Varignon’s theorem in statics

E923660

Varignon’s theorem in statics is a fundamental principle stating that the moment of a force about a point equals the sum of the moments of its components about that point, simplifying the analysis of mechanical systems.

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Varignon’s theorem in statics canonical 1

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Predicate Object
instanceOf principle of statics
theorem in mechanics
alternativeName Varignon’s principle of moments NERFINISHED
principle of moments
appliesTo concurrent force systems
coplanar force systems
nonconcurrent force systems
three-dimensional force systems
assumes force additivity
rigid body model
category engineering principle
physical law (approximate, classical)
coreStatement The moment of a force about a point equals the sum of the moments of its components about that point.
expressedAs The moment of a force about a point equals the algebraic sum of the moments of its rectangular components about that point.
field classical mechanics
engineering mechanics
statics
hasApplication aerospace engineering
civil engineering
machine design
structural analysis
historicalPeriod late 17th century
implies moment of a resultant equals sum of moments of component forces
mathematicalForm M_O(F) = r × F
M_O(F) = Σ M_O(F_i)
namedAfter Pierre Varignon NERFINISHED
relatedTo Newtonian mechanics NERFINISHED
equilibrium conditions ΣM = 0
parallelogram law of forces
relatesConcept force components
moment of a force
position vector
resultant force
vector cross product
requires vector decomposition of forces
taughtIn engineering statics textbooks
mechanical engineering curricula
undergraduate engineering courses
usedFor analysis of beams
analysis of frames
analysis of trusses
computation of resultant moments
equilibrium analysis
simplifying moment calculations
validIn three-dimensional vector mechanics
two-dimensional vector mechanics

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Pierre Varignon notableIdea Varignon’s theorem in statics