Average Shear Stress and Simple Connections – Mechanics of Materials

>>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.

34 thoughts on “Average Shear Stress and Simple Connections – Mechanics of Materials

  1. sorry i have a question at 11:35, you mentioned that for direct shear the shearing surface is parallel to the applied load but the hole puncher example you gave is not coherent to what you mentioned.

    Nonetheless good vid! Thanks!

  2. in the hole puncher example, the shearing surface is the cross section of the paper. I tried to make a diagram, but youtube refused. sorry if the failed attempts spam your inbox.

  3. Good video, even though I wish you would have done an example of double shear.  Thank you so much, didn't have to rely solely on my PoS textbook. 

  4. very good!!! And can you tell me which software you use to tech us? Is it the office microword or other Drawing software?

  5. How can a hole puncher give sheer stress? The force is perpendicular to the surface, it must give a normal stress. :L

  6. at 11.17 you said it's direct shear while on explaining from were the law of Tao is used you said it's only for indirect shear, or did I misheard?

  7. Sir i want to thank you from the bottom of my heart. Your Dynamics vids helped me a lot and it's the same with your Solid MECH.

  8. I would just like to ask about the double shearing stress, the formula they gave me was tao=V/2A. I would really like some clarifications with that. I love your vids, btw.

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