LAMI'S THEOREM Engineering Mechanics

Description of LAMI'S THEOREM 

Lami's Theorem states that if three coplaner forces acting at a point be in equilibrium, then each force is proportional to the sine of the angle between the other two forces. Mathematically

P/Sinα=Q/Sinβ=R/Siny

where P, Q and R are the three forces and α, β and γ are the angles as shown in Fig 1.2.

MOMENT OF A FORCE

Moment of a Force is the turning effect produced by a force, on the body, on which it acts. The moment of a force is equal to the product of the force and the perpendicular distance of the point, about which the moment is required and the line of action of the force. Mathematically, the moment of a force P about point O as shown in Fig 1.4,

=PXL

The unit of moment depends upon the units of force and perpendicular distance. If the force is in newtons and the perpendicular distance in meters, then the unit of moment will be Newton-metre (briefly written as N-m).

VARIGNON'S PRINCIPLE OF MOMENTS

Varignon's Principle of Moments (or Law of Moments)

It states that if a number of coplanar forces acting on a particle are in equilibrium, then the algebraic sum of their moments about any point is equal to the moment of their resultant force about the same point.

What are Parallel Forces, like parallel forces and unlike parallel forces?

The forces, whose lines of action are parallel to each other, are said to be parallel forces. if the parallel forces act in the same direction then these are known as like parallel forces. When the parallel forces act in opposite directions, then these are known as unlike parallel forces.

COUPLE - MOMENT OF A COUPLE

What is definition of Couple in engineering mechanics? Define moment of a couple?

The two equal and opposite forces, whose lines of action are different, form a couple, as shown in Fig. 1.4.

Couple - Moment of a couple

The perpendicular distance (x) between the lines of action of two equal and opposite forces is known as arm of the couple. The magnitude of the couple (i.e. moment of a couple) is the product of one of the forces and the arm of the couple. Mathematically,

Moment of a couple = P x X

A little consideration will show, that a couple does not produce any translatory motion (i.e. motion in a straight line), but a couple produces a motion of rotation of the body on which it acts.