# Sustainable Cross-Laminated Timber Structures in a Seismic Area: Overview and Future Trends
## 5 Modeling of Multi-Story Timber Buildings
### Mechanical Connections  
In multi-story CLT buildings the mechanical connections are usually modelled through links, trusses or frame elements.  
Figure 11: In-plane deflection of CLT floors under seismic actions.  
According to literature, uniaxial or biaxial behavior is generally considered to simulate the connections [23; 46; 50; 75; 76; 77]. In the first case, HDs and ABs resist only in their primary direction (e.g., HDs only in tension and ABs only in shear), in the second case both HDs and ABs resist axial and shear forces simultaneously. Uniaxial behavior is commonly used in the practical applications and leads to more conservative results with respect to the biaxial behavior. Moreover, for detailed analyses (e.g., time history analyses) the tension to shear force interaction domains are available to model the biaxial behaviour [61].  
The models discussed in Section 4.2 are used to schematize the panel to panel and the panel to foundation connection zones in finite element models of multi-storey CLT buildings. Both'simplified' or 'detailed' approaches discussed can be used to model the connection regions. Simplified methods do not consider the timber to timber contact contribution, then the connection model consists of: (a) HD truss or spring elements, which simulate the tensile behaviour of the hold-downs devoted to face tensile forces due to rocking of the panel; (b) AB truss or spring elements, which simulate the angle brackets devoted to resist shear forces due to translation of the panel. In such a model HD and AB are modelled as no-compression elements (due to buckling phenomena of the stem of HDs not interested by fasteners, when subjected to compression forces).  
To obtain more realistic analytical results, the contribution of the compressed timber should be included in the structural model. Thus, additional no-tension truss or spring elements devoted to simulate the timber to timber contact have been introduced in the structural model developed in references [50; 64; 75].  
Three different approaches to model the non-linear behaviour of the connections, and considered as representative for this paper's purpose, are reported in Table 4. An effective but sophisticated approach to model the cyclic behaviour of the connection has been presented by [PERSON] et al. [77]. The authors proposed the adoption of multi-linear hysteretic cyclic behaviour for both HDs and ABs, implemented thought a multilinear spring placed at the base of finite element model of the wall. Such schematization allows dynamic non-linear analyses to be carried out. Instead, a simplified monotonic trilinear model implemented within non-linear springs has been suggested by [PERSON] et al. [63] to carry out non-linear static analyses. Simplified elastic-perfectly plastic force-displacement behaviours have been also proposed in [PERSON] et al. [76] and [PERSON] et al. [50]. The first difference between these two latter models is that in [PERSON] et al. [50] the timber to timber contact takes into account the orthogonal to grain timber properties, while in [PERSON] et al. [76] only that in parallel to grain direction is considered. The second difference is that in [PERSON] et al. [76] the shear forces are faced through a couple of diagonal trusses joined at the corner of the panel, while in [PERSON] et al. [50] through frame elements.  
\begin{table}
\begin{tabular}{c c} \hline \hline \multirow{2}{*}{**Authors**} & **Structural Model** & **Connection Model** \\ \cline{2-3}  & **Trilinear Cyclic Behavior** \\ \hline \hline \end{tabular}
\end{table}
Table 4: Literature models for connections.  
These connection models are also valid to schematize the panel to panel and the panel to foundation connection zones in the case of coupled (or segmented) CLT wall, provided that additional shear springs to simulate the shear stiffness and strength of the fasteners in the vertical joints between the panels are included in the structural model [47; 49; 78].