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Chapter 1 : Introduction
- 1.1 Statics , what is it good for ?
- 1.2 Types of forces
- 1.3 Action and Re-action
- 1.4 What a force can do to a body
- 1.5 Graphical representation of forces
Let's say you as engineer are presented with all the design details
of a certain structure and your task is to make sure that this structure
- does not break under influence of the design load ( that includes
a certain safety factor ).
- no material is wasted
Here a structure can be just about anything of interest, the chair
you are sitting on, a
simple tower
for a power line or a
bridge
over a river.
Often a structure consists of many, sometimes thousands of members (parts)
which are connected ( glued , welded,
rivetted etc.) to each other.
Each individual member is subject to break.
So, how do you make sure that none does ?
Well, even if the design is already given to you this task can be difficult
enough. It can be roughly broken down into two steps
- Determine the forces acting on each member (this is the EMch 11 stuff ).
- Determine whether the member under consideration can withstand
the calculated forces with whatever safety margin is appropriate
(this is EMch 13 stuff and things coming after that).
Here is a sample problem,
take a peek. If this problem does not make much
sense to you now you may want to read Chapter 1 in its entirety first
and then come back to it.
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A force is the action of one body onto another.
We distinguish :
- Contact or support forces
- which occur whenever two bodies are in physical contact with each other.
They always depend on the details of how the two bodies are connected to
each other. You and the chair you are sitting on would be a nice
example, your ear being attached to your head and not falling
off would be another.
- Field Forces
- which may be due to gravity, electro-static,electro-magnetic or
nuclear interactions. No physical contact between the involved bodies
is necessary. Actually, the distance between two such bodies
can be rather large in comparison to size of the bodies themselves
(earth and moon for example).
Warning : Often there are forces of both types
acting simultaneously between two bodies.
My example :
Take a car sitting outside your house. The car is
pulled towards the center of the earth by gravity (we call that force
commonly "weight"). This force is constantly present even if the car drives
over a hump at high speed and its wheels are not touching the ground
momentarily. On the other hand (when the wheels are touching the ground)
the earth's surface is pushing upwards onto the car at the points where
the wheels touch the road surface. You can think of this force
as a kind of resistance force the earth's surface is exerting onto the wheels,
trying to prevent (resist) the wheels from penetrating the road surface.
If the surface is made out of a soft material (like mud or sand) which
has not much
resistance the car's wheels will actually sink into the ground until
enough resistance is encountered.
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We just looked at what kind of forces are acting on a car sitting on the ground
and argued that the earth exerts not only a gravitational pull onto the
car but that the ground is pushing upwards against the wheels of the car.
But what does the car do to the earth ? Well, the contact force is easy,
the car is pushing down onto the earth's surface and might even make
a dent into it. Obviously, the force the car exerts onto the ground
and the force from the ground onto the wheels are in
opposite direction (one upwards one downwards in this example).
How about the gravitational force and with that all other field forces ?
If I told you that the car is actually pulling the earth towards its own
center of mass, you would probably ask me to prove that, wouldn't you ?
Well, let me ask YOU to make up a thought experiment which clearly
shows that the gravitational forces between car and earth are
oppositely directed. Here is
my thought experiment.
Later we will learn that
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ALL forces acting between any two bodies come in
pairs and are exactly equal in value but exactly
opposite in direction. This law is often called
Newton's Third Law.
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The interaction between different bodies is not always easy to see
but is of utmost importance, so here is
an example you definitely should
have a look at.
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A force acting on a rigid body can in general cause the body to undergo
two different types of motion.
- The body starts to accelerate
- The body will start to rotate
Whether the body actually moves/rotates depends on
all the forces acting on the given body.
In statics we don't want any motion to
happen and therefore :
Statics : Study of bodies in equilibrium
The demand of bodies neither to translate ( = motion of its center of
mass if you will) nor to rotate ( = spinning around its center of mass )
will lead us to different types of equations relating the forces ( in magnitude
and direction ) acting on a body to each other. Once we have enough
equation we will solve for the unknown forces and we are done with
the EMch11-step of the designing process.
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Figure 1.5a
Graphical Representation of Forces
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In Figure 1.5a we have three forces acting on the box-like
body. Each force is represented by an arrow, pointing in
the direction the force is acting and having a length proportional to
the magnitude
of the force. Often the head or the tail of this arrow is placed at
the point where the force is acting on the body. This point is then
called the point of attachment.
Next to each arrow we have a symbol ( F1 etc. )
which we use later in equations or inside the text to indicate which of
several forces we are talking about. The letters F and subscript 1,2 etc.
are completely arbitrary although often used. Other letters which you find
in textbooks to represent forces are P, Q, and R.
The arrow next to each symbol is a reminder for us
that a force is a quantity which has a value and direction. It is the
same notation we use in vector algebra and vector calculus, because as we
will shortly see, the physical quantity of a force is as far as
mathematical properties are concerned equal to a vector.
NOTE : In Figure 1.5a we do not show the bodies which are exerting
the shown forces F1 etc.
Well, maybe now you'd like to have
another peek at the afore mentioned
sample problem.
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Zig Herzog, hgn@psu.edu
Last revised: 08/16/06