
Accurate modelling of the linear elastic flexure of composite beams warped by midlayer slip, with emphasis on concretetimber systems Lorenzo Bardella, Luisa Paterlini, Alessandro Leronni DICATAM, University of Brescia, Via Branze 43, Brescia 25123, Italy Abstract We focus on the modelling of the linear elastic flexure of composite beams in which the external layers are connected by a midlayer allowing a conspicuous slip between the external layers. In particular, we consider the case of concretetimber systems in which the midlayer consists of steel shear connectors passing through a wooden plank. To model these structures, we extend the Newmark theory, originally developed for connection of negligible thickness. Also, we apply Jourawski's technique to the Newmark model to obtain accurate analytic predictions of the shear stress. We provide analytic solutions for the cases of simplysupported, cantilever, and proppedcantilever beams, all subject to uniform load, and we compare the results with those obtained from both accurate plane stress Finite Element simulations and the FirstOrder Shear Deformation (FOSD) theory. For the latter we provide the explicit expression of the shearing rigidity based on a classical energy criterion. We show the inability of the FOSD modelling to accurately predict the deflection and explain the unexpected too large compliance characterising the FOSD estimate. Instead, the Newmark model turns out to be highly accurate for sufficiently slender beams, even in terms of shear stress if the "Jourawskilike" postprocessing proposed here is used. We also consider a further extension of Newmark's theory to accurately model nottooslender composite beams. In such an extension, henceforth called the NewmarkTimoshenko model, the wooden element is allowed to follow a Timoshenko kinematics, richer than the EulerBernoulli kinematics assigned to both the external layers in the Newmark model. The results of the novel NewmarkTimoshenko model are numerically obtained by the RayleighRitz method in which the analytic solution of Newmark's model is used to construct optimal approximating functions of the field entering the Total Potential Energy functional. Author Keywords: Composite beam; Warping; FirstOrder Shear Deformation theory; Zigzag Shear Deformation theory; Jourawski shear theory; Finite Element method
