Estimation of Geometrical Torsion Rigidity of Triangular and Rectangular Sections Using Interpolation Method

  • A. V. KorobkoEmail author
  • S. Yu. Savin
  • Yu. E. Balikhina
Conference paper
Part of the Lecture Notes in Mechanical Engineering book series (LNME)


The article considers the problem on a pure torsion of elastic prismatic beam with arbitrary convex contour in the isoperimetric form. It is proved that for isometric sections with a convex contour, the normalized geometrical torsion rigidity depends on one parameter only—the form factor. The sections in the form of isosceles and rectangular triangles, rectangles, and parallelograms are considered. Graphical comparison of the given geometrical rigidity of the examined sections with the value reciprocal of the form factor displayed the real similarity of these graphs. Analysis of these graphs provides the conclusion that all the range of values of the normalized geometrical rigidity of parallelogram sections is limited from above with values ik for rectangular sections, and from below—for the rhombic sections. Applying the method of geometrical modeling rigidity of the sections by a section form, we suggest the interpolation method to determine the given geometrical rigidity of the sections by the form factor. The obtained results are otherwise satisfactory when performing engineering calculations.


Pure torsion Elasticity Prismatic beams Torsion rigidity Form factor Interpolation method 


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • A. V. Korobko
    • 1
    Email author
  • S. Yu. Savin
    • 2
  • Yu. E. Balikhina
    • 1
  1. 1.Orel State University Named after I.S. TurgenevOrelRussia
  2. 2.South-West State UniversityKurskRussia

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