# Sustainable Cross-Laminated Timber Structures in a Seismic Area: Overview and Future Trends
## 5 Modeling of Multi-Story Timber Buildings
### Floors  
As well as for the shear-walls, the in-plane behavior of CLT floors can be schematized with 2D-shell elements having material properties calculated as descibed in Section 4.1.2, or through truss elements having diagonals (made with trusses or springs) to simulate the in-plane strength and stiffness of the floors [71,72].  
Lateral force transferring a diaphragm represents a topic still under study by researchers, then few indications can be found in both research papers and codes. For practical purposes, CLT floors are assumed as rigid diaphragms in the finite element model of the buildings: they are capable to transfer horizontal seismic actions to the vertical walls, provided that panel-to-panel connections are suffciently stiff and resistant.  
The assumption of a rigid diaphragm is of particular importance in seismic analyses, because flexibility of floors can influence the fundamental vibration modes of the structures  
Figure 10: Lintels configurations in case of: (**a**) monolithic wall, (**b**) segmented walls.  
changing the force transmission on the vertical elements [71]. When such an assumption is made, NDS [33] suggests verifying it by calculating the maximum in-plane deflection of the floors. For a simple supported floor, having length L and width W, maximum deflection can be determined as in the following (Figure 11):  
\[\delta=\frac{5 vL^{3}}{8 EAW}+\frac{wL^{2}}{8A_{clt}G_{ef}}+CLe_{n}+\frac{\sum(x \Delta_{c})}{2W} \tag{1}\]  
The first term of the Equation (1) represents the flexural deflection contribution, where v = wL/2B is the maximum shear at the edge of the diaphragm calculated from the uniformly distributed load w, B is the diaphragm width, E is the Young modulus and A the cross-section area of the effective lamination layers. The second term is the shear deformation of the CLT panels, where A\({}_{\text{clt}}\) is is the gross cross-sectional area of the CLT diaphragm resisting the shear load and G\({}_{\text{ef}}\) is the effective shear modulus; this latter can be estimated as in [PERSON] and [PERSON] 2013 [73]. The third term takes into account the slip contribution of the connection on the total deflection: the value of C is calculated as C = 0.5(1/P\({}_{\text{L}}\) + 1/P\({}_{\text{W}}\)) where P\({}_{\text{L}}\) and P\({}_{\text{W}}\) represent the length and the width of the typical panel respectively, while e\({}_{\text{n}}\) is the connection slip at the outer edge of the diaphragm under the maximum shear load v. The derivation of e\({}_{\text{n}}\) can be found in the ATC-7 [74], derived for application to typical wood structural panels diaphragms. The fourth term is the geometric translation of any chord slip under loading into lateral deformation of the diaphragm, where \(\Delta_{\text{C}}\) = 2(Tor C)/\(\gamma\)n (T and C are the maximum tensile and compression forces due to applied loads w, \(\gamma\) is the load slip modulus and \(n\) the number of fasteners) and \(x\) is the length considered for evaluating maximum deflection due to chord slip.  
By contrast, when the floors are modelled by means of 2D-shell elements or trusses the maximum in-plane deflection can be determined as a result of the numerical analyses.  
As regards the schematization of the out-of-plane behavior, it is limited to evaluate the amount of the out-of-plane flexural deflections or vibrations. Literature papers demonstrated that the analytical model described in the Section 4.1.2 gives back reliable results to calculate flexural deflections, vibrations and stress state, comparable with those obtained with finite element models composed of multi-layer material [52]. In any case, the adoption of the multi-layer material surely gives back more consistent results and allows conducting modal analyses to calculate accurately maximum vibrations.