Comparison of theoretical calculated deflections according to the Euler-Bernoulli andЕymoshenko beam models with experimentally obtained

The article presents the results of an experimental and theoretical study of the prediction of deflections of timber beams made of three types of wood: massive, glued laminated, and cross-laminated timber. The aim of the work is to compare the adequacy of the classical Euler-Bernoulli and the Timoshenko beam theory in predicting deflections under static loading. Deflections of simply-supported beams under concentrated loading in the middle of the span were experimentally investigated. Experimental values of deflections and mechanical characteristics were determined for each type of timber. Theoretical deflections were calculated according to the Euler-Bernoulli and Tymoshenko beam theories for identical conditions. Comparative analysis showed that the Euler-Bernoulli beam theory underestimates the deflections, with relative errors within 9%…15%, indicating a significant influence of shear deformations. On the other hand, the Timoshenko beam theory demonstrated much better convergence with experimental data, with errors within ‑2%…+4%. To increase the accuracy of prediction by Euler-Bernoulli beam theory, it is proposed to introduce averaged empirical shear coefficients determined on the basis of experimental results. The application of these coefficients allowed to significantly reduce the discrepancies between the theoretical and experimental values of deflections for all studied timber types. The obtained results confirm the importance of considering shear deformations in the analysis of beams made of timber-based materials. The application of the Timoshenko beam theory or the modified Euler-Bernoulli theory with consideration of empirical shear coefficients is more reasonable for accurately predicting their deformation behavior.