The concept of equilibrium is used for determining unknown forces and moments of forces that act on or within a rigid body or system of rigid bodies. The equations of equilibrium are the most useful equations in the area of statics, and they are also important in the dynamics and mechanics of materials. The drawing of appropriate free-body diagrams is essential for the application of these equations.
Conditions of Equilibrium
A rigid body is in static equilibrium when the equivalent force-couple system of the external forces acting on it is zero.
In vector notation, this condition is expressed as
where O is an arbitrary point of reference.
In practice, it is often most convenient to write Equation 1.2.13 in terms of rectangular scalar components,
Maximum Number of Independent Equations for One Body:
1. One-dimensional problem: ΣF = 0
2. Two-dimensional problem:
where xyz are orthogonal coordinate axes, and A, B, C are particular points of reference