Download Force - E

March 2016
Prof. VALENTINI GIOVANNI VITTORIO
LABORATORIO DI ARCHITETTURA
TOPIC OF THE MODULE: STATICS
How forces act on a building structure and their effects
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The aim of STATICS consists in analysing
the forces acting on balanced structures or
inside them.
The study of these forces allows
to establish if structures can sustain
forces without suffering significative
strains or stress.
Consider that
Forces have been remained the same
over the centuries, from the beginning
of Architecture.
Engineers and Architects must be
able to know and compute all the
forces affecting the structural
components in a building, as in
a bridge, and in any scaffold too.
A summary knowledge
about the forces acting on
a building structure can
cause a building collapse!
This apartment tower building, in China,
collapsed by itself while it was erecting
Buildings are not suitable
to dance rock’roll during
an earthquake.
But an appropriate
planning can save
many lifes.
CONSEQUENTLY WE NEED NOW A BIT KNOWLEDGE ABOUT FORCES.
Lesson 1 : What is Force?
A Force makes stationary objects
into motion.
A Force makes change speed
or direction of the moving objects
Force is an invisible one!
It is not something you
can see or touch, but you
can see it in action!
A force is a vector quantity.
A vector quantity is a quantity
which has both magnitude and
direction. To fully describe the
force acting upon an object,
you must describe both its
magnitude and direction. Thus,
10 Newtons of force is not a
complete description of the
force acting on an object
(DYNAMICS EFFECTS)
A Force makes change shape
of the objects that can not move
(STATIC EFFECT)
An arrow, with a name, length and direction
is used to represent a force.
A force diagram is usually used to show the
forces acting on an object
See this example below:
In a force diagram, the longer the arrow,
the bigger the force
Note: What is the difference between vector and scalar quantities?
A vector has both strength and direction, a scalar quantity can be described
using only 1 quantity, magnitude.
Examples of scalar quantities are: time, energy and volume since they only
represent magnitude and no direction.
A force usually results from an
interaction.
The interaction can be a physical
one, or a non-physical one.
For simplicity sake, all forces
(interactions) between objects
can be placed into two broad
categories: contact forces, and
forces resulting from
action-at-a-distance
Contact Forces include:
frictional forces, buoyant
forces, normal forces,
and air resistance forces
Action-at-a-distance
forces include: gravitation,
electrostatic and magnetic
forces.
In building structures we have both this kind on forces
So we can define Force exactly in this way:
Force is a push or pull
A force is that which changes or tends to change the state of rest
or motion of a body
Force is the capacity to do work or cause physical change
Force= Mass times acceleration (F = ma)
Key Words
Brain storming in groups:
Search and write all
the Key Words found above
English
Force
Shape
Vector
Magnitude
Direction
Interaction
Vector quantity
Scalar quantity
Italiano
Forza
Forma (sezione)
Vettore
Grandezza
Direzione
Interazione
Quantità vettoriale
Quantità scalare
How can we measure the Force?
Forces can be measured using a device called force meter, using the International
System of Units (SI). The unit of force is called the newton. It is represented by the
symbol N.
Force meters contain a spring connected
to a metal hook
The spring stretches when a force
is applied to the hook.
The bigger the force applied, the longer the
spring stretches and the bigger the reading.
A force of 2N is smaller that 7N.
1 Newton (N) of force is defined as the amount of force needed to accelerate 1
kilogram (kg) of mass at a rate of 1 meter per second squared (m/s2).
1 Newton = 1 kg m/sec2 (A kilogram is the amount of weight at which 1 N of force
will accelerate at a rate of 1 m/s2.)
Lesson 2 : What does applying a Force do?
Force causes acceleration.
Newton's Second Law states that: the acceleration (a) of an object is directly
proportional to the force (F) applied, and inversely proportional to the object's
mass (m).
That means that the more force you apply to an object, the greater the acceleration.
