Practice $4$: A two$-$members frame

Consider the frame represented in figure $(1),$ the two members $AB$ and $BC$ are pinned to the wall in A and $C$ and they are joined together through a pin in B$.$ The pins allow rotation but no translations.

Figure $1$: Representation of the frame.

$(12$ pts$)$ Briefly explain why the action$-$reaction between the two members in $B$ has two unknowns.

$(16$ pts$)$ Draw the FBDs of $AB$ and $BC$ on figure $(2).$ Replace the distributed loads with equivalent forces $($specify the point of application$).|$Figure $2$: FBDs to complete.

$(10$ pts$)$ Count the number of unknowns and equations of equilibrium when:

$($a$)$ We consider the whole frame as a system.

$($b$)$ We consider every member apart as a system

Then conclude which is the best choice to determine the unknowns.

$(22$ pts$)$ Determine the reactions in A and C$.$

$(20$ pts$)$ Determine the internal forces in point E$.$

$(20$ pts$)$ Draw the shear and couple moment diagrams for member AB$.$