You asked a good question. As long as your column meets the numerous assumptions made in deriving the Euler buckling equations, then yes, this analysis method is accurate in a real world scenrio. I have studied buckling for about 2 years now and if you are interested in more information, I would be happy to assist you.
If you are a researcher studying actual failure by buckling then no, Euler is too simple for the real world.
If you are a designer, designing to codes, then the anti buckling requirements of most codes are based on Euler. So in that sense, in the real world, a code design is (hopefully) a safe design and probably uses Euler.
Remember that Euler is based upon a static load. Buckling induced by dynamic or periodic loads require different treatment.
jrw66- I can usually understand these things better upon working it out a little bit. So "made" a little bar with circular cross sections on the ends. It is .2m long and the diameter is .01m. So I found the equation Fcr=[pi^2*(Modulus of Elasticity)*(second moment of inertia)]/(kL)^2.
I am pretending the beam is structural steel so my E=2*10^11 Pa. I calculated the second moment of inertia to be I=pi*(diameter)^4/64=pi*(.01^-8)/64. I also used k=.5 because the beam has two fixed ends. The equation came out to
I hate to ask you to do calculations but I am just curious if my procedure is correct and if this would indeed be the force which would cause such a bar to buckle. Thanks.
Studiot-You said that Euler's only works with static loads but not periodic. If I added 100N on linearly over the period of a second would that be periodic or static?
By static loads I mean those that are only loaded / unloaded a few times. A compression memeber in say an aircraft wing subject to continual fluttering will be subject to many load cycles. Yes one second is plenty slow wnough.
However for structural steel your slenderness ratio 0.2/0.005 = 40 is below the usual criterion (100) for applying Euler. So the critical stress will be the proportional limit.
A note to calculate the slenderness ratio this equals the effective length divided by the least radius of gyration of the section (=r/2 for circular) times a factor for end conditions. This factor is 1 for a hinge at each end, 0.5 for both ends fixed, 0.7 for one end fixed and one hinged, and 2 for one end free and one end fixed (flagpole)
Thank you, you really have been a lot of help in having me understand buckling. You guys have already answered my question but if you're interested in responding please do... I was just wondering if Euler's Buckling still holds under thermal stress? From the readings I've done it seems like yes it does. The thermal force will be F=(coefficient of thermal expansion)*(modulus of elasticity)*(temperature change)*(cross sectional area). Theoretically I am thinking that by setting this equal to the buckling force I can calculate what temperature change will buckle it. But i am thinking that the expansion caused by temperature increases my change the buckling force due to something like a change in the cross sectional area. Will Euler's hold true to predict this temperature or will it be inaccurate.
Things do buckle under thermal stresses, which can be quite large.
This sort of problem is more often seen in thin walled tubes, plates or shells where a more complicated analysis is appropriate when in plane forces are applied. With a plate there are usually three dimensions to consider. Euler is meant for columns and struts which are reduced to line beam ( 2 dimensional) analyses.
jrw66 has provided one reference.
The classics are
Timoshenko- Theory of plates and Shells
Southwell - theory of Elasticity