When I calculate section properties for a beam, I usually run AutoCAD's MASSPROP command on the section and then do any additional analysis in MathCAD. I'm often doing composite beams, beams with custom shapes, etc. so I can't rely on magic formulas for specific shapes. There are a few properties that I haven't been able to calculate as easily, such as the torsional constant, warping constant, plastic section modulus about plastic section centroid, and monosymmetry constant. These are found using finite element analysis. I have a python API written by Robbie van Leeuwen called SECTIONPROPERTIES, and it's great but my colleagues don't know how to use Python. So with that context, my question is "How can I use MathCAD Prime to cut a section into discrete elements and run a finite element analysis or solve differential equations o?
Here's the DE for the monosymmetry constant:
Here's the St. Venant torsion constant:
The warping constant, from Galambos, 1968:
Hi Kevin,
Part of your question was "How can I use MathCAD Prime to cut a section into discrete elements?"
SECTIONPROPERTIES by Robbie van Leeuwen uses six nodes per triangle.
I have also wanted to be able to do this. After looking around I have found this.
Using a program called Gmsh https://gmsh.info/ this is possible in PTC Prime by text processing for input and of output.
Gmsh is open source.
The second part of your question
and run a finite element analysis or solve differential equations
SECTIONPROPERTIES by Robbie van Leeuwen uses an Iterative Conjugate Gradient Scheme on Sparse Matrix for solution of the FEM.
This is beyond the capacity of Mathcad as it has no sparse matrix definition and algebra capabilities.
Cheers
Terry
Hi Kevin,
Step 2 taken the solution further by obtaining the section geometric properties from the six-node triangle triangulation.
I have not derived other geometric properties as this is trivial to do from the basic ones.
.If you want this extended to the calculation of J, and Cw I need some feedback that it is needed.
Cheers
Terry
Hi Bill,
FEM gets closer to analytical value the finer the mesh is used. This is with use of 9380 nodes and 4401 six node triangles in the approximation of a standard section 380 Parallel Flange Channel for which published data is available. Takes 15 GB of ram to hold the global dense form stiffness matrix so many laptops and PC's may not handle the memory requirements. Note how approximate the values are 🙂
Hi Kevin
A word about accuracy and Prime memory requirements.
With a drastic reduction in mesh size only a small loss of accuracy is achievable. It is a trade-off. With 1551 nodes (not 9380) you get a size that fits on a 4 or 8 GB machine.
