>>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.

very good! Thank you

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!

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.

Your drawings are beautiful lol, thanks mate!

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.

awesome video mate.. great explanation….

it finally makes sense !

thanks a lot, my official mechanics of machines channel

Very clear and informative, gonna help me for my engineering course! Thank you.

amazing courses… thanks.

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

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

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?

you are amazing! keep it up

man, after waching your video, I question myself; Do I even need to go to lecture? You are swesome

awesome

thank you for the video

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.

this fantastic. .extraordinary

thank you

can you please help me?

which book should i follow

Hiblers or bear & Johnson

Thank you so much..You are a great teacher

very very helpful tyvm

Taking Strength Of Materials online, which means that you are my teacher.

god bless your soul

the best teacher ever

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.

What does B/N mean? "Between"?

Thank you for amazing explanation.

do you help with suggesting solutions for real life engineering problems?

Just to be sure, Is the axial stress the same as the normal stress?

please can you turn up the sound ? I can barely hear you

That was Helpful.

Thanks a lot