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Optimization of Thin-walled Beams with Mono-Symmetric I-section subjected to torsion

A thin-walled beam with mono-symmetric I-cross-section fixed at its ends and loaded by the uniformly distributed torsion loads Pm is considered in this paper. The thin-walled beam is subjected to torsion with influence of shear and also to bending due to shear in the plane orthogonal to the plane of symmetry. The beam has small ratio length of the beam and length of the middle line. Because of that the shear influence especially on the angle of torsion, but also on the normal stresses in longitudinal direction, is significant. So, in this paper the normal stress and the angle of torsion we will calculate with the influence of shear. All geometrical properties of mono-symmetric I cross-section needed for calculation of the normal and shear stresses and the angle of torsion are given in numerical and graphical outputs. The optimization of the beam’s cross-section dimensions is done using MS Excel Solver GRG Nonlinear algorithm. The goal is the smallest mass of the beam and two criteria: strength and rigidity criteria were taken into consideration. For so obtained optimal cross-section the values of maximum normal stresses as well as the maximum value of the total angle of torsion for all types of materials according to the both criteria are given.

thin-walled beam, open cross-section, optimization, torsion with influence of shear

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