t the free body ab diagram the concurrent...
TRANSCRIPT
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 PARTICLEor 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
W
BCC
B
W
BA
A
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
Collinear SystemConcurrent System
Particle
General Coplanar System
Rigid Body
x
y
00
=Σ==Σ=
yy
xx
FRFR
0=Σ xF
0=Σ yF
0
00
=Σ
=Σ=Σ
i
y
x
M
FF
REAL LIFE CONCURRENT SYSTEM
Equilibrium of a Particle
Q=800#
P=?
Force in Boom= 4000#
?
A B
C
Problem
o30=θ
o60=θ o30=θ
W=100#
A
C D
E
B o30=θ
4
3
BA=?
BC=?
CD=?
CE=?
Problem
400#
F1
F2
300N
450N
F1
X
Y
X
XX
Y
Y Y
o30=θ
o60=θ
F
3 kN
7 kN
4.5 kN
7.5 kN2.25 kN
F
o60=θo30=θ
P P
PP
1
2
3
4
θθ
θ o20=θ
4
3
12
5
3
Line of action of CB
Line of action of CA
o30
o60X
Y
CB
CAW=200#
o30
o30o60
o60
RESULTANT EQUILIBRIANT
TIP-TO-TAIL METHOD
A B
C
Measure CB and CA
200 #
o60o30
o30
o30o60
o60PARALLELOGRAM METHOD
RESULTANTEQUILIBRIANT
A B
C
CB
CA
Measure CB and CA
200#
200 #
RIGID BODY SYSTEMS
ASimple Supported Beam A Cantilever Beam
A Mast with a PlatformHinged Beam with support
A CantileverTruss with Cable support
An Inclined Beam
A simply supported beam A simply supported beam
A Beam Supported by a Column and a Knee Frane
Hinged cantilever beam with cable support
Examples from Bio-Medical
Engineering – Human structural systems
APPLIED AND REACTIVE FORCES
Applied Forces
Reactive Forces
Applied and Reactive ForcesForces and Moments that act on a Rigid Body can be divided into two Primary types: appliedand reactive.
In common Engineering usage, applied forcesare forces that act directly on a structure ( like, dead, live load etc.) Reactive forces are forces generated by the action of one body on another and hence typically occur at connections or supports. The existence of reactive forcesfollows from Newton’s third law, which state that to every action , there is an equal and opposite reaction.
APPLIED AND REACTIVE FORCES
In the second figure the beam causes downward forces on the foundation, and upward reactive forcesare consequently developed. A pair of action and reaction forces thus exists at each interface between the beam and its foundations. In some cases, moments form part of the reaction system as well
More precisely, the law states that whenever one body exerts a force on another, the second always exerts a force on the first that is equal in magnitude and opposite in direction and that has the same line of action.
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
SUPORT CONDITIONS
The nature of Reactive Forces developed on a loaded body depends on the exact way in which the body is supported.
The Three Basic Ways in which Beams and other structures are supported are
ROLLER SUPPORT
PIN SUPPORT or PIN CONNECTION
FIXED SUPPORT or FIXED CONNECTION
Roller, Hinge and Fixed Supports
Hinge supports
Roller Supports
Fixed Supports
ROLLER SUPPORTApplied 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
Comp.
Half the strength of the Bridge is lost
Why Roller Support is Important?
300 ft.
300 ft. 1.3in
300 ft
T=35 deg
T=95 deg
T=95 deg
Why Hinge Support is Important ?
Why Fixed Support is Important?
A Cantilever has to be fixed to support a load
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
A B
F F F
Ay By
Ax
Free Body Diagram
Free Body Diagram
Free Body Diagram
Free Body Diagram
600 N200 N
100 N
Free Body Diagram
Free Body Diagram
Concrete Wall
Machine
Weight of floor slab
Concrete
Beam
Free Body Diagram
Actual Structure - A Truss Free Body Diagram
RIGID BODY SYSTEMS
ASimple Supported Beam A Cantilever Beam
A Mast with a PlatformHinged Beam with support
A CantileverTruss with Cable support
An Inclined Beam
A simply supported beam A simply supported beam
A Beam Supported by a Column and a Knee Frane
Hinged cantilever beam with cable support
Examples from Bio-Medical
Engineering – Human structural systems
Problem
4P
1P
10ft5ft5ft
RA=? RB=?
A B
15ft 5ft
Problem
4P
Problem
4P
A B
5’5’
o60
=
W= 50lb/ft
20’
Equivalent total load = 50 lb/ft x 20’= 1000 lb
10’ 10’
20 k
60k
12ft
20 k
60k
12ft
Resultant of Two Parallel Forces
A Bx
12’
R
R= -20 -60=-80k
Moment about A
-R.x = -60.12
x = 9 ft
F1
F2
F3
Question : Draw the Free Body diagram for the above beam
Common Supports
Ry
Rx
Mx
Fixed Support
Ry
Rx
Ry
Roller Support Hinge Support
Free Body Diagrams
F
Free Body Diagram
Applied Force
Reactive Force
0
00
=Σ
=Σ=Σ
i
y
x
M
FF
Statical Determinacy,Indeterminacy,Improper Constraints
Beams
Determinate
Indeterminate, O=1
Indeterminate, O=3
Unstable
Statical Determinacy,Indeterminacy,Improper Constraints
TrussesTrussesE I
b=2n-3 D D
DI
U D
D U
D I
Equilibrium of Rigid Bodies
w/ft wl=
=
l l
l l