3D deformed shape about pynite HOT 16 CLOSED

I'll post how I derived the beam segment deflection equations soon. I've been meaning to do it for a while now, along with other derivations I've used. I used direct integration to get the beam segment equations.

I used 'Jupyter Lab' and 'Sympy' to help me get the math right. You'll need to have those two libraries installed in order to view the notebook. Or you could install the Jupyter Notebook viewer.

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But do these formulations can be found in books of Structural mechanics theory ?

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The equations in PyNite are derived from the direct integration method, and the slope-deflection method, which are in just about every structural engineering textbook.

The derivations have been uploaded now.

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Your function AxialDeformation appears to return the axial strain at x. Don't we need to sum all the axial strains up to x instead? It appears that's what you're attempting to do with the self.AxialDeformation(x) * x term. That equation works if the strain is constant, but a summation or even integration may be required for variable axial loads.

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In order to handle the summation, the BeamSegZ class would need a variable added to it to track initial translation on each segment, the same way we track initial deflection.

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About AxialDeformation, it should be correct; it returns axial strain at x and I need this because I also introduce the function PlotAxialDeformation that is defined in Member.py.
About AxialTranslation, I'm agree with you. There is something that dosen't works and I think this is releated to formulation that I've used.

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Could you explain better what you want to say about additional variable?

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Initial translation (translation1) is defined in BeamSegZ class; it's calculated in Member3D.py for i=0:

SegmentsZ[0].translation1 = d[0,0]

and for i>0:

SegmentsZ[i].translation1 = SegmentsZ[i-1].AxialTranslation(SegmentsZ[i-1].Length())

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I see what you've done there. translation1 is the additional variable that tracks the initial translation at the start of each mathematically continuous segment. That works.

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Maybe I understand where I'm wrong! In Axial translation I have to use the integral of deformation (N(x)/EA) and not

translation1 - self.AxialDeformation(x) * x

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I think that's correct!

If you look at the derivations for BeamSegZ I posted you'll see how I integrated the distributed load to get the change in shear, and how I integrated the shear to get the change in moment, and the moment divided by EI to get the change in slope, and the slope to get the change in deflection. When you add the initial conditions to the change you get the total shear, moment, slope, and deflection. You can use the same procedure and EA to get the axial translation. Sympy will even take care of the calculus for you.

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Also, it's worth noting that translation1 - self.AxialDeformation(x)*x is the integral if the load is constant. That's why it worked for constant axial forces.

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Yes, now I have understood the derivations and I have followed the same procedure for axial translation. In this way I wouldn't need of Axial function but it can be used for axial deformation plotting. It can be also useful.

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I didn't see a pull request come through for this one. Were you planning to issue one?

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Yes of course, I'll open a pull request soon!

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