Understanding the Difference Between Bending Stress and Normal Stress in Beams

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Discussion Overview

The discussion centers around the distinction between bending stress and normal stress in beams, exploring the implications of these stresses on beam deformation. Participants examine the conditions under which bending occurs and the assumptions related to beam cross-sections during deformation.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • Some participants propose that bending stress can be considered a type of normal stress acting on the cross-sectional area of a beam, while others argue they are not the same due to their different effects on beam deformation.
  • It is suggested that normal stress causes elongation or shortening of the beam without bending, while bending stress involves a combination of tensile and compressive stresses that lead to curvature.
  • A participant questions the assumption that flat cross-sections remain flat after deformation, seeking clarification on how this is possible if the upper and lower parts of the beam experience different lengths.
  • Some participants acknowledge that shear deformation can occur, particularly in short beams, but emphasize that for long slender beams, normal bending is the dominant mode of deformation.

Areas of Agreement / Disagreement

Participants express disagreement regarding the interpretation of bending versus shear deformation, with no consensus reached on whether bending stress can be classified as normal stress.

Contextual Notes

The discussion highlights key assumptions about beam behavior under stress, particularly the condition of flat cross-sections during deformation, which remains unresolved.

chetzread
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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...
 

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chetzread said:

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.
 
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Chestermiller said:
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 said:
I agreed, but, it only means the beam is sheared , but not bent like U shape, right?
why you said that it's bent?
 
chetzread said:
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".
 
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Chestermiller said:
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)
 

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chetzread said:
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.
 
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