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A reliability approach applied to wood structures under seismic excitation is proposed in this paper.
Due to the advantages provided by its mechanical behaviour under seismic and fire loadings, to its aesthetic and environmental effects, timber is commonly employed in building and civil engineering structures.
The industrialized timber roof truss is composed by several timber members connected with punched metal plate fasteners.
The finite element model is composed of beam elements modelling the timber members connected with hysteresis elements modelling the punched metal plates. The finite element model is composed of 14 hysteresis elements modeling the punched metal plate fasteners. As it can be seen in figures 4 an 5, the obtained displacement in the nodes defining the same punched metallic plate fasteners takes different values. The main objective of the structural reliability analysis is to compute the probability of failure Pf of a mechanical system regarding a prescribed failure criterion which takes account for uncertainties arising from the geometry, the material parameters and applied load. In practical applications, the evaluation of the integral (1) is not a trivial task, because the reliability problems involve a very large random space dimension (i.e.
The first order reliability method (FORM) is based on the concept of the reliability index ft to estimate the probability of failure Pf. Generally, when dealing with dynamic reliability problem, the failure is defined as the maximum displacement response exceeding a critical threshold dcrit during the seismic excitation y(t). As indicated above, the timber roof truss is composed of several timber members connected with punched metal plate fasteners, as depicted in figure 8.
Based on the experimental tests presented in [10], the failure mode of the timber roof truss is composed of wood fracture on the top chord, as well as an anchor failure on the bottom chord. As it can be seen, the employed reliability method is not time consuming since the convergence of the reliability index is well achieved. We can observe that the reliability index increases fastely when the critical displacement increases. The reliability analysis methodology proposed in this paper can be used to predict the probability of failure of timber roof truss subject to earthquake events. TRUSSCO MFG has the right people in the right positions to provide you with the right design and the right product, built according to plan and delivered on time. Open web floor trusses allow longer spans with more access for HVAC, electrical and plumbing.
We can take your house plans and provide you with a free estimate for any floor or roof system. A new build roof with a wooden truss framework making an apex against a blue sky with cloud. In most cases of industrial and individual buildings, the timber structures are composed of wood members joint with connectors made of steel plates. Figure 1 gives the geometrical proprieties of the timber members and the punched metal plates ensuring the connection between those members. In these countries, timber housing represents more than 90% of the market of the private housing. Due to the complexity of the geometrical configuration of the timber roof truss and to the nonlinear behaviour of the metal joints, a finite element model is developed [10] to analyze the mechanical response induced by seismic excitation.
This can be explained by the nonlinear semi-rigid behaviour of the metallic connection (i.e.
As a geometrical interpretation, the reliability index is the distance defined by the closest point on the limit state surface H(U) = 0 to the origin of the standard random space.
The critical threshold displacement dcrit is defined as the displacement recorded when the yield stress is achieved.


