# Free body diagram

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