Problem $3(40$ points$)$

Consider $\backslash ($ w$\_\{0\}=30\backslash$mathrm$\{$kN$\}/\backslash$mathrm$\{$m$\}\backslash )$ and $\backslash ($ L$=12\backslash$mathrm$\{$~m$\}\backslash )$ for the beam shown in the figure.

a$)$ Determine the reaction force$/$moment at support A

b$)$ Find the moment function and draw the moment diagram

c$)$ Find the equation of the deflection $($using the integration method$)$

d$)$ Determine the maximum deflection in the beam

e$)$ Determine the maximum slope in the beam

NOTE: Keep E and I as variables for parts c$,$ d$,$ and e$.$

Your solution must include an FBD$.$