Talk:Buckling

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[edit] Emphasised the role of boundary conditions

I have added a point to help emphasise the importance of boundary conditions, so hopefully readers will appreciate that it is of critical importance to correctly judge the boundary conditions of a real life structure if they hope to achieve any accuracy in their structural analysis. I also added a picture of mine which I think illustrates this clearly Grahams Child 08:48, 25 May 2006 (UTC)

[edit] Picture Required

This needs a picture desperately. Also, the introduction could be a little less technical. Anyone up to the challenge?--Joel 18:18, 18 May 2005 (UTC)

--- different topic -----

1. that elasticity and not compressice strength . . .

In my opinion the above sentence is nonsense. Since a high value of E (Young's modolus, modulus of elasticity) signifies a high "compressive strength" (just as it signifies a high "tension strength").

Stiffness is not the same thing as strength. The sentence makes sense to me: E is in the equation and there's no strength/maximum stress term to be found. --Spindustrious 16:16, 6 October 2005 (UTC)

[edit] Axial vs. Eccentric loading conditions

   A short column under the action of an axial load will fail by direct compression but a long column loaded in the same manner will fail by buckling (bending), the buckling effect being so large that the effect of the direct load may be neglected.

I'm not sure this statement is correct. Any beam, regardless of the length, will fail in direct compression if the load is axial. A beam which fails due to buckling must have eccentric loading conditions in order to generate the bending moment required to buckle the beam. Axial loads provide no moment arm and therefore will never buckle a beam. In the real world, it is extremely difficult to create a true axial force and as a result it would appear that long columns fail under an "axial" load when in truth the load will be found to be eccentric due to some imperfection in the test.

The short of the long of it is that I don't think that the above statement is technically correct, and it might need a slight revision, perhaps something along the lines of:

   A short column under the action of an eccentric load will fail by direct compression before it buckles but a long column loaded in the same manner will fail by buckling (bending), the buckling effect being so large that the effect of the direct load may be neglected.

Any thoughts? Alangstone 00:54, 28 October 2005 (UTC)

Generally you are right but what you need is a load with infinitely small eccentricity (not exactly the same as eccentric load). I think that your proprosition could create some misunderstandings. Anyway before it buckles addition sounds reasonable and I will include it into the text. --Nk 12:06, 22 December 2005 (UTC)
I think Alangstone is missing the point: consider a perfectly straight beam with a perfectly axial load. Of course buckling could not actually happen in those conditions. What theory says is that, if there is a arbitrarily small deviation in the shape of the beam (not in the direction of the forces applied), if the compression exerted is smaller than the critical value given in the text, the deformation of the beam is stable and will not grow catastrophically due to the axial load. However, if the compression exerted is larger than the critical value, then it can be shown that an arbitrarily small deviation of the beam shape will grow catastrophically due to axial load because the problem becomes unstable. Since, in real life, beams cannot be perfectly straight, buckling always happens over the critical value in absence of other stabilizing factors.
I disagree with the comment above. The theory mentioned (the Euler buckling equation) is the result of the first eigensolution of the differential equation that relates lateral deflection (ie-buckling) to an applied compressive load. To set up the equation, you must assume that the load does not act through the center of gravity of the section, but rather through a slight eccentricity, which generates a moment. Then you equate that moment to the restoring moment caused by the material stiffness. At some critical value of the load, the restoring moment will exactly counteract the applied moment, increase the load and the member will buckle. The argument made above suggests that a deviation in shape will result in buckling. This is true under 2 cicumstances:
First, if the change in shape also means a change in center of gravity then by shifting the center of gravity, but leaving the load to act along the same line, you have in essence created a slight eccentricity and therefore also a moment. If the moment exceeds the restoring moment -- buckling occurs.
Secondly, if the change in shape does not result in a change of the center of gravity, but it does reduce the material stiffness (think of a cone shaped column vs. a cylindrical column with the same radius - both have their center of gravity acting in the center of the circle, but the cylinder is stiffer because it has more cross-sectional area at any given point), then provided the load is slightly eccentric and that the column buckles, what you have done in this case is changed the problem such that the column is no longer a short column, but is now an intermediate or long column. Either way, the definition of a short column is that it will crush before it buckles.
While I do agree that my original proposed change was flawed, I find that NK's reasoning is more valid that the one above. That being said, this isn't an engineering textbook, its an encyclopedia. I think that NK is right that if we introduce the concept of eccentricity it will confuse the issue for non-technical readers, thereby defeating the purpose of the article. Personally, I'm happy with the way it reads right now. Alangstone 00:10, 21 January 2006 (UTC)

[edit] Center of Gravity vs. Centroid; Moment of Inertia vs. Second Moment of Area

Comment on the following excerpt:

 "If the load on a column is applied through the center of gravity of its cross section it is called an axial load."

I am aware that "center of gravity" --U.S. spelling--is commonly used interchangeably with "centroid of cross section." People may understand the intent given the context of the discussion, but, considering that this is an encyclopedia, it seems that the technically correct term should be used. The need for this change is possibly made more urgent by the article on "center of gravity," which makes no mention of the misnomer.

To be clear, the centroid is the geometric center of an area (for buckling, we are interested in centroids of areas). The article on "centroid" seems quite good so no need to reproduce it here. Centroids do not require a knowledge of the volume or the density distribution in the column, nor of the gravitational field in which the column resides. Perhaps if the buckling article discussed the buckling of columns under their own weight, then these other terms would be relevant.

The center of gravity on the other hand, while a mathematically similar concept, does involve the length of the beam, the density distribution, and the variation of the gravitational field. It, however, does not generally have any relationship to the issue of buckling.

