Stress Level Prediction in Axially-Loaded Timber Beams Using Resonance Frequency Analysis: A Pilot Study

The structural integrity due to problems in the uncertainties of load, the load-carrying capacity of timber structures is of great importance, since peaks of increased loads might occur. One solution of these problems lies in the evaluation of timber structures using non-destructive testing (NDT) methods, and in this special case frequency based identification methods. This paper deals with the investigation whether it is possible to estimate the axial loads in timber beams using resonance frequency analysis to evaluate on whether the beams have sufficient load-bearing capacity. This was achieved by performing transversal frequency measurements on 32 timber specimens and an aluminium bar under tension. The latter hereby served as a homogeneous reference for better interpretation of results. The two first frequencies, together with different values for the E-modulus were then used to estimate the axial load S and the rotational stiffness k at the boundaries. The stress levels for the timber ranged from 2 MPa to 11 MPa, whereas for the aluminium reference bar the frequencies were measured for stress levels from 4 MPa to 32 MPa. The numerical model behind the calculations was based on Timoshenko beam theory, including effects of shear deformations and flexural stiffness. Finally, a sensitivity analysis was carried out to investigate the influence of errors in input parameters on the final results. The best results were obtained using the E-modulus derived from transversal vibration tests and showed a mean error ranging from 7.6% to 46.6%, where the results generally improved for higher loads. The results of the sensitivity analysis showed that the sensitivity of the estimated axial load decreases for higher stress levels, which could also be observed in the test results. The most influential parameters on the quality of the results were the measured frequencies and the clear beam length, followed by the density and the E-modulus.