Free Body Dig Ram

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T

A B

The Concurrent System

The Free BodyDiagram



Concept of Free Body

DiagramsParticle System

Rigid Body

Systems

Concept of

EquilibrantGraphical

Determination of

Equilibrant

Applied and

Reaction Forces in

Beams

Types of

Beam

Supports

Free Body diagram

of Rigid Bodies



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.



W

AB

C

W

BC

BA

Free Body Diagram



Draw the Free Body Diagrams



REAL LIFE CONCURRENT

SYSTEMS

Equilibrium of a Particle







1. Two cables support the traffic light weighing 250 pounds. Determine the tension in the

cables AB and BC.

Solution: Resolving T

1along x and y directions:

Resolving T2 along x and y directions:

.

r20 r30 A B

r20 r30

200lb

A C

BT1 T2

T1T2

T1Y T2Y

T1X T2X

T3=200lb

12

21

21

21

085.1

866.0*9396.0*

30cos20cos

0

T T

T T

T T

T T F R X X x x

!

!

r!r

!!!§

2005.0342.0

20030sin20sin

0200

21

21

21

!

!rr

!!!§

T T

T T

T T F R y y y y

1



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



Q=800#

P=?

Force in

Boom= 4000#

?

A B

C

Problem

Q30! U

Q60! U Q

30! U



W=100#

A

C D

E

B Q30! U

4

3

BA=?

BC=?

CD=?

CE=?

ProblemChange



400#

F1

F2

300N

450N

F1

X

Y

X

XX

Y

Y Y

Q30!U

Q60! U

F

3 kN

7 kN

4.5 kN

7.5 kN

2.25 kN

F

Q60! U

Q30!U

P P

PP

1

2

3

4

U U

UQ

20! U

4

3

12

5

3



CONCEPT OF THE EQUIBILIRIANT

Resultant

1 F

2 F

Equilibrant



Line of action of CB

Line of action of CA

Q30

Q60

X

Y

W=200#

Q

30

Q30

Q60

Q

60

RESULTANT EQUILIBRIANT

TIP-TO-TAIL

METHOD A B

C

Measure CB

and CA

200 #



Q60

Q

30

Q30

Q30

Q60

Q60PARALLELOGRAM

METHOD

RESULTANTEQUILIBRIANT

A B

C

CA

Measure CB and CA

200 #

200 #



ASimple Supported Beam

A Cantilever Beam

RIGID BODY SYSTEMS



A Propped Cantilever with Three

Concentrated Load

A Simply Supported Beam with

Three concentrated Loads



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 thecase of Beams.

Before we proceed further please study the animated

visuals on the next slide



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



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 DeadLoad, 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..



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- theAPPLIED FORCES and REACTION FORCES acting

on it

It is axiomatic that the Rigid Body must be in

equilibrium under the action of the APPLIEDFORCES 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



The above diagrams, which show the complete systemof 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 equilibriumdiagrams.

Drawing equilibrium diagrams and finding

reactions for loaded structural members is acommon first step in a complete structural

analysis



Roller, Hinge and Fixed Supports

Hinge

supports

Roller Supports

Fixed Supports



ROLLER SUPPORT

Applied Force

Reactive Forces

The Reactive Force must

always be perpendicular to

the surface for a ROLLER



Roller Support

Roller Support allows horizontal movement

It allows the beam to bend



Rocker Support

A Rocker Support is similar to the Roller Support



A variation of Roller Support



PIN or HINGE SUPPORT

Applied Force

Reactive Force

The Reactive Force can be in

any direction



Pin or Hinge Support

Pin support does no allow any movement

It allows the beam to bend



FIXED SUPPORT

No movement

No Rotation



Half the strength of the Bridge is lost by notallowing the Bridge to expand due to the

Temperature Rise

Why Roller Support is Important?

500 ft. 2.34´

T= 100 degT= 40 deg



Why Hinge Support is Important ?



Why Fixed Support is Important?

A Cantilever has to be fixed to support a load

Hinge



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



Question 1. What is the difference between aRigid Body and a Particle

Question 2: Explain the Difference between aRoller Support, Hinge Support and Fixed

Support



FREE BODY DIAGRAMS OF RIGID SYSTEMS







Free Body Diagrams

1. Try to draw the free body diagram for a axle of a bicycle wheel as shownbelow:

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



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

Water

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Free Body Dig Ram