Can you solve this using matlab

For the fixed$-$fixed beam subjected to the linear varying distributed loading acting over the whole beam shown in Figure $4-29($a$)$ determine the displacement and rotation at the center and the reactions.

Solution:

The beam is now modeled using two elements with nodes $1,2,$ and $3$ and the distributed load is replaced as shown in Figure $4-29($b$)$ using the appropriate load cases $4$ and $5$ in Appendix D$.$ Note that load case $5$ is used for element one as it has only the linear varying distributed load acting on it with a high end value of $\frac{w}{2}$ as shown in Figure $4-29($a$),$ while both load cases $4$ and $5$ are used for element two as the distributed load is divided into a uniform part with magnitude $\frac{w}{2}$ and a linear varying part with magnitude at the high end of the load equal to $\frac{w}{2}$ also.

$($a$)$

$($b$)$

Figure $4-29($a$)$ Fixed$-$fixed beam subjected to linear varying line load and $($b$)$ the equivalent nodal force replacement system