ON CALCULATING BUCKLING CRITICAL LOAD OF COLUMNS WITH GENERALLY DEFINED SEMI-RIGID END RESTRAINTS
Abstract
The purpose of this article is to present an approach for calculating exact critical buckling load of axially loaded column with generally defined semi-rigid end restraints (translational and rotational) with regard to convenient programming. The formulation of general boundary conditions to the buckling differential equation is explained and the corresponding matrix for finding eigenvalues (critical loads) is provided. A technique to account for absolutely rigid connections without the need to compute additional parameters and consider several end connection types, and as a result several matrices to include in programming, is demonstrated. The program composed in MATLAB environment was tested on five different cases with varying parameters of column length, flexural rigidity and values of translational and rotational stiffness of end restraints. The results of program computation (critical loads and K-factors) were contraposed to the results from FEM analysis, reference data and results from another scientific article. The results of comparison of computer program results, FEM analysis results and reference data showed relatively small deviation and none was observed for one available theoretical value from another article.
About the Author
V. V. Karnevich
Peoples’ Friendship University of Russia (RUDN University)
Russian Federation
Russian Federation
References
1. Stanton, J., Eberhard, M., Sanders, D., Thonstad, T., Schaefer, J., Kennedy, B., … Mantawy, I. (2014, July 21-25). A pre-tensioned, rocking bridge bent for ABC in seismic regions. Paper presented at the 10th National Conference in Earthquake Engineering: Frontiers of Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK.
2. Алфутов, Н. A. Основы расчета на устойчивость упругих систем. - М.: Машиностроение, 1978.
3. Гордон В.А. Красчету на устойчивость эволюционно поврежденного железобетонного элемента с «деградирующими» условиями опирания / В.А. Гордон, В.И. Колчунов // Строительная механика и расчет сооружений. - 2006. - №4. - С. 33-38.
4. Kartal, M. E., Basaga, H. B., Bayraktar, A., & Muvafik, M. (2010). Effects of semi-rigid connection on structural responses. Electronic journal of structural Engineering, 10(10), 22-35.
5. British Standards Institution. (2008). Eurocode 2: design of concrete structures: British standard. London: BSi.
6. Duan, L., & Chen, W. F. (1999). Effective length factors of compression members. Structural engineering handbook.
7. Chen, W. F. (2011). Semi-rigid connections handbook. J. Ross Publishing.
8. Aristizabal-Ochoa, J. D. (1994). K-factor for columns in any type of construction: nonparadoxical approach. Journal of Structural Engineering, 120(4), 1272-1290.
9. Adman, R., & Saidani, M. (2013). Elastic buckling of columns with end restraint effects. Journal of Constructional Steel Research, 87, 1-5.
10. Aristizabal-Ochoa, J. D. (2013). Stability of slender columns on an elastic foundation with generalised end conditions. Ingeniería e Investigación, 33(3), 34-40.
11. Birger, I. A., & Panovko, Y. G. (1968). Strength, stability, oscillations. Moscow: Mashinostroenie.
12. Карневич, В.В. Моделирование потери устойчивости прямого стержня на упругих опорах // Научному прогрессу - творчество молодых. - 2017. - №1-4. - С. 96-98.
13. Колллатц, К. Задачи на собственные значения с техническими приложениями. - М., 1968
14. Кривошапко, С.Н. Основы устойчивости упругих систем. - М.: Издательство РУДН,1992. - 80 с.
Review
For citations:
Karnevich V.V. ON CALCULATING BUCKLING CRITICAL LOAD OF COLUMNS WITH GENERALLY DEFINED SEMI-RIGID END RESTRAINTS. Building and Reconstruction. 2018;(1):38-44. (In Russ.)
Views:
84
Email this article 