UNCERTAINTY IN THE DYNAMIC BEHAVIOR OF TIMBER BEAMS WITH KNOTS

D.A. GARCIA; R. SAMPAIO; M.B. ROSALES

Rouen

Simposio; 2nd International Symposium on Uncertainty Quantification and Stochastic Modeling-UNCERTAINTIES 2014; 2014

French Society of Mechanical Sciences-ABCM (Brazilian Society of Mechanical Sciences)-SBMAC (Brazilian Society of Applied Mathematics)

The dynamic behavior of sawn timber beams of Argentinean Eucalyptus grandis using a stochastic model is herein presented. The aim of this work is to study the influence of the timber knots in the dynamical characteristics of timber beams. The presence of knots are the main source of the lengthwise variability and reduction of bending strength and stiffness in timber beams. The uncertainty in the stochastic model is presented in the following parameters of the timber knots: position along the beam span and within the beam cross section, their shapes and dimensions. The knots are modeled as holes in the beam with local reduction of the dynamic properties. Experimental data obtained from bending and density tests performed with 349 timber beams, classified in strength classes according to the Argentinean standard IRAM 9662-2:2006, are employed to find the timber modulus of elasticity (MOE) and density. On the other hand, experimental data obtained from a visual survey performed with 25 beams of the same species are employed to study the characteristic of the timber knots that are used in the stochastic model. The problem of the natural vibration frequencies of the timber beam is approximated with the finite element method. Numerical results are obtained by means of Monte Carlo Simulations (MCS) with a previous convergence study to determine the acceptable number of realizations. The uncertainties due to the timber knots presence and their influence are quantified with the probability density function (PDF) of the natural vibration frequencies. Statistical results obtained by means of MCS are compared with experimental results in order to assess the accuracy of the stochastic model. Frequently the presence of knots in sawn timber structures is disregarded, usually due to the lack of data and the availability of an adequate representations. The model herein presented contributes to attain a more realistic description of structures made out of sawn timber, due to the unavoidable presence of knots.