Approximate Torsional Analysis of Arbitrary Trapezoidal Bars by Kantorovich Method

Document Type : Research Article

Authors

1 Arak University, Arak, Iran

2 Department of Civil Engineering, Faculty of Engineering, Arak University, Arak, Iran

3 Arak University, Arak,, Iran

Abstract

A variety of structural members are expected to safely tolerate torsional moments. These include irregularly-shaped cross-sections (e.g., trapezoidal or triangular sections) in some industries which deserve special considerations for the analysis and design under torsional loading. Therefore, the development of novel methods as alternative approaches seems very necessary, partially because of the deficiency of analytical solutions in treating asymmetric solution domains. Semi-analytical and numerical methods appear as desirable alternatives in most cases. One of the proper tools for dealing with the boundary value problems encountered in the torsional analysis is the vibrational method. The Kantorovich semi-analytical method, known as an extension of the Rayleigh-Ritz method, has been proven advantageous among the others, mainly because of relaxing the conventional limitations in selecting the primary function for satisfying the boundary conditions. Therefore, the purpose of the present study is to extend the applicability of the Kantorovich method to estimate the warping and stress field of arbitrary trapezoidal sections directly. Finally, the efficiency and accuracy of the present solution is verified against a number of existing analytical and numerical methods. The results indicate high precision and rapid convergence of this semi-analytical method.

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Main Subjects

References

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Amirkabir Journal of Mechanical Engineering
Volume 53, Issue 10
January 2022
Pages 5203-5220

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