Beams braced with a welded flat steel plate 1

[BWally]

I have a pair of parallel beams that I'd like to brace with a flat steel plate (of at least 3/16" thickness) spanning between them. This plate would be continuously welded to the top flanges of the beams, and also to any cross-beams that might exist. This plate would also have angles welded beneath it to stiffen it for carrying live psf gravity loading. (For the purposes of this analysis, I'd like to ignore the contribution to beam bracing offered by the cross-beams and the angle stiffeners since there may be a situation in the future where these don't exist.)

So, I would like the plate to act as a beam brace and also be able to directly carry transverse loads itself.

I have researched the topic of "diaphragm-braced beams" by ordering and reading several papers published in the late 1960s to mid 1970s in the ASCE Journal of the Structural Division. The paper "Columns and Beams Braced by Diaphragms" by Errera, Pincus, and Fisher gives formulas for calculating the critical lateral-torsional buckling moment "Mcr" when diaphragm bracing is present. However, their equations are dependent on a quantity called "Q", the shear rigidity of the diaphragm, which is the product of diaphragm cross-sectional area "Ad" and effective shear modulus "Geff". The authors state that "Shear rigidity ["Q"] of diaphragms was determined experimentally because no general theory of diaphragm behavior was available. Such theory is necessary for the general application of the results of the investigation to practical design situations".

None of the other papers I reviewed presented a general theory of diaphragm behavior applicable to my welded flat steel plate.

Have any theories or data been published since then that I could use for my situation? The most helpful information would be values of "Q" to use in the equations presented by Errera, Pincus, and Fisher in "Columns and Beams Braced by Diaphragms". Also, is there any information on how the bracing capability of the diaphragm is diminished when it is loaded transversely?

 

[BWally]

jmiec,

The more I read your last post and think, the more I’m doubting my previous claim that the derivation by Errera et al is completely general. Perhaps it does apply only to corrugated light-gage metal deck, not to a solid flat plate. Their introductory sentence says this: “In many structures, shear-resistant light-gage metal diaphragms are connected directly to beams or columns of the steel framework, and may continuously brace these members along their length.” It’s hard to tell from their math. They use “energy methods”, starting with formulas for the ‘internal shear strain energy of a diaphragm’ and the ‘internal cross-bending strain energy of a diaphragm’, and then proceed to their solution from there.

Why doesn’t a flat steel plate behave the same way under shear as metal deck? Is it the corrugations, or the way it’s connected, or what?

The simple calculation of "Q" that you described apparently can’t be used for typical corrugated-type diaphragms connected intermittently with fasteners because of the difficulty in assessing the flexibilities of the components of the diaphragm assembly (sheet deformation, fastener slip, etc), according to another published paper I have here which describes basically the same calculation you suggested. That’s why “Q” has to be determined experimentally for these diaphragms. How can I be sure that this simple calculation applies in my case? For the cantilever length, why do you recommend using half the beam length?

Looking back at some of our old detail drawings here at work, I’ve noticed situations where we could not possibly have provided cross bracing at beam supports and were apparently forced to bolt the beam’s bottom (tension) flange to its supporting member (another beam), and count on this as a torsional brace. So in this kind of situation, the strength and stiffness requirements of Appendix 6 could be applied, or the “torsional stiffness = 20 x GJ/L” rule could be applied, right?

You’re correct—by transverse loads I meant out-of-plane loads.

 

[UcfSE]

There is an article in the November 1999 Journal of Structural Engineering by Helwig and Frank titled "Stiffness Requirements for Diaphragm Bracing of Beams". You may find it here at the ASCE website available for purchase.

I think there is a reason there is not much information on this in the building codes or steel codes: it has not been adequately researched. In the above referenced paper, the authors provide a statement: "Strength requirements for diaphragm bracing are still under investigation".

I think you should design your plate as you would a roof or floor diaphragm and anchor it independent of the beams like you would a roof to a shear wall and provide a load path for the brace force. Then the plate will have someplace for the bracing force to go without trying to send it back into the same beams it is trying to support. That may well be overkill, but at least you won't be using unproven equations in a real-world situation. That or switch your cross section to something not suceptable to LTB, like a standard tube, or just design an I-section that will work for your case.

 

[miecz]

BWally-

It sounds as though the solution presented by Errera is specific to metal decks. As I said in an earlier post, it can't be applied to your case. I believe it's both the corrugations and the intermittant puddle welds that result in the difference. I'm not sure how much each contributes.

If the derivation I suggesed has been published in a reputable engineering journal, then I think it applies to your case. After all, the codes only say to provide bracing with enough stiffness. They don't say how to provide that bracing. Lateral bracing is provided in many different ways; struts, cantilever beams (see the pony truss solution), metal deck...In fact, most lateral bracing has been designed using a 2 percent rule that doesn't even check the stiffness.

Half the beam length: If you loaded your beam with a lateral load (or axial load) and provided lateral support by use of metal deck, the maximum deflection would be at the mid point. That's the stiffness you're trying to provide.

Appendix 6: I don't have Appendix 6 here (at home), so I can't say for sure, but I don't think the torsional stiffness rule applies at the support.

The more I think about it, the more I wonder why you couldn't consider your beams and plate to be a single built up section with no lateral bracing, but a large ry.