Buckling of a circular hollow section?

I am trying to determine the critical load for a circular hollow post of diameter 42.4mm and thickness 4mm. The 2nd moment of area is 8.99cm^4 and the cross section area is 4.816x10^-4. I will be making this from aluminium with Youngs modulus is 67GPa and the yield stress of 190MN/m2.





Will the post fail by Euler or Johnson method??





Think I have to use the eualer euquation to find critical load, then check that value against the point of intersection with the Johnson curve to determine if the post is in actual fact going to fail by the Euler method? Something about slenderness ratio?

Buckling of a circular hollow section?
Critical loads are usually provided by the manufacturer.
Reply:Well first off, if you have a machine design textbook, or a design book, u could find all this info in there. But for your question, u have to determine how your column will be loaded to determine the effective length..





for round-rounded: Leff=1


pinned-pinned: Leff=1


fixed-free: Leff=2.1*L


fixed-pinned: .8*L


fixed-fixed: .65*L





then to determine whether to use euler or johnson you need to determine the slederness ratio:





Sr=Leff/k





k=SQRT(I/A) I is moment of inertia, A is cross sect. area





Compressive yield strength:





Syc=2*pi^2*E/(Sr^2)





Then:


(Sr)D=pi*SQRT(2*E/Syc)





If Sr%26lt;10 (short column) use:





sigma=Pcr/A





if Sr%26gt;=10 and Sr%26gt;(Sr)D (long) use Eulers:





Pcr=pi^2*E*I/(Leff^2)





if Sr%26gt;=10 and Sr%26lt;=(Sr)D (intermediate) use Johsnon%26#039;s:





Pcr/A=Syc-(1/E)*(Syc*Sr/(2*pi))^2





Factor of Safety:





Fs=Pcr/Pall Pall is how much the column will hold





and uhh, there u have it. Oh, and make sure you convert your I and A dimensions to meters so all your units are the same. good luck!!
Reply:You haven%26#039;t said how you were applying the load. Can%26#039;t help.



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