Given a two$-$span beam. Joint $"1"$ is pinned, joint $"3"$ is fixed, and simple support is located at joint $"2".$ The beam is loaded by a linearly distributed load acting on the right span as shown in the figure. The beam is linear elastic with constant bending stiffness EI$.$

$1)$ Use the slope$-$deflection method to determine the rotations at joints and bending moment at joint $"3".(5$p$)$

$2)$ Determine and draw the distribution of the moment and shear force. $(2$p$)$

Hint. Remember the sign convention for the bending moment.