Lecture #4
Equilibrium of a Particle and Intro to Free Body
Diagram (ref: Chapter 3.1, 3.2)
ΣFx = 0
ΣFy = 0
ΣFz = 0
Required for Static
Equilibrium!!
R. Michael PE 8/14/2012
Particle vs. Rigid Body
Particle – Very small amount of matter
compared to the system being
analyzed.
 The volume of the particle and area it
occupies is negligible to the problem
and has no bearing on the solution.
 Can be modeled as a single point in
space.

Particle vs. Rigid Body
Rigid Body – A combination of a large
number of particles occupying fixed
positions with respect to each other.
 Must use a rigid body model when the
area that the body of the object
occupies has an affect on the
outcome of the problem.
 Have additional requirement for
equilibrium (moment)

Rigid Body Analysis

Must be used:
If the mass of the body comes into
effect
 If there are forces with different points
of application on the body
 If the size of the body has to be taken
into account

Explanation of Rigid Body
 For Statics we define a Rigid Body as a body that has no
deformation.
 A Rigid Body differs from a Particle because size comes
into play:
Both weigh 50 lb, which one is
a rigid body and which one is
a particle?
A
B
W = 50 lb
W = 50 lb
Concepts to be Introduced
for Rigid Body Analysis






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Internal vs. External Forces
Free Body Diagrams (applies to Particles
and Rigid Bodies)
Translational Equilibrium (applies to
Particles and Rigid Bodies)
Principle of Transmissibility
Moments (Couples) acting on the bodies
Force – Couple Systems on Rigid Bodies
Equilibrium in Six degree of freedom
situation (Rigid Body Equilibrium)
External vs. Internal Forces
 External Forces – Represent the action of
other bodies on the Particle or Rigid Body.
Entirely responsible for the motion of lack of
motion of the Particle or Rigid Body as
described by Newton’s First Law of Motion.
 Internal Forces – The forces holding the
individual particles of a rigid member together.
Can also be used to define the forces holding
members of a composite structure together.
Types of Forces:
Small contact area;
treat as a point
FR is
resultant of
w(s) = area
under curve,
acts at
centroid
Acting on
narrow area
One body
acting on
another
One body
acting on
another w/o
contact
3.1 Free Body Diagram
Introduction
 Free Body Diagram – A diagram of
the Particle or Rigid Body of interest
with all Forces acting ON the body
and all measurements pertinent to the
solution of the problem.
THE WHAT, WHY AND HOW OF A
FREE BODY DIAGRAM (FBD)
Free Body Diagrams are one of the most important things for
you to know how to draw and use.
What ? - It is a drawing that shows all external forces acting
on the particle.
Why ? - It is key to being able to write the equations of
equilibrium—which are used to solve for the unknowns
(usually forces or angles).
FBD for Rigid Body:
This is a FBD
of the truck!!
=
simplified
Truck External Forces

The Forces can be shown by Vectors acting
on the Truck



W – Weight of the truck acting in the
negative vertical direction and acting at the
center of gravity of the truck
R1 and R2 – Contact Force of the ground
holding the truck from falling toward the
center of the Earth
Fr – Force of the Rope pulling the truck
forward
COPLANAR FORCE SYSTEMS
(Section 3.3)
This is an example of a 2-D or
coplanar force system.
If the whole assembly is in
equilibrium, then particle A is
also in equilibrium.
Draw a FBD for the mass, C
Draw a FBD of Ring A
To determine the tensions in
the cables for a given weight
of the cylinder, you need to
learn how to draw a free body
diagram and apply equations
of equilibrium.
Steps in Making the Free
Body Diagram

The most important part of making a Free
Body Diagram is that a clear decision must
be made as to what part of the Space
Diagram or System is being analyzed
VS.
External Force Vectors




Represent the forces acting ON the Free
Body BY the surroundings. This is very
important.
Must be applied to the body where they are
acting on the body
Must be represented with Direction and
Magnitude.
The weight of the object (if applicable)
should be placed at the center of gravity of
the object.
REACTION Forces

Unknown external forces are known as
reactions or constraining forces and must
be shown on the Free body Diagram

Reactions are forces that constrain one or
more degrees of freedom of motion and
must be indicated on the Free Body Diagram
where it is supported or connected to an
external body
Unknown External Forces
Unknown External Forces
Practice FBD’s!!!
APPLICATIONS
The crane is lifting a load. To decide if the
straps holding the load to the crane hook
will fail, you need to know the force in the
straps. How could you find the forces?
Straps
APPLICATIONS (continued)
For a spool of given weight, how
would you find the forces in
cables AB and AC ? If designing
a spreader bar like this one, you
need to know the forces to make
sure the rigging doesn’t fail.
APPLICATIONS (continued)
For a given force exerted on the boat’s towing pendant, what are the forces in
the bridle cables? What size of cable must you use?
Principle of Transmissibility

The conditions of equilibrium or
motion of a Rigid Body will remain
unchanged by moving a force along
its line of action provided the force
magnitude and direction does not
change
Equivalent Forces
 If F and F' have the same direction,
magnitude, and line of action, they are
said to be Equivalent Forces