force scalars and vectors: the characteristics of a force: … · 2019. 5. 31. · 4.nonconcurrent,...
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FORCE
Scalars and Vectors:
The characteristics of a force:
Principle of transmissibility:
Classification of the force system:
Composition and Resolution of Force
Rectangular components in 2-D
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Scalars and Vectors:
Scalar: A quantity like mass, time, volume and temperature which only has a magnitude (not direction). Vector: A quantity like weight or force which has both a magnitude and a direction.
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FORCE
A force may be defined as the action of one body on another body
which changes or tends to change the motion of the body acted
on.
A force is a vector quantity that, when applied to some rigid
body, has a tendency to produce translation (movement in a
straight line) or translation and rotation of body. When
problems are given, a force may also be referred to as a load or
weight.
The characteristics of a force:
• Magnitude;
• Direction (sense and slope);
• Location of any point on its line of action.
The unit of force: N, kN, Pound (lb), Kilopound (kip=1000 lb).
F=450N
3 4
A
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Force exerted on a body has two effects:
• The external effect, which is tendency to change the motion of the body or to develop resisting forces in the body
• The internal effect, which is the tendency to deform the body.
Principle of transmissibility: The external effect of a force on a rigid body
is independent of the application of the force along its line of action.
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Principle of Transmissibility
Line of action
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1. Point loads - concentrated
forces exerted at point or
location
2. Distributed loads - a force
applied along a length or
over an area. The
distribution can be uniform
or non-uniform.
Types of Forces(Loads)
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Classification of the force system: 1. Collinear. All forces of the system have a common line of action.
2. Concurrent, coplanar. The action lines of all the forces of the system
are in the same plane and intersect at a common point.
3. Parallel, coplanar. The action lines of all the forces of the system
parallel and lie in the same plane.
4. Nonconcurrent, nonparallel, coplanar. The action lines of all the
forces of the system are in the same plane, but they are not parallel
and they do not all intersect at a common point.
5. Concurrent, noncoplanar. The action lines of all the forces of the
system intersect at a common point, but they are not all in one plane.
6. Parallel, noncoplanar. The action lines of all the forces of the system
are parallel, but they are not all in the same plane.
7. Nonconcurrent, nonparallel, noncoplanar. The action lines of all the
forces of the system do not all intersect at a common point, they are
not all parallel, and they do not all lie in the same plane.
When several forces act in a given situation, they are called a
system of forces or a force system.
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Collinear
F1
F1
F2
F2 Action Line
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Concurrent, coplanar
F1
F2 F3
O x
y
F1
F2
F3
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Parallel, coplanar
F1
F2 F3
O x
y
F1
F2
F3
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Nonconcurrent, nonparallel, coplanar
F1
F2 F3
O x
y
F1
F2
F3
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Concurrent, noncoplanar
O x
y
z
F1
F2
F3
F1 F2
F3
x
y
z
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Parallel, noncoplanar
O x
y
z
F1
F2 F3
F1
F2
F3
x
y
z
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Nonconcurrent, nonparallel, noncoplanar
O x
z
F1
F3
F2
F1
F3
F2
x
y
z
y
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Composition and Resolution of Force
Composition : replacing a force system by its resultant.
The resultant force is proportional to the diagonal of the
parallelogram whose sides are proportional to the two forces.
(Parallelogram law)
Q
P β
Q
P
α R
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Resolution: A force may be resolved into two components
having knowing lines of action by using parallelogram law.
F
β
α
a
b
F
β
α
Fa
Fb
a
b
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Rectangular components in 2-D:
A rectangular component of a force is equal to the product
of the force and the cosine of the angle between the force and the
component.
See examples 2-1 to 2-4
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