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Originally Posted by Paul Copioli
This equation is based on some assumptions, but the criteria for validity is, generally, that L/r must be greater than 100.
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for clarity, if L/r is greater than 100 it will buckle before it yields. You would always want to keep L/r (called the slenderness ratio) less than 100.
The equation we used per structural pipe code was kL/r had to be <120 for steel structures (E~30 Mpsi, Sy~45 ksi)), where k is dependant on the end constraints. Since worst case k=1.5 for pinned ends, it's conservative to just use L/r <80. I ran the numbers for 6061 aluminum and it seems to me it was L/r <60 ; I have the calcs at work and I'll post them tomorrow if I can find them.
It's actually a pretty simple calc to derive. From Eulers equation given by Paul, setting the stress at the critical buckling load equal to the yield strength Sy, L/r = pi*(E/Sy)^1/2.
For steel (properties given above) L/r = 81
For 6061-T6 Aluminum (E~10 Mpsi, Sy~36 ksi), L/r = 52