Determine magnitude of the couple:

A square block having each side 1.5 m is acted upon by system of forces along its sides as shown in the adjoining figure. If system reduces to couple, determine magnitude of the forces P and Q, and couple.

Sol.: If the system is reduces to couple, the resultant force is zero,

(that is  ∑H = ∑ V = 0) but ∑M = 0,

i.e. the moment of the force system or couple is the resultant of the force system.

∑H = 150 - 150 cos 45º - P = 0

P = 43.95N                                                                               .......ANS

∑V = 300 - 150 sin 45º - Q = 0

Q = 193.95N                                                                            .......ANS

Now moment of couple = Algebraic sum of moment of forces at any corner, say A

= -300 × 1.5 - 43.95 × 1.5 = -515.925 Nm             .......ANS

negative means moment is anticlockwise.