statics, - angelo filomeno · 2014-09-18 · 2 2 our body contains a number of these contrivances...
TRANSCRIPT
![Page 1: Statics, - Angelo Filomeno · 2014-09-18 · 2 2 Our body contains a number of these contrivances which through long ages have been adapted by nature to our needs. If we lift a weight](https://reader033.vdocuments.us/reader033/viewer/2022042012/5e72b739b20fc659da36e76a/html5/thumbnails/1.jpg)
1
1
The object of studying structural mechanics is to
enable architects and engineers to learn how to
build structures with a view to stability, the safety of
human life and financial economy. Mechanics is a
branch of knowledge covered by applied
mathematics and deals with the motion of bodies,
with ‘the forces by which those motions are
conditioned and with the balance of forces on a
body at rest. The word 'Mechanics' is derived from
the Greek Mechanikos meaning 'contrivance'.
![Page 2: Statics, - Angelo Filomeno · 2014-09-18 · 2 2 Our body contains a number of these contrivances which through long ages have been adapted by nature to our needs. If we lift a weight](https://reader033.vdocuments.us/reader033/viewer/2022042012/5e72b739b20fc659da36e76a/html5/thumbnails/2.jpg)
2
2
Our body contains a number of these contrivances which
through long ages have been adapted by nature to our
needs. If we lift a weight or raise a foot from the ground,
we are employing mechanisms which are admirably suited
by nature for these purposes. Therefore, mechanics may
be defined as the constituent part of applied mathematics
where we study the conditions under which bodies around
us move or remain at rest. In this course we are going to
consider in particular structural mechanics, which is mainly
concerned with forces-how they combine together, how
they keep a body at rest, and in general with the effect
they have on the stability of the part of the building or
structure to which they are applied. Also, we will have to
pay attention to the effect a force has on the size and
shape of the material upon which it acts. The word 'body'
is meant to include all things which have weight, and
throughout this course it will enter into our discussions and
into many of our calculations.
![Page 3: Statics, - Angelo Filomeno · 2014-09-18 · 2 2 Our body contains a number of these contrivances which through long ages have been adapted by nature to our needs. If we lift a weight](https://reader033.vdocuments.us/reader033/viewer/2022042012/5e72b739b20fc659da36e76a/html5/thumbnails/3.jpg)
3
3
In the definition of mechanics two aspects have
been mentioned: first, the conditions under which
objects remain at rest; and second, the conditions
under which objects move. These two aspects have
brought about the division of the subject into two
parts: Statics, which is concerned with solid bodies
at rest, and Dynamics, which is concerned with solid
bodies in motion. There is a further branch of the
subject called Hydrostatics, which deals with the
application to liquids and gases of those principles
which have been mentioned above in relation to
solid bodies. Hydrostatics is a study in its own right
and is outside the scope of this course.
![Page 4: Statics, - Angelo Filomeno · 2014-09-18 · 2 2 Our body contains a number of these contrivances which through long ages have been adapted by nature to our needs. If we lift a weight](https://reader033.vdocuments.us/reader033/viewer/2022042012/5e72b739b20fc659da36e76a/html5/thumbnails/4.jpg)
4
4
Take a small fairly heavy body such as a
weight, suspend it by a piece of string and hold
the free end of the string between the thumb
and first finger. If you do this simple experiment
yourself, you will be aware of the forces
involved, and I would suggest that the way to
get the most out of this experiment is to use
different weights at the end of the string.
