On Saint-Venant's principle in pin-jointed frameworks
On Saint-Venant's principle in pin-jointed frameworks
Numerical experiments performed by Hoff 50 years ago on the application of Saint-Venant's principle to frameworks are extended, and his conclusions qualified. Guided by these results, a general treatment is formulated employing a state variable approach; this leads directly to an eigenvalue problem in which the decay rates are the eigenvalues of the cell transfer matrix. Unity eigenvalues correspond to the transmitting modes of rigid body displacement and the stress resultants of tension, bending moment, shearing force and twisting moment. Consideration of the associated eigenvectors and principal vectors gives exact values for the equivalent “continuum” beam properties of the framework, such as equivalent cross-sectional area, Poisson's ratio, second moment of area, shear coefficient and torsion constant.
79-97
Stephen, N.G.
5390e21f-11b3-4334-8da6-7bd611acc4a0
Wang, P.J.
ba2106da-fcd3-4768-bc81-c596e1d48e9a
1996
Stephen, N.G.
5390e21f-11b3-4334-8da6-7bd611acc4a0
Wang, P.J.
ba2106da-fcd3-4768-bc81-c596e1d48e9a
Stephen, N.G. and Wang, P.J.
(1996)
On Saint-Venant's principle in pin-jointed frameworks.
International Journal of Solids and Structures, 33 (1), .
(doi:10.1016/0020-7683(95)00019-7).
Abstract
Numerical experiments performed by Hoff 50 years ago on the application of Saint-Venant's principle to frameworks are extended, and his conclusions qualified. Guided by these results, a general treatment is formulated employing a state variable approach; this leads directly to an eigenvalue problem in which the decay rates are the eigenvalues of the cell transfer matrix. Unity eigenvalues correspond to the transmitting modes of rigid body displacement and the stress resultants of tension, bending moment, shearing force and twisting moment. Consideration of the associated eigenvectors and principal vectors gives exact values for the equivalent “continuum” beam properties of the framework, such as equivalent cross-sectional area, Poisson's ratio, second moment of area, shear coefficient and torsion constant.
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Published date: 1996
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Local EPrints ID: 21174
URI: http://eprints.soton.ac.uk/id/eprint/21174
ISSN: 0020-7683
PURE UUID: fcf8be21-2be7-470f-814d-7aa0f906dd0b
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Date deposited: 08 Nov 2006
Last modified: 15 Mar 2024 06:28
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Author:
N.G. Stephen
Author:
P.J. Wang
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