shear and

bending moment diagram, that is$,$ draw the diagrams. To solve this problem, use

the method of minimum work, that is$,$ the Castigliano method.

$7\mathrm{.}32.$ A propped cantilever beam with an overhang is subjected to a concentrated

load P$,$ as illustrated in Fig. P$7\mathrm{.}32.$ The beam has a constant flexural rigidity El$.$

Determine $($a$)$ the stiffness matrix for each element; $($b$)$ the system stiffness matrix;

$($c$)$ the nodal displacements; $($d$)$ the forces and moments at the ends of each

member; $($e$)$ the shear and moment diagrams.

$L=4$ meters

$P=11\mathrm{.}5k\frac{N}{m}$

Figure P$7\mathrm{.}32.$