![Page 5: Statics, - Angelo Filomeno · 2014-09-18 · 2 2 Our body contains a number of these contrivances which through long ages have been adapted by nature to our needs. If we lift a weight](https://reader033.vdocuments.us/reader033/viewer/2022042012/5e72b739b20fc659da36e76a/html5/thumbnails/5.jpg)
5
5
Now look at Fig 1. First, in order to keep the weight from falling to the ground you must exert an upward force by means of the muscles of your thumb, finger, wrist and arm. It is an upward force because, if you take the weight in your other hand, then your thumb, finger and arm--on being relieved of the weight--will shoot upwards. Second, this upward force is necessary to counter-balance a force which is acting vertically downwards on the suspended body, a force which we call the weight of the body. This downward force or weight is called the Force of Gravity. It is the attraction which the Earth exerts on all bodies and makes them fall to the ground. Now let us return to the experiment with the body suspended by a piece of string. Fig 2 explains the method which is employed to represent the forces involved. A represents the body and the straight lines show the vertical gravitational forces acting on it, the arrowheads indicating the direction of each of them. The forces are as follows: the weight acting vertically downwards is marked w and the balancing force acting vertically upwards exerted by the thumb and finger through the string is marked F. Now, so long as the pull upwards which you exert is equal to that of the weight w, the body will remain stationary, that is, at rest. If you increase the pull upwards, the body will move upwards; if you decrease the pull upwards, the body will move towards the ground.
![Page 6: Statics, - Angelo Filomeno · 2014-09-18 · 2 2 Our body contains a number of these contrivances which through long ages have been adapted by nature to our needs. If we lift a weight](https://reader033.vdocuments.us/reader033/viewer/2022042012/5e72b739b20fc659da36e76a/html5/thumbnails/6.jpg)
6
6
Here is a summary of these principles. Thus an
alteration in the forces acting on the body results in
the body being at rest or in motion. So far the term
'Force' has been used without giving a definition of
it. The experiment described earlier and the simple
results gained from it have now made this possible.
Force is that which tends to produce motion in a
body, to change that motion or to keep the body at
rest. The mental picture of a pull or push is for the
moment a sufficient conception of force.
![Page 7: Statics, - Angelo Filomeno · 2014-09-18 · 2 2 Our body contains a number of these contrivances which through long ages have been adapted by nature to our needs. If we lift a weight](https://reader033.vdocuments.us/reader033/viewer/2022042012/5e72b739b20fc659da36e76a/html5/thumbnails/7.jpg)
7
7
Familiar examples of forces are to be found in life around
us. It is necessary to measure the amount of pull or push.
This is called the measurement of the magnitude of a force
and it is convenient to express this in terms of Newtons. In
this course the measurement of a force will be in Newtons
or Kilonewtons.
The Newton (N) is the unit of force which acting on a
mass of one kilogramme (kg) imparts to it an
acceleration of one metre per second per
second (1 m/s2).
thus 1 N = 1 kg x 1 m/s2 = 1 kgm/s2
weight = mass x acceleration due to gravity
weight of 1 kg = 1 kg x 9.81 m/s2 = 9.81 kgm/s2
but 1 kgm/s2 = 1 N
Hence 1 kg = 9.81 N
![Page 8: Statics, - Angelo Filomeno · 2014-09-18 · 2 2 Our body contains a number of these contrivances which through long ages have been adapted by nature to our needs. If we lift a weight](https://reader033.vdocuments.us/reader033/viewer/2022042012/5e72b739b20fc659da36e76a/html5/thumbnails/8.jpg)
8
8
Let us again refer to the experiment. The upward
pull through the thumb and finger to maintain the
weight at rest is apparent, but if the string is
attached to a nail in a wall and the weight is left
hanging downwards, the upward pull through the
nail is not apparent. This phenomenon forms the
basis for all static theory in mechanics. If we push
against a wall we are conscious of an opposite force
acting against our hands, and the harder we push,
the greater will be the counter force. In other words,
there is some hidden force balancing our pushing.
Similarly, there must be a hidden counter force
acting through the nail in the wall to balance the
vertical force acting downward through the weight.
