Keywords: timber joint, anisotropic hysteresis law, uncertainty, stochastic collocation method, reliability.

In this paper, a probabilistic methodology is presented to assess the behaviour of timber joints under seismic loading. The considered hysteresis anisotropic behaviour law [1] allows us to describe the behaviour of the punched metal plate fasteners in timber joints. Its originality lies in taking into account the damage under cycles of constant amplitude and in describing the bidimensional behaviour of timber joints. The parameters of the proposed hysteresis law are determined from experimental results [2], which are then used to validate the numerical model. The stochastic collocation method [3], based on third order Stroud integration formulas [4], is used to compute the statistical moments (i.e. mean, standard deviation) of the relevant mechanical response of the timber joint such as the maximal force and the dissipated energy. We have shown that high correlation exists between these two quantities and the relevant parameters of the hysteresis law, namely the initial elastic stiffness and the peak force. Based on these results, the reliability analysis is conducted by considering these two variables as random. The proposed reliability approach is based on direct coupling of the finite element model with the first order reliability method. The numerical application is carried out for an industrial timber joint with hysteresis anisotropic behaviour. The failure is defined by the increase of the force induced by seismic loading until reaching the resisting capacity of the joint. The failure probability strongly decreases with the increase of the joint capacity, with high sensitivity with respect to the peak force of the hysteresis behaviour. We have shown that the proposed methodology is low time consuming since the convergence is well achieved using a limited number of finite element analyses. The ongoing research aims at developing a coupling method able to deal with higher order reliability problems for complex engineering structures such as timber roof trusses used in individual housing and taking into account the variability due to seismic ground motion.

1

J. Humbert, "Caractérisation du comportement des structures bois à assemblages métalliques sous sollicitations sismiques: Essais experimentaux, Modelisation numerique, Analyse de sensibilité", Thesis, Grenoble, France, 2010.

2

FCBA Technological Institute, "Testing reports on metallic connectors according to NF EN 1075", Internal reports, 4 vol, 1999-2001.

3

Ph. Bressolette, M. Fogli, C. Chauvière, "A stochastic collocation method for large classes of mechanical problems with uncertain parameters", Prob Eng Mech, 25, 255-270, 2010. doi:10.1016/j.probengmech.2010.01.002

4

A. Stroud, "Approximate calculation of multiple integrals", Prentice-Hall, Englewood Cliffs NJ, 1971.

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