I recently noticed that the iterative linear algebra solvers in my pyLinAlgfuncs3.xlsb spreadsheet had stopped working. It turned out that the optional tolerance argument had been renamed ‘rtol’. Changing all the occurrences of the name in the Python code fixed the problem. The revised code and updated spreadsheet can be downloaded from:
For more details of the included functions, and links to related topics see: Scipy Functions with Excel and pyxll 7 – Linear Algebra.
Following the previous post, I found some errors in the Python code:
These problems have now been fixed, and updated code and a revised spreadsheet have been added to the download file at:
The screenshots below show results with end point loads, compared with results from Strand7 and the 3DFrame spreadsheet:
In 2018 I posted Beam geometric non-linear effects with a VBA based spreadsheet to calculate beam actions and deflections under combined transverse and axial load, allowing for geometric non-linear effects. I have now converted the code to Python, linking to Excel with pyxll, with several added features:
Typical input and results are shown in the screenshots below. See the previous post for background on the analysis method used. The spreadsheet and required Python code can be downloaded from:
The first examples are based on a beam with two different cross sections, fixed for rotation and transverse deflection at both ends, and with an axial load close to the buckling load. The spreadsheet results are compared with results from Strand7 and from my 3DFrame spreadsheet.
Specifying moment-curvature tables, and an increased number of iterations significantly increases the deflections:
Doubling the number of beam segments improves the match between the alternative softwares used:
The results below are for a 20 m long beam with different end conditions:
Moment and transverse deflection fixed at both ends.
Transverse deflection restraint removed at the right hand end.
Moment restraint removed at both ends
… with very different renditions.
First from 1967, Martin Carthy and Dave Swarbrick join Julie Felix:
Then a new version of Tam Lin from 2022, by Fiona Gillespie and Elliot Cole and performed by Makaris:
For more om Makaris see their web site: MAKARIS
This post was prompted by an Eng-Tips question: Statically Indeterminant Beam Problem, asking for reactions due to a triangular distributed load on the middle span of a continuous beam with 3 equal simply supported spans. This could be simply solved with a frame analysis program, or continuous beam analysis (such as ConBeamU or py_ConBeamU), but it is useful to analyse this problem from first principles to get a better understanding of the procedures used.
The procedure used in my continuous beam spreadsheets is:
Since the spans are equal in the given problem, the analysis can be simplified by
Note that:
An alternative process is to remove the two end supports, and find the deflections at these locations due to the applied load on the middle span:
Finally a simple version of standard frame analysis procedure can be set up:
The calculated reactions are exactly the same from each of the three calculations. Copies of the spreadsheets used can be downloaded from: 3 Span triang load.zip
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