Varignon theorem - mechanics, Mechanical Engineering

Varignon theorem:

State Varignon's theorem. How it helps in determining of the moments? In which type of condition is it used?

Sol.: Varignon's theorem also called Law of Moment.

The application of varignon's theorem practically is to find the position of the resultant from any point of the body.

It states "If number of coplanar forces is acting simultaneously on a particle, algebraic sum of moments of all the forces about any point is equal to moment of their resultant force about same point."

Proof: Let us consider, two concurrent forces P and Q represented in magnitude and direction by AB and AC as shown in the figure given below.

Let 'O' be the point, about which moment are taken, through O draw line OD parallel to direction of force P, to meet line of action of force Q at point C. Now with AB and AC as the two adjacent sides, complete Parallelogram ABDC as shown in the figure given below. Join the diagonal AD of the parallelogram and OA and OB. From parallelogram law of forces, we know that diagonal AD represents in the magnitude and direction, resultant of two forces P and Q. Now we see that moment of the force P about O: = 2. Area of triangle AOB  ...(i)


133_Varignon theorem.png

Likewise, moment of the force Q about O:  = 2. Area of ΔAOC                                     ...(ii)

And moment of resultant force R about O:  = 2.Area of ΔAOD                                     ...(iii)

But from the geometry of the figure, we find that

Area of ΔAOD = Area of ΔAOC + Area of ΔACD

But the Area of ΔACD = Area of ΔABD = Area of ΔAOB

(As the two "AOB and ADB are on same base AB and between same // lines)

Now Area of triangle AOD = Area of triangle AOC + Area of triangle AOB

Multiply both the side by 2 we obtain;

2. Area of triangle AOD = 2.Area of triangle AOC + 2. Area of triangle ACD, that gives

Moment of force R about O = Moment of force P about O + Moment of force Q about or,

Where R . d =     ∑M

∑M = Sum of moment of all the forces

d = Distance between resultant force and point where moment of all the forces are taken. This principle can be extended for any number of the forces.


Posted Date: 10/16/2012 7:20:04 AM | Location : United States

Related Discussions:- Varignon theorem - mechanics, Assignment Help, Ask Question on Varignon theorem - mechanics, Get Answer, Expert's Help, Varignon theorem - mechanics Discussions

Write discussion on Varignon theorem - mechanics
Your posts are moderated
Related Questions
(1) Huckel Theory: Using Huckel theory, write a program that solves for the molecular orbitals and energy levels in a conjugated or aromatic hydrocarbon (i.e. ethylene, butadiene,

A hydraulic pipe is 20 cm internal diameter and 5 cm thick. It is needed to sustain an intensities of radial and hoop stress at several radii and plot their variation.

The Leader Command The Leader command can be used to annotate at any point on a drawing. The command sequence below was used to draw the leader shown in the Figure Below.

The round tensile specimen given  below has a diameter of 0.5 in. A load, F, is applied and the deflection, g , is calculated. Given the following                    d = 0.5 in

When you arrive at Duke's Dude Ranch, you are greeted by the large wooden sign shown.  The left end of the sign is held in place by a bolt and the right end is tied to a rope that

what is cone friction?

Reversible and irreversible processes: Thermodynamic system which is capable of restoring the original state of it by reversing the factors responsible for occurrence of proc