A $2-$D frame as shown is loaded by a $30$ lb force $$t D $.$ The segment $AB$ and $BD$ are assumed rigid.

$($a$)$ Determine the reactions at A and C $,$ and the internal forces at joint B$.[20$ PTS$]$

$($b$)$ Determine the bending moment at C $[10$ PTS$].$

You are required to draw clear FBDs with all relevant forces marked.