Computational Technology Resources - CCP

Keywords: critical load, elastic stability, geometric stiffness, finite element method, buckling, self-weight.

Summary

The consideration of the bar self-weight in the buckling critical load problem was first discussed by Euler, who could not obtain a satisfactory solution. This problem was definitely solved by Greenhill in 1881. The main difficulty found by Euler was that the differential equation for the curvature considering a uniformly distributed compressive force is not as simple as the constant coefficients of the differential equation for the normal external force buckling problem [1]. The solution of first case requires either the application of infinite series or the application of approximate methods (e.g. the energy method). Modern procedures utilize matrix linear analyses based on a non-trivial solution by eigenvalues and eigenvectors, and offer numerical solutions easily implemented using a finite element (FE) environment [2]. However, it is important to understand that the stiffness matrix of structures subjected to axial loads is different from the conventional stiffness matrix. Axial loads produce the effect of reducing the stiffness of the structural members [3]. Hence, the buckling critical load determination now requires some of the aspects peculiar to non-linear analysis. That can be conveniently done, for several engineering problems, by the introduction of the geometric stiffness concept [4]. He present work evaluates the critical load of bars exclusively subjected to their self-weight, utilizing Euler's formulation and the finite element method eigenvalue solution via computational analysis.

References

1: Timoshenko S., "Theory of Elastic Stability", McGraw-Hill Book Company Inc, New York and London, 1936.
2: Cook R.D., Plesha D.S.M., Witt R.J., "Concepts and Applications of Finite Element Analysis". John Wiley and Sons, Inc., NJ, USA, 2002.
3: Gambhir M.L., "Stability Analysis and Design of Structures", Patiala Índia, Springer, 2004.
4: Wilson E.L., Habibullah A., "Static and Dynamics Analysis of Multi-Story Buildings, Including P-Delta Effects", Earthquake spectra, Vol.3, No 2., 1987. doi:10.1193/1.1585429

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £145 +P&P)

	Computational & Technology Resources an online resource for computational, engineering & technology publications
	not logged in - login
Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 88 PROCEEDINGS OF THE NINTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping and M. Papadrakakis Paper 13 Evaluation of the Buckling Critical Load of Bars Subjected to their Self-Weight A.M. Wahrhaftig, R.M.L.R.F. Brasil and M.A.S. Machado Department of Structural and Geotechnical Engineering, Polytechnic School, University of São Paulo, Brazil doi:10.4203/ccp.88.13 purchase the full-text of this paper Full Bibliographic Reference for this paper A.M. Wahrhaftig, R.M.L.R.F. Brasil, M.A.S. Machado, "Evaluation of the Buckling Critical Load of Bars Subjected to their Self-Weight", in B.H.V. Topping, M. Papadrakakis, (Editors), "Proceedings of the Ninth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 13, 2008. doi:10.4203/ccp.88.13 Keywords: critical load, elastic stability, geometric stiffness, finite element method, buckling, self-weight. Summary The consideration of the bar self-weight in the buckling critical load problem was first discussed by Euler, who could not obtain a satisfactory solution. This problem was definitely solved by Greenhill in 1881. The main difficulty found by Euler was that the differential equation for the curvature considering a uniformly distributed compressive force is not as simple as the constant coefficients of the differential equation for the normal external force buckling problem [1]. The solution of first case requires either the application of infinite series or the application of approximate methods (e.g. the energy method). Modern procedures utilize matrix linear analyses based on a non-trivial solution by eigenvalues and eigenvectors, and offer numerical solutions easily implemented using a finite element (FE) environment [2]. However, it is important to understand that the stiffness matrix of structures subjected to axial loads is different from the conventional stiffness matrix. Axial loads produce the effect of reducing the stiffness of the structural members [3]. Hence, the buckling critical load determination now requires some of the aspects peculiar to non-linear analysis. That can be conveniently done, for several engineering problems, by the introduction of the geometric stiffness concept [4]. He present work evaluates the critical load of bars exclusively subjected to their self-weight, utilizing Euler's formulation and the finite element method eigenvalue solution via computational analysis. References 1 Timoshenko S., "Theory of Elastic Stability", McGraw-Hill Book Company Inc, New York and London, 1936. 2 Cook R.D., Plesha D.S.M., Witt R.J., "Concepts and Applications of Finite Element Analysis". John Wiley and Sons, Inc., NJ, USA, 2002. 3 Gambhir M.L., "Stability Analysis and Design of Structures", Patiala Índia, Springer, 2004. 4 Wilson E.L., Habibullah A., "Static and Dynamics Analysis of Multi-Story Buildings, Including P-Delta Effects", Earthquake spectra, Vol.3, No 2., 1987. doi:10.1193/1.1585429 purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £145 +P&P)
Back to top	©Civil-Comp Limited 2023 - terms & conditions