Section Properties with MeshPY, including torsion and warping

I recently discovered robbie van leeuwen’s structural engineering blog, which has an open-source set of Python routines for calculation of section properties, including torsion and warping constants.  The program uses the MeshPY Library for generating the finite element meshes required for the torsion and warping calculations.   The Python code for generation of the input to MeshPY, and for carrying out the finite element analyses, is all by Robbie van Leeuwen.

I have written an Excel front-end for these routines, allowing most of the functionality to be accessed quickly and easily, with no programming required.  The spreadsheet, including full open source code, can be downloaded from:

The spreadsheet requires the following software to be installed:

  • Windows version of Excel
  • Python version 2.7 or later (not checked with version 3)
  • xlwings version 0.11.4 or later
  • Matplotlib, Numpy and Scipy
  • The required MeshPY and other Python files are included with the download

The spreadsheet includes two calculation sheets:

  • Twelve defined shapes
  • Any shape defined by a series of coordinates

The screenshots below show the list of defined shapes and input and output for a rectangular hollow section:

Input cells are shaded blue.  Select a section type by number (1-12) and the required dimensions will update.  The optional input, Nu (Poisson’s Ratio) and mesh size (maximum area of each generated mesh element), is only required for the warping results.  The applied actions are only required for display of stress results.

The section properties output is shown in the two screen-shots below.  More detailed descriptions can be found at the on-line documentation.

For graphic display of the generated cross-section, element meshes, and stress plots under the input actions, click the “Display Stress Results” button:

17 images are shown in sequence in an external window.  Close each image to move on to the next.  There is currently no way to automatically save the images to the spreadsheet, but any image may be manually saved to disk as a png file.  At present each image must be viewed in sequence before control is returned to the spreadsheet.

The image window may be dragged to any required size (or made full-screen):

Stress distributions are generated for each of applied actions, and combined stresses:

The image window has tools to zoom and pan, and edit output format:

Sections defined by co-ordinates may be analysed on the second sheet.  The Python code has provision for analysis of sections with holes, but this is not yet implemented in the spreadsheet version:

The numerical results are as for the defined shapes:

The download file contains output for an asymmetrical I section, compared with the same section analysed in Strand7.  The geometric results are in exact agreement, to machine accuracy, except for the plastic modulus results, which have larger, but still very small differences.  The shear area, and torsion and warping constants have larger differences, due to different implementations of the finite element analysis, but are generally within 1%.

The output torsion and shear stress results from the spreadsheet are compared below with the equivalent results from Strand7:


Posted in Beam Bending, Concrete, Excel, Finite Element Analysis, Frame Analysis, Link to Python, Maths, Newton, Numerical integration, NumPy and SciPy, Strand7, UDFs, VBA, xlwings | Tagged , , , , , , , , | Leave a comment

Brent’s Method; Update and Examples

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If so, please contribute to the Raw Impact charity group providing practical help to poor communities in Cambodia:

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Brent’s Method is a refinement of Newton’s Method for the numerical solution of any equation with one variable.  The User Defined Function (UDF) QuadBrent was described in:  The Inverse Quadratic Method 3 – Brent’s Method

Following a recent question, I have updated the function and added some simple examples and additional documentation, linking to the Wikipedia article.  The new spreadsheet can be downloaded from:

The main update is that in addition to calling a VBA function to solve, the equation may be entered as text on the spreadsheet.  There is also a new function, QuadBrentT, for which this option is the default.

A simple example, solving a trigonometric equation, is shown in the screen-shot below (click on any image for full size view):

The function to be solved is entered as text in cell B4.  Using the original QuadBrent function, the default function type is the name of a VBA function.  To solve a text function on the spreadsheet, the new “EvalTxt” argument must be set to True.  The full list of arguments is now:

QuadBrent(Func, Ak, Bk, Coefficients, YTol , MaxIts , Subr, XTol, EvalTxt , ParamA , SolveFor )

  • Func: Name of VBA function, or function entered as text on the spreadsheet
  • Ak: Minimum x value
  • Bk: Maximum x value
  • Coefficients: value of fixed parameters used in the function; default = none
  • Ytol: solution tolerance on Y value; default = 1E-12
  • MaxIts; maximum iterations, default = 20
  • Subr: solution type; 1= Inverse Quadratic (default), 2 = Quadratic
  • XTol: solution tolerance on X value; default = 1E-12
  • EvalTxt: evaluate the entered text string; default = False
  • ParamA; list of fixed parameters (required if EvalTxt = True only); default = none
  • SolveFor: variable character (required if EvalTxt = True only); default = “x”

For the new QuadBrentT function the argument order and defaults are changed for greater convenience when evaluating text functions on the spreadsheet:

QuadBrentT(Func, Ak, Bk, ParamA, Coefficients, SolveFor, YTol , MaxIts , Subr, XTol )

Arguments are as listed above, except EvalTxt is no longer required, since it is always true.

