Question $1$: Beam ABCD is loaded as shown below. The beam is simply supported $($pin support at A and roller at $B).$

a$)$ Determine the support reactions at A and $B.$

b$)$ Construct the shear force and bending moment diagrams. Label the shear force and bending moment values at cross$-$sections $A,B,C,$ and $D,$ and at the locations of maximum and minimum values. Mention the order of the curve in each section $($first order$/$linear$,$ second order$/$quadratic$,$ third order$/$cubic$,$ etc.$)$ as well.

c$)$ Indicate the coordinate $x,$ within segment $AB,$ at which the bending moment is maximum.

Parameters: $L=2m,p_0=200k\frac{N}{m},P_C=170kN,M_C=40kN.m$ and $M_D=80kN.m$