For the beam and loading shown, use discontinuity functions to compute $($a$)$ the deflection of the beam at A and $(b)$ the deflection of the beam at $C.$ Assume a constant value of EI $=23000kN*m^2$ for the beam. Also, assume $P=15kN,w_B=23k\frac{N}{m},w_C=78k\frac{N}{m},a=2\mathrm{.}2m,b=3\mathrm{.}8m,$ and $c=1\mathrm{.}3m.$

Calculate the reaction forces $B_y$ and $D_y$ acting on the beam. Positive values for the reactions are indicated by the directions of the red arrows shown for the forces $B_y$ and $D_y$ on the free$-$body diagram below. $($Note: Since $B_x=0,$ it has been omitted from the free$-$body diagram.$)$

$\backslash$table$[[|$P$,,],[,,],[,,],[,,]$

$,[,,],[D_y,$

$($