GNGTS 2019 - Atti del 38° Convegno Nazionale

468 GNGTS 2019 S essione 2.2 The transversal walls were also represented as overlapping logs of with the same cross section of the longitudinal one and smaller length 1m. The characteristic notches and protrusions along the top and bottom surfaces were reasonably neglected while the corner joints with the transversal outrigger has been accurately reproduced. The top steel beam was also accounted. The decision to perform an Explicit analysis comes from the necessity to assess the different sources of non-linearity in the FE model and the presence of small mounting gaps. Two different materials have been considerated; steel in plate and cable is considerated as isotropic, linear elastic ( ρ s =7,500 kg/m 3 , E s = 130 GPa, and ν s = 0.32) (Eurocode 3 (CEN, 2004)). C24 Scot Pine has been modelled as orthotropic, elasto-plastic material. The contact is assessed as a boundary non-linearity; moreover, in a finite element analysis, contact conditions are a special class of discontinuous constraint, allowing forces to be transmitted from one part of the model to another. Using a formulation available inABAQUS/Explicit library, general contact interactions were automatically detected between overlapping logs, along their entire length, and between main logs and orthogonal logs based on the nominal geometry of adopted joints. For all of them, appropriate mechanical behaviour were specified, to correctly reproduce possible relative sliding between two adjacent surfaces (tangential behaviour) or interactions because of loads perpendicular to surfaces in contact (normal behaviour). In the first case (tangential behaviour), the main input parameters is the static friction coefficient μ (value μ = 0.5 was used in further parametric simulations). At the same time, the slip tolerance F f was set to 0.0005, so that possible reversible sliding between overlapping logs could be avoided ( γ f ≈ 0.05% l mesh ). The typical finite-element (FE) model used in this investigation consisted of 8-node, linear brick, solid elements with reduced integration (C3D8R), available in the Abaqus element library. The interpolation used is of the first order, there are no nodes interposed to those of the corner. This alternative is preferable to the interpolation of the second order, more effective in the problems in which concentrations of effort are generated but which requires greater computational burden. The vertical 10mm-diameters cable was modelled using truss elements (T3D2 type). The cable was placed in the tensile stress side of the wall. The connection between the cable and the wall top log was then modelled by means of a rigid link, fixed at the top timber log ( w x = w y = w z =0 and r x = r y = r z =0, where w i are the displacements in the x; y; z directions and r i signifying the rotation around the axis i , with i = x, y, z ). At the same time, the cable and the bottom timber log were restrained at the base ( w x = w y = w z =0). The steel plate was tied to the top log surface. The vertical compression load was described by means of a uniformly distributed, constant vertical pressure applied to the upper surface of the steel beam, the amount of load was defined for each log-wall. An horizontal in-plane lateral displacement was applied to the edge surface of the steel beam as a uniform, quasi-static, linearly increasing time-varying displacement BC. The maximum displacement was set equal to 200mm for each wall. Geometrical imperfections were taken into account in ABAQUS numerical model, as small gaps representative of possible mounting tolerances or geometrical defects affecting the standard joints. Nominal log dimensions were modified by introducing a vertical gap d gap between each main log and its orthogonal interceptions. The gap amplitude was assumed equal to to d gap = 1 mm. An Elasto-plastic model was formulated in order to define the load displacement behavior at the top of the wall using a linear SDOF spring. The envelope response of a wooden shearwall is modeled by the following three-parameter nonlinear Equation: Where K 0 is the initial tangent stiffness of the backbone curve, F b , represents the restoring force, F u is the maximum load-carrying capacity associated with the last displacement, δ u .