… 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
Links to the Scipy statistics functions were last presented here. The functions have since had extensive updates:
The py_Stats spreadsheet, with associated Python code in PythonStatsFuncs3.py and pyScipy3.py, are included in the download file:
Details of the required pyxll package (including download, free trial, and full documentation) can be found at: pyxll
For those installing a new copy of pyxll, a 10% discount on the first year’s fees is available using the coupon code “NEWTONEXCELBACH10”.
The py_Stats function can be used to call any function in the Scipy.stats module. Alternatively the functions can be called with specific py_ functions. The screenshot below shows the describe function called with py_Stats and py_describe.
The examples of each function have now been extended to cover every available function:
Help on any function can be displayed as text on the spreadsheet, using the get_docs function:
The Scipy on-line help for any function can now be displayed by clicking on “Help on this function” at the bottom left of the function wizard:
The function wizard now displays a brief description of the function purpose, and the data required for each argument, as for the built-in Excel functions:
The spreadsheet also has functions to return the arguments for each function (get_args and get_argtab, and to list every available function in any Python module (get_funcs):
Finally there is a list of every Scipy.ststs function that can be called from Excel with a py_ function. This list now also includes the row number where the function example can be found:
The py_Numpy spreadsheet, and the associated Python module have been updated. The new files are included in:
The download contains full open-source Python code and example spreadsheets for a wide range of Scipy functions, as well as the Numpy functions covered in this post. For more details, see the series of posts starting at: Scipy functions with Excel and pyxll.
The update was prompted by use of the norm function, which has versions in both Numpy and Scipy, which are very similar, but not identical. The Numpy version is now called from Excel with py_npNorm, with py_Norm calling the Scipy version.
Links to the Numpy on-line help have also been extended. When any of the py_Numpy functions are entered, from any spreadsheet, the on-line help can be displayed by clicking on “help on this function”, at the bottom-left of the Function Wizard:
This takes you directly to the on-line help for the selected function:
Alternatively, the Numpy help can be displayed on the spreadsheet using the get_docs function. In the py_Numpy spreadsheet this is linked to the list of available functions, so that entering the index number for any function will display the associated help text:
Note that the get_docs function can be used from any spreadsheet, and will return the help text from any available Python function. The screenshot below shows it used for the Numpy norm function and also the Scipy version:
… or perhaps one more. Following the previous post I have modified the py_BeamAct3D function to fix some problems with the non-linear analysis.
The latest version, together with an additional spreadsheet comparing results with Strand7, can be downloaded from:
Also, see Python and pyxll for details of the pyxll package required to link the Python code to Excel, including a 10% discount code for new users.
The screenshots below show results for a 32 metre long beam with 2 different cross sections loaded with a uniform transverse load, and a high axial load.
The function allows for the beam alignment to be defined in 3 dimensions, but for the purposes of comparison with Strand7 results it was aligned with the X axis:
Output results (for the first 12 metres) are shown below for a linear analysis, ignoring geometric non-linear effects:
Setting the analysis to non-linear significantly increased the beam action and deflections:
Beam deflections and actions are plotted below comparing the linear and non-linear results with Strand7 geometric non-linear results:
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