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.

M_A = -150 × 60 - 100 × 80, both are anticlockwise

Then, Resultant moment = couple = -17000N-mm                                                      .......ANS