Calculate for the resultant of the force system:
A rectangle ABCD is having sides AB = CD = 80 mm and BC = DA = 60 mm. Forces of 150 N each of them act along AB and CD, and forces of 100 N each acting along the directions BC and DA. Calculate for the resultant of the force system.
Sol.: Let R be the resultant of given system. And ∑H and ∑V be horizontal and vertical component of the resultant. And resultant makes θ angle with the horizontal.
Resolving all the forces horizontally
∑H = 150 - 150
∑H = 0KN ...(i)
Resolving all the forces vertically
∑V = 100 - 100
∑V = 0KN ...(ii)
Since ∑H and ∑V both are 0, then resultant of system is also zero.
But in Non concurrent forces system, the resultant of system can be a force, a couple or a force and a couple that is in this case if couple is not zero then couple is resultant of the force system.
MA = -150 × 60 - 100 × 80, both are anticlockwise
Then, Resultant moment = couple = -17000N-mm .......ANS