![Page 9: Statics, - Angelo Filomeno · 2014-09-18 · 2 2 Our body contains a number of these contrivances which through long ages have been adapted by nature to our needs. If we lift a weight](https://reader033.vdocuments.us/reader033/viewer/2022042012/5e72b739b20fc659da36e76a/html5/thumbnails/9.jpg)
9
9
This hidden balancing force, or counter force, is known as
the Reaction. This is a force which we seldom see at work,
and because it is unseen, fail sometimes to appreciate fully.
Stop this tape; then Go to the nearest solid wall and push
against it with your hands and then with your shoulder. If you
push against a wall with a force of 100 N, the reacting force
back through the wall will be 100 N. If you push lightly
against the wall through your thumb with a continuous
pressure of 5 N, the wall will press back with a continuous
reaction of 5 N.
Now we have arrived at an important principle: Force and
reaction are opposite in direction and equal in amount. You
must never consider that reaction, because it is not
apparent, is a purely imaginary force invented by
mathematicians to help them to solve problems.
![Page 10: Statics, - Angelo Filomeno · 2014-09-18 · 2 2 Our body contains a number of these contrivances which through long ages have been adapted by nature to our needs. If we lift a weight](https://reader033.vdocuments.us/reader033/viewer/2022042012/5e72b739b20fc659da36e76a/html5/thumbnails/10.jpg)
10
10
In the experiment in which a weight was suspended by a
piece of string held by your finger and thumb no weight
value was used. Let us now assume that the body is an
actual weight of 10 N. The piece of string is now subject to
a pulling or tensile force of 10 N. The vertical force acting
downwards is 10 N, the reacting force upwards through
your finger and thumb is 10 N and this must be so since
there is no motion. The body is at rest. You may ask, very
rightly, 'Why is the pulling or tensile force in the string not
20 N?', that is, 10 N downwards added to 10 N upwards. If
we want to determine the actual force in the string, all we
have to do is to insert a spring balance somewhere along
the length of the string, as illustrated in the next slide.
![Page 11: Statics, - Angelo Filomeno · 2014-09-18 · 2 2 Our body contains a number of these contrivances which through long ages have been adapted by nature to our needs. If we lift a weight](https://reader033.vdocuments.us/reader033/viewer/2022042012/5e72b739b20fc659da36e76a/html5/thumbnails/11.jpg)
11
11
If we carried out this experiment we would find that
the spring balance would indicate a force of 10 N,
no more and no Less. We can now further extend
this experiment to determine the value of the
reaction force which is taking place through the
muscles of our f~irst finger and thumb.
![Page 12: Statics, - Angelo Filomeno · 2014-09-18 · 2 2 Our body contains a number of these contrivances which through long ages have been adapted by nature to our needs. If we lift a weight](https://reader033.vdocuments.us/reader033/viewer/2022042012/5e72b739b20fc659da36e76a/html5/thumbnails/12.jpg)
12
12
Here is an experiment which I want you to carry out.
Fix a smooth- running pulley to a wall or to a
drawing board or to a piece of apparatus. Pass a
piece of string over the pulley and on the vertical
length fix the 10 N weight. Along the horizontal
length of string insert a spring balance and hold the
free end of the string again between your first finger
and thumb. Note carefully that the spring balance
shows a tensile force in the string of 10 N, not 20 N.
![Page 13: Statics, - Angelo Filomeno · 2014-09-18 · 2 2 Our body contains a number of these contrivances which through long ages have been adapted by nature to our needs. If we lift a weight](https://reader033.vdocuments.us/reader033/viewer/2022042012/5e72b739b20fc659da36e76a/html5/thumbnails/13.jpg)
13
13
Next take a metal ring of about 3 cm in
diameter and where the finger and thumb held
the string, attach the string to the ring and hold
the ring in position by placing it over a nail
fixed in the wall or in the drawing board or, as
shown here, on the apparatus. The spring
balance again shows a tensile force of 10 N in
the string.
