Torsion/warping properties 2

[EngDM]

Hey all,

I'm curious if properties Cw and J are additive, meaning if I find the constants for each individual shape in the build up section and sum them, it's equivalent to if FEA solved the warping and torsion constant.

For instance, an I beam reinforced with angles either side, can I just calculate for the angles and then calculate for the I beam and add them?

 

[JoshPlumSE]

It's additive for J.... Unless the shapes form a "closed" section, then you get a huge increase in J.

I'm not sure about Cw.

You've probably already looked at the AISC design guide 9 for torsion of open cross sections. There is a similar (maybe even better) design manual that the British steel guys have.

 

[canwesteng]

CISC used to put out a guide on calculating torsional properties that was pretty good, you can find it here.

http://www.labciv.eng.uerj.br/pgeciv/files/Torsion Properties.pdf

 

[handofthelion]

The assumption of adding torsion constants (J) for built-up sections is valid for sections that are not connected at a given cross-section. The assumption is conservative if the sections are connected, the actual value for J will depend on how the built-up section allows for a closed shear flow under torsion.

Also not sure about the warping constant, but it appears to also be conservative for this example to assume addition of individual properties. Here's an example using my python package sectionproperties. You can execute the entire notebook by selecting Run->Run All Cells (you may have to wait a minute for it to execute).

For the given geometry assuming full connectivity between the angles and the I-section, adding the torsion constants gives 36% of the FEA calculated torsion constant, and adding the warping constants gives 92% of the FEA calculated warping constant. There are some stress plots at the bottom to visualise how torsion is resisted in the section (the built-up section creates a torsionally stiff thicker section at the junction of the angle and I-section webs).

If you're interested you can modify any of the values in the notebook and run your own scenario!

 

[JoshPlumSE]

The assumption is conservative if the sections are connected, the actual value for J will depend on how the built-up section allows for a closed shear flow under torsion.

True, but it's not conservative by very much. Summation of bt^3/12 is reasonably good for most open shapes... as mentioned in that excellent link provided by Canwesteng.

 

[Lomarandil]

For more discussion of how connectivity of sections affects torsional properties, make sure to also see Agent's blog series starting here



----
just call me Lo.

 

[le99]

You need to calculate the torsional stress and torsion warping stress separately at a location and then add the stresses together. Luckily, the wrapping stress is usually much smaller than the torsional stress and can be ignored. Here is a good article about it. Link