And, the more mass the object has, the lower the acceleration.
Newton's Second Law can be written in equation form: F = ma.
For falling objects we can write F=mg where g is the acceleration due to gravity.
The force of gravity is what causes free falling objects to accelerate. These objects
all accelerate at the same rate of 9.8 meters/sec2
Resultant force
A force acting on an object may cause the object to change shape, to start moving,
to stop moving, to accelerate or decelerate.
When two objects interact with each other, they exert a force on each other,
the forces are equal in size but opposite in direction.
The forces acting on an object can be replaced with a single force that causes
the object to behave in the same way as all the separate forces acting together did,
this one overall force is called the resultant force. Remember: all forces (F) are
measured in Newtons (N).
Make note of following:
Newton’s First Law:
Any time a stationary object stays still, its' resultant force is zero.
As soon as force is applied, acceleration begins.
The speed of the acceleration will depend on the force applied
and the mass of the object.
In a similar way, each time an object in motion (in constant speed and same
direction) stays in motion, its' resultant force is zero too. As soon as a force is
applied, it can make it stop, change direction, move slower or move faster.
The resulting effect will depend on the force applied and the mass of the object.
It is worth noting that an object may have several different forces acting on it.
To understand resultant forces better, let us see these two scenarios:
See example in the illustration below:
All these different forces, F1, F2, F3
can be added up to know the resultant
force, F4. The resultant force is the
single force that has the same effect on
the object as all the individual forces
acting together.
If different forces are acting in different
directions, a resultant force can be
determined as well.
To recap:
If the forces are in the same direction, they add up;
If the forces are in the opposite direction, they subtract.
If the resultant force acting on a stationary object is zero,
the object will remain stationary.
If the resultant force acting on a moving object is zero,
the object will carry on moving at the same speed in the
same direction (i.e. at constant velocity).
Balanced Forces
When forces are balanced, they are of equal size, but opposite in direction.
Note: that this does NOT mean there is no force. It simply means that the total
of the forces add up to the value in the graphic above is zero.
When 2 Forces acting on the same object, in the same direction, with the same
magnitude, but in opposite way, have the resultant equal ZERO, they are
BELANCED. The object can’t move.
Video: Belanced Forces http://learning.alfriston.bucks.sch.uk/mod/url/view.php?id=1104
1) The sum is zero. The object stays.
Look at the forces acting on the object
and describe what happen.
Are all the example relate to balanced forces?
2) The difference is 1N to left.
The object moves to left. Slowly.
3) The difference is 4N to right.
It moves to right.
4) The difference is 4N to left.
It moves to left.
5) No difference. The only one force
of 20N make the object accelerate
quickly to left
Peer to peer:
Make your own example,
about balanced forces only.
1) The sum is _____. The object __________
2) The sum is _____. The object __________
Exercise!
3) The sum is _____. The object __________
Peer to peer :
Make your own example,
about unbalanced forces.
4) The sum is _____. The object __________
5) The sum is _____. The object __________
Lesson 3 :
Unbalanced Forces
Unlike balanced forces, we say unbalanced forces when two forces
acting on an object are not equal in size.
(or in equal direction, or in opposite way)
Unbalanced forces causes can cause:
- a still object to move
- a moving object to speed up or slow down
- a moving object to stop
- a moving object to change direction
As we have seen, just few pages before, Forces sum to a resultant force:
If the forces are in the same direction, they add up;
If the forces are in the opposite direction, they subtract.
If the forces are in the same direction, they add up to make a resultant force.
In this picture the resultant force is shown in black:
If the forces are in opposite directions they take away.
The resultant is in the direction of the bigger of the two forces.
Note that in this case the bigger force is from right to left, so the resultant force
is from right to left.
The resultant force is the single force that would have the same effect as all the
forces acting on the object.
We can have as many forces as we like, but they would all sum to a single
resultant force.
