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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 PrinciplesNewton’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 PrinciplesNewton’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.
EquilibriumStatic 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
x
y
F =0
F =0
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Balanced 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©iStockphoto.com
Remember Moment = F x D
Statics Principles
Scalar Quantities:A physical quantity that has magnitude only
Examples: Mass, length, 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 temperature and it shows 101 F. The magnitude of your temperature is 101, degrees Fahrenheit is the unit of measurement.
O
Statics Principles
Vector Quantities:A physical quantity that has both a magnitude and direction
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?
A vector quantity defined by its known magnitude, direction, and point of application
A
45 lbf
21.8°NE
The pushing or pulling interaction of objects
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 Systems1lbf = 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.
a
F a
Fay
Fax
a
Resultant Force
A single force that has the same effect as two or more concurrent forces
2lbf5lbf
5lbf
2lbf
7lbf
Resultant
3lbf
Resultant
=
=
Free Body DiagramVisual representation of force and object interactions
Individual objects or members are isolated from their environment or system, illustrating all external forces acting upon them
Free Body Diagram Components
Vector quantity has direction and magnitude
ForceA straight line push or pull acting upon an object
Direction is illustrated by arrowhead
Magnitude is illustrated by length of line segment and is the amount of push or pull
Free Body Diagram Components
The twisting effort about a point or axis when a force is applied at a distance
Arc with an arrowhead acting about a point indicating direction of CW or CCW
Moment
• Distance (d) is called the moment arm. It must be measured perpendicular to the line of action of the force.
Moment Review
Line of ActionF
Point of Rotation
d
Moment (M) = Force (F) x distance (d)
Free Body Diagram Procedure
A stack of three books, each weighing 5 lb, is sitting on top of a table. Draw the Free Body Diagram (FBD) of the top book.
Free Body Diagram Procedure• 1. Sketch the isolated object.
What is the isolated object?
Top Book
Free Body Diagram Procedure• 2. Sketch the applied and norm
forces.
When an object is in contact with and is supported by a second object, the second object can be replaced with a normal force which is perpendicular to the surface of the second object.
Free Body Diagram Procedure• 2. Sketch the applied force and norm
forces.
Applied Force Weight of top book
Normal Force Reaction force pushing up on the book, causing it not to fall
Free Body Diagram Procedure• 3. Label objects and forces.
N=5 lbf
W=5 lbf
PLTW – DE book
Free Body Diagram Procedure• 4. Label dimensions.
N=5 lbf
W=5 lbf
PLTW – DE book
For more complex free body diagrams, proper dimensioning is required, including length, height, and angles.
45°
8 ft
8 ft10 ft
38.6°
Free Body Diagram Practice
Fapp
FN
W W
Ff
θ
θ
Create a FBD for the sled pictured below.
Fapp
Ff
FN
Free Body Diagram Practice
FN
W W
FN
Fapp
Fapp
F f
F f
θ
θ
Create a FBD for the refrigerator pictured below.
Free Body Diagram Practice
M1
M2
FBD of Mass 1:
FT
FBD of the movable pulley:
W1
W2 + W pulley
FT
FT
Tension Forces (FT ) are equal throughout the system.
Create a FBD for the pulley system pictured below.