The connections are represented in the two dimensional finite element model by hysteresis elements where the behaviour is defined by three parameters namely the horizontal stiffness Kx, the vertical stiffness Kz and the rotational stiffness Kg. For a precision level of 10"4, we need only 10 iterations which correspond to 99 finite element analysis.
Obviously, the critical displacement represents the capacity of the timber roof structure to resist the seismic excitation.
This approach is based on coupling the numerical model stemming from the finite element modeling of timber roof truss and the First Order Reliability Method. We are also an authorized dealer for engineered wood products: I-Joists, Rimboard, LVL beams and headers. We also offer Boise Cascade engineered wood products for flooring and roof systems as well as stock a large selection of hangers used in the construction industry. The mechanical, model which represents a timber roof truss used in individual housing, is detailed and the mechanical nonlinear behavior of the timber joints is defined by hysteresis elements. From the mechanical point of view, the combination of the nonlinear behaviour of wood and the ductility of steel components inevitably generate energy dissipation phenomena [1] during the seismic loading. In France, there are more and more interest to use this configuration of timber roof trusses in individual housing.
We assume that the nonlinearity is not due to the geometrical configuration of the timber roof truss but mainly induced by the behaviour of the metal fasteners. This point is called the most likely failure point P*, its coordinates in the standard random space are denoted by the vector u*. The mechanical response is defined by the displacements of the nodes N14 and N19 in the direction OX (see figure 2).
For instance, the target probability of failure suggested by the design code is about 10 5. The mechanical response is represented by the displacements of the nodes Nn, N17 and N1S in the direction OX (see figure 2).
From the obtained results, we can conclude that the risk of anchorage failure on the back truss is more important than the failure by the fracture of wood on the front truss. The finite element model has been based on the assumption that the main nonlinearity is due to the punched metal plate fasteners employed in the timber joints (i.e.
Some items that are available are engineered laminated beams (LVL's), I-joists systems, glulam beams, and specialty hangers. The uncertainties are taken into account in the numerical model through random variables representing the stiffness parameters at timber joints. At each location, one or more hysteresis elements are used, depending on the number of connected timber beams.
The main idea of these approaches is to approximate the limit state function G(X) = 0 to provide an estimation of the probability of failure Pf (Figure 7). In order to reduce the dimension of the random space, we assume perfect correlation between the horizontal stiffness Kx, the vertical stiffness Kz and the rotational stiffness Kg.
The limit state function is defined as stated by equation (7) and the critical displacement is dcrit =1,8 10"4 rn. Those information collected trough the reliability analysis can help the engineers to take better decision concerning the choice of the convenient technological solution for the connection elements. The reliability analysis allows us to compute the failure probability and their sensitivity to various random parameters. This value is chosen as the lower bound of the range given by the mechanical grading of timber members achieved in experimental tests.
The obtained results concerning the reliability analysis for different values of the critical displacement dcrit are summarised in table 2.


We note that the orthotropy of the wood is not taken into account, as the beam elements are slender, thus the load remains collinear to the principal beam’s direction and shear loads in wood are limited. The choice of the parameters used for eachjoint is based on experimental tests on metallicjoints. The limit state surface corresponds to the points verifying the condition G(X) = 0, in other word, it defines the boundary between the safe and the failure domains as shown in figure 6. Unfortunately, the mechanical behaviour of timber joints is highly nonlinear mainly due to the metal plate fasteners which ensure the connection between the timber members.
The developed finite element model allows us to obtain the displacement fields at each node during the seismic excitation. Hence, the random variable representing the rotational stiffness is defined as Kg = AK + Xh where Xt is the random variable defining the joint uncertainties. Based on experimental results, the failure mode of the timber roof truss is composed of wood fracture on the top chord, as well as an anchor failure of the bottom chord. In spite of the important scientific work devoted in this context, the mechanical behaviour of timber joints is still misunderstood.
In this study, the seismic excitation corresponds to Kobe earthquake in Japan which occurred in January 17, 1997.
These two failure modes have been considered in the reliability analysis and the probability of failure against the failure critera has been estimated. Contrary to the approximations made in considering the timberjoints either completely rigid or flexible, the behaviour of punched metal plate fasteners is now described by semi-rigid behaviour law.
We have shown that the risk of anchorage failure on the back truss is more important than the failure by fracture on the top chord.
In this way, several nonlinear models have been developed including those in [2, 3, 4], Although, these models have been widely used, the obtained predictions are conservative since the parameters of the behaviour law have been considered as deterministic.
We have also shown that the proposed methodology is not time consuming since the convergence of the quantities of our interest (i.e. However, probabilistic approaches must be used in order to take into account the variability observed in material properties, fluctuations of seismic excitation and uncertainties in geometrical properties.
In this context, several works already took into account these uncertainties [5, 6, 7, 8], In the present work, an alternative to these approaches is proposed on the basis of reliability analysis. Figure 4 illustrates the displacement in the nodes related to metallicjoints at the top and the supports of the truss. The ongoing research aims to develop a coupling method able to deal with higher order reliability problems.
The mechanical behaviour under seismic loading is simulated by nonlinear finite element model, the parameters defining the stiffness of the timberjoints in the roof truss are considered as random variables and the probability of failure against a prescribed failure mode is estimated using the First Order Reliability Method (FORM).
This paper is organized in three sections: in the first one, we describe the methodology adopted to construct the finite element model dealing with timber roof truss under seismic excitation.
The performance of the proposed approach is depicted in section 4, based on numerical applications. Finally, conclusions based on the obtained results and some prospects for a further work are presented.



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