In this example the solution to the equation could of course easily be found using the ASin function, but the method is easily applied to more complex equations, as shown below:

In this case two additional array arguments are required: the symbols representing constant values, and their associated values.

The next example illustrates the use of the QuadBrent function calling a VBA function to solve the same equation as above.  The code for VBA_1 is:

Function VBA_1(Coeffa As Variant, x As Double)
VBA_1 = Coeffa(1, 1) * Sin(x) - Coeffa(2, 1) * Cos(x) - Coeffa(3, 1)
End Function

Note that all required data must be passed as a single variant array, followed by the function variable.

The algorithm for Brent’s Method (taken from the Wikipedia page) is shown below:

This is applied to the first simple example on the spreadsheet, showing the results for each step of each iteration:

The Wikipedia page has a more complex example, solving a cubic equation.  This is solved with the QuadBrentT function below, and also with the Cubic UDF:

The step by step method is also shown on the spreadsheet:

This can be compared with the listing of the results at each iteration on the Wikipedia page:

Not that, at the time of writing, steps 7 to 9 have corrected results shown at the end of the line, and these corrected values agree with the spreadsheet results shown above.

Posted in Arrays, Excel, Maths, Newton, UDFs, VBA | Tagged , , , , , , | Leave a comment

Update to AL-Spline-Matrix

Has the free software at this site saved you time and/or money?
If so, please contribute to the Raw Impact charity group providing practical help to poor communities in Cambodia:

 Everydayhero – Cambodia 2018

  • All contributions gratefully accepted.
  • Contributions are tax-deductible for Australian tax payers

The AL-Spline-Matrix spreadsheet contains a large number of VBA user defined functions (UDFs) performing spline fitting and matrix operations, using the free and open source ALGLIB library. It was recently pointed out that the Excel interface code for the CSplineFitCW1da function had an error. The function fits a cubic spline to scattered data, with provision for weighting and specified constraints, but the code error resulted in the constraints not working properly. The code has now been fixed, and an example with constrained data is shown below.

The revised spreadsheet, including full open source code, (Version 1.33; 27 Nov 2017) can be downloaded from: (Excel 2003 version) (Excel 2007 and later)

The screen-shot below shows results with constraints applied at the minimum and maximum x-values, compared with unconstrained results, and the Hermite Fit function:

Posted in AlgLib, Excel, Maths, Newton, UDFs, VBA | Tagged , , , , , , | Leave a comment

Raw Impact in Cambodia – Please Donate

Raw Impact is a charity group providing practical help to poor communities in Cambodia:

Sustainable and innovative projects with a hand-up model, focusing on simple yet powerful ways to change the game for the poorest of the poor by equipping and inspiring them forward.

In January next year I will be joining a Northridge Vineyard Church group helping to construct a Raw Impact project in Cambodia.

Please help Raw Impact to continue and expand their work with a charity donation through:

Everydayhero – Cambodia 2018 – Please Donate

All donations are welcome, and are tax deductible for Australian tax payers.

Posted in Bach, Newton | Tagged , , , | 1 Comment

Composite Beam Spreadsheet Update 1.01

Following a comment here, I have modified the Composite Beam spreadsheet to correct the stage 1 stresses forces in the reinforcement as listed in Columns 6 and 7, when the tensile face is the top.  The output has also been modified to list from top face to bottom (as for the other output), rather than compressive to tension face.  The updated spreadsheet can be downloaded from:

Composite Design Functions

The version posted recently at Stress increments in prestressed concrete beams has also been updated, and can be downloaded from:

Composite Design Functions-Stress Inc


Posted in Beam Bending, Concrete, Excel, Newton, UDFs, VBA | Tagged , , , , , , , | Leave a comment

Tables and VBA

I don’t use Excel Tables much, and not at all from VBA (where they are known as ListObjects), but that should probably change, so here are four links with comprehensive help on using Tables from VBA:


Posted in Arrays, Excel, VBA | Tagged , , , , | 3 Comments

A Hard Rain

I happened to be looking at an old post here; Various routes to and from Nottamun Town, featuring Bob Dylan’s performance of A Hard Rain’s Gonna Fall, which led me to Patti Smith’s performance of the same song at last year’s Nobel Prize ceremony, and this is a unique performance in very many ways:

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