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.