See the examples in the illustrations below:
When Forces have the same
point in, but different direction
and way, to find their resultant
we use the parallelogram of forces:
Different forces, F1, F2, F3, F4
for example, can be added up to
know the resultant force, R. The
resultant force is the single force t
hat has the same effect on the
object as all the individual forces
acting together
Two workers have to collocate a barrel in another place. They can’t roll it,
but they have a long rope. So they connect the rope to the barrel with a knot
and begin pulling it. Now, they have a double choice:
They can use one rope and apply
the sum of their force, by pulling
both in the same direction;
…or they can use two different
ropes and, pulling in different
direction, make the barrel moving
towards a resultant direction,
which they want.
To sum up:
If we have two forces that are not in the same direction, or in opposite direction,
we can't simply add or take away. We have to do a vector sum to find the resultant.
We can recognize, in the illustration below, the triangle of forces.
This aeroplane is flying with a wind blowing across its path.
It will actually move along the grey arrow, the resultant of the two vectors.
Key Words
Brain storming in groups:
Search and write all
the Key Words found above
English
Acceleration
Deceleration
Mass
Newton
(unit measure)
Newton Isaac
(Physicist)
Resultant Force
Balanced Forces
Unbalanced Forces
Parallelogram of
Forces
Italiano
Accelerazione
Decelerazione
Massa
Newton
(unità di misura)
Newton Isacco
(Fisico)
Forza risultante
Forze in equilibrio
Forze disuguali
Parallelogramma delle
Forze
Lesson 4: What is Friction?
Friction is the force that opposes the relative motion or tendency to such motion
of two bodies in contact.
If we try to push a block of wood across a table, there are two opposing forces that
act: the force associated with the push, and a force that is associated with the
friction which acts in the opposite direction.
As frictional forces are decreased (for example, by placing oil on the table) the
object moves further and further before stopping.
This demonstrates Galileo's law of inertia, which states: an object in a state of
motion possesses an ``inertia'' that causes it to remain in that state of motion unless
an external force acts on it.
More simply, we can define Friction as a Force that stops things from moving
easily .
Whenever an object moves or rubs against another object, it feels frictional forces.
These forces act in the opposite direction to the movement. Friction makes it harder
for things to move.
In the illustration by side, the smooth
base of the snowblades slides smoothly
on the snow. The boy on the grass is
having difficulty sliding, because the
grass is not smooth and his shoes are
getting stuck in the grass. There is more
friction between the shoes and the grass
than the snow and the snowblades.
Without frictional forces, a moving object may continue moving for a longer period.
Frictional forces are usually greater on rough surfaces than on smooth surfaces
Frictional forces can be good and helpful.
For example:
- A basketball star can grip a ball and control it
better in a dunk because of greater friction.
- When we walk, we don’t slip easily because of
the friction between our shoes and the floor.
- Each time you ride your bike, friction between
the tires and the road help you not to skid off.
Brainstorming!
Make more examples
Sometimes frictional forces can be unhelpful.
- If you don't lubricate your bike regularly with oil,
the friction in the chain and axles increases.
- When you run in a smooth surfaces like snow.
Your bike will be noisy and difficult to pedal.
Video: Bikes and fiction from the air
http://learning.alfriston.bucks.sch.uk/mod/url/view.php?id=1107
Sports
Brain storming in groups:
Compare some sports,
seeming similar, but where
frictional forces acting different.
Choice the sport where friction
has less or more importance
Curling
Less
Bocce
More
Wheel
Skating
More
Ice
Skating
Less
?
Bob/Sledge
Cart
Grass ski
Ski
Again…
I suggest: Sailing and Glider
work in the same way and they
both need air and wind to move.
But the boat floats in the water,
so his friction is MORE than
flying glider.
Swimming
Sub
Rowing
Paddle boat
Glider
—
Sailing
+
BACK TO STATICS
Remember: our topic is the knowledge of Forces acting in a building frame.