![Page 14: Statics, - Angelo Filomeno · 2014-09-18 · 2 2 Our body contains a number of these contrivances which through long ages have been adapted by nature to our needs. If we lift a weight](https://reader033.vdocuments.us/reader033/viewer/2022042012/5e72b739b20fc659da36e76a/html5/thumbnails/14.jpg)
14
14
Now attach another length of string to the metal ring
and then pass it over a second pulley (at about the
same distance as the first pulley from the ring) and
tie it to a 10 N weight hanging vertical- ly
downwards. Allow the metal ring to move away from
the nail so that the ring is free of it. Again the spring
balance shows a tensile force of 10 N. We have
now quantified the forces involved in our first
experiment. This may be stated as follows: first, a
vertical force downwards of 10 N; second, a vertical
force upwards through the muscles of our first finger
and. thumb of 10 N; and third, a tensile force in the
string of 10 N.
![Page 15: Statics, - Angelo Filomeno · 2014-09-18 · 2 2 Our body contains a number of these contrivances which through long ages have been adapted by nature to our needs. If we lift a weight](https://reader033.vdocuments.us/reader033/viewer/2022042012/5e72b739b20fc659da36e76a/html5/thumbnails/15.jpg)
15
15
Here are one or two more examples to illustrate what we have
been discussing. At the top we see a man pulling on a rope which
is tied to a stake driven into the ground. If the man pulls on this
rope with a force of 400 N, his back and back muscles will be
conscious of making an effort of 400 N. Suppose he now removes
the stake and asks another man to pull with a force of 400 N on
the rope, again his back and back muscles would be conscious of
reacting with an effort of 400 N. If the second man suddenly drops
his end of the
rope to the ground, the first man cannot apply a force Qf 400 N to
his end of the rope, since he will fall to the ground because there
is no equal and opposite force at the other end. It takes two people
to make a quarrel and it takes tWQ equal and opposite forces to
make what we understand as Simple Tension.
![Page 16: Statics, - Angelo Filomeno · 2014-09-18 · 2 2 Our body contains a number of these contrivances which through long ages have been adapted by nature to our needs. If we lift a weight](https://reader033.vdocuments.us/reader033/viewer/2022042012/5e72b739b20fc659da36e76a/html5/thumbnails/16.jpg)
16
16
Here we see that it takes two equal and opposite forces
to make what we understand as Simple Compression. A
man is carrying a
weight Won his head. This weight acts vertically
downwards through his body. There is an opposing force
acting vertically upwards from the ground through his
feet and legs. The man's body is being compressed
between the downwards action of the weight and the
upwards reaction of the ground. On the right is a man
holding a block of wood in his hand. The block is being
compressed between the downward action of the weight
of the timber and the upward reaction of the muscles in
the man's hand and arm.
![Page 17: Statics, - Angelo Filomeno · 2014-09-18 · 2 2 Our body contains a number of these contrivances which through long ages have been adapted by nature to our needs. If we lift a weight](https://reader033.vdocuments.us/reader033/viewer/2022042012/5e72b739b20fc659da36e76a/html5/thumbnails/17.jpg)
17
17
One of the most important properties about a material is whether it is heavy or light. We think of steel as a heavy material and aluminium as a light one. But what happens when aluminium is cOm- pared with, say, timber? It would appear, therefore, that calling a material heavy or light is not enough; a more accurate method of comparison is needed. You know that two bricks weigh more than one--in other words, that the weight of a body varies directly as the quantity of matter in it. This quantity of matter is called Mass. We all know that steel is heavier than wood and therefore that if we lift a cubic centimetre of steel it is heavier than a cubic centimetre of wood. This means that the mass of a cubic centimetre of steel is greater than the mass of a cubic centimetre of wood. The word used to express this idea is Density.
