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XI.—Matrix Analysis of Beam-Columns by the Method of Finite Elements*

Published online by Cambridge University Press:  14 February 2012

R. G. Smith  and
J. A. Webster
R. G. Smith
Affiliation:
Marischal College, University of Aberdeen.
J. A. Webster
Affiliation:
Marischal College, University of Aberdeen.
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Synopsis

A matrix analysis is derived, using the concept of finite elements, for beam-columns of continuously varying cross-section and “small” initial curvature subject to tangential and normal forces acting at discrete points along the centroidal axis.

The relationships between loads applied to the ends of the member and their corresponding deformations are established in the form of stiffness matrices, which are the basis of the Equilibrium Method of Analysis of linear or non-linear elastic plane frames composed of such membeis. In addition, the end loads induced by the tangential and normal forces for various types of boundary conditions are obtained.

Finally, it is shown that the buckling load may be calculated by the determination of the lowest eigenvalue of a certain matrix, provided there is no lateial translation of the ends of the member.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 67 , Issue 2 , 1965 , pp. 156 - 173
Copyright
Copyright © Royal Society of Edinburgh 1965

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References

References to Literature

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