How is a cantilever beam loaded at the end in uniaxial stress?

[Altairs]

When the term uniaxial comes I imagine something being pulled or pushed in one direction only. Confusion is that I read online http://enpub.fulton.asu.edu/imtl/HTML/Manuals/MC105_Cantilever_Flexure.htm" that a cantilever beam loaded at the end is also in uniaxial stress. This is what I can not understand. How? The point at the end where it is being loaded is free and the cantilever will bend so how can it be in uniaxial stress ?

Please explain (not in terms of principal stresses as it is even more confusing :-( )

thx.

 

[Q_Goest]

Hi Altairs,

When the term uniaxial comes I imagine something being pulled or pushed in one direction only.
...
Please explain (not in terms of principal stresses as it is even more confusing :-( )

thx.

Not in terms of principal stress? hmmm... that makes it a bit more difficult. I think you'll need to understand what a principal stress is, but for the example under consideration (cantilevered beam) it might be easier to ignore that for a moment.

For the beam, let's consider the typical x,y,z directions (x is left/right, y is up/down, z is into/out of the plane).

The statement is:

Another characteristic of the cantilever beam used in this experiment is that the stress is uniaxial everywhere on the [top and bottom] beam surface except in the immediate vicinity of the loading point and the clamped end.

I added the "top and bottom" because that's what they mean when they talk about the beam surface. They're not talking about the side surfaces which are subject to both normal stresses in the x direction plus shear stresses. These other locations result in stresses in more than 1 direction (not uniaxial). But for the top and bottom surface of the beam, there are no shear stresses (on an infintesimal element). The stresses on the top and bottom are all in the x direction. There are no stresses in the y or z direction and there are no shear stresses on the surface. Note however that there are shear stresses where the beam meets the wall which is mentioned in the statement on that link you gave.

I think that might also help define what a http://vacaero.com/Glossary-P.html" is:

Principal stress (normal)
The maximum or minimum value of the normal stress at a point in a plane considered with respect to all possible orientations of the considered plane. On such principal planes the shear stress is zero. There are three principal stresses on three mutually perpendicular planes. The state of stress at a point may be (1) uniaxial, a state of stress in which two of the three principal stresses are zero, (2) biaxial, a state of stress in which only one of the three principal stresses is zero, and (3) triaxial, a state of stress in which none of the principal stresses is zero. Multiaxial stress refers to either biaxial or triaxial stress.

Then the http://vacaero.com/Glossary-U.html" can be defined as:

Uniaxial stress
A state of stress in which two of the three principal stresses are zero.

 

[Altairs]

Hi Altairs,

Not in terms of principal stress? hmmm... that makes it a bit more difficult. I think you'll need to understand what a principal stress is, but for the example under consideration (cantilevered beam) it might be easier to ignore that for a moment.

For the beam, let's consider the typical x,y,z directions (x is left/right, y is up/down, z is into/out of the plane).

The statement is:

I added the "top and bottom" because that's what they mean when they talk about the beam surface. They're not talking about the side surfaces which are subject to both normal stresses in the x direction plus shear stresses. These other locations result in stresses in more than 1 direction (not uniaxial). But for the top and bottom surface of the beam, there are no shear stresses (on an infintesimal element). The stresses on the top and bottom are all in the x direction. There are no stresses in the y or z direction and there are no shear stresses on the surface. Note however that there are shear stresses where the beam meets the wall which is mentioned in the statement on that link you gave.

I think that might also help define what a http://vacaero.com/Glossary-P.html" is:

Then the http://vacaero.com/Glossary-U.html" can be defined as:

Got it.

Thx a lot. *thumbs up*