1. CE Statics
Lecture 9

2. Three-Dimensional Force Systems
Particle will be in equilibrium if F = 0
In 3-D problems, this can be expressed as:
Fx i + Fy j + Fz k = 0
Therefore, for a particle to be in equilibrium:
Fx = 0
Fy = 0
Fz = 0

3. Procedure for Analysis
Free-Body Diagram
Establish the x, y, and z axes
Label known and unknown forces (magnitude and direction)
Assume the direction of unknowns
Equations of Equilibrium
For any force that can be resolved into x, y, and z components, use Fx = 0; Fy = 0; and Fz = 0.
If problem looks difficult, express forces in Cartesian vector form and use F = 0 and set i, j, and k components to zero.