Following another buckling discussion at Eng-tips I have modified my Frame4-buckle spreadsheet to allow input of multiple axial loads at any point along the column, along with any number of sections with different section properties. Background on the method used in the spreadsheet, and installation of the Alglib solver (if desired) can be found at: Buckling of columns with varying cross section and Using Frame4Buckle with the Alglib solver and the new spreadsheet (Frame4buckle-multiload.xlsb) can be downloaded from:
Input and results for a column with a top load and one intermediate load are shown in the screen-shots below:
Note that for multiple loads the input allowing varying section properties must be used. The cell E24 in the Constant Section input (“Number of Segments”) must be blank.
Any consistent units may be used. In the example above lengths are in inches and force in kips.
The calculated buckled shape may be plotted:
The example shown above was taken from a spreadsheet published by Alex Tomanovich, available from: StepCol
This spreadsheet uses a different analysis method, but gives very close results for the column effective lengths:
L1 = 19.25 ft = 231 in. (compared with 230.8 in.)
L2 = 29.08 ft = 349 in. (compared with 348.6 in.)