DINAME 2017 - Proceedings of the XVII International Symposium on Dynamic Problems of Mechanics A. T. Fleury, D. A. Rade, P. R. G. Kurka (Editors), ABCM, S˜ ao Sebasti ˜ ao, SP, Brazil, March 5-10, 2017 DYNAMIC BEHAVIOR OF TIMBER FOOTBRIDGES WITH UN- CERTAIN MECHANICAL PROPERTIES AND STOCHASTIC WALKING LOADS Diego A. Garc´ ıa 1,2,3 , Marta B. Rosales 1,3 , Rubens Sampaio 4 1 Department of Engineering, Universidad Nacional del Sur, Bah´ ıa Blanca, Argentina; garciadiego@fio.unam.edu.ar; mrosales@criba.edu.ar. 2 Department of Civil Engineering, Universidad Nacional de Misiones, Ober ´ a, Argentina. 3 CONICET, Argentina. 4 Department of Mechanical Engineering, Pontif´ ıcia Universidade Cat ´ olica do Rio de Janeiro, Rio de Janeiro RJ, Brazil; rsampaio@puc-rio.br. Abstract: A dynamic study of timber footbridges with uncertain mechanical properties under the action of stochastic walking loads is presented in this paper. These structural systems made of timber are increasingly employed due to the high relation stiffness/weight that wood exhibits in relation to others structural materials. More, the development and implementation of laminated beams permits larger spans. These features can lead to lightweight structural systems in which the acceleration levels can exceed the human comfort limits. The sources of uncertainty of this structural model are the timber mechanical and physical properties, Modulus of Elasticity (MOE) and mass density. Also, the geometrical design of the boards that compose the laminated timber beams supporting the floor involves variability in the distances between finger joints. Probability Density Functions (PDFs) of the timber properties are formulated from the Principle of Maximum Entropy (PME). The finger joints distance generates the lengthwise variability of the MOE and mass density functions in each board of the laminated beams. The influence of these stochastic variables in the structural response on a forced vibration problem that includes a stochastic model of the load induced by the human walking is assessed. Pedestrians arrive to the footbridge under a Poisson distribution. The arrival velocity is such that a medium/low transit density is achieved in accordance with the footbridge dimension. The PDFs of the natural frequencies of the structure, the mode shapes and the structural response are numerically obtained through the Finite Element Method (FEM) and Monte Carlo Simulations (MCS). Values of peak accelerations produced at the mean span of the footbridge are evaluated in relation to the footbridge occupancy at each instant. The present stochastic model contributes to obtain a more realistic description of the response of this type of structures. Keywords: Dynamics, Timber footbridge, Uncertain properties, Stochastic walking load, Poisson process. INTRODUCTION Pedestrian footbridges are one of the most common timber structures mainly due to the high relation stiffness/weight that this material presents in comparison to other construction materials and the possibility of covering long spans owing to the development and implementation of laminated beams. This type of beams has become greatly employed, and has allowed the construction of slender timber structures. The footbridges are composed of a deck and longitudinal laminated beams. In this work, the complete structure is made of Argentinian Eucalyptus grandis, one of the most important renewable species cultivated in Argentina. A simple method for visually strength grading sawn timber of these species has been developed by Piter (2003). As reported in this paper, the presence of pith and knots are considered the most important visual characteristic for strength grading this material by the Argentinian standard IRAM 9662-2 (2006). Experimental studies related with the bending strength and stiffness in Eucalyptus grandis laminated beams have been presented by Piter et al . (2007) and Saviana et al . (2009). The stochastic approaches employed for the modelling of timber mechanical properties are derived from the probabilis- tic theories of random variables and processes. They allow simulating the timber mechanical properties within a structural analysis. K¨ ohler et al . (2007) presented a probabilistic model of timber structures where the MOE is represented as a random variable with a lognormal PDF and the mass density through a random variable with normal distribution, both assuming a homogeneous value within a structural element. Recently, Fink and K¨ ohler (2015) present a probabilistic approach for modelling the tensile strength and stiffness properties of timber boards and finger joint connections. Timber footbridges must satisfy both strength and serviceability requirements. Generally, due to its lower weight, the serviceability requirements in terms of peak accelerations constitute the most restrictive condition in the design. The control of the structural system maximum acceleration can just be made by increasing the structural damping or mass.