The non-linear analysis routines in 3DFrame-py have now been updated to work with beams with end-releases at one or both ends.  Updated files are at:

3DFrame-py.zip

See the previous two posts for details of other software required for installation.

To check the spreadsheet results, 7 portal frames with different end conditions were analysed in Strand7:

From left to right the rotational end releases were specified at:

• Top beam, both ends
• Top beam, right
• Top beam, left
• Top of both columns
• Top of right column
• Top of left column
• None

Results are shown below for a vertical distributed load of 7500 kN/m applied to the top beam, with a horizontal point load of 2000 kN applied at the top of the left column. For Case 1 and 4 (rotation release at both ends) these loads are close to the buckling load, resulting in horizontal deflections of well over 1 metre (click on image for full-size view):

For this case there are significant differences between the Strand7 and spreadsheet results for both horizontal and vertical deflections and bending moments at the base of the columns. The programs use different approximations for the non-linear geometric effects, and with very large deflections close to the buckling load these result in significant differences in the results.

To display results for other cases, enter the “frame no.” (1-7) in cell C9, and update the end releases on Sheet Input1:

The spreadsheet results are then updated by clicking the “Recalculate” button and can be compared with the Strand7 results:

For this case there is still a significant difference in the vertical deflections at the top of the columns, but the horizontal deflections and forces are all much closer, with a maximum difference of about 1%. The actions at the beam ends are also in good agreement:

Results are also included for linear elastic analyses. These are in near exact agreement: