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Civil-Comp Proceedings
ISSN 1759-3433 CCP: 79
PROCEEDINGS OF THE SEVENTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping and C.A. Mota Soares
Paper 246
Static and Dynamic Stability of Frames with Linearly Tapered Columns S.C. Kim+, S.G. Lee*, Y.J. Moon+ and C.Y. Song#
+Department of Architectural Engineering, Dongshin University, Naju, Korea
Full Bibliographic Reference for this paper
S.C. Kim, S.G. Lee, Y.J. Moon, C.Y. Son, "Static and Dynamic Stability of Frames with Linearly Tapered Columns", in B.H.V. Topping, C.A. Mota Soares, (Editors), "Proceedings of the Seventh International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 246, 2004. doi:10.4203/ccp.79.246
Keywords: linearly tapered column, taper parameter, sectional property parameter, elastic critical load, natural frequency of lateral vibration, regression analysis.
Summary
In the case of single prismatic members, the axial thrust,
![]() ![]() ![]() where ![]() ![]() For the rectangular frames with nonprismatic columns, however, the two (eigenvalues elastic critical load and fundamental natural frequency) are hard to determine and the above relationship is in question. This paper aims to examine whether Equation (72) is also applicable to the rectangular frame shown in Figure 1. The following shows the parameters and other factors considered in the eigenvalues analysis of the frame by the finite element method.
The shape functions for the linear element having two degrees of freedom at
each node is utilized in the formulation of element matrices [3,4]. When the element
matrices are assembled for the whole structure, the external force, where ![]() ![]() ![]() Due to the large size of assembled matrices, the eigenvalues are determined by a computer-aided iteration method. The determinations of the first mode eigenvalues by the iteration method easy when Equation (73) is transformed into the following form: where ![]() To generalize the changes of eigenvalues obtained by the finite element method, the following form second order algebraic equations is proposed: The constants ![]() ![]() where ![]() ![]() ![]() ![]() References
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