- 2074 Asoj · 6 marks
Equilibrium and its equations in 2D and 3D
Short answer
Equilibrium means the resultant force and moment on a body are zero, so it stays at rest or moves uniformly. For a particle: 2D ΣFx=0, ΣFy=0; 3D ΣFx=ΣFy=ΣFz=0. For a rigid body: 2D ΣFx=0, ΣFy=0, ΣM_O=0; 3D ΣFx=ΣFy=ΣFz=0 and ΣMx=ΣMy=ΣMz=0.
Define equilibrium and its essence. What are the equations of static equilibrium for 2D and 3D analysis of particle and rigid body?
Equilibrium
A body is in equilibrium when the resultant of all forces and moments acting on it is zero, so it remains at rest (static equilibrium) or moves with constant velocity.
Its essence
The essence of equilibrium is that the body has no tendency to translate or rotate. The forces are balanced, so ΣF = 0, and the moments are balanced, so ΣM = 0. In engineering, structures must be in static equilibrium under their loads. The equations are used to find unknown loads and support reactions.
Equations for a particle
| Case | Equations |
|---|---|
| 2D | ΣFx = 0, ΣFy = 0 |
| 3D | ΣFx = 0, ΣFy = 0, ΣFz = 0 |
A particle has no size, so moments do not arise.
Equations for a rigid body
| Case | Equations |
|---|---|
| 2D | ΣFx = 0, ΣFy = 0, ΣM_O = 0 |
| 3D | ΣFx = ΣFy = ΣFz = 0; ΣMx = ΣMy = ΣMz = 0 |
In 2D there are 3 independent equations, and in 3D there are 6. A properly supported body is statically determinate when the number of unknown reactions equals the number of available equations. If there are more unknowns than equations, it is statically indeterminate.
✓ Answer checked by Claude Opus 5.5 (high effort)
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