1. 5.5 Equilibrium in Three
Dimensions (FBD)
Consider types of reaction that can occur at the
supports
Support Reactions
Important to recognize the symbols used to
represent each of these supports and to clearly
understand how the forces and couple moments
are developed by each support
As in 2D, a force that is developed by a support
that restricts the translation of the attached
member
2. 5.5 Equilibrium in Three
Dimensions (FBD)
Support Reactions
A couple moment is developed when rotation
of the attached member is prevented
Example
The ball and socket joint prevents any
translation of connecting member; therefore,
a force must act on the member at the point
of connection
This force have unknown magnitude Fx, Fy
and Fz
Magnitude of the force is given by
F = Fx2 + Fy2 + Fz2
3. 5.5 Equilibrium in Three
Dimensions (FBD)
Support Reactions
The force’s orientation is defined by the
coordinate angles α, β and γ
Since connecting member is allow to rotate
freely about any axis, no couple moment is
resisted by a ball and socket joint
Single bearing supports, single pin and single
hinge are shown to support both force and
couple moment components
4. 5.5 Equilibrium in Three
Dimensions (FBD)
Support Reactions
However, if these supports are used with
other bearings, pins or hinges to hold a rigid
body in equilibrium and the supports are
properly aligned when connected to the
body, the force reactions at these supports
alone may be adequate for supporting the
body
Couple moments become redundant and not
shown on the FBD
9. 5.5 Equilibrium in Three
Dimensions (FBD)
Ball and socket joint
provides a
connection for the
housing of an earth
grader to its frame
Journal bearing
supports the end of
the shaft
10. 5.5 Equilibrium in Three
Dimensions (FBD)
Thrust bearing is
used to support the
drive shaft on the
machine
Pin is used to
support the end of
the strut used on a
tractor
11. 5.5 Equilibrium in Three
Dimensions (FBD)
Example 5.14
Several examples of objects along with their
associated free-body diagrams are shown. In
all cases, the x, y and z axes are established
and the unknown reaction components are
indicated in the positive sense. The weight of
the objects is neglected.
