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Above is a chart from a Eurocode handbook. It gives a correct buckling curve depending on cross section and its dimensions. I noticed that for hollow sections, the choice depends on whether the section is hot finished or cold formed. Why does it matter how the beam is manufactured? Shouldn't the buckling behavior depend just on cross section geometry and the material used? Why does it matter how the beam is made?

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  • $\begingroup$ What about welded seam or seamless? do you think that will have an effect? $\endgroup$
    – Solar Mike
    Jul 15, 2020 at 18:29
  • $\begingroup$ Probably, but I don't know why. Why does anything besides geometry have an effect on buckling? $\endgroup$
    – S. Rotos
    Jul 15, 2020 at 18:41
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    $\begingroup$ Have you checked any books on heat treatment? That may give you an insight. $\endgroup$
    – Solar Mike
    Jul 15, 2020 at 18:45
  • $\begingroup$ @Solar Mike I am aware of heat treatment; they are used to reduce residual stress. But how is that related to buckling? And why is the difference made only with hollow sections and not L sections for example? $\endgroup$
    – S. Rotos
    Jul 15, 2020 at 18:48
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    $\begingroup$ Manufacturing processes create internal stresses in the component. Buckling depends on the actual stress, not just the stress from the applied loads. The internal stresses may be beneficial (e.g. pre-stressed reinforced concrete) or they may not, but either way they make a difference. $\endgroup$
    – alephzero
    Jul 15, 2020 at 18:55

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Manufacturing methods for structural steel shapes result in stresses that remain in the material after the section has been formed. Those residual stresses have an impact on the buckling curve and are a major reason the design curves are distinct from the theoretical Euler buckling curve.

In hot-rolled sections and welded sections, the residual stresses are principally due to uneven cooling. For example: in a hot-rolled wide flange beam, the flanges, being thicker than the web, cool more slowly. But the flange tips also cool more quickly than the flange where it joins to the web because the tips have more surface exposed to air. The result is residual compressive and tension stresses in the section, and this means that when the member is subjected to a compressive load, the fibers in the section are not all under the same stress. This gives rise to the inelastic buckling portion of the buckling curve. This is being accounted for in the rolled sections listed in the table you included, but all those sections will be hot-rolled so there's no need to distinguish between manufacturing methods.

The figure below (obtained here) shows the typical arrangement of residual stresses in sections fabricated by various methods.

residual stresses

The cold forming process by which HSS are produced also introduces residual stresses, particularly at the corners. The Steel Tube Institute has a nice overview of this. If the piece is subsequently hot finished, this will relieve some of these residual stresses and the buckling curve will be changed. I don't possess a copy of Eurocode 3, but my expectation is that buckling curve "a" for the hot finished sections will lie closer to the theoretical elastic buckling curve than curve "c" for the cold formed sections.

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  • $\begingroup$ Great answer, thank you! $\endgroup$
    – S. Rotos
    Jul 20, 2020 at 17:36
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The cold-formed pieces will exhibit less elongation before yielding because cold work has been performed on them. The hot-formed pieces will exhibit more elongation before yield because they have been annealed into their unworked state.

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  • $\begingroup$ Why does it matter only for hollow sections and not for L sections or I sections? Only hollow sections have different curves for hot formed and cold formed pieces in that picture. $\endgroup$
    – S. Rotos
    Jul 16, 2020 at 4:32
  • $\begingroup$ do not know. -NN $\endgroup$
    – niels nielsen
    Jul 16, 2020 at 4:32
  • $\begingroup$ Okay, thanks anyway. I was wondering, aren't the buckling curves plotted against non dimensional slenderness, which is a function of yield stress? So if the treatment of the metal changes changes elongation before stress, in another words its yield stress, would be just get a different slenderness and a different point on a curve? Why do we now use a different curve? $\endgroup$
    – S. Rotos
    Jul 16, 2020 at 4:51
  • $\begingroup$ do not know. - NN $\endgroup$
    – niels nielsen
    Jul 16, 2020 at 4:59
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The only material factor is the material strength, The themo-mechanical processing to get to the strength makes no difference. All oil well casing designs have a buckle calculation,they are round but I expect the same principles apply. For thinner sections such as in the shown figures , the yield strength was used . For thick sections the tensile strength was used . I forget the exact boundary for thick/thin , maybe about 15 : 1 ,diameter /wall thickness.

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