Least Squares Weighted Residual Method for Solving the Generalised Elastic Column Buckling Problem

Least Squares Weighted Residual Method for Solving the Generalised Elastic Column Buckling Problem

Charles C. IkeClifford U. Nwoji Benjamin O. Mama Hyginus N. Onah  

Department of Civil Engineering, Faculty of Engineering, Enugu State University of Science and Technology, Enugu, 400001, Enugu State, Nigeria

Department of Civil Engineering, University of Nigeria, Nsukka, Enugu State, Nigeria

Corresponding Author Email: 
19 January 2019
15 March 2019
31 March 2019
| Citation



In this work, the least squares weighted residual method (LSWRM) was used to solve the generalised elastic column buckling problem for the case of pinned ends. Mathematically, the problem solved was a boundary value problem (BVP) represented by a system of three coupled linear ordinary differential equations (ODEs) in terms of three unknown displacement functions and subject to boundary conditions. The least squares residual method used formulated the problem as a variational problem, and reduced it to an algebraic eigenvalue problem which was solved to obtain the characteristic buckling equation. The characteristic stability equation was found to be a cubic polynomial for the general asymmetric sectioned column. The buckling modes were found as coupled flexural – torsional buckling modes. Two special cases of the problem were studied namely: doubly symmetric and singly symmetric sections. For doubly symmetric sections, the buckling loads and the buckling mode were found to be decoupled and the buckling mode could be flexural or flexural – torsional. For singly symmetric section columns, one of the bucking modes becomes decoupled while the others are coupled. The buckling equation showed the column could fail by either pure flexure or coupled flexural – torsional buckling mode. The results of the present work agree with Timoshenko’s results, and other results from the technical literature.


Least squares weighted residual method, generalised elastic column buckling problem, asymmetric section, singly symmetric section, doubly symmetric section, characteristic buckling equation, algebraic eigenvalue eigenvector problem

1. Introduction
2. Theoretical Framework
3. Methodology
4. Results
5. Discussion
6. Conclusion

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