Lab · Engineering Mechanics
Statics & Equilibrium
A planar force system, its resultant, and the support reactions that hold it — solved from the same three equilibrium equations throughout.
Presets
Forces
Couples
Uniform distributed loads
Supports
Reference member
Drawn from (0, 0) to (L, 0). Use 0 for no member.
L is reference geometry for reading the diagram. Changing it redraws the member only: it does not move any force, support, couple or distributed load, and it never enters ΣFx, ΣFy or ΣM. Application points stay free anywhere in global x–y, inside or outside [0, L].
Moment reference point
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 |
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 |
Assumptions
- · Planar rigid-body statics: +x right, +y up, moments positive counter-clockwise.
- · The horizontal member from (0, 0) to (L, 0) is reference geometry only: it is drawn, never solved, and it does not constrain where loads or supports act.
- · A uniform distributed load is replaced by its equivalent force w·L acting at the segment midpoint.
- · Supports are ideal; a negative reaction acts opposite the assumed direction.
- · Indeterminate and inconsistent systems are reported as such — no extra assumption is invented to force a solution.
What this Lab models
A planar rigid body under applied forces, couples and uniform distributed loads, held by idealised supports — reduced to a resultant about a chosen point and, separately, solved for support reactions from the same three equilibrium equations.