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 = 0Variables 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
- Draw the isolated component and supports.
- Write force equations in each relevant direction.
- 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.