Analysis of Thin-Walled Straight Beams with Generally Shaped Closed Sections Using Numerically Determined Sectional Deformation Functions
Publication: Journal of Structural Engineering
Volume 138, Issue 12
Abstract
This investigation presents one-dimensional static and eigenvalue analyses of thin-walled straight beams with generally shaped closed single-cell or multicell sections. For accurate beam analysis, sectional warping and distortional deformations should be considered in addition to the standard Timoshenko displacement field, but it is difficult to obtain the deformation functions analytically for arbitrarily shaped sections. Thus, a numerical method is proposed to obtain sectional deformations for any arbitrarily shaped sections. Once the deformations are identified, they can be integrated over a cross section to yield one-dimensional higher order beam equations. For the numerical determination, the cross section of a thin-walled beam is modeled as a beam frame, where the warping and distortional deformation functions of the section are identified as the eigenmodes of the frame model; the lowest few energy mode sets of in-planar and out-of-planar modes are selected as the distortional and warping deformation functions, respectively. The validity of this approach is checked by comparing the present results with shell finite-element results. For numerical tests, several thin-walled closed sections, including those with flanges or varying wall thicknesses, are considered. The effect of the number of selected warping and distortion sets on solution convergence is also investigated.
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Acknowledgments
The first writer was supported by the National Research Foundation of Korea (Grant No. 2011-0026851). The other writers were supported by the National Research Foundation of Korea (Grant No: 2011-0017445) contracted through the Institute of Advanced Machinery and Design at Seoul National University and the World Class University program (Grant No. R31-2009-000-10083-0) through the National Research Foundation of Korea, funded by the Ministry of Education, Science, and Technology.
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© 2012 American Society of Civil Engineers.
History
Received: Dec 27, 2010
Accepted: Feb 17, 2012
Published online: Feb 21, 2012
Published in print: Dec 1, 2012
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