Again, NACA provides a the solution to another problem. The theoretical derivation of plate compression buckling coefficients. I had a simple derivation, which uses this equation for the simply supported plate buckling coefficient
NACA-Report-733 has the expression that give the general curve for any edge restraint condition:
The free spreadsheet is available here and has the simple expression in the first tab and the expression for the general curve in the second tab.
All thanks and credit is due to NACA. Enjoy!
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