Pure Bending: Understanding the Effects of Shear Force on Beam Behavior

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Discussion Overview

The discussion revolves around the effects of shear force on beam behavior during pure bending, specifically examining the conditions under which shear forces are present or absent in relation to stress concentrations and cross-sectional changes in beams as depicted in figures from a textbook.

Discussion Character

  • Homework-related
  • Debate/contested
  • Technical explanation

Main Points Raised

  • Some participants assert that during pure bending, there is no shear force acting on the beam.
  • One participant notes that the bending moment is constant in the section experiencing pure bending, but questions the presence of stress concentrations due to a change in cross section.
  • There is a contention regarding whether there is a change in cross-sectional area in the figures referenced, with some participants claiming it is constant while others argue that it does change.
  • Participants discuss the implications of stress concentrations at changes in cross section and whether this affects the breaking point of the beam.
  • Some participants express confusion over which figures represent pure bending and the conditions under which shear forces are zero.
  • There is a repeated assertion that the absence of shear force does not directly cause stress concentrations, leading to further debate on the relationship between shear force and stress distribution.

Areas of Agreement / Disagreement

Participants do not reach consensus on the presence of cross-sectional changes in the figures, nor on the implications of shear force absence for stress concentrations. The discussion remains unresolved with multiple competing views on these topics.

Contextual Notes

Participants reference specific figures (3.10 and 3.11) from their notes, which may contain assumptions or definitions that are not fully articulated in the discussion. The relationship between shear force and stress concentration is also not clearly defined, leading to ambiguity in the arguments presented.

chetzread
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Homework Statement


in the notes , i was told that when pure bending occur, there is no shear force acting...
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Homework Equations

The Attempt at a Solution


refer to diagram 3.11 , does it mean the center of beam (between 2 forces P) will break? since there's no shear force acting
 
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Fig. 11 shows the portion of the beam experiencing pure bending. This is the portion of the beam where there is no (internal) shear force. The bending moment M throughout this section of the beam is constant. However, because there is a change in cross section in the middle, there will be a stress concentration in close proximity of the location where the cross section changes. Most of the section to the right of the change will have a stress distribution independent of distance along the beam, and most of the section to the left of the change will have a stress distribution independent of distance along the beam. Only in the region very close to the change will the stress distribution change as a result of the cross section change. The equation they give is supposed to approximate the tensile stress distribution over the cross section where the change has occurred. I assume this is the distribution over the smaller cross section.
 
Chestermiller said:
Fig. 11 shows the portion of the beam experiencing pure bending. This is the portion of the beam where there is no (internal) shear force. The bending moment M throughout this section of the beam is constant. However, because there is a change in cross section in the middle, there will be a stress concentration in close proximity of the location where the cross section changes. Most of the section to the right of the change will have a stress distribution independent of distance along the beam, and most of the section to the left of the change will have a stress distribution independent of distance along the beam. Only in the region very close to the change will the stress distribution change as a result of the cross section change. The equation they give is supposed to approximate the tensile stress distribution over the cross section where the change has occurred. I assume this is the distribution over the smaller cross section.
why there's a cross sectional area change in the middle ? i didnt see it . I just noticed that the cross sectional area is constant throughout the beam ...

and is it true that the center of beam (between 2 forces P) will break? since there's no shear force acting
 
chetzread said:
why there's a cross sectional area change in the middle ? i didnt see it . I just noticed that the cross sectional area is constant throughout the beam ...
You're saying you didn't notice a cross sectional area change in Fig. 3.11?
and is it true that the center of beam (between 2 forces P) will break? since there's no shear force acting
It has nothing to do with no shear force acting there. I has to do with the stress concentration at the change in cross sectional area.
 
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Chestermiller said:
You're saying you didn't notice a cross sectional area change in Fig. 3.11?

It has nothing to do with no shear force acting there. I has to do with the stress concentration at the change in cross sectional area.
yes , is there any cross sectional area change ? it's a straight beam , am i right ?
 
chetzread said:
yes , is there any cross sectional area change ? it's a straight beam , am i right ?
Are we looking at the same figure? I'm looking at Fig. 3.11. Do you not see a cross section change in the figure?
 
Chestermiller said:
Are we looking at the same figure? I'm looking at Fig. 3.11. Do you not see a cross section change in the figure?
which is pure bending??.3.11 or 3.10 ?
the cross section area in 3.1 isn't change , while the 3.11 change...
 
chetzread said:
which is pure bending??.3.11 or 3.10 ?
Both.
the cross section area in 3.1 isn't change , while the 3.11 change...
Yes. So??
 
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Chestermiller said:
Both.

Yes. So??
so , in 3.10,
there's no stress concentraion at the middle , thus no shearing force ？
 
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chetzread said:
,,,,,,,,,,,

so , in 3.10,
there's no stress concentraion at the middle , thus no shearing force ？
Why do you persist in saying that a shear force is the cause of the stress concentration? It is not. In the center of the beam in both Fig. 3.10 and 3.11, there is no shearing force. In Fig. 3.11, there is no shearing force throughout the entire length of the beam. In Fig. 3.10, the shearing force is zero throughout the section that is inboard of the two loads P.
 

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