FORCE COUPLEA system of two equal and unlike parallel forces, whose lines of action are not the same, is called a couple or a torque.* Moment of Couple: The moment of a couple is the product of one of the forces forming the couple and the arm of the couple. The perpendicular distance between the forces is called the arm of the couple.* The moment of the couple is regarded as positive or negative according as it has a tendency to turn the body in the anti-clockwise of clockwise direction.* The algebraic sum of the moments of the two forces forming a couple about any point in their plane is constant, and equal to the moment of the couple.* Two couples, acting in one plane upon a rigid body, whose moments are equal and opposite balance one another.* Any number of couples in the same plane acting on a rigid body are equivalent to a single couple, whose moment is equal to the algebraic sum of the moments of the couples.* If three forces, acting upon a rigid body, are represented in magnitude, direction, and line of action by the sides of a triangle taken in order, they are equivalent to a couple whose moment is represented by twice the area of the triangle.Solved Example 1:

Two unlike parallel forces each of magnitude 20√3 units acting on a rigid body form an anticlock

couple. If these forces lie in the xy-plane and act at the points A (–1, 0), B (3, 0) and are inclined at 600 to the x-axis, find the moment of the couple.

Solution: From B, draw BM perpendicular to the line of action of the force passing through A.Since, AB = 4 units and ∠MAB = 600

From right angled triangle AMBMB = AB sin 600 = 2√3 unitsTherefore, the moment of the couple= 20√3 × MB = 20 × 2√3 units= 120 units

MOMENT OF A FORCEThe moment of a force about a point is the product of the force and perpendicular distance of its line of action from the point.

If F be a force and p the perpendicular distance of its line of action from the fixed point O, then moment of F about O = F × p.

Properties Of Moments

* Positive and Negative Moments: The moment of a force about a point measures the tendency of the force to cause rotation about that point. If the tendency of the force is to turn the lamina in anti-clockwise direction then usual convention is to regard the moment as positive and that in clockwise direction as negative.

* The algebraic sum of the moments of a set of forces about a given point is the sum of the moments of the forces, each moment having its proper sign prefixed to it.

* The algebraic sum of the moments of any two forces about any point in their plane is equal to the moment of their resultant about the same point.

* If any number of forces in one plane acting on a rigid body have a resultant, the algebraic sum of their moment about any point in their plane is equal to the moment of their resultant.

* The moment of a force about an axis is the product of the resolved part of the force in a direction perpendicular to the axis (the other component being the product of force parallel to the axis and the shortest distance between the axis and the line of the force.

Solved Example 1:A uniform beam AB is 18 feet long and weighs 30 lb. Masses of 20 and 45 lb are suspended from A and B respectively. At what point must the beam be supported so that it may rest horizontally?

Solution: Let the weight of the beam AB acts at its middle point C. when masses of 20 and 45 lb are suspended from A and B respectively, then let resultant of these three passes through O.

Since, AB = 18 ft => AC = BC = 9ft

Let CO = x ft, then AO = (9 + x) ft and

BO = (9 – x) ft

Since, the resultant passes through O, therefore moments of the acting force at point A, B and C about O will be zero.

=> 20 . AO + 30 . CO – 45 . BO = 0

=> 20 (9 + x) + 30 x –45(9 –x) = 0

=> 19x –45 = 0 => x = 45/19

=> Beam should have support at a distance of (9+ 45/19) ft i.e. 11 7/9 ft from A.