$(45$ pts$)$ The frame below supports a weight $P$ at joint $D.$ The bars are rigid and their self

weight can be neglected.

a$.$ Determine the reactions in the supports and the force in each member when $P=$

$20k.$ Indicate if each member is in tension or compression.

b$.$ Determine the maximum value for $P$ if the force in any member cannot exceed $30$

$k$ and the reactions at A and $B$ cannot exceed $40k.$