Static equilibrium

How force and moment balance determines support reactions before component stresses are considered.

ENGINEERING PRINCIPLE

A body in static equilibrium has zero resultant force and zero resultant moment about any point.

ΣFx = 0; ΣFy = 0; ΣM = 0
FundamentalsVerifiedReviewed 2026-08-09

Variables and units

  • F = applied or reaction force (N)
  • M = moment (N·m)
  • x = lever-arm distance (m)

Worked example

A 12 kN central load on a simply supported beam gives 6 kN vertical reaction at each support when the beam and loading are symmetric.

Calculation method

  1. Draw the isolated component and supports.
  2. Write force equations in each relevant direction.
  3. Take moments about a point that removes unknown reactions where practical.

Practical applications

  • Support reactions
  • Bracket loading
  • Lifting and fixture layouts

Review boundary and reference

  • Check the assumed support type and load direction.
  • Equilibrium alone does not check strength, deflection or stability.

Formula and displayed units independently checked for the stated conditions. This is not a code-compliance design method.

Source: Classical statics and strength-of-materials derivations; SI conventions follow NIST SP 811.

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