Thin-Walled Rods with Semi-Opened Profiles

  • Vladimir Kobelev


A thin-walled beam is an extraordinary type of the torsion spring. This type of torsion spring serves as the cross-connection member in several industrial and automotive structures. The thin-walled beam is an elongated elastic structural element whose distinctive geometric dimensions are all of different orders of magnitude. Thin-walled beams can be classified by their geometric features. Two classes of thin-walled beam cross-sections are notable, namely thin-walled beams with the open cross-section and thin-walled beams with the closed cross-section (Vlasov 1961; Timoshenko 1945; Flügge and Marguerre 1950). In the Chap.  10 an intermediate class of thin-walled beam cross-sections is studied. The cross-section of the beam is closed, but the shape of cross-section is elongated and curved. The walls, which form the cross-section, are nearly equidistant. The Saint-Venant free torsion behavior of the beam is similar to the behavior of closed cross-section beams. However, the total warping function of the semi-opened cross-section is similar to the warping function of open cross-section beam.

Generally speaking, particular difference between thin-walled rods is in the presence of warping of cross-section and the corresponding force factor, the bi-moment. It is shown, that the thin-walled beams with closed profiles behave differently, depending on the form of the cross-section. There exist two types of the thin-walled beams with closed profiles. The first type of thin-walled beams possesses closed profiles with nearly equal diameters in all directions, so that there is no distinguished direction. The torsion of such closed beams is predominantly of Saint-Venant type. The effect of bi-moment on the twist behavior of the thin-walled beams of the first type is in most cases negligible in comparison to the Saint-Venant torsion. The second type of thin-walled beams embraces closed profiles formed by equidistant walls, elongated profiles and star-like profiles. The contribution of Saint-Venant torsion stiffness of beams with this type of profile is of the same order of magnitude, as the contribution of sectorial stiffness and the effect of bi-moment should be accounted.


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© Springer International Publishing AG 2018

Authors and Affiliations

  • Vladimir Kobelev
    • 1
  1. 1.Faculty of EngineeringUniversity of SiegenSiegenGermany

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