Dynamic analysis of beams including warping and shear deformation effects: application in bridge deck analysis

摘要

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.