Engineering Mechanics

Proceedings Vol. 27/28 (2022)

ENGINEERING MECHANICS 2022

Copyright © 2022 Institute of Theoretical and Applied Mechanics of the Czech Academy of Sciences, Prague

 

Baláž I., Koleková Y., Partov D.
pages 17 - 20, full text

Calculation of the critical moments M_cr of the beams under various combinations of the uniform loading q and the end moments. Solution of the differential equations is presented in the graphical form. Two diagrams enable to obtain the factors C₁ and C₂, which depend on the parameters M and ψ . Approximate formula for calculation of the critical moments depending on three factors C₁, C₂, C₃ and three dimensionless parameters κ_wt , ζ_g , ζ_j was derived before. The values of the factors C₁, C₂, C₃ for basic loadings of the beams with the various combinations of the boundary conditions in vertical and horizontal bending and torsion for the monosymmetric I-sections were published before. They were later accepted for Eurocode (2007) and many national annexes. The presented results are valid for the beams simply supported with double symmetric I-sections. They may be used also for the continuous beams being slightly on the safe side. Numerical examples show that our results equal to the exact results of commercial computer programs. The procedure gives quickly practically exact results and therefore it is efficient tool for designers.

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