Description of behaviour of timber-concrete composite beams including interlayer slip, uplift, and long-term effects: Formulation of the model and coefficient inverse problem. (1st September 2019) - Perkowski, Zbigniew; Czabak, Mariusz
Highlights: Correct model description of the long-term behaviour of timber-concrete beam. Non-invasive estimation of the beam stiffness and moisture shrinkage parameters. Concentration of tensile stress in the beam top layer under a concentrated load. Abstract: The research paper presents a model of a two-layer, timber-concrete composite beam, taking into account the rheology of the issue and the hygrothermal impact. The description of the beam layers' mechanical features and the interlayer joint was adopted as per the assumptions of standard linear solid model of viscoelasticity. In the case of the joint, the possibility of its slip, as well as uplift were taken into account. The result was a system of 4 integro-differential equations with respect to functions of deflections and horizontal displacements of beam layer axes. The second essential objective of the research was to develop a coefficient inverse problem in terms of the proposed model which would enable a natural-scale, non-invasive (e.g. for diagnostic purpose) estimation of the parameters of a timber-concrete beam, determining its initial and long-term stiffness, and moisture shrinkage/swelling of the layers. For this purpose, the following methods were applied in the experimental domain: measurements of the deflections, curvatures of layer axes, and interlayer slip at selected points of beam, ultrasonic tests of the top concrete slab, and monitoring of the ambient temperature and air relative humidity. The proposed inverse problem involves minimizing the objective function defined as a sum of relative square errors between given deflection, slip, curvature measurements and the corresponding model outputs. Tikhonov regularization was applied in order to improve the problem posing, and solutions of the system of integro-differential equations were obtained by using numerical integration and the finite difference method. The correctness of the formulated issue description was verified with the use of experimental creep data for 4 beams being inside a building over a 2-year period. For these cases, a satisfactory conformity of the measurements and theoretical results was obtained. The research paper is concluded with a presentation of the results obtained based on the model which depict the redistribution of the rheological nature of internal forces in the layers and the interlayer joint of the tested beams as well as changes over time of these magnitudes originating from changes of ambient air humidity. In particular, it was demonstrated that an adverse accumulation of tensile stresses at the bottom of the top slab of timber concrete composite beam may occur under the concentrated load, which cannot be predicted when using a beam model assuming a typically infinite stiffness of the joint for tension/compression in the perpendicular direction to its surface.