Varignon's Theorem

Varignon's theorem [var·ən′yōnz ‚thir·əm]

(mechanics)

The theorem that the moment of a force is the algebraic sum of the moments of its vector components acting at a common point on the line of action of the force.

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Varignon’s Theorem 

a theorem in mechanics that establishes the dependence between moments of forces of a given system and the moment of their resultant force. This theorem was first formulated and proved by the French scientist P. Varignon. According to Varignon’s theorem, if a system of forces F_i has a resultant force R, then the moment M₀(R) of the resultant force relative to any center O (or z-axis) is equal to the sum of the moments M₀(F_i) of the component forces relative to the same center O (or the same z-axis). Mathematically, Varignon’s theorem is expressed by the formulas

M₀(R) =ΣM₀(F_i)

or

M_z(R) =ΣM_z(F_i)

Varignon’s theorem is used for solving a series of problems in mechanics (especially statics), resistance of materials, construction theories, and other areas.