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:
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: