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?

 

[Stillerz]

Does this post get the blue ribbon for Eng-Tips' all time longest forum discussion?

 

[trainguy]

dhengr,

Would like to correspond, but I'm not sure how while maintaining some degree of anonimity(sp?) in this very public space. FYI, I work in engineering consulting, clients being primarily Eastern Canadian rail vehicle re-work shops, the passenger rail authority, and some vehicle OEM's on occasion.

tg

 

[cntw1953]

Stillerz:

Final effort to answer your OP question.

wrt Plane Stresses from Strength of Material - there are two types of stresses acting on a plane element taken out from a beam, namely "Normal Stress & Shear Stress". The former came from Mc/I, that result in compressive or tensile stresses acting normal to the sides of the plane element; the latter came from VQ/I, the result is shear stresses acting on the sides of the plane element.

I think it is simpler to treat the shear stress as glue, or bond, necessitated for things stay together as a whole, otherwise the adjacant pieces could slide freely if no friction in between. On the other hand, the normal stress pushes things together, or pulls things apart, quite different phenomenon, isn't it?

 

[Stillerz]

Indeed they are quite different, however, one cannot exist without the other in statical equilibrium.

 

[cntw1953]

Yes, they do coexist while minding their's own business.

 

[Stillerz]

I'd like to crawl inside a stressed out beam web and see what the hell is really going on in there.
I'd probably have to push Timoshenko out of the way.

 

[dhengr]

cntw1953:

You beat me to it! I was hoping someone would look in a strength of materials text and scan that page or two. Surprise, surprise, my texts say exactly the same thing, although the ones by Timoshenko are called theory of elasticity texts, talk about stress at a point, and have a lot more ??’s and dx/dy’s in them than I like to deal with in my old age. Seems we agree again, I certainly couldn’t have said it any better, although I am sure it would have taken me far more verbiage, my hat’s off to you. Except, your 14:27 post, I might have worded it: yes they do coexist.... now mind your own business and get the hell back to work, or I’m gona tell your boss your playing with his expensive computer. I think we are all getting pretty stressed out, beam web or not and who ever’s in there, on this one. Let’s give Stillerz the award for longest thread, would you please second that, so we can all get back to work. And, so the world wide supply of shear flow will come back to normal, because this thread and that supply can not coexist in a state of “statical equilibrium.”

 

[cntw1953]

dhengr:

I concur. I am running short on supply as well. Wish Santa bring some with him this time around. Cheers!

 

[BAretired]

Shear flow is illustrated in this page from "Elements of Strength of Materials" by Timoshenko and McCullough.

In this example, the shear flows horizontally along the top flange, then down the web and finally horizontally to the tip of the bottom flange.

The value of shear flow varies from one point in the cross section to another. Shear flow in the web carries the shear V. Shear flow in the flanges creates a pair of equal and opposite horizontal forces which create a moment. The shear center of the channel may be determined by finding the point where the moment is zero.

Except for csd72, this point appears to have been missed by contributors to this thread.

BA

 

[cntw1953]

Hope the attached sketch makes the cut.

 

[BAretired]

cntw1953,

If you are illustrating flexural and shearing stress, f = Mc/I is a stress but VQ/I is not. The shear stress in your sketch is VQ/Ib where b is the width of the rectangular beam.

BA

 

[cntw1953]

Yes, I should have b under the denominator. Thanks.

Isn't this shar stress a part of the shear flow? I think Timoshenko's book has similar illustration shown in the chapter dealing with shear.

 

[Stillerz]

I think maybe there should be a new forum for "Shear Stress/Flow Engineering" and universities should work on new ABET accredited curriculums for Shear Engineers.

 

[cntw1953]

Stillerz:

Make a book on this thread, it could be the best seller of the year, and you can sell to whoever has shortage of it, such as dhengr Cheers.

 

[tigermoth]

In the interests of making this thread even longer: If a simply supported beam experiences zero shear load (ie constant moment) over say the central 50% of its span, is there any need for connection between the web and flanges in this region (apart from the need to avoid buckling of the compression flange)? Is there any need for a web at all in this part of the span if the compression flange is stable?

 

[cntw1953]

Then you have seperated parts rather than an unit beam, that affects moment of inertia.

For the 2nd question, try to bend two chopsticks with space in between, then you will see what is missing.

 

[rowingengineer]

tigermoth,
Cntw has this covered, but if you want to see what is the least amount of web you can get away with I recommend you look at castellated beam design.

Arguing with an engineer is like wrestling with a pig in mud. After a while you realize that they like it

 

[tigermoth]

Thanks for your replies. I wouldn't seriously consider removing the mid-span web in this way; it was more of a thought experiment. If we assume a beam or length L simply supported at each end, with point loads at say .25L in from each end, what function is the web actually performing doing in the central 50% of the span? It can't be resisting shear load because there is none. It will be resisting a small bending moment (but not much compared with the flanges). If there were air gaps between web and flanges over the central 0.5L only, would those gaps tend to close as load is applied? I would imagine they would, perhaps due to the web being stiffer in bending than the flanges (like a ruler on edge vs chopsticks). If so, there must in a 'normal' beam (with no gap between flanges and web) be a vertical load transfer between flanges and web: hence a need for welds. Not sure how I would quantify this by manual calculation.

 

[KootK]

Tigermoth,

For what it's worth, I think that your assessment is bang on. For the highly idealized thought experiment that you proposed, there would be no need for web/flange welds nor for the web plate itself.

In residential wood floor trusses, often the diagonal web of a panel near the middle of the truss will be omitted to create a mechanical chase. This is justified in a similar fashion. I'm not sure that I agree with it (assumed loading vs. real loading) but it is done, without incident at far as I know. I imagine that the trusses are probably saved by some minimal vierendeel truss action across the
affected panel.

KK

 

[BAretired]

In the tigermoth example, the web carries no shear in the middle half of the span, but it adds stability to the structure.

The tension flange could be replaced by a cable in the middle half. The compression flange could be replaced by a compression strut. If the connections are hinged at the quarter points, the structure has four hinges and is unstable, so a diagonal brace is needed for stability.

BA