On the Mechanics of Thin-Walled Laminated Composite Beams

*DcparllllL'nt Ill" MechanICal and Aerospace Engineering. **Ocp;,Jftment of Civil Engineering. EVER 1. BARBERO,* ROBERTO LOPEZ-ANIDO** AND JULIO F. DAVALOS** Ui'st Virginia University Morgantown, WV 26506-6101 On the Mechanics of Thin-Walled Laminated Composite Beams sible to optinlize the material itself by choosing among a variety of resins, fiber systems, and fiber orientations. Changes in the geometry can be easily related to changes in the bending stiffness through the moment ofinertia. Changes in the material do not lead to such obvious results, because composites have properties that not only depend on the orientation of the fibers but also exhibit modular ratios that could differ considerably from usual values in conventional isotropic materials (Barbero [2]). Although beams and columns are the most commonly used structural elements, the theory of laminated beams has been less developed than the theory of laminated plates. Laminated beam theories were initially derived as extensions of existing plate or shell theories. Bert and Francis [3] presented a comprehensive review of the initial beam theories. Berkowitz [4] pioneered a theory of simple beams and columns tor anisotropic 1l1aterials. Vinson and Sierakowski [5 J applied classical lamination theory along with a plane strain assumption to obtain the extensional, coupling and bending stiffness for an Euler-Bernoulli type laminated beam (All,B•.,Dtt ). A theory for orthotropic thin-walled composite beams was proposed by Bank and Bednarczyk [6], where the in-plane material properties were obtained using classical lamination theory or coupon tests. A Vlasov theory for thin-walled open cross sections conlposed of plane symmetric laminates was proposed by Bauld and Tzeng [7] disregarding shear strains in the middle planes. Massonnet [8] addressed the problem of warping in a transversely isotropic beam by complementing a mechanics of materials approach with corrective terms derived using theory of elasticity. Bauchau [9] and Bauchau et al. [10] provided a more comprehensive treatment to the problem of warping by using variational principles to model anisotropic thin-walled bealTIs with closed cross sections. A general finite element with 10 degrees of freedom per node was derived by Wu and Sun [11] for thin-walled laminated composite beams by modifying the assumptions of the Vlasov theory. Skudra et al. 112] proposed a theory for thin-walled symmetrically laminated beams of open profile, and they illustrated the distribution of forces in a flat homogeneous anisotropic strip. Tsai [13] defined engineering constants from the laminate compliances, and employed them to obtain deflections for laminated beams. He further employed lanlinated plate theory to determine ply stresses. In the present work, kinematic assumptions consistent with the Timoshenko beam theory are employed in order to generate beam stiffness coefficients. A distintictive feature of the present approach with respect to existing formulations [7,9,10,12] is the possibility of considering not only membrane stresses but also flexural stresses in the walls. This assunlption seems to be more appropriate for moderately thick laminated beams enlployed in civil engineering-type structures. The bending extension coupling that may result froln material and/or geometric asymmetry is usually taken into account by bending-extension coupling stiffness coefficients. In this work, the position of the neutral axis is defined in such a way that the behavior of a thin-walled beanl-column with asymnletric material and/or cross-sectionaJ shape is conlpJetely described by axial, bending, and shear stiffness coefficients (Az,D.v,F.v) only. While the importance of considering a consistent shear coefficient in the Journal a/COMPOSITE MATERIALS, Vol. 27, No. 8/1993