Knots Influence on the Buckling Load of Timber Columns with Uncertain Properties

Abstract

In this work, the static buckling problem of a timber column with geometric and material uncertainties is analyzed. The knots are assumed randomly shaped, sized and located. Also, the Modulus of Elasticity (MOE) is considered as a random field given by a Probability Density Function (PDF) and an exponential correlation function. Two methods are employed to find the PDF of the MOE: the Principle of Maximum Entropy (PME) and a statistical fit using the Kolmogorov-Smirnov (K-S) test, both leading to a Gamma PDF. Meanwhile, the dimensional parameters of the knots are modeled through the Joint Probability Mass Function (JPMF). Experimental data found with bending tests performed on timber beams, classified in strength classes according to the Argentinean standard IRAM 9662-2:2006 are employed to find the PDF parameters of the MOE. On the other hand, experimental data obtained from a visual survey are employed to study the dimensional characteristic of the timber knots and to determine their JPMF. The Nataf transformation and the non-Gaussian Karhunen-Loeve expansion are employed in order to generate and simulate the random field of the MOE and the inverse transform method for the knots parameters. The static buckling load of the timber columns is numerically approximated with the finite element method. Statistics of the response are obtained by means of Monte Carlo Simulations (MCS) with a previous convergence study to determine the acceptable number of realizations. The propagation of the geometric and material uncertainties on the critical load is evaluated through the PDF of the static buckling load. Results obtained by means of MCS are compared with previous numerical outcomes found in limiting cases in order to assess the accuracy of the stochastic model herein presented.
Frequently, the presence of knots in sawn timber structures is disregarded, usually due to the lack of data and the availability of an adequate representation. The present approach contributes to attain a more realistic description of the structural components made out of sawn Eucalyptus grandis timber.