Net force

In mechanics is called the resultant force of two or more forces, the forces equivalent to the original, so is equivalent in their effects on the rigid body, short Resulting or resultant.

Intersect the lines of action of all forces at a point ( central force system ), then the resultant passes through this point. In the general case ( common power system ) in addition results in a torque that can be represented, for example, by two forces of a force couple. The point of application of the resultant single force is selected, the size of the force couple is dependent on this choice.

A method for determining the resultant

The resultant is determined by vector addition. For this purpose, various methods exist.

The analytical method

Analytically, the resultant is determined from the following conditions:

• The components of the resultant with respect to a Cartesian coordinate system are equal to the sum of the components of the individual forces, and
• The components of the moment of the resultant with respect to any point is equal to the sum of the moments of the individual components of the forces.

If the vectorial sum of the individual forces disappears, the resultant force is zero. That is, for example, in a case of the couple of forces (Figure d ); There remains a single moment with the lever rule applies.

Graphical method

For the graphical determination of the resultant of two forces to use the force polygon (Figure b. ) Or the parallelogram of forces (Figure c. ).

The three- forces method used to determine the resultant or the provision of a third, unknown force when knowing two of the three forces. The resultant forces at two or more can be determined, for example, with the aid of Seileckverfahrens.

The four- forces method according to Karl Culmann serves as the Cremonaplan for graphic determination of the resulting bar or rod forces, for example in the design of trusses.