Problem $2$

Numerical Problem $(20$ points$)$: For this problem, you will create a generalized formula to find reactions for a simply supported beam $($hinge on one side, and roller on the other$)$ subjected to a trapezoidal load somewhere along its length. Then, you will use the generalized formula that you created to solve some typical loading that the simply$-$supported beams can encountered in real$-$life. This process of creating generalized procedures and applying to problem$-$specific conditions is how engineering codes are made!

Please create a generalized formula$($s$)$ to compute the reactions $($and all the components$)$ for the figure shown below. Your generalized formulas should in terms of load magnitudes $\text{'}$a$\text{'}$ and $\text{'}$b$\text{'},$ and lengths $\text{'}{L}_a\text{'},\text{'}{L}_b\text{'},$ and' $L\text{'}.$ Start by creating a global free body diagram for the system.

Using the formula derived in part $1,$ please solve the following beams.

$($a$)$ Ream $1$

$\frac{V}{m}$

$($h$)$ Ream $?$