Equilibrium
Once a FBD system is constructed, the next step is to apply the conditions of equilibrium. A
body in static equilibrium is not accelerating, so the forces and moments
acting on it must sum to zero in any direction. Equilibrium requires that:
 the sum of the forces in any direction must be zero: S F = 0.
 the sum of the moments about any nonaccelerating point must be zero: S M_{O}= 0.
In 3dimensions, six equations must be satisfied:
S F_{x} = 0 ; S F_{y} = 0 ; S F_{z} = 0
S M_{x} = 0 ; S M_{y} = 0 ; S M_{z} = 0 
In 2dimensions, only three equilibrium equations are required.
When the object is in the xy plane, one of the following three
sets of equations may be used:
S F_{x} = 0
S F_{y} = 0
S M_{z,A} = 0

S F_{x} = 0
S M_{z,A} = 0
S M_{z,B} = 0

S M_{z,A} = 0
S M_{z,B} = 0
S M_{z,C} = 0

The sum of forces in x and in y, and the
sum of moments about any Point A (about a zaxis through Pt. A), each equal zero 
Points A and B are two
different points. 
A, B and C are
three points, not all on the same line. The points define a plane. 
Many 3Dproblems can be reduced to 2D. 