Static and Dynamic Response of Helically Curved Thin-Walled Girders
Bauman, Robert Anthony
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https://hdl.handle.net/2142/66904
Description
Title
Static and Dynamic Response of Helically Curved Thin-Walled Girders
Author(s)
Bauman, Robert Anthony
Issue Date
1981
Department of Study
Civil Engineering
Discipline
Civil Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Civil
Language
eng
Abstract
This dissertation presents a finite element method of analysis for the static and dynamic response of helically curved thin-walled girders. The girder is assumed to possess a doubly symmetric, open cross-section with principal axes oriented in the directions of the normal and binormal vectors to the helical curve described by the cross-section center of gravity.
Differential equations of motion are derived bassed on A. E. H. Love's curvature and strain relationships modified to include warping effects. A closed form solution to the free vibration problem of a simply supported helical beam is used to study the effect on natural frequencies of varying the slope angle. Approximate frequency equations for all four coupled natural frequencies are also presented for the case of simple supports.
A helical beam finite element is developed using quintic hermitian shape functions to approximate each of the four displacements, axial, radial, vertical, and twisting, of a point on the beam's centerline. The strain energy due to bending about either principal axis, to axial deformation, to St. Venant torsion, and to the bimoment (warping effects) are included in the formulation of the element. The resulting 24 degree of freedom helical beam element is tested for in-plane and out-of-plane response by comparison to various static and dynamic solutions for curved thin-walled beams. Results of static analyses are also compared to flexibility method solutions for prismatic helical beams is also studied.
Finally, impact factors due to a moving load are compared for horizontally and helically curved single and two span continuous girders. The load is idealized as a single concentrated force moving at constant velocity. The equations of motion are solved by the Newmark Beta method of numerical integration. Conclusions are presented concerning the effect of increased helix angle on impact factors and the applicability of the present method to cross-sections having only a vertical axis of symmetry.
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