Problem $1(40$ points$)$: For the beam shown in Fig. $1,$ let EI be constant throughout the beam. Use the

FEA method to determine $($a$)$ the rotation at pin support A; $($b$)$ the rotation and displacement at the mid$-$

point where the load P is applied; $($c$)$ Draw the shear force and bending moment diagram; $($d$)$ Sketch the

deformed shape of the beam.