Calculator · Engineering Mechanics
2D Equilibrium Calculator
Reactions of a planar rigid body from the three equilibrium equations. When the system is indeterminate or inconsistent, that is stated rather than solved around.
Applied forces
Applied couples
Supports
Moment reference point
Any reference point gives the same reactions; it only changes how the moment equation is written.
Free-body diagram
Select a vector, support, couple or distributed load to inspect its exact values.
Verdict
Statically determinate
The three planar equilibrium equations determine every unknown reaction.
3 equations · 3 unknowns · rank 3 · cond ≈ 4.2656
Reactions
| Ax | 0 N → (0, 0) N |
|---|---|
| Ay | 500 N → (0, 500) N |
| Bn | 500 N → (3.0616e-14, 500) N |
Equilibrium equations
- ΣFx:Ax = 0[N]
- ΣFy:Ay + Bn − 1000 = 0[N]
- ΣM:4·Bn − 2000 = 0[N·m]
Equilibrium check
| ΣFx | 3.0616e-14 N |
|---|---|
| ΣFy | -1.7053e-13 N |
| ΣM about O | 4.5475e-13 N·m |
| Verdict | Equilibrium satisfied within tolerance |
Technical reference
ΣFx = 0
ΣFy = 0
ΣM_O = 0
- ΣFx, ΣFy
- sum of force components, including reactions[N]
- ΣM_O
- sum of moments about the reference point, including reactions[N·m]
Each support contributes scalar reaction unknowns along its fixed directions: a pin gives two components, a roller one along its stated normal, and a fixed support two components plus a moment. These unknowns are assembled into the three equations above and solved together, not one support at a time.
A negative solved reaction is a valid answer: the reaction acts opposite the assumed positive direction, it is not an error.
Any choice of moment reference point O gives the same reactions; whether the system is determinate, indeterminate or inconsistent depends only on the rank of the assembled system, not on O.
Assumptions
- · A single planar rigid body: ΣFx = 0, ΣFy = 0, ΣM = 0, with +x right, +y up and counter-clockwise moments positive.
- · Supports are ideal and frictionless; a roller reacts only along its stated normal direction.
- · Statically indeterminate systems are reported, not solved: equilibrium alone does not determine them.
- · Deformation, member internal forces and stresses are outside this tool.
Continue
Same system, plus distributed loads, presets and the resultant view.