Elastic modulus about the geometric or principal axis? 4

[CivilSigma]

The elastic sectional modulus is S= Ix/ymax.

For symmetric cross sections, the geometric (centroidal) axis = principal axis, and the calculation is trivial.
However, for asymmetric sections, the principal axis can be rotated with respect to the geometric axis.
This post here (

https://www.eng-tips.com/viewthread.cfm?qid=245739)

mentions that asymmetric sections (e.g. angles) bend about their principal axis.

So, that begs the question: What values do you use to determine the elastic modulus then? and would the section neutral axis coincide with that of the principal axis?

I think in the case of asymetric sections, I would use Imin/ymax as a conservative value for the elastic modulus of bending.

Any input is greatly appreciated.

Thank you,
CS

 

[Denial]

Determine your principal axes and their orientations.[ ] (They will be perpendicular to each other.)
Decompose your applied moment into components about each of the two principal axes.
For any point of interest on your cross-section calculate the stresses resulting from each of the components, then sum them.
Note that in general the plane in which your beam will deflect will not be the plane in which your moment acts.

 

[Agent666]

I second what Denial has outlined.

If you're after a comprehensive & free cross section analysis tool to help you work out the principle axes and any other cross section properties imaginable, I highly recommend this python package. Even without any python knowledge, the examples in the documentation should be enough to get you up and running with the built in section types.

 

[rb1957]

3rd that … that's what I'd've done in school

another day in paradise, or is paradise one day closer ?

 

[CivilSigma]

Thanks for the input ! I never really thought about it like that before, and it makes sense.
So, the same thing would apply to plastic bending too, with stress = M/Z.

The package is great, thanks for the source @Agent666.

I am actually working on my own thin-walled element analysis application, with the premise that you can create any thin-walled cross section, and it will output design variables that you would need as required, for example, by CSA S16, or other steel design standards. My application is based on Vlasov's thin-walled element theory and is intended to compliment non-standardized beam cross section design using code equations.

 

[Denial]

So, the same thing would apply to plastic bending too, with stress = M/Z

If that is a question, the answer is "NO".

The situation is a lot more complicated for plastic bending of sections that lack symmetry, and also for symmetric sections under biaxial bending.[ ] I started to investigate this many years ago, but was taken off the exercise before I made much progress and have never returned to it.[ ] Hopefully there will be other EngTippers able to be more helpful.

 

[Agent666]

To be honest, I would be reluctant to rely on an angle section for development of plastic section strengths unless it was being bent about the minor axis principle axis (no flexural torsional buckling issues). This practical uses for this is likely to be limited.

Most codes that I'm familiar with do not address the flexural torsional buckling of angles, your mileage might vary depending on where you are situated, but there is probably a reason for this. They simply are not an efficient/dependable bending member, and are likely unstable when it comes to resisting flexural torsional buckling effects.

About the most bending you want them to carry is the moment developed due to eccentricity at which any axial load is applied. Some codes have means of addressing this aspect (NZS3404, and I believe British steel standards) depending on how slender the member is and what restraint end connections provide all feed into these checks.

 

[CivilSigma]

Yea I agree, I wouldn't design an angle or asymmetric sections to undergo plastic stress.
When it comes to thin-walled steel structures, I would use doubly symmetric members.

 

[rscassar]

Thanks Agent666, those python packages u linked to a pretty amazing. I've been experimenting a little writing a FEA solver in pythons, frames a fairly straightforward but always struggled when it came to FEA formulations for plate elements. Looks like a lot of good work by the author of the package.