Torsion diagram of curve beam 1

To get meaningful answers here, you're probably going to have to post sketches of the situations that are producing the results that you're seeing. In my experience, most beams with torsion will have their maximum torsion at the ends. There are probably exceptions though, particularly if the beam is torsionally braced along its length.

dccd said:

I think the part which have the highest curvature (most curve) has the highest value of torsion, correct me if I am wrong...

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While that may be true in some instance, I don't think that it's a principle that can be applied generally.

What about the more usual case where the beam is bent in a circular curve? Curvature is constant throughout the span. Where is the maximum value of torsion?

BA

You need to consider the loading on them too for the curved torsionally unbraced members.
In case they carry their own weight and uniformly loaded with the same UDL so KootK has already given the answer above.

I think the maximum torsion would be at the ends. Similar to a straight beam with applied torsion along its length with the maximum applied torsion at the center. The below torsion moments are linear for each step along the beam and not parabolic in magnitude for each applied torsion moment. But the point moments could be manipulated based on points along a curve to get the magnitude of each applied point torsion load for an estimate, with more points if you want to get more accurate in the diagram.

Conservatively, I believe you could take the length of the straight beam to be equal to the total length along the curved beam. I would use a different straight beam diagram to estimate/superimpose the direct bending component.

The actual internal stresses are more difficult to estimate along the curved beam and would need a 3d FE model or a decent amount of hand calc time. The outside perimeter along the circular beam should have higher stresses than the interior part of the beam.

Depends how the beam is supported and how it is resisting the torsion. For a close section the torsion the torsional stresses are highest at the supports. For open section that isn't warping restrained at the ends, the warping torsional moment is highest at the centre.

Warping on a curved beam is an interesting wrinkle. I'm not sure that we even know how to do that in a rigorous sense since you'd develop something like lateral arching / catenary action in the flanges.