What is Shear? Understanding Pure Shear

[lavster]

what is shear? from looking at books etc i understood that the shear of a direction was the change of angle. but then pure shear doesn't have a change in angle between the axes, its just stretched in one direction and contracted in the other. so why is this called pure shear? I am rather cofused...

thanks

 

[Mapes]

Can you point out an example online? What you're describing sounds like pure tension or compression. Pure shear does indeed always involve a change in angle.

 

[tiny-tim]

Hi lavster!

Shear is is when parallel layers slide past each other.

For example, a pile of papers, or a pack of cards, with rectangular cross-section, can be pushed so as to have a parallelogram cross-section …

in that sense, the angle between the sides has changed, but all that has actually happened is some parallel sliding.

See also http://en.wikipedia.org/wiki/Shearing_(physics)"

 

[Mapes]

Hi lavster!

Shear is is when parallel layers slide past each other.

For example, a pile of papers, or a pack of cards, with rectangular cross-section, can be pushed so as to have a parallelogram cross-section …

in that sense, the angle between the sides has changed, but all that has actually happened is some parallel sliding.

Well, actually, this is shear flow. I had assumed the question was about solid mechanics, but I could be wrong.

 

[Andy Resnick]

Are you referring to, for example, this:

http://www-odp.tamu.edu/publications/193_IR/chap_02/images/02_f12.gif

Shear can be a little tricky, because 'simple shear' also has a rotation.

 

[Studiot]

Shear is really an adjective not a noun and should not be used on its own.

This is because it can be applied to different nouns (physical quantities) to mean different things.

If you think of a force applied to a body you probably know we can resolve this force into two components at right angles to each other. I have shown this in the sketch.

We call the force at right angles to the body surface the normal force and the force parallel to the surface the shear force.

Note that there need be no movement (ie the body is rigid).

If the body distorts as a result of this force, as in the second sketch, the angle gives the shear strain as has been noted.

So shear refers to something in some sense parallel to something else, usually as distinguished from something perpendicular or normal.

 

[Mapes]

Are you referring to, for example, this:

http://www-odp.tamu.edu/publications/193_IR/chap_02/images/02_f12.gif

Shear can be a little tricky, because 'simple shear' also has a rotation.

Ugh, that diagram is missing a pair of forces that apply tension horizontally. Pure shear can't be transformed into a single compressive or tensile load. http://www.codecogs.com/users/13108/img__ss6_0004.jpg" is complete.

But also, I should have been more precise earlier. A shear strain $\gamma_{xy}$ always involves a change in angle between lines drawn along the original x and y axes. Other pairs of lines (specifically, ones drawn in the directions $\bm{\hat{i}}\pm\bm{\hat{j}}$) will not feature a change in angle.

 

[lavster]

hi, thanks for all your help! I am def understanding the concept better now!

however

For example, a pile of papers, or a pack of cards, with rectangular cross-section, can be pushed so as to have a parallelogram cross-section …

If the body distorts as a result of this force, as in the second sketch, the angle gives the shear strain as has been noted.

are these not example of simple shears (of something)?

Are you referring to, for example, this:

http://www-odp.tamu.edu/publications/193_IR/chap_02/images/02_f12.gif

Shear can be a little tricky, because 'simple shear' also has a rotation.

yes, this is the kind of diagram i was looking at :)


This is what i was reading:

NB i don't no how to write the symbol for tensor product so I've just used X

homogeneous pure shear is defined by e.g. $$F=\lambda U_1 X U_1+\lambda^{-1} U_2 X U_2 + U_3 X U_3$$ where $$\lambda$$ is the principal stretches

 

[Andy Resnick]

Ugh, that diagram is missing a pair of forces that apply tension horizontally. <snip>

Yeah... it was just the first pic that came up.

 

[tiny-tim]

Hi lavster!

Looking at your question again, and at Andy Resnick's diagram …

… from looking at books … pure shear doesn't have a change in angle between the axes, its just stretched in one direction and contracted in the other. so why is this called pure shear?

Are you referring to, for example, this:

http://www-odp.tamu.edu/publications/193_IR/chap_02/images/02_f12.gif

… you're obviously describing the "pure shear" in the diagram.

I have never seen this usage before.

(though I see from http://en.wikipedia.org/wiki/Shear_(geology)" it appears to be standard in geology)

I'm not challenging its correctness, but I have to agree with you that it is confusing, and inconsistent with the usual meaning of shear (as an adjective), to describe "sideways" force and movement, as Studiot says …

Shear is really an adjective not a noun and should not be used on its own.

This is because it can be applied to different nouns (physical quantities) to mean different things.
…
We call the force at right angles to the body surface the normal force and the force parallel to the surface the shear force.
…
If the body distorts as a result of this force, as in the second sketch, the angle gives the shear strain as has been noted.

If you're studying geology, or if your professor tells you to use the terms "pure shear" and "simple shear", then of course you must do so.

But if you're just coming across this in books, my recommendation would be to understand it, but not to copy it … for simple shear, just use "shear" on its own, and for pure shear, as Mapes says …

… What you're describing sounds like pure tension or compression.

so, instead, use "tension and compression in perpendicular directions" (presumably of equal amounts, to keep the density constant).

 

[Studiot]

I am sorry my offering was rather scrappy, last night but it was half past my midnight so I rather dashed it off.

Anyway it is probably worth looking at a few more examples.
Don’t forget shear force may act vertically as well as horizontally, or indeed in any direction.

It is perfectly possible for shear force to be exerted without any shear displacement or shear rotation. Structural Engineers commonly meet this situation as in my sketch 1.

Here I have shown a cantilever loaded with some load W. It is embedded in a concrete wall and supported by a reaction R in the wall. The cantilever is subject to breaking or snapping at the face of the wall because of the shear force, V, existing across the section at the wall.
If we consider vertical equilibrium we can see that the load W is balanced by the reaction R. Vertical equilibrium also tells us that the internal shear force V at the wall equals either the load W in the right hand section or the reaction, R in the left.
It is this force that causes the fracture or break of the cantilever.
Because the support at such a situation is considered rigid there is no displacement or rotation until fracture.
It should be noted that there are other forces/moments also acting that I have not considered here.

A good example of significant shear displacement appears in sketch 2, which shows a simple fault as familiar to geologists. This fault presumably occurred when the support of the right hand section of rock subsided for some reason.

Meteorologists also say just shear when they mean shear displacement as sketch 3 shows. Here the top of a cloud is being pushed over by a high altitude wind.

Finally shear may present as a traveling wave, rather than being static, as happens in earthquakes and seismological testing. Geologists distinguish two types of waves S-waves or shear waves and P-waves or pressure waves. The correspond to transverse (S-waves ) and longitudinal (P-waves) types of wave, as shown in sketch 4.
This example emphasises the nature of two orthogonal effects.