Introduction to Statics
Forces in Equilibrium
Tall buildings are an impressive example of
equilibrium, or the balancing of forces.
A modern office tower is constructed of steel
and concrete beams that are carefully
designed to provide reaction forces to
balance against wind, gravity, and people.
All forces acting on the building must add up
to zero.
Statics
The study of forces and their effects
on a system in a state of rest or
uniform motion
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Equilibrium
• The concept of equilibrium is important to
the design of bridges, buildings and
virtually any technology invented by
humans.
• In order for a bridge to stay in place, ALL
the forces acting on the bridge must add
up to produce a net force of zero.
Statics Principles
Newton’s First Law of Motion (law of inertia):
An object in a state of rest or uniform
motion will continue to be so unless
acted upon by another force.
If the net force of an object is zero
(equilibrium), an object at rest will
stay at rest and an object in motion
will stay in motion with constant
speed and direction.
Statics Principles
Newton’s Second Law of Motion:
The acceleration of an object is proportional
to the net force acting on the object and
inversely proportional to the object’s mass
Force = Mass x Acceleration
The acceleration of an object in equilibrium is zero
because the net force acting on the object is zero.
Zero acceleration means neither the speed or the
direction of motion can change.
Statics Principles
Newton’s Second Law of Motion:
Any object at rest is in equilibrium and has a net force
of zero acting on it.
Imagine a book sitting on a table. Gravity
pulls the book downward with a force equal
to the books weight.
But what force balances the weight?
The table exerts an upward force on the book
called the Normal Force.
In mathematics, Normal means perpendicular.
The force the table exerts is perpendicular to the
table’s surface.
Statics Principles
Newton’s Third Law of Motion:
For every action force, there is an
equal and opposite reaction force
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Statics Principles
Newton’s Third Law of Motion:
The third law explains why normal forces exist.
The book pushes down on the table, so the
table pushes up on the book. The book’s
force on the table is the action force, and the
table’s force on the book is the reaction
force.
These forces are equal in strength. If the
book is at rest, these forces must be equal
but opposite in direction.
Equilibrium
Static Equilibrium:
A condition where there are no net external
forces acting upon a particle or rigid body
and the body remains at rest or continues at
a constant velocity
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Equilibrium
Translational Equilibrium:
The state in which there are no
unbalanced forces acting on a body
 F =0
 F =0
x
y
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Balanced
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Unbalanced
Equilibrium
Rotational Equilibrium:
The state in which the sum of all the
clockwise moments equals the sum of all
the counterclockwise moments about a
pivot point
M=0

Remember
Moment = F x D
Statics Principles
Scalar Quantities:
A physical quantity that has
magnitude only
Examples: Mass, length,
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time, volume, temperature,
pressure, and speed
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Scalars
• Scalars have Magnitude
• A scalar is a quantity that can be completely
described by a single value called a magnitude.
• Magnitude means the size or amount and always
includes units of measurement
• Temperature is a good example of a scalar
quantity. If you use a thermometer to check your
O
temperature and it shows 101 F. The magnitude
of your temperature is 101, degrees Fahrenheit is
the unit of measurement.
Statics Principles
Vector Quantities:
A physical quantity that has
both a magnitude and
direction
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Examples: Position,
velocity, force, and moment
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Vectors
• Vectors have direction
• If you are giving someone directions to
your house, you could not just say drive 5
miles. You must also add the direction to
drive those 5 miles.
• A force vector has units of Newtons, like
all forces; the force vector also includes
the direction of the force.
What Is a Force?
The pushing or pulling interaction of objects
A vector quantity defined by its known
magnitude, direction, and point of
application
A
21.8°NE
A force vector is drawn as an arrow.
Force Units
British System of Units
Pound-force (lbf)
International System of Units
Newton (N)
Conversions between Unit Systems
1lbf = 4.448 N
1N = 0.2248 lbf
Static Equilibrium Force Principles
Forces always occur in pairs.
Force pairs act in opposite directions
and have the same magnitude.
Force Components
A single force can be replaced by
component forces if their combination
produces the same effect as the
original force.
Fay
a
a
Fax
Resultant Force
A single force that has the same effect
as two or more concurrent forces
Resultant
5lbf
2lbf
=
Resultant
2lbf
5lbf
7lbf
=
3lbf