Deflections in sawn timber beams with stochastic properties

A stochastic model is proposed to study the behavior of structural sawn beams of Argentinean Eucalyptus grandis with the aim of improving the predictability of the elastic deformations. The enhancement of the mid-span deflection calculation is based on a probabilistic model of the Modulus of Elasticity (MOE) and the representation of its lengthwise variability through a random field. The standard model that uses a MOE variable assumed random from piece to piece but deterministic (constant) within each piece is obtained as a particular case. In order to obtain a statistical representation of the MOE, the Principle of Maximum Entropy (PME) is employed. Experimental data obtained from bending tests are employed to find the parameters of the derived Probability Density Function (PDF). The PDF of the mid-span deformations is numerically obtained through the Stochastic Finite Element Method (SFEM) and Monte Carlo Simulations (MCS). Numerical results are validated with experimental values. Deflections of structural sized beams under usual loads are obtained. Finally, the stochastic model is used to compare with the serviceability requirements established in the Argentinean design code. It is shown that the structural performance of timber beams is found through a more realistic material approach.