3.FORCE SYSTEMS
FORCE
SYSTEMS
Characteristics of a Force
θ
F
A
Force is
characterized by
1. Point of
application (A)
-θ ( 100
2. Magnitude
N)
3. Direction (from x-axis)
Objective: To bring out the characteristics of a Force as applied in Statics
Sense of Force
y
y
x
Tension
x
Compression
Objective: To bring out the two senses in which a Force can act
RIGID BODIES AND FLEXIBLE
BODIES
Rigid Body
Steel, Wood, Concrete, Stone are rigid bodies, we
neglect their deformation in Statics
In Statics we deal
with
Flexible Body
Rigid bodies alone
Foam is Flexible material, which undergoes
large deformations under loading
Objective: To bring out the difference between a Rigid Body and a Flexible Body
Transmissibility
F
F
Hence Pulling is
equal to Pushing,
provided the Forces
are on the same
horizontal line
(same line of action)
This is known as the Principle of Transmissibility
Objective: To explain the concept of Transmissibility
P
=
P
From the viewpoint of Statics, the Arch which is
loaded on the top is equivalent top the arch which
is loaded from beneath – this is an application of
the principle of Transmissibility
Objective: An example which illustrates the principle of Transmissibility
Red Forces
are Applied
Forces
Blue Forces
are
Reaction
Forces
The dotted line the Reference Boundary for the
Structural System under consideration
Objective: To describe, System Boundary, Applied Forces and Reaction Forces
The Green Forces are the Internal Forces
Objective: To describe Internal Forces
External Force
Internal
Forces
Reference
Boundary of the
Structural System
Reaction Forces
Objective: An example to illustrate: System Boundary, External ,Reaction & Internal
Forces
CONCLUSIONS
1. The System
boundaries can
be defined
arbitrarily
2. What the
Applied Forces,
the Reaction
Forces and the
Internal Forces
are, will be
clarified
accordingly
Objective: To explain the idea that the System Boundary is defined, depending on the
portion of the structure one wishes to focus on
Vector Addition
Characteristics of a Vector
An important characteristic of vectors is that
they must be added according to the
parallelogram law . This is necessary because
vectors have both magnitude and direction .
Using parallelogram law, we may add vectors
graphically or by trigonometric relationships.
First we will see the graphical method and
then the trigonometric method.
Objective: To explain how Vectors can be added graphically
V=900 N
PARALLELOGRAM
LAW OF VECTOR
ADDITION
H=900 N
N
1000
600
400
200
V=900 N
800
300#
1
=
R
θ = 22.6o
200
400
H=900 N
600
800
1000 N
A box is being pulled up
by a Force of 900 N and
pulled to the right with a
Force of 900 N. We want
to know the Resultant.
50
0#
PARALLELOGRAM LAW OF ADDITION OF VECTORS
75
R
θ
900#
15
Objective: To illustrate the parallelogram method of addition of vectors using triangles
TIP –TO – TAIL METHOD
Another Method of Vector Addition
A
R
θ
O
B
z
A
R
O
θ
B
Determining the Resultant by Analytical Method.
Sometimes it is more convenient to determine the Resultant by using the cosine
law as shown in the following example.
30o
F1 = 100lb
30
x
45o
y
F2 = 140lb
F1 = 100lb
30
o
o
φ = 105o
θ
R
45o
75o
F2 = 140lb
R 2 = F12 + F22 − 2 F cos φ
= 100 2 + 140 2 − 2(100)(140)(−0.259)
= 192lb
R
F2
=
sin 105o
sin θ
F2 sin 105o
sin θ =
R
140 × 0.966
=
192
= 0.704
θ = sin −1 (0.704)
= 44.8
o
VECTOR ADDITION
600 lb
35
900 lb
45°
°
R= 1413 lb, Angle=50.8
R=1413 lb, Angle=50.8
900 lb
600 lb
R
600 lb
45°
35
°
R
900 lb
Parallelogram Method
Tip-to-tail method
Graphical addition of Three or More Vectors
y
R12
y
F1
F2
x
F3
F1
F2
R123
F3
x