A beam theory for open and closed section, thin-walled, composite beams is presented. The layup of each wall segment is arbitrary, the effects of shear deformation and restrained warping are neglected. Closed form expressions are developed for the calculation of the 4×4 stiffness matrix. It is also shown that the local bending stiffnesses of the wall segments may be neglected when the laminate is either symmetrical or orthotropic.
This paper compares the results of different beam theories with finite element calculations and determines simple rules which designers may apply to insure simplified theories give acceptable results. Specifically, we analyze the effect of shear deformation and restrained warping. For thin-walled beams with layups that may be symmetrical or unsymmetrical, orthotropic or unorthotropic, simple expressions are developed to determine the effect of shear deformation. We also demonstrate that the effect of restrained warping in balanced, anisotropic open-section beams may be determined using the warping stiffness derived for orthotropic beams.
The paper presents a theory for thin-walled, closed section, orthotropic beams which takes into account the shear deformation in restrained warping induced torque. In the derivation we developed the analytical (''exact'') solution of simply supported beams subjected to a sinusoidal load. The replacement stiffnesses which are independent of the length of the beam were determined from the exact solution by taking its Taylor series expansion with respect to the inverse of the length of the beam. The effect of restrained warping and shear deformation was investigated through numerical examples.
In the design of composite sections, beam theories are used which require the knowledge of the cross-sectional properties, that is, the bending-, the shear-, the torsional-, warping-, axial stiffnesses and the coupling terms. In the classical analysis, the properties are calculated by assuming kinematical relationships (e.g. cross sections remain plane after the deformation of the beam). These assumptions may lead to inaccurate or contradictory results. In this paper, a new theory is presented in which no kinematical assumption is applied, rather the properties are derived from the accurate (three dimensional) equations of beams using limit transition. The theory includes both the in-plane and the torsional-warping shear deformations. As a result of the analysis, the stiffness matrix of the beam is obtained which is needed for either analytical or numerical finite element (FE) solutions. Applications for open section and closed section beams are also presented.
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