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Abstract
A method for calculating the dynamic transfer and stiffness matrices for a straight Timoshenko shear beam is presented. The method is applicable to beams with arbitrarily shaped cross sections and places no restrictions on the orientation of the element coordinate system axes in the plane of the cross section. These new matrices are needed because, for a Timoshenko beam with an arbitrarily shaped cross section, deflections due to shear in the two perpendicular planes are coupled even when the coordinate axes are chosen to be parallel to the principal axes of inertia.
Highlights
INTRODUCTIONTwo recent studies of the Timoshenko shear beam by Romano, Rosati, and Ferro (1992) and Schramm et al (1994), have reconsidered some fundamental aspects of shear deformation coefficients
Two recent studies of the Timoshenko shear beam by Romano, Rosati, and Ferro (1992) and Schramm et al (1994), have reconsidered some fundamental aspects of shear deformation coefficients. It is shown in Schramm et al (1994) that the shear deformation coefficients
The beam element and the righthanded Cartesian coordinate axes x, y, and z are shown in Fig. 1; the x axis is parallel to the axis of the beam and the orientation of the y and z axes may be chosen arbitrarily in the plane perpendicular to the x axis
Summary
Two recent studies of the Timoshenko shear beam by Romano, Rosati, and Ferro (1992) and Schramm et al (1994), have reconsidered some fundamental aspects of shear deformation coefficients. For a symmetrical cross section, the shear deformation coefficients form a diagonal tensor when referred to the principal axes of inertia, so that if the chosen coordinate axes are parallel to these axes, both The purpose of this article is to develop a method for determining two such element matrices for a straight Timoshenko shear beam in any Cartesian coordinate system. The first of these matrices is a dynamic transfer matrix and the second, which is expressed in terms of the entries of the first, is a dynamic stiffness matrix. The context of linear system theory, the reader is referred to Chen (1970), Lewis (1977), and Johnson and Johnson (1975)
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