Question $1(50\%)$

Forces are acting on a rigid pipe frame with a built$-$in joint at O as shown. Hint: Write down coordinates of A$,$ B$,$ C$,$ and D$.$

$($a$)$ Draw a free body diagram of the overall pipe system. $(5\%)$

$($b$)$ Draw a free body diagram of the pipe ABC $.$ You should derive the numerical values of all forces and moments acting on the free body ABC and show them in the FBD$.(5\%)$

$($c$)$ Find vector moment of the $100$ N force at A about junction D$.(5\%)$

$($d$)$ Find the vector of reaction force at O$.(15\%)$

$($e$)$ Find the vector of reaction moment at O$.(15\%)$

$($f$)$ Find the angle between the reaction force at O $($i$.$e$.$ answer to part $($e$))$ and the $100$ N force at A$.(5\%)$