Problem $3(25$ points$)$

The beam is used to support a dead load of $\backslash (2\backslash$mathrm$\{$k$\}/\backslash$mathrm$\{$ft$\}\backslash ),$ a live load of $\backslash (0\mathrm{.}8\backslash$mathrm$\{$k$\}/\backslash$mathrm$\{$ft$\}\backslash )$ and a concentrated live load of $10$ k $.$ The support at A is a pin and B is a roller.

$(1)$ Determine the maximum positive $($upwards$)$ reaction at A $.$

$(2)$ Determine the maximum positive bending moment at C $.$

$(3)$ Determine the maximum negative shear force at D $.$