The behaviour of open and closed section carbon fibre composite beams subjected to constrained torsion

Abstract

A simple engineering theoretical approach is presented in this paper which is able to predict the initial constrained torsional response of a specific class of thin-walled open-section and single-cell closed-section carbon fibre composite beams. The flat walls of the composite beams are symmetrically laminated about their own mid-planes and possess membrane orthotropy. The laminated flats are assembled in such a way that the stiffness distribution round the section is of a symmetrically disposed nature and thus the flanges of a composite box-section, for example, can have a different lay-up configuration to that of the section webs. Beams of this type are essentially uncoupled in their overall stiffnesses and thus it is possible to apply axial load or bending to the sections without inducing torsional behaviour. The analysis procedures for such beams will, of course, be considerably less complex in nature than those associated with beams of a more general lay-up configuration. Indeed, the analysis approach adopted in this paper simply makes use of the existing theories of torsion appropriate to isotropic construction and these are then suitably modified to account for the non-isotropic nature of the composite material. The torsional and warping rigidities for use in the analysis of the composite beams are thus duly determined through the use of the appropriate equivalent engineering elastic constants of the individual thin composite walls and the concept of effective thickness is employed to account for the different stiffnesses in the walls. In the paper some detailed attention is paid to the effects of primary and secondary warping restraint on the torsional response of open section beams and the distinct differences between sections whose behaviour is governed predominantly by primary effects and those whose response is associated solely with secondary effects are discussed. The stress systems set up in open-section and single-cell closed-section carbon fibre composite beams when subjected to torsion with variable twist are examined in the paper and in particular it is shown that although the shear flow due to primary warping restraint in open-section beams serves in part to equilibrate the applied torque, that in closed box section beams is completely self equilibrating. Comparisons are given in the paper between theory and experiment and between theory and finite element solutions and these are shown to give good agreement for the Z, angle and box section beams considered.