Dead loads are the self weight of the structural materials and members which make up a building. These dead loads include roof and roof finishes, roof trusses and frames, floors and floor finishes, ceiling finishes, beams, columns, load-bearing walls and parti- tions, staircases, lift shafts, foundations etc. Loads of this kind are present throughout the life of the structure or building, and must be accurately determined before proceeding with detailed calculations appertaining to design. Self weights of materials can be obtained in textbooks and tables which you will probably find in your school or college library.
![Page 18: Statics, - Angelo Filomeno · 2014-09-18 · 2 2 Our body contains a number of these contrivances which through long ages have been adapted by nature to our needs. If we lift a weight](https://reader033.vdocuments.us/reader033/viewer/2022042012/5e72b739b20fc659da36e76a/html5/thumbnails/18.jpg)
18
18
Density is Mass, that is, quantity of matter per unit volume, and is
expressed by the simple formula shown here. By knowing the densities of
different materials we are able to compare their self weights or Dead
Loads, as they are commonly called. This inform- ation is important
because the self weight of a timber beam would be very much lighter than
a steel beam of the same dimensional proportions. Dead loads are those
considered as the weight of the structure itself and parts of the structure.
Superimposed or live loads are all loads other than dead loads.
They cover all movable weights in a building including the occupant
(human or animal), machines, furniture, fittings, storage materials and
goods, non-structural partitions and walls, rain, ice and snow on roofs etc.
Since the structure has to support these loads, it is necessary to
determine them as accurately as possible in relation to the type or
occupancy of the building. Fortunately Codes of Practice and Building
Regulations specify the minimum loads in kN.m2 which must be taken into
consideration on roofs and floors whether the floor be in an office block,
hospital, flats or ware- house. Reference should be made to British
Standard Code of Practic CP3, Chapter V, Loading, where all of these are
clearly stated.
![Page 19: Statics, - Angelo Filomeno · 2014-09-18 · 2 2 Our body contains a number of these contrivances which through long ages have been adapted by nature to our needs. If we lift a weight](https://reader033.vdocuments.us/reader033/viewer/2022042012/5e72b739b20fc659da36e76a/html5/thumbnails/19.jpg)
19
19
This slide gives examples of the densities of some common
materials You will note that the density of mild steel is 14 times
greater than timber and almost 5 times greater than dry sand.
In a multi-storey building, other than those used primarily for
storage purposes, it is obvious that the superimposed loads will
not occur simultaneously throughout the entire building; in such
circumstances the superimposed load can be reduced on all
floors by proportional amounts from 10%, but not exceeding
40%, with regard to columns, piers, walls and foundations each
giving support to one, two, three, four and five or more floors.
Snow loads vary but depend upon the geographical location
and climate of the country or region where the building is to be
sited.
![Page 20: Statics, - Angelo Filomeno · 2014-09-18 · 2 2 Our body contains a number of these contrivances which through long ages have been adapted by nature to our needs. If we lift a weight](https://reader033.vdocuments.us/reader033/viewer/2022042012/5e72b739b20fc659da36e76a/html5/thumbnails/20.jpg)
20
20
Now I want to talk about another kind of weight or load which we call Superimposed Load. All structural members are required to support loads other than their own dead loads. These are known as superimposed loads or Live Loads. A floor in a house, for example, is required to support the weight of people moving across it, sitting on it and also the furniture which is positioned on it. The amount of furniture may increase or decrease, the number of people may increase quite considerably for a party whereas it may support no people at all on other occasions.
