Analytical method for torional constant

[JoeH78]

Dear Colleauges,

I'd like to calculate the torisonal constant for general shape with analytical methods. I googled for a while with deep and through search to find the solution but sitll didn't come up with anything useful other than some torsional constants for specific shapes. Computer algorithms for that is also wellcome.

Regards,

 

[Retrograde]

I do not believe that there is a general elasticity solution for torsion. There are only particular solutions for specific cross sections.

 

[JoeH78]

Yes quite interesting I also never seen any generic function other than that Link but this seems to be torque dependent, I can not foresee whether that torque can be eliminated by some math methods, but that truly renders it to be very difficult.

To narrow down the problem, I specifically would like to calculate I-shaped universal beam including the fillets, generally most of the formulas are given for I -shapes without fillets, so I'd like to include the fillets, then if I succeed proceed further to channels, angles etc.. including fillets.

Any guidance on that?

Regards,

 

[Retrograde]

My understanding is that warping dominates the torsional response of I beams - and as such including the fillets will make a negligible difference.

 

[JoeH78]

Yes I completely I agree with you, I also believe that practically fllets will not make any difference at all. But for time being I've been assigned a task to calculate the torsional constants on theoritical basis. I have to prove it on white paper no matter whether it has slight effect or not and I relly don't know where to start.

Regards,

 

[prex]

You need to solve a Laplace equation for K. See here, where a finite difference method is used.

prex
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[JoeH78]

@prex thank you very much, it seems that its a closed form javascript formulation, but how can I get explicit formulation?

 

[Hokie93]

Appendix C of AISC Design Guide 9 (Torsional Analysis of Structural Steel Members) provides a torsional constant equation for several typical structural shapes (WF-, S-, C-, and Z-shapes) that includes the fillet at the flange-web junction.

 

[KootK]

It depends how general you want to get. For a truly general solution, you're looking at an FEM-ish approach rather than a closed form solution to solve the differential equations (Link Link). It's so damn complex that you have to get NASA involved (Link).For general formulations within certain categories of cross sections, this may be useful: Link.

Whoever's telling you to include the cross section fillets needs a talking to themselves. That's a fruitless waste of human effort and/or computational power.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[Guest262653]

If you don't mind reading in French, there's an excellent free tool from the CTICM (Centre Technique Industriel de la Construction Métallique) that calculates sectional properties, including torsional properties, based on a FEM approach. The link for the program is the following:

https://www.cticm.com/content/propsection-v103