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

[chetzread]

Homework Statement

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

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

 

[Chestermiller]

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.

 

[chetzread]

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

 

[Chestermiller]

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.

 

[chetzread]

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 ?

 

[Chestermiller]

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?

 

[chetzread]

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...

 

[Chestermiller]

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??

 

[chetzread]

,,,,,,,,,,,

Both.

Yes. So??

so , in 3.10,
there's no stress concentraion at the middle , thus no shearing force ？

 

[Chestermiller]

,,,,,,,,,,,

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.