Wind loading or pressure on vertical surfaces of multi-storey buildings placed normal to the wind direction is an important consideration in structural design. The active wind force is based upon the geographical location, height and degree of exposure of the building, eg on the coast, top of a mountain or in a naturally protected area where shielding is possible. The wind pressure (p) on a vertical surface of a building is calculated in so many Newtons per square metre which is divided into two parts:
(a) positive pressure on the windward side (+) and, (b) negative pressure or suction on the leeward side (-)
![Page 21: Statics, - Angelo Filomeno · 2014-09-18 · 2 2 Our body contains a number of these contrivances which through long ages have been adapted by nature to our needs. If we lift a weight](https://reader033.vdocuments.us/reader033/viewer/2022042012/5e72b739b20fc659da36e76a/html5/thumbnails/21.jpg)
21
21
The type of structure will detenfline the
intensity of the super- imposed loading and the
form of the loading. For example, the deck of
a bridge will be required to support a moving
load, that is, the movement of the traffic across
it from one side to the other. The floor of a
warehouse storing bags of flour will have to be
stronger than a warehouse storing cardboard
boxes. The floor of the auditorium in a cinema
will have to carry a greater loading of people
than, say, the floor of a bedroom in a house.
![Page 22: Statics, - Angelo Filomeno · 2014-09-18 · 2 2 Our body contains a number of these contrivances which through long ages have been adapted by nature to our needs. If we lift a weight](https://reader033.vdocuments.us/reader033/viewer/2022042012/5e72b739b20fc659da36e76a/html5/thumbnails/22.jpg)
22
22
Here is a table of a few superimposed or live loads
which are used in the design of buildings. I would
like you to note the differ- ences; for example, the
superimposed load on the floor of a work- shop
making lightweight goods is 5 times greater than
that for a floor in a house and 3 times greater than
that for a floor in a general office. There are other
loads on structures which have to be considered,
such as wind loads and snow loads, but I do not
intend to discuss these at this early stage in the
course.
![Page 23: Statics, - Angelo Filomeno · 2014-09-18 · 2 2 Our body contains a number of these contrivances which through long ages have been adapted by nature to our needs. If we lift a weight](https://reader033.vdocuments.us/reader033/viewer/2022042012/5e72b739b20fc659da36e76a/html5/thumbnails/23.jpg)
23
23
Here as a reminder is a list of the loads I have
just described. It is important to remember
them, since they are the loads to be
considered when designing a building.
![Page 24: Statics, - Angelo Filomeno · 2014-09-18 · 2 2 Our body contains a number of these contrivances which through long ages have been adapted by nature to our needs. If we lift a weight](https://reader033.vdocuments.us/reader033/viewer/2022042012/5e72b739b20fc659da36e76a/html5/thumbnails/24.jpg)
24
24
Finally, here is a section through an office
building. You will see the live loading in the
building due to the people and the furni- ture
and the way the forces generated by these
loads are transferred to the foundations and
the reactions through the foundations by the
subsoil. Similarly, the dead loads of the
materials which form the roof, the floors and
the walls generate forces which are transferred
to the foundations. Again the subsoil sets up
reactions through the foundations so that all
the forces are balanced.
![Page 25: Statics, - Angelo Filomeno · 2014-09-18 · 2 2 Our body contains a number of these contrivances which through long ages have been adapted by nature to our needs. If we lift a weight](https://reader033.vdocuments.us/reader033/viewer/2022042012/5e72b739b20fc659da36e76a/html5/thumbnails/25.jpg)
25
QUESTIONS
1 Describe the difference between dynamics, statics
and hydrostatics.
2 What is density and how is it determined?
3 (a) Explain as clearly as you can the difference
between forces and reactions.
(b) A man carries a load of 30 kg on his head. If the
man weighs 70 kg determine the amount of the
reactions through his feet when he is standing still
and when he is standing on his left leg only.
4 (a) A stone column supports a vertical load of
1000 kN including the self weight of the column. If
the vertical reaction through the foundation to the
column is 1000 kN determine the amount and
nature of the force in the column.
(b) A rope which is fixed to a pole is pulled by a man
who exerts a force of 50 N. Determine the
magnitude and nature of the force in the rope.
5 (a) When designing a building, what kinds of
external forces have to be considered?
(b) Make two lists, one of dead loads and the other
of superimposed or live loads. Place the loads in
each list in order of magnitude, ie the heavier loads
at the top and the lighter loads to the bottom. Try to
memorize these loads.