Continuous beam with varying stiffness

Previous Splinebeam post

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  Since a step in the section stiffness will result in a step in the curvature, the curvature has been replaced by the bending moment, and the governing equation becomes:

SplineBeam2_1-1

SplineBeam2_1-2

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)

then:

SplineBeam2_1-3

Typical output for a 3 span beam is shown below:

SplineBeam2_1-4

Typical output; Click to view full size

A Strand7 analysis with the same input gives identical results:

SplineBeam2_1-5

Strand7 Output, Click to view full size

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This entry was posted in Arrays, Beam Bending, Excel, Finite Element Analysis, Maths, Newton, UDFs, VBA and tagged , , , , , , , . Bookmark the permalink.

3 Responses to Continuous beam with varying stiffness

  1. 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.

    Like

  2. Pingback: SplineBeam update « Newton Excel Bach, not (just) an Excel Blog

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