We don’t have to calculate the structures, this is an assignment for Engineers
and Architects. But we have to know how these forces acting on structures and
which task the different frames work for.
Lesson 5: Deformation
We must avoid any deformation on the structural elements of a building frame.
All the deformations are due to stress. So we analyze now what stress is and
what involves.
Stress
Stress is "force per unit area" - the ratio of applied force F and cross section –
defined as "force per area".
tensile stress - stress that tends to stretch or lengthen the material –
acts normal to the stressed area
compressive stress - stress that tends to compress or shorten the material –
acts normal to the stressed area
shearing stress - stress that tends to shear the material - acts in plane to the
stressed area at right-angles to compressive or tensile stress
To recap:
What happen to beam in stressing?
If stress is not equal from all directions, then we say that the stress is a
differential stress. Three kinds of differential stress occur:
Tensional stress (or extensional stress), which stretches material;
Compressional stress, which squeezes material; and
Shear stress, which result in slippage and translation.
When materials deform they are said to strain.
A strain is a change in size, shape, or volume of a material.
Tensile or Compressive Stress - Normal Stress
Tensile or compressive stress normal to the plane is usually denoted "normal stress"
or "direct stress"
For example: we have a simple beam with a weight over.
When a force is applied to the top of the beam, it causes compression
on the top surface and tension on the bottom surface
Shear Stress
Stress parallel to the plane is usually denoted "shear stress"
Strain
Strain is defined as "deformation of a solid due to stress"
Young's Modulus - Modulus of Elasticity (or Tensile Modulus) - Hooke's Law
Most metals deforms proportional to imposed load over a range of loads.
Stress is proportional to load and strain is proportional to deformation
as expressed with Hooke's law E = stress / strain
Collapsed bridge
Bridge fell down in the course of test,
due to much weight.
Stages of Deformation
When a material is subjected to increasing stress, it passes through 3 successive
stages of deformation.
Elastic Deformation — wherein the strain is reversible.
Ductile Deformation — wherein the strain is irreversible.
Fracture – irreversible strain wherein the material breaks.
Modulus of elasticity
Each material has an own modulus of elasticity, over which the deformation
became permanent. Under it, when stress ends, deformation too ends, and
the material turns back to his original shape and length. (Reversibile strain).
Over modulus, the material can’t turn in original shape, even if the stress ends.
(Irreversibile strain).
Then, if the strain goes on with stressing, the material breaks.
Each material has an own braking modulus, we ask breaking point.
We can divide materials into two classes that depend on their relative behavior
under stress.
Brittle materials have a small or large
region of elastic behavior but only a small
region of ductile behavior before they
fracture.
Ductile materials have a small region of
elastic behavior and a large region of
ductile behavior before they fracture.
Engineers and Architects, to avoid fractures that could bring building
to collapse, check materials in order to their task and which material
Is the most suitable for the use.
Key Words
English
Stress
Tensile stress
Compressive
stress
Strain
Elastic
deformation
Ductile
deformation
Fracture
Reversible strain
Irreversible strain
Modulus of
elasticity
Italiano
Sforzo
Trazione
Compressione
Sforzo di taglio
Deformazione
reversibile
Deformazione
irreversibile
Frattura
Tensione reversibile
Tensione irreversibile
Modulo di elasticità
Brain storming in groups:
Search and write all
the Key Words found above
Lesson 6: Statics and Building Structures
We started lesson 5 about Statics with a figure, showing the
frame of a building, in which some structural elements were
identified. Now, after a necessary introduction on forces,
we see what are these structural components
and which tasks they have.
Do you remember?
The purpose of the static is the calculation
of forces acting on structures or within
structures that are balanced.
The study of these forces enables you
to determine whether the structures can
support the forces without suffering significant
deformations or fractures.
Engineers and architects must be able
to calculate the forces acting on the structural
components of a building.
What is a Building Frame?
