It was recently reported that the VBA version of the biaxial bending spreadsheet was returning incorrect results when the neutral axis was exactly parallel to the Y axis. This problem has now been fixed, and the revised spreadsheet can be downloaded from:
For more information on the spreadsheet, and discussion of options for algorithms to find the neutral axis angle, see:
Newton Excel Bach, not (just) an Excel Blog 
Hi Doug,
I am currently developing an Excel VBA tool to generate Biaxial Interaction Diagrams (M-M Diagrams) for arbitrarily shaped reinforced concrete sections. The tool will allow users to input the section’s corner coordinates, material properties, steel rebar coordinates, and load cases (Pu, Mux, Muy). Based on these inputs, it will generate the corresponding biaxial interaction diagram.
The tool is designed to accommodate various stress-strain relationships for both concrete and steel. The approach for stress calculation involves dividing the compressed region of the concrete section (above the neutral axis) into smaller horizontal fibers to integrate stresses accurately. One of the key challenges I am facing is detecting the coordinates of the compressed region and efficiently dividing it into slices for stress integration. I plan to use the bisection method to determine the neutral axis position that satisfies equilibrium conditions.
If you have any suggestions, references, or methodologies that could help refine this approach, I would greatly appreciate your input.
Thank you for your valuable content and contributions to the advancement of structural engineering.
https://imgur.com/a/7sCF2fZ
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Another thing, The values of concrete and steel material reduction factors (Safety factors) are not always 1.50 and 1.15 and change by changing load cases. A while-loop is used to iterate and search for final values by trial and error.
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Abdullah – you might like to have a look at:
Brent’s Method; Update and Examples
Brent’s Method is a refinement of Newton’s Method that automatically switches to the bisection method for cases where Newton’s Method fails to converge.
My biaxial spreadsheet currently only allows for a rectangular stress block, but the ULS Design Functions spreadsheet:
ULS Design Functions 2.16
also allows for a parabolic-rectangular stress block, and allows for integration of the stress function over trapezoidal or triangular elements, as well as rectangular, so can give an accurate solution without subdividing into very small layers.
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Thank you very much doug. I really appreciate your help. I’ll have a look at your posted links.
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