Column Buckling - Half in compression, Half in tension
Column Buckling - Half in compression, Half in tension
(OP)
Hello everyone,
I've been trying to solve this problem for a while but can't seem to find a solution.
I went through Galambos and Timoshenko but can't seem to find a case that would apply.
I'm trying to figure out which effective length to use for a column that is in tension for half the column and in compression for the other half.
This effectively means that a load upwards of P would be applied at top, and a load downwards of 2P at the middle with no bracing at mid-height.
If anyone has any references that they know of that could be of help, that would be much appreciated.
Thanks in advance.
I've been trying to solve this problem for a while but can't seem to find a solution.
I went through Galambos and Timoshenko but can't seem to find a case that would apply.
I'm trying to figure out which effective length to use for a column that is in tension for half the column and in compression for the other half.
This effectively means that a load upwards of P would be applied at top, and a load downwards of 2P at the middle with no bracing at mid-height.
If anyone has any references that they know of that could be of help, that would be much appreciated.
Thanks in advance.






RE: Column Buckling - Half in compression, Half in tension
The effective length is the column length assuming it is pinned top and bottom.
BA
RE: Column Buckling - Half in compression, Half in tension
RE: Column Buckling - Half in compression, Half in tension
BA
RE: Column Buckling - Half in compression, Half in tension
1.when the load is applied at the top of col it's final location is fixed/known after the assumed buckling deflection of the column because of the col being braced at that location..
2.when applied at mid-height the location of the load is dependent on the assumed lateral deflection of the col at mid-height and is a so-called "following load" which in itself adds to to the destabilizing affect..so by assuming the load is applied at the top of the col would be unconservative and consequently reduce the conservatism of assuming the effective length as the full length...
I would consider the final result to be more accurate than you claim...ofcourse, you may prove me totally misguided on this....
RE: Column Buckling - Half in compression, Half in tension
In a practical design situation, I would likely do exactly the same as you suggested, but if I wanted to predict the result more precisely, I would use the method I suggested above. While it may not be an exact solution to the problem, it can be as exact as you wish by simply repeating the cycle as often as required to find the buckled shape of the column.
BA
RE: Column Buckling - Half in compression, Half in tension
Mike McCann
MMC Engineering
RE: Column Buckling - Half in compression, Half in tension
Whether or not this has practical value is another matter, but there may be some application where it is of value.
BA
RE: Column Buckling - Half in compression, Half in tension
RE: Column Buckling - Half in compression, Half in tension
RE: Column Buckling - Half in compression, Half in tension
The question is a theoretical one although I am trying to potentially use it for design applications.
An example for a design application would be an unbraced beam in a chevron braced bay.
The beam would be braced along its strong axis at mid-point but not along its weak axis. Half of the beam could also hypothetically be in tension and half in compression.
There's very detailed solutions for point loads at mid point where designers can use a buckling length of ~0.8L but none for one portion of the column in tension and the other in compression.
The problem I was having is defining the buckling shape for such a case to arrive at a solution.
Thanks again for all your input; I'll definitely look at Timoshenko's book more closely this week.
RE: Column Buckling - Half in compression, Half in tension
Setup 1. Downwards load of 1 applied at top. Predicted buckling load factor 15.3 (which is exactly what Prof Euler would have told me).
Setup 2. Upwards load of 1 applied at top, and downwards load of 2 applied at midpoint. Predicted buckling load factor 61.2 (which is exactly four times the prediction for setup 1).
Something in my bones tells me that this is not a coincidence, and that there is some simple theoretical truth underpinning what is going on. Maybe a few lines of algebra will shine a light on it?
RE: Column Buckling - Half in compression, Half in tension
RE: Column Buckling - Half in compression, Half in tension
But your half-length column is not a pin-ended column as per Euler. It is partially free to sway at its top, and that freedom to sway is partially limited by the tension in the half-length member above it. What I want the algebra to show is why these two partial effects exactly cancel each other out.
RE: Column Buckling - Half in compression, Half in tension
Setup 3. No load applied at top, and downwards load of 1 applied at midpoint. Predicted buckling load factor 28.9 (which probably doesn't help us all that much other than to rule out the unlikely possibility of it being 30.6, which would have been "a coincidence too far").
RE: Column Buckling - Half in compression, Half in tension
RE: Column Buckling - Half in compression, Half in tension
In practice the system would also become laterally soft at the same time, which in real trellis type frames is the issue.
Cheers
Greg Locock
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RE: Column Buckling - Half in compression, Half in tension
In other words, to mis-quote Gilbert & Sullivan, "it was the very model of a modern Euler column".
RE: Column Buckling - Half in compression, Half in tension
Another way to model it which should produce the same result: Node at very bottom restrained against X and Y translations, but fully free to rotate. Node at very top restrained against X and Y translations and also fully free to rotate. Node at midpoint unrestrained in any way. Downward load of 2P applied at midpoint. No other load applied.
Beam elements as before.
BA
RE: Column Buckling - Half in compression, Half in tension
RE: Column Buckling - Half in compression, Half in tension
Quando Omni Flunkus Moritati
RE: Column Buckling - Half in compression, Half in tension
You are correct. As expected (because of the small-displacement nature of a linear buckling solution) the model you defined gives identical results to my setup-2 above.
RE: Column Buckling - Half in compression, Half in tension
But in a non-linear analysis (and reality) having the top node restrained in the Y direction will make a big difference, it will prevent buckling. As the lower part of the column approaches the buckling load a greater proportion of the applied load will be transferred to the top support, and the top half of the column, which is in tension, will restrain the lower half. The behaviour will be non-linear, but there will be no buckling until the top column reaches its yield stress.
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: Column Buckling - Half in compression, Half in tension
RE: Column Buckling - Half in compression, Half in tension
the extreme model would be a column (like a flag pole) loaded at the free end (fixed at the base), which is a known solution. the real problem is better than this as there is some lateral stiffness and some moment continuity (allowing the "free" end to react with the rest-of-the-world).
Quando Omni Flunkus Moritati
RE: Column Buckling - Half in compression, Half in tension
"An example for a design application would be an unbraced beam in a chevron braced bay.
The beam would be braced along its strong axis at mid-point but not along its weak axis. Half of the beam could also hypothetically be in tension and half in compression."
This is a system where the force in the beam is applied by a pair of braces, one in tension, one in compression. You can see continuity between the compression brace and the compression half of the beam. The system needs lateral restraint unless a conservative effective length factor is used.
However, the beam is often in compression, carrying load to the bracing, not the other way around.
Michael.
"Science adjusts its views based on what's observed. Faith is the denial of observation so that belief can be preserved." ~ Tim Minchin
RE: Column Buckling - Half in compression, Half in tension
I would definitely be exercising caution in such a design case but here is an example (allowed by code) where this scenario would occur.
If you're designing a tubular EBF (ie. totally unrestrained along its length except at the ends and at the braces along the y-axis). The code demands a minimum Iy/Ix ratio for design but does not give guidance as to how to design the beam portion outside of the link.
Again, in this instance, there would be a portion of the beam in tension and a portion of the beam in compression (very similar to chevron braces).
In my opinion, it would be too conservative to consider the typical pinned-pinned Euler weak axis buckling load for the entire length but it is hard to justify any other case.
It sounds like designers should not tempt fate in such a design scenario and just design the beam-column by considering the entire laterally unbraced length along the weak axis.