Varignons principle of moments

Varignons principle of moments

1. TOPIC:    Varignon’s Principle Of Moments            NAME:KALINGO AUROBINDO NAYAK REGD NO:20010112022 SEC:D BRANCH CAMPUS:PARLAKHMUNDI

2. Varignon’s Theorem  Varignon’s Theorem states that the moment of a force about any point is equal to the  algebraic sum  of the moments of its components about that point. Principal of moments states that the moment of the resultant of a number of forces about any point is equal to the  algebraic sum  of the moments of all the forces of the system about the same point.

3. Proof:- 1.let  us consider two concurrent forces F1 and F2 represented in magnitude and direction by AB and AC as shown in diagram. 2. let 'O' be the point about which the moments are taken . 3.though 'O' draw a line OD parallel to the direction of force F1 to meet the line of action of the force F2 at C. 4. with AB  and AC  as two adjacent slides ,complete the parallelogram ABDC as shown in diagram.

4. 5. where AD is the diagonal of the parallelogram. 6. from the parallelogram law of force , the resultant of F1 and F2 is AD as shown in dia. 7. moment of force =2 x area of triangle,                            Whose base line represented force  and whose vertex is the pt. About which the moment is taken. * moment of force F1 about O = 2 x area of   AOB             moment of force F2 about O= 2 x area of    AOC   Moment of resultant R about O = 2 x area of  AOD            => from same base and equal height , Area of   AOB = area  of    ADB ---------------1 Because ABDC is a parallelogram ,  Area of    ADB= area of    ACD---------------2

5. From eq 1 & eq 2   Area of  AOB = area of  ACD--------3 From the diagram Area of   AOD = area of   AOC + area of    ACD                                                     ----------- 4 From eqn no   -----3      Area of  AOD = Area of  AOC + area of   AOB Multiply both side by 2 2 x area of   AOD = 2 x area of  AOC  + 2 x area of    AOB Moment of force R about O = moment of force F1 about O + moment of force F2 about O

6. QUE: four coplanar forces 2KN,3KN,5KN& 7KN are acting on a square body of side 1m.determine magnitude ,direction & position of resultant force from point A, which will keep the body in equilibrium

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