If you think I’m wrong, try looking at it from a different perspective.
The picture above came from an optical illusion blog at:
http://www.anopticalillusion.com/
and I was led there from:
http://www.josleys.com/index.php
which is an amazing collection of mathematical imagery by Jos Leys, of which I have posted a very small sample below (visit the link for higher resolution images, and much more).
3D Mandelbrot 1
3D Mandelbrot 2
Newton Fractal
Escher inspired “Engineer’s Nightmare”
Still on Frame4, Julien asked if provision could be made for application of local loads, i.e. loads perpendicular to sloping members, rather than just horizontal or vertical. This will actually be incorporated in the spreadsheet “real soon now”, but it makes a good example of how the program can be made more versatile with the use of formulas on the spreadsheet, so that’s what I have done in this example. The example is a simple twin portal frame structure, with perpendicular downward loads of 10 kN/m applied to the beams facing left, and perpendicular upward loads of 5 kN/m applied to those facing right.
Twin Portal Frame Structure
The formulas entered to calculate the equivalent global loads are shown below:
Calculation of global loads, click for full size view
For each roof member two load lines are required, to calculate the X and Y loads, from the input perpendicular loads, and the beam slope. The calculated global load can then be transferred to the input area. The resulting output results and deflected shape are shown below:
Output Results
Deflected shape
This technique can be extended to allow quite sophisticated analyses; for instance it would be possible to include geometric non-linearity by adjusting the node coordinates after each run, or material non-linearity by adjusting the section properties. The only word of warning is that the rows below the designated data entry areas must not be used for other purposes.
Hot on the heels of Version 3.04 comes Version 3.05.
A few days ago Julien asked if the Frame4 allowed for specified support deflections, to which I replied it would be added in the future. Searching Google on the topic I found:
https://newtonexcelbach.wordpress.com/2009/05/11/frame-analysis-with-excel-%E2%80%93-7-shear-deflections-and-support-displacements/
from which I discovered that it had been done already!
Download from: http://www.interactiveds.com.au/software/Frame4.zip
The new version has some small amendments to make it compatible with the Alglib solver, and adds some brief documentation. The screen shots below show example input and output, and results from Strand7 for the same problem, which are in near exact agreement.
Support displacement input
Support displacement and reaction output
Deflected shape x 200
Horizontal beam moments
Strand7 output, reactions for Node 1
In preparation for adding 3D functionality to the Frame4 spreadsheet I have rearranged the load input sheet, and in doing so I noticed that the fixed end reaction calculation was incorrect for cases where loads were applied to one member over two or more lines, and the fixed end moments were not equal. That has now been fixed, along with some other minor amendments, and the new files (in xls and xlsb versions) may be downloaded from: Frame4.zip.
For details of installing the link to the compiled Alglib solvers see: https://newtonexcelbach.wordpress.com/2012/11/16/frame4-now-with-added-alglib ,
and in the event of problems registering the dll files see the comment from Tom dated December 5 2012.
New load input sheet
I wrote about this function 2 1/2 years ago, and promptly forgot about it, but a few days ago brian provided an answer to a question that was raised shortly after it was first posted, concerning how to apply the function to secondary chart axes.
I have updated the spreadsheet to incorporate brian’s code (slightly modified), and the new version (including full open source code) can be downloaded from: SetScale2.zip
I have also added an example of the technique for plotting a function entered as text on the spreadsheet. The procedure is:
Newton Excel Bach, not (just) an Excel Blog 