We can define the frame of a building as a structural system composed of beams,
pillars, and foundations making up the backbone of the building
The term structural system in structural engineering refers to the load-resisting
sub-system of a structure.
Structural system transfers loads to the foundation or supporting structure through
interconnected structural components or members
What is a beam?
It is a horizontal structural component, used to support and distribute the weight
of roof or other structure to the vertical pillars. It is made of metal, reinforced
concrete, bricks, wood, and usually looks like a bar with a square shape.
What is a pillar?
The pillar is an upright shaft or structure, of stone, brick, metal, renforced concrete,
or other material, relatively slender in proportion to his height, and of any shape in
section, used as a building support.
What is a foundation?
A foundation (or, more commonly, foundations) is the element of an architectural
structure which connects it to the ground, and transfers loads from the structure
to the ground. Foundations are generally considered either shallow or deep.
Foundation engineering is the application of soil mechanics and rock mechanics
(Geotechnical engineering) in the design of foundation elements of structures
How can we consider their use?
Beam:
Because the beam (or sometimes lintel) is a horizontal architectural element,
not pushing and taken by pillars (that does not touch the ground, but download
your weight on other elements), it is most often in turn for top points that overlook.
The lintel typically relies on two piers, sometimes through a joint, which transmits
its weight and hopefully that of the structures above it claims.
Being typically facilities that in the central part are suspended in a vacuum,
they are limited to use by weight that is placed above and to the strength of the
material.
Pillar:
The pillar is a vertical load-bearing architectural element, which transfers
the loads of the superstructure to underlying structures (foundations)
empowered to receive it.
The pillar can have different forms in section .
The span (distance between two pillars) depends on the geological nature
of the ground, on the length of the beams, and on the loads they must endure.
Foundation:
The foundations have the purpose to receive the loads from the superstructure
and forward them to the ground. For that role it is necessary that these are carried
out in such a way as to be rigid. To have stiffness, foundations must be massive.
For ordinary foundations, therefore, do not use high-strength concrete (except for
areas deemed seismically active, in which need to be used high-strength concrete)
precisely because of the overflowing masses to be used to achieve the required
stiffness.
The type of foundation, whenever employed, depends on the stress acting on it
and on the type of terrain it is connected; the foundation must be laid on a ground,
able to bear the load of the structure.
Key Words
Brain storming in groups:
Search and write all
the Key Words found above
English
Beam
Lintel
Pillar
Foundation
Frame
Building frame
Stiffness
Seismic
That’s all folks!
End of the Module!
Italiano
Trave
Architrave
Pilastro
Fondazione
Telaio
Telaio strutturale
Rigidezza
Sismico
Summary exercises
Six easy questions:
Question 1
What will be the total value of the forces above?
The answer is_______________ The 10 force_____________________________out the ten force.
Question 2
What would happen if your weight was more than the upwards force from
the chair?
The answer is: You ____________________________________through the chair!
Question 3
Why is it harder to cycle into the wind than cycle at the same speed in still
air?
The answer is: the wind is_______________against you more. Therefore it is causing more
drag (backwards force).
So you have to pedal _______________ to increase the forward force.
Summary exercises
Six easy questions:
(part 2)
Question 4
The answer is:
Question 5
Work out the resultant of these forces and state the direction of the
resultant.
(a) 25 N from left to right and 20 N from left to right;
(b) 25
N from left to right and 20 N from right to left.
(a) Resultant = ____________ = ___ N (from left to right)
(b) Resultant = ____________ = ___ N (from left to right)
What happens when a force is applied to the top of the beam?
The answer is: it causes___________________on the top surface and__________________
on the bottom surface.
Question 6
What kind of stress corresponds to the diagram below?
The answer is: An ________________ deformation or __________________one.
Beam to not breaks down!
Student: Name_____________________Surname_________________________Class_________
Summary exercises
Cloze
CLOZE EXERCISES
Fill the gap with one of a), b), c) solutions indicated on the right side boxes
1.
