>> Hey what's going everyone?
Welcome back to our mechanics of material sequence.
And in this video we're going to address --
we're going to talk about shearing stress.
And hopefully by the end of this video you will be able
to define shear stress and average shearing stress.
And then take a look at some simple connections draw the
[inaudible] diagram of those
and identify what is single shear and double shear.
And then lastly we'll just take -- we'll talk about what direct
and indirect shear are and that we know which formulas apply
or appropriate in each case.
But here just to get started off in terms of shear stress.
Whenever I think of shear stress, you know,
I think of something sliding by something else.
So I think the image I have in my head is
like is a book, right?
If a book is resting on a table and it's attached
to that table right here, and I put my hand on top of the book
and I force I push along the side of it I know
that this thing will deform like this right here.
It'll essentially shear right here.
And if all the pages were bonded together, you know,
I would have shear stress develop in between each layer
within the material, or within the book between the pages.
And that would be kind of like shear stress, right?
Other things you might think
of are scissors whenever they slide past each other
to cut something or even fluid flow.
And especially where the fluid touches the structure that's
containing the fluid like a pipe or like a river bank I guess.
The river bank and the fluid, right,
there's some shearing action going
on where the fluid is sliding by the body or the structure.
Okay. So fluid flow right here.
So that's what I think of, you know,
and officially it's whenever you have a force that's causing your
body, the structure, you know, to slide by each other.
And I'm rubbing my hands right now, but you can't see it.
I'm rubbing my hands together and that's, you know,
that's causing shearing, you know.
Shearing action going on there too.
But, you know, the thing I think of here --
let's take an example.
Let's take a connection here.
So here I predrew a -- if you can imagine a bolted connection
with two plates here or -- one, two, three, plates here.
And then let's say I have some force.
We'll call that p here.
And if this whole thing is an equilibrium right here,
this connection, I know that each
of these forces here is going to be p over 2.
Okay, on this place right here.
And then if I isolate and cut right here.
If I were able to cut
and I isolated this one center plate right here,
I can see that I have this force p here.
And here for this to be an equilibrium I have this shear
stress acting along the area of the bolt --
the cross sectional area this bolt here.
And this would be p over 2.
These would be p over 2, and this would be p and equilibrium.
So this p over 2 is a shear stress acting
on the cross section or the surface of my bolt.
And if I were to look here --
if I look down at this bolt right here what I might see is I
would see -- if I look at the bolt right here.
If I can draw the bolts, bam, and let's --
and again, you know, I'm looking down at this bolt right here.
Right there.
And what I would see is that I have this p
over 2 acting on the top of it.
This p over 2 which, you know,
which induces essentially a stress,
a shear stress that's rubbing,
if you will, on top of this bolt.
Okay. The area of this bolt here.
And this right here this is --
this would be my shear stress we'll call this tau average.
This is my shear stress, and I have a diameter
of this bolt right here, okay?
Diameter of the bolt.
I'll call it db right here.
And if I want to calculate the average shear stress tau
average, I'm going to take the shear force
over on my bolt divide it by the cross sectional area
of the bolt right here which in this case,
would be p over 2 divided by the area of the bolt
which would be pi db squared over 4.
Okay. Right here tau average.
Now, this equation here represents the average
shear stress.
This is kind of a generic equation
for average shear stress
which is essentially is the shear force acting
on the surface divided by the area.
Okay. So we can take this as -- if I take the bolt part off.
If I take that off let's see.
And I erase that right there so this would be an equation
to calculate the average shear stress.
One thing you have to note is that this equation assumes
that the shear stress on the surface --
the shear stress is acting on top of the surface is uniform
which it is not, okay?
And this equation usually only works for simple connections
or bolts or small areas where you don't have a lot
of other things going on.
But really for -- and typically in direct shear cases.
And direct -- and this is an example of direct shear
which we'll get into some more in a little bit.
Okay. So now that we have a feel
for what the average shear stress, you know.
Let's talk about a simple connection,
some simple connections.
This right here, this connection here,
is called a double shear connection --
double shear, double shear.
And the reason it's called double shear is
because it has two planes of shear.
One -- I'll do it in green.
One -- oh, can you even see that?
No. Let's see, can you see that one plane
and two planes of shear here?
So that's called the double shear connection.
Okay. And the force that's applied here gets distributed
over this shear planes and, you know, by equilibrium each
of the shear forces acting over each area
of the bolt is p over 2.
The -- for single shear.
Let's call it single shear as you might be able to imagine.
Single shear is where you have two plates --
and let me draw that real fast.
Yeah, here, bam, bam, and then another.
Let's put another plate here like that,
and then right here, okay?
And so I have two plates here,
and a bolt going through that plate.
Let's put it right here.
Using my straight edge.
Having nice clean drawings.
Hopefully they're clean.
Okay. Right here, bam.
We'll make that a little bit longer for the bolt and nut.
Okay, bam.
All right.
