Example$)$

As shown in Fig. $2,$ three loads vec$(F{)}_1,$vec$(F{)}_2,$vec$(F{)}_3$ and a couple moment vec$(M)$ are acting on a beam

supported by a roller and a pin joint. The mass and thickness of the beam are negligible.

$($i

$($b$)$ If the beam is in static equilibrium, write the equations of motion at point $B.$

$($c$)$ If the magnitudes of the loads and the couple moment are given as $|vec(F{)}_1|=2P,|vec(F{)}_2|=P$ and

$|vec(M)|=2Pb,$ respectively, determine the maximum magnitude of the load vec$(F{)}_3$ required to keep

the beam in static equilibrium, and also determine the support reactions at points A and $B.$

Express your answer in terms of $P$ and $.$ Use the given coordinate system.