The main Structural Components of a building are beams,
__________________and foundations.
a) windows
b) pillars
c) floors
2.
The Foundation is a construction below the ground that
______________________ the load of building
a) increases
b) minimizes
c) distributes
3.
The Deformation can be reversible when inside the
____________________modolus.
a) tensile
b) elastic
c) tension
4.
Belanced forces are forces of _____________size but
opposite in direction.
a) different
b) equal
c) disequal
5.
A __________is the force needed to accelerate 1 Kg of
mass at a rate of 1 meter per second squared (m/s2)
a) Kilogrammeter
b) Higgs
c) Newton
Summary exercises
Cloze
CLOZE EXERCISES (part 2)
Fill the gap with one of a), b), c) solutions indicated on the right side boxes
6.
A Force can be definite as the action of pushing or
_________________ .
a) punching
b) pulling
c) pumping
7.
The ___________is a structural component of a building
used as an horizontal structural memberwell.
a) beam
b) bean
c) bear
8.
A _____________structure is a structure enabled to
support all the forces acting on
a) collapsed
b) reinforced
c) deformed
9.
Friction is a force that _____________the relative
motion or tendency to such motion of two bodies in
contact
a) improves
b) resists
c) helps
Statics is a science consisting in analysing the forces
acting on the structures or _____________them.
a) outside
b) around
c) inside
10.
Student: Name_____________________Surname_________________________Class_________
Match Up
Linkage exercise.
Connect with an arrow the words on the left line to their definitions.
Summary exercises
Match Up
1)
BEAM
→
a)
Distortion of shape when subjecting to forces acting on or inside.
2)
STATICS
→
b)
The construction below the ground that distributes the load of a building.
3)
TENSIONAL STRESS
→
c)
The single force that would have the same effect as all the forces acting on the object.
4)
BELANCED FORCES
→
d)
When the strain is irreversible
5)
FRACTURE
→
e)
The horizontal structural component of a building frame, connecting pillars.
6)
FOUNDATION
→
f)
The science consisting in analysing the forces acting on building structures or inside
them
7)
DEFORMATION
→
g)
The force that opposes the relative motion or tendency to such motion of two bodies
in contact, and stops things to moving easily.
8)
RESULTANT FORCE
→
h)
When forces are of equal in size, but opposite in direction.
9)
DUCTILE
DEFORMATION
→
i)
When forces acting in opposite directions stretches beam.
FRICTION
→
l)
The third stage of deformation, an irreversible strain wherein the materials breaks.
10)
Answers:
1) is:____; 2) is:____; 3) is:____; 4) is:____; 5) is:____;
6) is:____; 7) is:____; 8) is:____; 9) is:____; 10) is:____.
Student: Name_____________________Surname_________________________Class_________
Summary exercises
Crossword
CROSSWORD
Summary exercises
Crossword
CROSSWORD (definitions)
Summary exercises
Solutions
SOLUTIONS
Six easy questions
1) The answer is: Zero. The 10 N force has cancelled out the 10 N force.
2) The answer is: You would sink through the chair.
3) The wind is pushing against you more. Therefore it is causing more drag (backwards force).
So you have to pedal harder to increase the forward force.
4) (a) Resultant = 20 N + 25 N = 45 N (from left to right)
(b) Resultant = 25 N -20 N = 5 N (from left to right)
5) The answer is: it causes compression on the top surface and tension on the bottom surface.
6) The answer is: An elastic deformation or a ductile one. Beam to not breaks down!
Cloze Exercises
The right answers are:
1b; 2c; 3b; 4b; 5c; 6b; 7a; 8a; 9b; 10c.
Match Up
The right answers are:
1e; 2f; 3i; 4h; 5l; 6b; 7a; 8c; 9D; 10g.
Summary exercises
Solutions
Summary exercises
Solutions