Here are the free body diagrams for the given systems: 1. Axle of bicycle wheel: F_app R_1 R_2 2. Propped cantilever: W_1 W_2 R 3. Neoprene pad bearing functions like a roller support. 4. Circled part of building: W R_1 R_2 R_3 5. Dam: W_water R

1. T
A B
The Concurrent System
The Free Body
Diagram

2. Concept of Free Body
Diagrams
Particle System
Rigid Body
Systems
Concept of
Equilibrant
Graphical
Determination of
Equilibrant
Applied and
Reaction Forces in
Beams
Types of
Beam
Supports
Free Body diagram
of Rigid Bodies

3. Free Body Diagrams
• Essential step in solving Equilibrium problems
•Complex Structural systems reduced into concise
FORCE systems
WHAT IS A FREE BODY DIAGRAM?
A FBD is a simplified representation of a PARTICLE
or RIGID BODY that is isolated from its surroundings
and on which all applied forces and reactions are
shown.
All forces acting on a particle original body must be
considered, and equally important any force not directly
applied on the body must be excluded.

4. W
A
B
C
W
BC
BA
Free Body Diagram

5. Draw the Free Body Diagrams

6. REAL LIFE CONCURRENT
SYSTEMS
Equilibrium of a Particle

9. 1. Two cables support the traffic light weighing 250 pounds. Determine the tension in the
cables AB and BC.
• Solution:
• Resolving T1 along x and y directions:
• Resolving T2 along x and y directions:
• .
°20 °30A B
°20 °30
200lb
A C
B
T1 T2
T1
T2
T1Y
T2Y
T1X T2X
T3=200lb
12
21
21
21
085.1
866.0*9396.0*
30cos20cos
0
TT
TT
TT
TTFR XXxx
=
=
°=°
=+== ∑
2005.0342.0
20030sin20sin
0200
21
21
21
=+
=°+°
=−+== ∑
TT
TT
TTFR yyyy
1

10. • Substituting equation 1 in the above equation, we get
.342T1+.5425T2=200
.8845T1=200
T1=226lb
• From equation 1 we get
T2=1.085*226
T2= 245.56lb
Answers:
Tension in cable AB = 226lb
Tension in cable BC = 245.56lb

11. W=100#
A
C D
E
B 
30=θ
4
3
BA=?
BC=?
CD=?
CE=?
Problem
Change

12. 400#
F1
F2
300N
450N
F1
X
Y
X
X
X
Y
Y Y

30=θ

60=θ
F
3 kN
7 kN
4.5 kN
7.5 kN
2.25 kN
F

60=θ

30=θ
P P
PP
1
2
3
4
θ
θ
θ

20=θ
4
3
12
5
3

13. CONCEPT OF THE EQUIBILIRIANT
Resultant
1F
2F
R
E
Equilibrant

14. ASimple Supported Beam
A Cantilever Beam
RIGID BODY SYSTEMS

15. A Propped Cantilever with Three
Concentrated Load
A Simply Supported Beam with
Three concentrated Loads

16. APPLIED AND REACTION FORCES IN BEAMS
In the Chapter on Force Systems, we discussed the concept
of APPLIED FORCES, REACTION FORCES and
INTERNAL FORCES
Here we well discuss the relevance and importance of
APPLIED FORCES and REACTION FORCES in the
case of Beams.
Before we proceed further please study the animated
visuals on the next slide

17. APPLIED FORCES AND REACTION FORCES ON
RIGID BODY SYSTEMS
A Foundation resting on Soil, with
APPLIED FORCES and REACTION
FORCES
A Simple Supported Beams with APPLIED
FORCES and REACTION FORCES
A Cantilever Beam with APPLIED
FORCES and REACTION
FORCES

18. A Beam is an example of Rigid Body. Generally loads are
applied on the beams. And the beams develop reactions. We
named the loads hat are applied on the beams like Dead
Load, Live Load, Wind Load. Earthquake Loads as
APPLIED FORCES, and the consequent reactions that are
simultaneously developed as REACTION FORCES. These
REACTION FORCES generally develop at the supports. We
use the same color code as described earlier for clarity.
The reactions develop as a direct consequence of Newton’s
Third Law,. Which states that for every action there is an
equal and opposite reaction. In the three examples
presented, if we separate the rigid body for its supports we
can see equal and opposite forces acting at the supports..

19. From the above we can describe the concept of the
FREE BODY DIAGRAM of a Rigid Body as folows. It
is representing the rigid body with all the Forces- the
APPLIED FORCES and REACTION FORCES acting
on it
It is axiomatic that the Rigid Body must be in
equilibrium under the action of the APPLIED
FORCES and the REACTION FORCES. Hence the
FREE BODY DIAGRAMS can also be called as
EQUILIBRIUM DIAGRAMS, even though the former
name is more popular.
Finding the REACTION of beams for various types of
APPLIED LOADS is a basic requirement in STATICS

20. The above diagrams, which show the complete system
of applied and reactive forces acting on a body, are
called free body diagrams.
The whole system of applied and reactive forces acting
on a body must be in a state of equilibrium. Free-body
diagrams are, consequently ,often called equilibrium
diagrams.
Drawing equilibrium diagrams and finding
reactions for loaded structural members is a
common first step in a complete structural
analysis

21. Roller, Hinge and Fixed Supports
Hinge
supports
Roller Supports
Fixed Supports

22. ROLLER SUPPORT
Applied Force
Reactive Forces
The Reactive Force must
always be perpendicular to
the surface for a ROLLER

23. Roller Support
Roller Support allows horizontal movement
It allows the beam to bend

24. Rocker Support
A Rocker Support is similar to the Roller Support

25. A variation of Roller Support

26. PIN or HINGE SUPPORT
Applied Force
Reactive Force
The Reactive Force can be in
any direction

27. Pin or Hinge Support
Pin support does no allow any movement
It allows the beam to bend

28. FIXED SUPPORT
No movement
No Rotation

29. Half the strength of the Bridge is lost by not
allowing the Bridge to expand due to the
Temperature Rise
Why Roller Support is Important?
500 ft. 2.34”
T= 100 degT= 40 deg

30. Why Hinge Support is Important ?

31. Why Fixed Support is Important?
A Cantilever has to be fixed to support a load
Hinge

32. REAL LIFE HINGES
A Steel Hinge A Concrete Hinge A Neoprene Pad Hinge
The shear deformation of
the Neoprene pad mimics
the horizontal movement of
a Roller
The close confinement of the
steel rods will not allow moment
transfer, but only Vertical &
Horizontal Forces
Top part
Bottom
part
Pin
The rotation of
the top part
about the pin
allows a Hinge
action

33. Question 1. What is the difference between a
Rigid Body and a Particle
Question 2: Explain the Difference between a
Roller Support, Hinge Support and Fixed
Support

34. FREE BODY DIAGRAMS OF RIGID SYSTEMS

37. Free Body Diagrams
1. Try to draw the free body diagram for a axle of a bicycle wheel as shown
below:
2. Draw the free body diagram for a propped cantilever shown below:
3. Does a Neoprene pad bearing function like a Hinge or a Roller.
4. Attempt to draw the Free body diagram for the circled part of the building
P
Axle

38. 5. Draw the Free Body Diagram for the following Dam:
Water