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

Abstract:

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. The aim of this paper was to investigate if 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 rotary inertia. 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.

• Periodical: Advanced Materials Research (Volume 778)
• Pages: 454-461
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.778.454
• Online since: September 2013
• Authors: Thomas Lechner, Steve Laux, Daniel Sandin
• Keywords: Axial Load, Dynamic E-Modulus, Modal Analysis, Nondestructive Testing (NDT), Parameter Estimation, Resonance Frequency Analysis, Timber Beams, Timoshenko Beam Theory

References

[1] T. Livingston, J. Béliveau, and D. Huston: Estimation of axial load in prismatic members using flexural vibrations. Journal of Sound and Vibration. 179 (5), 899-908, (1995).

DOI: 10.1006/jsvi.1995.0060

[2] N. Maille: Assessing the Roof Structure of the Breeding Barn Using Truss Member Resonant Frequencies, The University of Vermont, (2008).

[3] M. Amabili, S. Carra, L. Collini et al.: Estimation of tensile force in tie-rods using a frequency-based identification method. Journal of Sound and Vibration. 329 (11), 2057-2067, (2010).

DOI: 10.1016/j.jsv.2009.12.009

[4] P. Avitabile: Experimental modal analysis. Sound and vibration. 35 (1), 20-31, (2001).

[5] P. Crovella, and G. Kyanka, Use of vibration techniques to determine the rotational stiffness of timber joints, College of Environmental Science and Forestry, State University of New York, USA, (2011).

[6] Y. Chui, and I. Smith: Influence of rotatory inertia, shear deformation and support condition on natural frequencies of wooden beams. Wood Science and Technology. 24 (3), 233-245, (1990).

DOI: 10.1007/bf01153557

[7] J. McGuire: Notes on semi-rigid connections. NASA, USA, (1995).

[8] S. Laux: Estimation of axial load in timber beams using resonance frequency analysis, Master's Thesis, 2012: 60, Civil and Environmental Engineering, Chalmers University of Technology, Gothenburg, (2012).