Continuing from Frame Analysis with Excel 2 – Single inclined beam
Download Beam3.zip - the download file includes complete open source code.
The spreadsheet for a single inclined beam presented in the previous post has been modified to deal with up to six continuous horizontal or inclined beams. Examples of a 5 span beam and a four member portal frame have been compared with a frame analysis in Strand7 and show near exact agreement.
The procedure used in the new spreadsheet is:
- The stiffness matrix for each beam is generated as before.
- The beam matrices are combined into a global matrix, adding coefficients for the beams meeting at each node.
- The stiffness matrix for active freedoms is extracted from the complete global matrix
- This matrix is inverted using the Excel Minverse() function
- The inverted matrix is matrix multiplied by the applied nodal actions, giving the nodal translations and rotations.
- The complete stiffness matrix is multiplied by the complete nodal deflection vector, giving the net load for each freedom.
- Reactions at the fixed freedoms are found by deducting the applied loads from the net loads.
Formation of the global matrix for beams 1 and 2 of a continuous beam are shown below:
Global Stiffness Matrix
Screenshots below show Strand7 models for a 5 member continuous beam, and a portal frame, and comparisons of the Strand7 analysis and the spreadsheet output:
Strand7 continuous beam analysis
Continuous beam results
Strand7 Portal Frame Analysis
Portal Frame results
Filed under: Excel, Frame Analysis, Newton, VBA | Tagged: Excel, Finite Element Analysis, Frame Analysis, VBA
Great thing to learn matrix method for continous beam or frame analysis. I used Mathcad for this type of computations (involving matrixes) before but it looks Excel aided by VB programming works well.
Thanks, Tomasz
I am not able to give input for 3 beam portal. Explain, how to reduce your programm for 3 member portal frame.
In 3 member portal if the last dof is constrained then your programm is giving error. check
Mahesh
Yes, the program crashes if the last node is fixed against rotation. I have fixed the problem and added a 3 member portal frame example to the download file:
http://interactiveds.com.au/software/Beam3.zip
Note that the beam3 spreadsheet was intended mainly for educational purposes, and was set up so the matrices etc are all visible on the spreadsheet. There is a frame analysis spreadsheet at:
http://interactiveds.com.au/software/Frame4.zip
which is much more versatile, and should be easier to use for problems other than the provided example.
Thanks for the feedback.
Doug
Here is the Blog post with more details of the frame analysis spreadsheet:
http://newtonexcelbach.wordpress.com/2009/05/11/frame-analysis-with-excel-%e2%80%93-7-shear-deflections-and-support-displacements/