One of my aims in developing the splinebeam function is to carry out non-linear analysis of reinforced concrete beams, allowing for the greatly reduced flexural stiffness of reinforced concrete sections after cracking of the concrete. To that end, I have added the facility to specify the section stiffness span by span. Later versions will allow for the stiffness of individual segments to be specified, or for a non-linear moment-curvature relationship to be used. Dowload SplineBeam2_1.zip
The standard cubic spline formulation is based on the curvature and slope of the spline being continuous at nodes. Since a step in the section stiffness will result in a step in the curvature, the curvature has been replaced by the bending moment, and the governing equation becomes:
The coefficients of the cubic splnie function must also be changed:
if: y = a + b(x – x(n)) + c(x – x(n))^2 + d(x – x(n))^3
where x lies between x(n) and x(n+1)
Typical output for a 3 span beam is shown below:
A Strand7 analysis with the same input gives identical results:
I think that would be more useful if in your interesting spreadsheet includes a scheme or draws for the beams.
Thanks in advance, and regards from Guadalajara México.
Manuel, I’m not exactly sure I understand you, but this spreadsheet might be of interest:
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