Vibrational problems of timber beams with knots considering uncertainties

A stochastic model of the dynamic behavior of sawn timber beams of Argentinean Eucalyptusgrandis is herein presented. The aim of this work was to study the influence of the timber knots in the dynamical response of timber beams. The presence of knots is known to be the main source of the lengthwise variability and reduction in bending strength and stiffness in timber beams. The following parameters of the timber knots are considered stochastic: position along the beam span and within the beam cross section, shape and dimensions. Experimental data, obtained from bending and density tests, are employed to find the timber modulus of elasticity and density. On the other hand, the characteristics of the timber knots used in the stochastic model were obtained from a visual survey performed with 25 beams of the same species. The problem of the natural vibration frequencies of the timber beam is approximated with the finite element method. Numerical results are obtained using Monte Carlo simulations (MCS). The uncertainties of the timber knot parameters and their influence are quantified with the probability density function of the frequencies. Statistical results obtained by means of MCS are compared with experimental measurements in order to assess the accuracy of the stochastic model. The present approach that gives a more realistic description of timber structures correlates better with experiments.

[1]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[2]  Claude E. Shannon,et al.  The mathematical theory of communication , 1950 .

[3]  Reuven Y. Rubinstein,et al.  Simulation and the Monte Carlo Method , 1981 .

[4]  K. Bathe.  Finite Element Procedures , 1995 .

[5]  Ireneusz Czmoch,et al.  Influence of structural timber variability on reliability and damage tolerance of timber beams , 1998 .

[6]  Tord Isaksson,et al.  Modelling the Variability of Bending Strength in Structural Timber - Length and Load Configuration Effects , 1999 .

[7]  J. C. Piter.  Clasificación por resistencia de la madera aserrada como material estructural , 2003 .

[8]  Michael Havbro Faber,et al.  Probabilistic modeling of graded timber material properties , 2004 .

[9]  Michael Havbro Faber,et al.  Probabilistic modeling of timber structures , 2005 .

[10]  Wilson H. Tang,et al.  Probability Concepts in Engineering: Emphasis on Applications to Civil and Environmental Engineering , 2006 .

[11]  Dirk P. Kroese,et al.  Simulation and the Monte Carlo method , 1981, Wiley series in probability and mathematical statistics.

[12]  Jochen Köhler,et al.  Reliability of timber structures , 2007 .

[13]  Jochen Köhler,et al.  Reliability of Timber Structures , 2007 .

[14]  M. Guaita,et al.  Prediction of bending load capacity of timber beams using a finite element method simulation of knots and grain deviation , 2011 .

[15]  Manuel Guaita,et al.  A three-dimensional wood material model to simulate the behavior of wood with any type of knot at the macro-scale , 2012, Wood Science and Technology.

[16]  V. Baño,et al.  Determinación de la curva tensión-deformación en madera de Pinus sylvestris L. para la simulación numérica de vigas de madera libre de defectos , 2012 .

[17]  Francisco Arriaga,et al.  Determination of the influence of size and position of knots on load capacity and stress distribution in timber beams of Pinus sylvestris using finite element model , 2013 .

[18]  Manuel Guaita,et al.  The analytical influence of all types of knots on bending , 2014, Wood Science and Technology.