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>> Hello, everyone. Welcome back to engineering
mechanics. Our discussion is on process. If
you recall, in the last session, we discussed
about structural analysis. You may recall
structural engineering or structural analysis
is probably the oldest form of engineering
that humans have practiced. The oldest human-made
structure is still in France. It is about
5,000 years old BC. Since the stone structure
built long time ago to the skyscrapers that
we are building now, we have made a tremendous
progress in designing and building structures.
There are various kinds of structures. Our
focus today is on trusses. What is a truss?
Well, truss is a structure that is entirely
made of two-force members. Now, you may recall
what a two-force member. Two-force member
is a structural element that is either in
tension or in compression. The loads are applied
at the ends at those joints, and typically
for two-force members, we ignore the weight,
all right? So a structure completely made
of two-force member is a truss. Where are
trusses used? Well, you see them in your everyday
life. If you visit a supermarket or a warehouse,
just look up. You will see lots of beams crisscrossing
the entire structure on top, and those are
roof trusses. They support the roof. Similarly,
trusses are also widely used in bridges construction.
For example, a railroad bridge. It's typically
a truss. Here is an example. This is a railroad
bridge made entirely of two-force member,
and therefore, this is a truss. As you can
look at, as you can see, here is a truss made
of two-force members, and each three two-force
members are making a triangle and more triangle,
and this is a simple truss, okay. Now, all
these truss elements are connected at the
joint, typically a pin joint, and those joints
are here, all right. Now, these truss structures
are so important that we see them in our everyday
life, like railroad bridges, roof trusses,
and many other structures. But you also talk
about structures, I wanted to keep it in mind,
it is not that stationary structures we are
talking about. Moving systems, such as a plane
or an automobile or other transportation devices,
have also a structure, and those-- Hello,
everyone. As we move on to talking about truss
structures, let's briefly review two-force
members. Remember, truss is a structure entirely
made of two-force members. That's by definition,
right. Otherwise, it won't be a truss. If
there is a non-two-force member, a multiforce
member, then that becomes a frame. It won't
be a truss. And we are dealing with truss,
which means all the members of the structure
is made of two-force member, and what is a
two-force member? Well, recall our discussion
from the past. A two-force member is a member
that is either in tension, as shown now, or
in compression, all right. There is no other
force applied anywhere along the line, and
two-force members that make a truss joint
are connected by pin joints at the ends. Now,
these are all pin joints and we're going to
assume these pins are smooth, all right. One
thing that confuses people a lot of time is
what about the weight? Remember, a bridge
is a huge structure. It's very heavy, and
even each member that makes that bridge is
heavy. In our normal understanding, this could
weigh hundreds and thousands of pounds. And
yet, we do not want to consider the weight
of that member because if I draw the weight
of this member, it's going to be applied somewhere
in the middle. And if this is the weight and
the beam is loaded here and here again, it
is not a two-force member. This is not a two-force
member. So in our truss calculations, for
that matter, any truss calculation, we are
going to ignore the weight of that beam or
the weight of that member. Now, you may ask
why we ignore it. Well, if you consider the
loads involved in this truss design, the weight
is relatively small and can be ignored for
all practical purposes. And that's the reason
we ignore the weight and still get a fairly
good solution to the problems. Now, if you
do have to account for the weight, then it
can be done. What you do is take this weight,
divide by two, and apply at the ends, all
right. So, again, to repeat, a two-force member
is a member that is in tension or in compression,
and the weight of the member is not accounted
or ignored. And if you do have to account
for it, you'll have to apply at the ends because,
by definition, a two-force member is loaded
only at the ends, which mean those joints,
all right. And the last point I wanted to
keep it in mind is two-force members may not
have to look exactly like a straight member.
A two-force member could look like this, okay.
And if it looks like this, and let's say these
are all the two joints connecting, then the
line of action of the two-force member is,
line of action of the forces acting on the
two-force member will be created by the lines
connecting those two joints, all right. So
in this case, this two-force member may look
like this. This is just for you to know a
two-force member doesn't have to look like
a straight member. Even though this will be
the case for most part in trusses, all right.
All right, so we are talking about trusses.
We just briefly mentioned about two-force
members. And before we go to trusses, I wanted
to show you a simple two-force member made
out of a Lego beam. Here I have a simple beam.
It's made out of Lego and it can be assumed
as a two-force member and is going to be connected
by two pin joints at these ends, all right.
So I can find another beam. This beam alone
doesn't make any structure. If I take this
beam and attach to another beam, this is still
not a structure, all right. So two-force members
connected in this fashion is still not forming
a structure, but let's say I take a third
member and connect it now. I get a nice triangle
and see -- actually, I broke it. All right.
Watch this now. This is actually a rigid structure,
all right. This is stable, rigid, and therefore,
a triangle structure is the simplest structure
that is possible, all right. In fact, it is
rigid, stable, and it is made of three members
-- two two, three two-force members. So triangle
structure is the simplest possible structure,
and for those of you who you think, "How about
we make a structure with four members?" If
you look at four members here, clearly if
I give a push here, this is losing its geometry.
It actually collapses. So when you have four
members like this, what you have is not a
structure. It's a mechanism, all right. So
if you want to make this as a structure, you
need to put a crossbeam, making as a triangle
structure. So if you look at trusses, most
trusses are made with simple triangle members.
For example, if you want to make a truss,
you can start with the triangle like this.
Now, you know this is a simple structure.
You can add two more members here and you
get another triangle. It becomes a structure.
And I can add two more members like this.
And you get another structure. Two more members
like this. Two more members like this. And
you can keep going. This kind of structures
is known as simple truss, all right. And,
of course, the truss will be finally supported
by maybe a pin joint and a roller joint. An
example of such a truss is right here, you
have seen it a few minutes ago, all right.
That's a simple truss. Actually, it's a bridge.
And you can see the truss elements made of
triangles. All right. So that's how truss
analysis is done, and truss analysis can be
done in two different ways. One is matter
of joints. That's one matter. Another matter
is matter of section. Two matters to solve
truss problems. And the objective of truss
analysis is to find the forces in each of
those members. Are they in tension or in compression?
All right. So your answer should include the
member forces and, in addition, you should
include whether the member is in tension or
compression. So let's do an example involving
matter of joints, and we will do this on the
whiteboard.
