Accurate modelling of the linear elastic flexure of composite beams warped by midlayer slip, with emphasis on concrete-timber systems
Lorenzo Bardella, Luisa Paterlini, Alessandro Leronni
DICATAM, University of Brescia, Via Branze 43, Brescia 25123, Italy
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 concrete-timber 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 simply-supported, cantilever, and propped-cantilever beams, all subject to uniform load, and we compare the results with those obtained from both accurate plane stress Finite Element simulations and the First-Order 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 "Jourawski-like" post-processing proposed here is used. We also consider a further extension of Newmark's theory to accurately model not-too-slender composite beams. In such an extension, henceforth called the Newmark-Timoshenko model, the wooden element is allowed to follow a Timoshenko kinematics, richer than the Euler-Bernoulli kinematics assigned to both the external layers in the Newmark model. The results of the novel Newmark-Timoshenko model are numerically obtained by the Rayleigh-Ritz 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; First-Order Shear Deformation theory; Zig-zag Shear Deformation theory; Jourawski shear theory; Finite Element method