Free body diagram
T
A
B
The Free Body
Diagram
The Concurrent System
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.
Free Body Diagram
C
BC
BA
W
B
A
W
Draw the Free Body Diagrams
Learning Objectives
1.
To be able to explain the equilibrium of Rigid Body Systems
2.
You will be able to draw the FBD of Simple Rigid Body Systems
Concurrent System
Particle
Collinear System
General Coplanar System
Rigid Body
ΣFx = 0
ΣFy = 0
ΣM i = 0
ΣFx = 0 x Rx = ΣFx = 0
R y = ΣFy = 0
ΣFy = 0
y
REAL LIFE CONCURRENT SYSTEM
Equilibrium of a Particle
Problem
Force in
Boom= 4000#
C
θ = 30o
?
Q=800#
P=?
θ = 60o
A
θ = 30o
B
Problem
E
4
3
A
B
D
C
θ = 30o
BA=?
W=100#
BC=?
CD=?
CE=?
1
Y
400#
Y
3
300N
o θ=30 12
P
5
P
X
θ
3
θ = 60o
θ = 20o
X
F1
4
450N
F2
F1
2
Y
7 kN
Y
4
F
3
P
X
θ
P
4.5 kN
θ θ = 60
o
o θ=30 F
2.25 kN
3 kN
7.5 kN
X
TIP-TO-TAIL
METHOD
A
B
60
30o
o
Y
60o
Line of action of CA
30o
C
200 #
X
60o
W=200#
CB
RESULTANT
Line of action of CB
CA
30o
Measure CB and CA
EQUILIBRIANT
A
PARALLELOGRAM
METHOD
60
30o
o
60o
C
B
30o
200#
30o
60o
200 #
CA
CB
EQUILIBRIANT
RESULTANT
Measure CB and CA
RIGID BODY SYSTEMS
ASimple Supported Beam
A Cantilever Beam
A Mast with a Platform
Hinged Beam
A
B
The Free Body
Diagram
The Concurrent System
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.
Free Body Diagram
C
BC
BA
W
B
A
W
Draw the Free Body Diagrams
Learning Objectives
1.
To be able to explain the equilibrium of Rigid Body Systems
2.
You will be able to draw the FBD of Simple Rigid Body Systems
Concurrent System
Particle
Collinear System
General Coplanar System
Rigid Body
ΣFx = 0
ΣFy = 0
ΣM i = 0
ΣFx = 0 x Rx = ΣFx = 0
R y = ΣFy = 0
ΣFy = 0
y
REAL LIFE CONCURRENT SYSTEM
Equilibrium of a Particle
Problem
Force in
Boom= 4000#
C
θ = 30o
?
Q=800#
P=?
θ = 60o
A
θ = 30o
B
Problem
E
4
3
A
B
D
C
θ = 30o
BA=?
W=100#
BC=?
CD=?
CE=?
1
Y
400#
Y
3
300N
o θ=30 12
P
5
P
X
θ
3
θ = 60o
θ = 20o
X
F1
4
450N
F2
F1
2
Y
7 kN
Y
4
F
3
P
X
θ
P
4.5 kN
θ θ = 60
o
o θ=30 F
2.25 kN
3 kN
7.5 kN
X
TIP-TO-TAIL
METHOD
A
B
60
30o
o
Y
60o
Line of action of CA
30o
C
200 #
X
60o
W=200#
CB
RESULTANT
Line of action of CB
CA
30o
Measure CB and CA
EQUILIBRIANT
A
PARALLELOGRAM
METHOD
60
30o
o
60o
C
B
30o
200#
30o
60o
200 #
CA
CB
EQUILIBRIANT
RESULTANT
Measure CB and CA
RIGID BODY SYSTEMS
ASimple Supported Beam
A Cantilever Beam
A Mast with a Platform
Hinged Beam