Shear Flow 15

[Stillerz]

I am sure most here are familiar with the concept of shear flow as it related to horizontal shear stresses in beams.
When designing a I-Shaped plate girder, most references, if not all, will design the weld between the flange and web using the shear formula VQ/I to determine the force on the welds.
My question is, isn't there bending stress on the weld as well in the form of MC/I?
If one had a simply support girder with a uniformly distributed load, the shear at the center of the beam would be = zero and the moment at a maximum. This would imply that no weld would be needed at the center, yet this is the section where having the entire cross-section engaged in bending is most critical.
What am I missing here?

 

[BAretired]

shin25,

Your statement of total horizontal shear between a support and midspan is true if and only if the moment at the support is zero. If the support moment is not zero, it is not true. Moreover, if the beam is subjected to constant moment throughout its length, the horizontal shear at every section from end to end of the beam is zero.

That is easily verified, because at every point along the span, V = 0. Therefore, VQ/I = 0.


BA

 

[BAretired]

Compositepro,

What is the point? The only point, so far as I can see is to determine how much weld is required. If there is horizontal shear to resist, the weld must be capable of resisting it. If the weld is only for the purpose of holding the web and flange together, then a stitch weld may be sufficient.

In the case of a simple span with symmetrical cantilever each end, when the cantilevers are identically loaded and the span is unloaded, the span has a constant moment and zero shear. The welds between web and flange in the span carry no horizontal shear but they are required to hold the pieces together...a nominal weld should be adequate.

BA

 

[apsix]

Which leads us back nicely to my problem of last week.

- Members in pure bending will have shortening of the compression face and lengthening of the tension face.
- This will occur in your example above, at the flange/web interface, unless there is a (shear) connector forcing the elements to act compositely, ie. both elements will have the same tension or compression at the interface.
- The force this connection is resisting could be called horizontal shear and will occur wherever there is curvature, as I see it.
- I understand that my argument isn't compatible with the horizontal shear = VQ/I version.

Feel free to point out my mistake.

 

[ishvaaag]

No. For a segment with the shape of a part of a ring, the longitudinal forces along the tangent are compression (or tension for the tensile face), where the circumferential faces sustain in any case normal forces to them. For these, at the limit, faces, you have a triaxial state of tensions where the stresses are principal. The need of the welds doesn't come from any variation along the fiber of tangential (along the shape of the curved beam) longitudinal stresses, where in the varying moment, yes, because the difference in resultant for a cut rectangular segment in that case exacts that equilibrium be restored by a shear force in the cut along the paralell to the beam's axis.

However the tensions perpendicular to the axis of the beam at the compression side are tensile, and if you do not show physical opposition to the tensile force there provided by a weld, the flange may buckle away from the interface web-flange.

 

[DaveAtkins]

Can we all agree that the welds which connect a web to a flange (in a bending member with shear) are designed for VQ/I, and nothing else? The weld does experience some longitudinal stress due to bending, and does prevent buckling of parts which are in compression, but is only designed for VQ/I.

DaveAtkins

 

[cntw1953]

I didn't read through the entire discussion, my thoughts below might cross someone's before.

Shear flow is consistent with "flexural displacements between segments within a section". If two or more segments stacked together without bond, under load, which produces vertical shear, the segments deflect and the relative displacement is greatest at the end, zero in the middle. THe horizontal shear is therefore required to prevent the relative displacements with magnitude varying from maximum at the ends, zero in the middle.

Make sense?

 

[paddingtongreen]

DaveAtkins, I agree, except sometimes it is governed by the vertical force transfer from flange to web, typically from a point load on the flange.

Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[Lion06]

BA-
It is true that there are principal shear stresses even at locations where there is only bending stress, but those stresses are on a plane that is 45 degrees from the horizontal, right? These wouldn't be considered in a weld design.

 

[BAretired]

apsix said:

- The force this connection is resisting could be called horizontal shear and will occur wherever there is curvature, as I see it.

Not true! In the case of a simple span of length L with cantilever of length 'a' each end, if load P is placed at the end of each cantilever, M = P*a at each support. The same moment occurs throughout the span L. Each support carries a vertical reaction of P.

Weld is required between flange and web throughout the length of each cantilever to resist horizontal shear and develop the combined section. Weld is not required in the span because every fiber of the beam has been strained to P*a*c/EI immediately outside each support, where 'c' is the distance from the neutral axis to the fiber.

If the beam was actually built without weld in the span, it would fail, but not because of horizontal shear. Compression elements would buckle because they lacked lateral support, so a nominal weld is required across the span just to hold everything together.

Curvature in the cantilevers varies from 0 at the ends to P*a/EI at the supports. Curvature throughout the span is P*a/EI with no help from the welds.

BA

 

[BAretired]

StructuralEIT,

Yes, I agree.

BA

 

[hemis]

Dave Atkins

I am not sure that horizontal shear should not be considered in addition to vertical shear at the flange weld. I design ply web-beams and I would certainly check the glue line for a combination of both. I think in the Eurocodes, a test for a combination of both stresses would have to tried.

 

[Lion06]

hemis-

The horizontal shear is a result of the vertical shear? That's like saying you should check for the moment and the normal stresses associated with that same moment. Am I missing something?

I've never seen any standard spec, code provision, or textbook advocate doing that.

Can you describe the beams you're referencing and exactly what you're checking for?

 

[Stillerz]

E.I.T.-

Horizontal shear stress are the direct result of applied vertical shear forces, no?

 

[Lion06]

Yes, I don't know why I have a question mark. That should be a period. I was making a statement and following it up with an example.

 

[Stillerz]

i see...makes more sense....i started this post and even i am sick of it!!!!!

 

[JAE]

I looked but couldn't find the "beating a dead horse" gif icon.

 

[JAE]

But there were a lot of good posts here...don't get me wrong.

 

[hemis]

StructuralEIT

In timber, bending and shear stresses are considered together - its the nature of the materials. Maybe not necessary in steel unless you castellate the beam - maybe. Check out shear deflection.

 

[IJR]

stillerz

I had the same problem when I started learning. Until I saw a heavy riveted steel girder, the kind you find in old bridges.

Have a look at that, some time.

By the way, JAE,StructuralEIT,BAretired, ishvaag and all, thanks for the great posts

respects
IJR

 

[Stillerz]

I guess I never really had a problem with the concept of horizontal shear...that was basic stuff from mechanics of materials. I just had a hard time justifying ignoring the bending stresses in the weld design.
After this exhuastive chat, it's pretty clear to me now.