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

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.

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

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.

Principle of Transmissibility

Line of action

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)

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.

Collinear

F1

F1

F2

F2 Action Line

Concurrent, coplanar

F1

F2 F3

O x

y

F1

F2

F3

Parallel, coplanar

F1

F2 F3

O x

y

F1

F2

F3

Nonconcurrent, nonparallel, coplanar

F1

F2 F3

O x

y

F1

F2

F3

Concurrent, noncoplanar

O x

y

z

F1

F2

F3

F1 F2

F3

x

y

z

Parallel, noncoplanar

O x

y

z

F1

F2 F3

F1

F2

F3

x

y

z

Nonconcurrent, nonparallel, noncoplanar

O x

z

F1

F3

F2

F1

F3

F2

x

y

z

y

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

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

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