So here is a proposed improvement to the above quote:

 "If the load on a column is applied along its centroidal axis it is called an axial load."

Would this change add value to the article?


On a related note, I have long wondered how "moment of inertia" became synonymous with both "second moment of mass" and "second moment of area." The "moment of interia" article does identify usage of "moment of inetia" for the the latter term as a misnomer. So given the widespread use of the phrase "area moment of inertia," would it still be helpful to replace it with the (perhaps less familiar) more technically sound "second moment of area?" That article is quite good also.

AJOS 22:19, 19 March 2006 (UTC)

[edit] Design of members in compression

In the article it is stated: "Examination of this formula [the Euler load] reveals the following interesting facts with regard to the load bearing ability of columns: that elasticity and not compressive strength of the materials of the column determines the critical load."

On this backgriound I am wondering why in Codes of Practice such as BS 5950 the load-carrying capacity of members in compression is dependent on material strength and not Young's modulus? The article does hint at a number of possible reasons ("a number of empirical column formulae have been developed to agree with test data" and "buckling will generally occur slightly before the theoretical buckling strength of a structure due to plasticity of the material"), but it would benefit the article to devote an entire section to this question. Does anyone know the answer? Is it already in the article? --Ahnielsen 21:11, 26 June 2006 (UTC)

I have replied on your talk page Alangstone 22:55, 26 June 2006 (UTC)

[edit] First paragraph

I don't want to start a revert war here, so I will explain why I am changing the opening paragraph back to the prior edit.

1) a member that fails as a result of buckling will fail at a lower load than the ultimate compressive strength of the material. It is _not_ possible for the member to carry a load above the ultimate compressive strength, as it would have failed in direct compression once the load reached ultimate. I tried to disambiguate this by adding the word "ultimate" into the opening sentence.

2) I have removed the sentence that read "If the actual compressive stresses were lower, it would not exceed the design requirements." This statement is not accurate. Just because a column is subjected to a load below critical for buckling, it does not necessarily mean that the member meets design requirements - there are other possible failure modes that must be considered which can occur well below the buckling load. (ex - Connection failure) Alangstone 03:16, 9 August 2006 (UTC)

[edit] Doug Roland's Neck

Happened across this page while looking for information on buckling of curved columns... While I'm sure Mr. Roland's neck is quite long and slender, and his head is sufficiently massive as to cause buckling in Earth's gravitational field, I'm not sure that this information is encyclopedic. I removed the link to the non-existant article.--156.68.7.124 15:21, 4 October 2006 (UTC)

[edit] Elastic Bending Before Buckling

A quick question on something that I have difficulty in finding anywhere in internet. What relationhsip is there between the change in length of the column, and the force applied, before the maximal load is applied? Foe example, I applied a force to a carbon fibre tube (thin walled and long), which caused it to bent. The force needed to start it bending was close to 20kg. As I increased the force slightly, it bent more. At about 22kg it was bent like a "U" and then broke. Or am I too deep in the dark to see that it is already answered? Harry Marx

[edit] Selfbuckling

Where does this formula come from? Doing some quick back of envelope equations seems to imply to me that it should in fact be pi^2 / 4 (~2.47) rather than 2.5. Is this an unnessesary approximation, or am I mistaken?

[edit] Comment on Axial vs. Eccentric loading conditions

Euler's theory merely determines the conditions for stability under load. Below a certain load, the tendency is for the deflection in response to any (lateral) perturbation is to return to zero. Above the critical load deflection will keep on increasing until catastrophic failure occurs. As with all ideas on stability, some infinitesmal displacement is implicitly assumed. Perfection in alignment, straightness and homogeneity of material is unfortunately beyond us mere mortals. Real life engineers do not have access to the mathematican's stock of inextensible strings, massless pulleys, frictionless pegs, etc..Gordon Vigurs 06:55, 10 April 2007 (UTC)

[edit] The second order surface moment of inertia...

If you are saying, in section Buckling in columns, that K=2 for hinged bar than your equation for stress is correct. Equation for surface moment of inertia is not correct. That is, the second equation is for the polar moment of inertia and that is not the one used here.

I_y=I_x=\frac{1}{2} A R^2

I\neq A R^2

Marko Raodosavljevic152.88.80.79 09:53, 25 May 2007 (UTC)


[edit] LTB section

Not only is the following section quite clearly copy and pasted from somewhere else, assumadly a lecturers notes, but it has been done so extremely lazily:

"When a beam is loaded in flexure, the compression side is in compression, and the tension side is in tension. If the beam is not supported in the lateral direction (i.e., perpendicular to the plane of bending), and the flexural load increases to a critical limit, the beam will fail due to lateral buckling of the compression flange. In wide-flange sections, if the compression flange buckles laterally, the cross section will also twist in torsion, resulting in a failure mode known as lateral-torsional buckling.

Any problems with this come and see davie boyce in room 801"

Removal of the bottom line will not change the fact that it has been copied, the section will need rewriting completely.Pledger166 (talk) 23:58, 10 January 2008 (UTC)

"The maximum load, sometimes called the critical load, causes the column to be in a state of unstable equilibrium;" - At Pcrit (critical buckling force) the strut will actually have neutral stability - this are not the same things as unstable equilibrium. Imagine a ball on the perfect top of a perfect hill - any lateral displacement will cause it to roll off - this is unstable equilibrium...then switch to a ball on a perfectly flat surface - it will displace with any lateral force but will not further displace once the lateral force is removed - as is the case here Sam Lacey (talk) 02:54, 29 February 2008 (UTC)