Dynamic Analysis Of Beams Including
Warping And Shear Deformation Effects:
Application In Bridge Deck Analysis
Author(s)
E. J. Sapountzakis, V. G. Mokos & A. D. Koroneou
Abstract
In this paper the dynamic analysis of 3-D beam elements restrained at their edges
by the most general linear torsional, transverse or longitudinal boundary
conditions and subjected to arbitrarily distributed dynamic twisting, transverse or
longitudinal loading is presented. For the solution of the problem at hand, a
boundary element method is developed for the construction of the 14x14
stiffness matrix and the corresponding nodal load vector of a member of an
arbitrarily shaped simply or multiply connected cross section, taking into account
both warping and shear deformation effects, which together with the respective
mass and damping matrices lead to the formulation of the equation of motion. In
order to account for shear deformations, the concept of shear deformation
coefficients is used, where these factors are defined by a strain energy approach.
Eight boundary value problems are formulated and solved employing a pure
BEM approach, which uses only boundary discretization. Free and forced,
transverse, longitudinal or torsional vibrations are considered, taking into
account both rotatory inertia and damping resistance. The influence of the
warping effect especially in members of open form cross section is analyzed
demonstrating the importance of the inclusion of the warping degrees of freedom
in the dynamic analysis of a space frame. Moreover, the discrepancy arising from
ignoring the shear deformation effect necessitates the inclusion of this additional
effect, especially in thick walled cross section members.
Key words: nonuniform torsion, warping, shear deformation, bar, beam,
dynamic analysis, boundary element method, stiffness matrix, mass, damping.
Keywords
nonuniform torsion, warping, shear deformation, bar, beam,
dynamic analysis, boundary element method, stiffness matrix, mass, damping.
Related Book
Other papers in this volume
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