Understanding the Difference Between Bending Stress and Normal Stress in Beams

[chetzread]

Homework Statement

https://en.wikipedia.org/wiki/Bending
[/B]
form the link, we know that σ represent the bending stress, I'm wondering can I call the bending stress as normal stress act at the cross sectional area of beam?

Homework Equations

The Attempt at a Solution

IMO, they are not the same...Because the normal stress act on the cross sectional of beam will only cause the beam to elongate or shorten, it will not cause it to bend , so they are not the same...

 

[Chestermiller]

Homework Statement

https://en.wikipedia.org/wiki/Bending
[/B]
form the link, we know that σ represent the bending stress, I'm wondering can I call the bending stress as normal stress act at the cross sectional area of beam?

Homework Equations

The Attempt at a Solution

IMO, they are not the same...Because the normal stress act on the cross sectional of beam will only cause the beam to elongate or shorten, it will not cause it to bend , so they are not the same...

If there is tensile stress perpendicular to the beam cross sections in the upper half of the beam, and compressive stress in the bottom half of the beam, the upper half of the beam will get longer and the bottom half of the beam will get shorter. This geometrically means that the beam is bent.

 

[chetzread]

If there is tensile stress perpendicular to the beam cross sections in the upper half of the beam, and compressive stress in the bottom half of the beam, the upper half of the beam will get longer and the bottom half of the beam will get shorter. This geometrically means that the beam is bent.

I agreed, but, it only means the beam is sheared , but not bent like U shape, right?

 

[chetzread]

I agreed, but, it only means the beam is sheared , but not bent like U shape, right?

why you said that it's bent?

 

[Chestermiller]

why you said that it's bent?

The key assumption involved here is the flat cross sections of the beam remain flat after the deformation has occurred. Can you tell me how the cross sections can remain flat while the upper part of the beam gets longer and the bottom part of the beam gets shorter without the beam developing curvature (i.e., bending)?

Your reference fails to mention this key assumption (that is actually observed in practice). Therefore, I can see the source of your confusion regarding the deformation being shear. "Shear bending" does actually occur in very short beams, but in long slender beams, the dominant mode of deformation is "normal bending".

 

[chetzread]

The key assumption involved here is the flat cross sections of the beam remain flat after the deformation has occurred. Can you tell me how the cross sections can remain flat while the upper part of the beam gets longer and the bottom part of the beam gets shorter without the beam developing curvature (i.e., bending)?

initially, i was thinking that the author mean this, so the object is sheared , but not bent (figure above)
But, it should look like this,right? (figure below)

 

[Chestermiller]

initially, i was thinking that the author mean this, so the object is sheared , but not bent (figure above)
But, it should look like this,right? (figure below)

Yes.