Warping constant (Cw) of cellular beams

[StaVis]

I am quite unfamiliar with cellular beams and I am looking for a way in which to calculate the warping torsion constant Cw.

I am aware that for symmetrical I and H sections the following formula can be applied:

Cw = (Iy.h^2)/4

Can this be adapted to accommodate the cross section of a cellular beam?

 

[BAretired]

Cw = 0.0 for Hollow Structural Sections.

BA

 

[JoshPlumSE]

I'm not sure that I agree with BA retired. I recall doing some relatively complex torsion calculations back in college for an aerospace course.... Which is the only time I've worked on members with a multi-celled cross section. That is the type of member that you're getting at, right StaVis?

I'm fairly confident that BAretired is correct for all standard pipes and tube that AISC uses. But, I'm just not sure about the odd mult-celled cross sections that you get in other fields.

 

[BAretired]

Can you provide a cross section of the shape you are using?

BA

 

[StaVis]

Thanks, I appreciate the feedback, but perhaps I posed my question ambiguously. To rephrase: I am considering a standard steel I beam with voids in its web. Please see the attachment for an example.

I'm looking for a method to calculate this constant without the use of software if possible.

Any suggestions regarding useful literature would be much appreciated as well.

 

[ToadJones]

BA-
I believe a "cellular" beam is the same as a castellated beam

 

[ToadJones]

Blodgett section 4.7 covers open web beams....not sure about Cw however.

 

[paddingtongreen]

Strange, they are/were called castellated in the UK and here. I haven't heard them called cellular, before, I thought of cellular deck and assumed similarity.

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

 

[ToadJones]

Pad-
The only difference I can think between Castellated and Cellular is Castellated are cut and welded from one beam where Cellular maybe simply a beam with holes cut in the web with no welding as seen in a Castellated beam.....just guessing here.

 

[BAretired]

I misinterpreted the meaning of cellular beam. Cw for a regular WF (wide flange beam) is given as:

Cw = t_fh²b³/24

Since this expression does not involve web thickness, it seems to me that Cw is the same for a castellated beam.

BA

 

[ToadJones]

BA-
I was thinking the same thing, but haven't had a chance to look it up.

 

[BAretired]

Toad,

I have never calculated Cw for a castellated beam, but it seems to make sense that it should be the same as for a WF, H or I section. The top flange bends in one direction while the bottom flange bends in the other when the section is exposed to torsion.

The web plays no role in warping, but it does contribute to torsional resistance and is included in the 'J' term.

BA

 

[ToadJones]

BA-
Makes sense to me.

 

[StaVis]

Thanks for the all the help. After all of this I'm rather curious as to how this constant was derived, as I've realised that I obviously don't understand it all too well. Will probably have to do some digging in the old classic elastic theory, as I suspect the formulae given in the codes etc are just safe approximations. But thanks again.

Yes, one could say that Cellular beams are the modern version of Castellated beams - they are fabricated in much the same way (also by flame cutting and then welding). I think the Cellular beams are possibly easier to bend (done before welding) to form curved or precambered members.

For interest's sake, I've included a picture showing the cutting pattern.

 

[ishvaaag]

An interesting pattern, giving the most of inner diameter for mechanical services. From the structural viewpoint it also has as good the elimination of corners of the typical hexagonal/octogonal patterns, with the only drawback of weakened chords relative to the hexagonal cut, what is not much if limiting to reasonable use the members.