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

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SUMMARY

The discussion centers on the concept of pure bending in beams, specifically addressing the absence of shear force and its implications on stress concentration. Participants clarify that in the context of pure bending, as illustrated in Figure 3.11, the bending moment remains constant while stress concentration occurs at any changes in cross-sectional area. The confusion arises from the interpretation of figures 3.10 and 3.11, where it is established that both figures depict scenarios without shear force, yet only figure 3.11 shows a change in cross-section that leads to stress concentration.

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  • Familiarity with stress concentration concepts
  • Knowledge of bending moment diagrams
  • Ability to interpret engineering diagrams (e.g., Figures 3.10 and 3.11)
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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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