The document summarizes key points about free-body diagrams and their use in solving equilibrium problems in 2D and 3D: - A free-body diagram shows all forces and couple moments acting on a body, including those from supports preventing translation or rotation. - Forces are resolved using angles and moments taken using dimensions on the diagram. - For 2D problems, the equations ΣFx=0, ΣFy=0, ΣM0=0 can be applied, eliminating unknown forces along a chosen axis. - For 3D, Cartesian vector analysis expresses known and unknown forces and moments as vectors. Setting force and moment sums to zero provides six scalar equations of equilibrium.

1. Chapter Summary
Free-Body Diagram
Draw a FBD, an outline of the body which
shows all the forces and couple moments
that act on the body
A support will exert a force on the body in a
particular direction if it prevents translation
of the body in that direction
A support will exert a couple moment on a
body is it prevents rotation

2. Chapter Summary
Free-Body Diagram
Angles are used to resolved forces and
dimensions used to take moments of
the forces
Both must be shown on the FBD

3. Chapter Summary
Two Dimensions
∑Fx = 0; ∑Fy = 0; ∑MO = 0 can be
applied when solving 2D problems
For most direct solution, try summing
the forces along an axis that will
eliminate as many unknown forces as
possible

4. Chapter Summary
Three Dimensions
Use Cartesian vector analysis when applying
equations of equilibrium
Express each known and unknown force and
couple moment shown on the FBD as a Cartesian
vector
Set the force summation equal to zero
Take moments about point O that lies on the line
of action of as many unknown components as
possible

5. Chapter Summary
Three Dimensions
From point O, direct position vectors to each
force, then use the cross product to
determine the moment of each force
The six scalar equations of equilibrium are
established by setting i, j and k components
of these force and moment sums equal to
zero

6. Chapter Review

7. Chapter Review

8. Chapter Review