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Evaluation of Mathematical Solutions for the Determination of Buckling of Columns Under Self-weight

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Abstract

Propose

Investigation of mathematical solutions for including the self-weight of a column for calculating buckling critical load. The complexity of including self-weight resides in the fact that the mathematical formulation depends on elliptical integral solutions related to differential equations of the problem.

Method

Comparing the analytical solutions with computation modeling. The obtained results with these computational models are approximate since they depend on the discretization of the domain of the problem while analytical solutions tend to be exact. An experimental activity was carried out for analyzing mathematical accuracy.

Results

The investigation of buckling was performed through static as well as dynamic analysis. The results found shown differences smaller than 5% among the mathematical investigated solution. Besides that, all solutions represented well the problem in comparison with a laboratory test.

Conclusion

It has been evaluated solutions for stability analyses of bars under self-weight, using Euler–Greenhill analytical approach, solutions with the eigenvalues from FEM analysis, and also a dynamic solution based on the Rayleigh’s method, comparing them with dynamic laboratory tests. Can be concluded that the mathematical ways and the experimental investigation had a good agreement.

Level of evidence

IV, evidence obtained from multiple mathematical methods, static and dynamic, is experimentally confirmed.

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Authors and Affiliations

  1. Department of Construction and Structures (DCE), Polytechnic School, Federal University of Bahia (UFBA), Rua Aristides Novís, 02, 5º andar, Federação, Salvador, BA, 40210-910, Brazil

    Alexandre de M. Wahrhaftig & Kaique M. M. Magalhães

  2. Center for Engineering, Modeling and Applied Social Sciences, Federal University of ABC (UFABC), Rua Arcturus, 03 (Jd. Antares), Edifício Delta, Sala 386, São Bernardo do Campo, SP, 09606-070, Brazil

    Reyolando M. L. R. F. Brasil

  3. In Autonomous Collaboration, Warsaw, Poland

    Krzysztof Murawski

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  1. Alexandre de M. Wahrhaftig
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  2. Kaique M. M. Magalhães
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Correspondence to Alexandre de M. Wahrhaftig.

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Appendix 1

Appendix 1

Dynamic and Static Experimental Results Obtained in Testing

See Tables 1 and 2.

Table 1 Results from dynamic analysis
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Table 2 Results from static analysis
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Wahrhaftig, A.d.M., Magalhães, K.M.M., Brasil, R.M.L.R.F. et al. Evaluation of Mathematical Solutions for the Determination of Buckling of Columns Under Self-weight. J. Vib. Eng. Technol. 9, 733–749 (2021). https://doi.org/10.1007/s42417-020-00258-7

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