Static Equilibrium Calculator
Check static equilibrium using ΣF = 0 and Στ = 0 — find unknown force or torque.
For a beam on two supports: enter load F at distance d from left support, and beam length L.
What Is Static Equilibrium Calculator?
The formula Check static equilibrium using ΣF = 0 and Στ = 0 — find unknown force or torque., is fundamental to this topic in physics.
This relationship is derived from first principles and applies broadly across scales and materials.
Engineers and scientists use this daily. The calculator automates arithmetic so you can focus on physical reasoning.
Ensure SI units throughout for correct results.
Formula Reference Table
| Solve For | Formula | Notes |
|---|---|---|
| Force equilibrium | ΣFx = 0, ΣFy = 0 | No net force |
| Torque equilibrium | Στ = 0 about any point | No net torque |
| Simple beam (R₁) | R₁ = F×(L−d)/L | Taking moments about right support |
| Simple beam (R₂) | R₂ = F×d/L | Taking moments about left support |
| Check | R₁ + R₂ = F | Sum of reactions = total load |
| Distributed load (UDL) | Acts at centroid (L/2 for uniform) |
3 Worked Examples
F = 1000 N at d = 2 m from left, L = 5 m.
- R₁ = F×(L-d)/L = 1000×3/5 = 600 N
- R₂ = F×d/L = 1000×2/5 = 400 N
- Check: 600+400 = 1000 N ✓
F = 800 N at center (d = L/2).
- R₁ = R₂ = F/2 = 400 N each (symmetry)
F = 500 N. Measured: R₁ = 200 N, L = 4 m.
- Στ about left: F×d = R₂×L → R₂ = F-R₁ = 300 N
- d = R₂×L/F = 300×4/500 = 2.4 m from left
Real-World Applications
Common Mistakes to Avoid
SI units required.
Use correct form for geometry.
Ideal conditions assumed.
Check conventions.
Verify squared/sqrt.
Frequently Asked Questions
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Formula Explorer connections
Interpretation: This relationship connects motion, force, momentum, work or energy in a mechanical system. Assumption: Choose a consistent reference direction and unit system. The model may assume constant acceleration, rigid bodies, negligible losses or an isolated system.