Conditions of equilibrium
A rigid body is in equilibrium the following conditions must be satisfied:
if the sum of the external forces acting on the body equals zero and the sum of the moments of the external forces about an arbitrary chosen point O equals zero:
| Σ F = 0 |
the sum of the external forces acting on the body must be equal to zero in order to obtain translation equilibrium |
| Σ M0 = 0 |
the sum of the moments of the external forces about an arbitrary chosen point O must be equal to zero in order to obtain rotation equilibrium |
Three-dimensional problem
In a three-dimensional problem the above conditions result in the following six scalar equations:
| Σ Fx = 0 |
Σ M0x = Σ (yFFz - zFFy) = 0 |
| Σ Fy = 0 |
Σ M0y = Σ (zFFx - xFFz) = 0 |
| Σ Fz = 0 |
Σ M0z = Σ (xFFy - yFFx) = 0 |
where Fx, Fy, Fz represent the force components in the x, y, z directions and xF, yF, zF are the projections of the force arms in the x, y, z directions.
Two-dimensional problem
In a two-dimensional problem the equilibrium equations result in the following three scalar equations:
Σ Fx = 0
Σ Fy = 0
Σ M0z =Σ (xFFy - yFFx) = 0
