In engineering, we deal with various bodies,
frames, machines and other structures.
Eventually, all systems transfer their loading
to the ground.
This is accomplished by connecting a series
of elements.
It is very important we understand what these
connections are.
These connections are typically knowns as
supports.
The supports can also be called as joints
or constraints.
Each of this connection is designed to support
a specific type of loading condition.
Since support hold the bodies in place, they
resist unwanted motion and therefore create
reaction forces, which we will call as support
reactions.
Quite often our goal is to determine the support
reactions in equilibrium problems
Let us start with cable supports.
Take a look at this example, where a traffic
light is supported by two cables.
Or another example, where a weight is supported
by a cable system.
Cable, wires and ropes are widely used in
the industry.
They can support only tensile loads.
So anytime you see a cable in your system,
you can replace the cable with a force along
the cable in the direction that pulls the
cable.
When it comes to right bodies, they can be
supported not only by cables but other means.
The three common supports, which join two
bodies, are pin support, roller support and
fixed support.
There are also other supports but in this
session, we will limit our discussion to cable,
pin, roller, and fixed supports.
Let us consider the pin support.
A pin support is typically represented by
the figure as shown here.
A pin support is very popular.
Take a look at this beam with holes.
Here I have a Lego compatible part made of
metal.
It has many holes.
And here I have a black pin.
I can insert this pin into one of the holes
of this beam, and this beam is now supported
by a pin.
Now, watch this.
This beam can rotate about z axis but it cannot
move along x direction, or y direction.
Let us take a look at another example of pin
support.
Here I have a scissor, and it has two parts.
Upper handle with the blade and the lower
handle.
These two are parts are connected by a pin
right here.
This pin allows the parts to rotate.
Notice this.
The pin does not allow the parts to move horizontally
or vertically with respect to each other.
It only allows rotation.
So, this is a pin support.
In other words, pin support resists both vertical
and horizontal forces but not a moment.
So, this is how we treat pin support from
now onwards.
Any time you see a pin support, replace that
with two forces, one horizontal and one vertical.
Let us consider the roller support.
A roller support is typically represented
by the figure as shown here.
Roller support allows rotation and translation
along the surface upon which the roller rests.
This support is widely used in the industry
to account for thermal expansion of structural
elements such as beams.
This support allows the body to rotate as
well as move along the surface.
Here is an example for roller support.
This is a slotted beam.
You can see the two slots and it is used in
many experiments.
You can see there are some parts in the slot.
In this case, you see a disk connected to
a pin.
As you can see these parts can rotate, you
can see this pin can rotate, and slide along
the slot.
This is a roller support.
This support resists translations motion along
the axis perpendicular to the surface.
This means it has only one support reaction
along this vertical axis.
So this is how we treat roller support from
now onwards.
Any time you see a roller support, replace
that with a force in the direction, where
the motion is resisted.
All right.
Now, let’s consider fixed support.
A fixed support is typically represented by
the figure shown here.
A fixed support is also called a built-in
support or a rigid support.
This support is very common.
A beam built into a structure is a fixed support.
Or, you can imagine fixed support like a tree
that grows from the ground.
Fixed supports can resist vertical and horizontal
motion as well as the moment so they will
have three support reaction.
So this is how we treat fixed support from
now onwards.
Any time you see a fixed support, replace
that with two forces, one horizontal and one
vertical and a moment.
With a good understanding of how to model
support reactions, we are now ready to solve
two-dimensional rigid body equilibrium problems.
