Example $5\mathrm{.}3$: A crane consisting of a vertical post, a horizontal boom, and an inclined brace supports a vertical load of $10,000lb,$ as shown in Figure $5\mathrm{.}16$ a $.$ The crane is supported by a pin connection at A $.$ The support at B permits only a horizontal reaction $($smooth vertical surface$).$ The members of the crane are pin$-$connected at points C$,$ D$,$ and E$.$ The members have weights as follows: post, $1400$ lb ; boom, $1500$ lb ; and brace, $900$ lb $.$ The member weights may be considered to be acting at their respective midpoints. Calculate all the forces acting on each of the three members.

$($a$)$ Crane framework