I have updated the Frame4 spreadsheet to allow a rotational spring stiffness to be specified for members with a rotational end release. The new file can be downloaded from:
See Installing C# dll files, reminder for details of installing the supplied dll files, which provide much better performance for large frames. If these are not installed the spreadsheet will default to the built in VBA solver.
The previous version allowed insertion of beam end releases with zero rotational stiffness, which resulted in additional nodes being inserted in the frame model. This allowed the addition of springs to the model, in effect inserting additional zero length spring members, connecting the rotational freedom at released ends to the rest of the model, by inserting the following values into the frame stiffness matrix:
using the following code:
'Add hinge stiffness factors k = BeamA(i, 5) If k > 0 Then For j = 1 To 2 HingeK = BeamA(i, j + 2) If HingeK > 0 Then gj = BeamER(k, (j - 1) * 2 + 8) gk = BeamER(k, (j - 1) * 2 + 9) KGCA(gj, gj) = KGCA(gj, gj) + HingeK KGCA(gk, gk) = KGCA(gk, gk) + HingeK KGCA(gj, gk) = KGCA(gj, gk) - HingeK KGCA(gk, gj) = KGCA(gk, gj) - HingeK End If Next j End If
The screenshot below shows the input for the spring restraints:
I have compared results from the spreadsheet with those from the FEA program Strand7, using the model shown below:
The screenshot below shows near exact agreement for both beam end actions and deflections:
The spreadsheet also allows a lot of the frame deflected shape, and plots of arch actions and/or deflections along any slected beams.
Strand7 graphical output:
Spredsheet deflected shape plot:
Spreadsheet bending moment plots: