Eigenproblems in timber structural elements with uncertain properties

A stochastic model of sawn timber structural elements of Argentinean Eucalyptus grandis is applied to the study of two eigenproblems. One is the free vibrations problem which, after being solved, yields the natural frequencies and modes. The other problem is the buckling of columns. Its solution leads to the buckling loads and modes. The governing differential equations are stated starting from the Euler–Bernoulli beam theory. Then, they are discretized and numerically approximated through the finite element method. The stochasticity is given by the mechanical properties involved in each problem. The lengthwise variabilities of the modulus of elasticity and of the second moment of the cross-sectional area are simulated to account for the presence of knots. The variability of the mass density among structural elements is also considered. The statistics of the solutions are obtained. The probability density functions of the natural frequencies and the buckling loads are numerically obtained through a stochastic finite element concept using Monte Carlo simulation. Numerical results for the first natural frequency are validated with experimental values. The mode shape statistics are also analyzed. 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 model herein presented contributes to attain a more realistic description of structures made out of sawn timber due to the unavoidable variability of the properties, in particular the presence of knots .