Convergence of the Rayleigh–Ritz Method for buckling analysis of arbitrarily configured I-section beam–columns

  • Hakan OzbasaranEmail author


Design of the slender members requires calculation of buckling loads in addition to stress and deflection demand/capacity ratios. The Rayleigh–Ritz Method, which allows one to present approximate closed-form solutions for certain cases, is one of the simplest methods for this purpose. This study evaluates the buckling analysis of the I-section prismatic beam–columns with the Rayleigh–Ritz Method in detail. First, algebraic, trigonometric, and exponential trial functions for various restraint configurations are derived carefully in finite series form. Then, an iterative procedure to calculate buckling loads and modes is described. Finally, a software is developed with Mathematica and the sensitivity of the results and performance to trial function type and the number of terms is investigated over 1000 computer-generated numerical examples, which include doubly and singly symmetric sections, simply supported and cantilever members, intermediate torsional and lateral restraints, transversal concentrated and distributed loads acting above/below the shear center, and axial loads.


Buckling I-section Beam–column Rayleigh–Ritz Trial function Intermediate restraint 



This study is supported by the Eskisehir Osmangazi University’s Scientific Research Projects Department (Project ID: 2015-806).


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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Civil EngineeringEskisehir Osmangazi UniversityEskisehirTurkey

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