And here -- so if I have this single shear right here
and I have this force p by equilibrium I know each
of these forces to transfer, you know, to transfer the force
in this plate or bar across to the other bar connected to it.
You know I have to -- it's all going
to be p. The normal force is going to be p in each.
And if I make a cut right here, if I make a cut let's see.
What did I use before?
I used red before.
So if I make a cut and isolate one of these plates
so that I have -- let's say I isolate the bottom plate
right here.
And bam like this.
I'll make a cut through the bolt.
I have here the bolt [inaudible] connection.
Let's say it's sticking out right here like this.
Here's the nut holding it in place.
And here is that surface right here of the bolt.
And I know that shear force acting across here is going
to be equal to p because of the equilibrium.
This is p right here.
And so here the average shear stress here tau equal
to v divided by A would be p divided by the area of the bolt,
the cross sectional area of the bolt here or tau average.
Okay. And this is a single shear because I have only one plane
of shear in this connection.
And I can do the same for glued surfaces.
If I had let's say two plates.
Let's see if I can draw this in 3D a little bit.
I'm going to kind of forego my eraser.
If I had this, let's see right here.
Hey, that's not bad.
Okay. Not bad.
Maybe all right.
Right here.
But if I had maybe glued on these two things together --
these two plates or wood pieces whatever.
If I glue it on I isolate just one.
Let's see can I isolate just one?
I need another page.
And isolate just one and I look at one right here.
So if I look at the bottom piece right here.
Okay, and I have, bam, bam, right here.
And let's say that I had a force p and the force p acting
on here then if this is my glued right here.
This is an area of the gluing right here.
And if I have my [inaudible] diagram just the bottom piece
right here I know that this has the shear force acting
over the glued surface is equal to p right here.
And then the average shear stress tau average
for this would also be v divided by area -- the glued area.
The area of the glue right here.
And this would just be v divided by a --
p divided by a because v equals p,
and that's how I would calculate the average shear stress.
[inaudible] how much glue area I need
to make sure I can carry this load if I have, you know,
the shear strength of the glue, okay?
And this is the basic idea behind bolted connections
and steel construction and something you might find
in ASME or AISC codes.
And the formulas are basically the same.
You know, there's this idea of tau average equal to v over a.
So there's some code modifications depending
on the surface or the materials that are used.
And other ways besides just [inaudible] in the bolt.
There's other ways that a connection can fail.
But we're not going to address that here.
What we want to get into next now is really just as we move
on here, you know, we've covered --
we've talked about shear stress.
We've talked about simple or single shear --
simple connections and single shear and double shear.
And now really, you know, we want to be able to differentiate
between direct and indirect shear.
Now, everything that we've done here --
if I go back up [inaudible].
Okay. If I go back up right here to this double shear
and single shear this is an example of direct shear, okay?
Direct shear because the applied load is causing the stress,
the shear stress directly, okay?
It's right here.
In terms of direct shear, let's see, direct shear.
Okay. So the applied load causes, you know, shear stress
by direct action or directly.
Let's see, you know, typically not all the time, but typically
that shearing surface --
that shearing surface is parallel to the applied load.
And the other examples might be like a hole puncher.
I'm sure all of you've have worked
with a paper hole puncher -- that's direct shear.
You know, that's the -- causing shear stress.
And the idea is the same behind punching holes
through metal plates, okay?
So you punch a hole through a metal plate, you know,
you got that's also direct shear.
There are some direct shear tests for wood
like wood specimen to measure transfer shear.
But anyway, I think the hole puncher,
the hole punching thing is more relevant to you.
Some examples of indirect shear it would be the shear stress
caused by axial loading, torsion, bending, okay.
Or bending right here.
So if I think of something -- let's see.
Like if I think of a traffic sign or a beam that's bending.
And a beam that's bending I'm going
to have shear forces develop.
You know, if I have a beam let's say here like this --
here and here like that.
And I apply a concentrated load here.
I'm going to have shear stresses developing throughout the beam.
You know, if I make a cut I'm going
to have [inaudible] shear forces and shear stresses
in between the layers of the beam,
and as well as in the vertical planes as well as.
And then if -- or if I think
of like maybe something more relevant
like a traffic sign that you look at.
So if I can draw a traffic sign looks
like this here is my traffic sign right here.
And I'll fix it here, and I have this bam, like this right here.
So I've got lots of things going on in a traffic sign.
I've got the weight of the sign pulling it down this way.
I've got the wind that's blowing into it
and causing this whole thing to twist,
and that always causes shear stresses
within the pole that's holding it, okay?
So I have lots of things going on here that can --
and also this load right here causes bending.
You know, causes a moment reaction here
that will also induce -- that also has shear stresses
that are going to develop within the beam
or the [inaudible] lever that's holding up the sign.
So that's -- these are indirect shear and then direct shear.
So hopefully this video was helpful in giving you, you know,
a little bit of introduction to shear stress
and calculating the average of shear stress.
We'll do some examples in the next video.
All right.
Talk to you later.