## 4 Case-Study Building
### Modal-DBD Design Steps
#### 4.2.1 Definition of the Target Performance Level  
The first step of Modal-DBD method requires one to define the displacement limits for different hazard levels. For each displacement level, literature values of Non-Exceedance (NE) probability are generally taken into account for the design of ordinary buildings. The ASCE/SEI-7 [5] provisions, for example, require that the displacement targets of Table 2 are satisfied for \"other than masonry\" structures.  
As far as these general modal-DBD rules are taken into account and extended to wooden buildings, a first design issue must be properly assessed for Blockhaus systems. Currently, no specific drift limits are recommended by standards in use for timber structures, in particular regarding the detection of \"damage\" and the quantification of inter-story drift levels at collapse.  
For light-frame buildings, for example, [PERSON] et al. [18] conveniently adjusted the limits suggested in Table 2 for \"other than masonry\" systems. Later on, [PERSON] et al. [26] concluded that laterally braced wooden shear-walls could remain stable up to 7%-10% inter-story drift values, depending on the magnitude of the vertical compressive loading. Even different drift limits were adopted by the NEESWood [27] project team. There, a fixed 4% inter-story drift was recognized as an acceptable threshold for Maximum Credible Earthquake (MCE) hazard, while a conventional 7% drift was taken into account for collapse prevention against near fault ground motions.  
For the case-study system examined in this paper, based on the evidences of past experiments available in the literature for Blockhaus structures, it is clear that the \"other than masonry\" drift limits presented in Table 2 would result in extremely conservative design assumptions. The intrinsic flexibility of the examined log-assemblies (as also demonstrated in [20; 21]) was thus taken into account for the selection of key parameters of the Modal-DBD analysis.  
Regarding the Immediate Occupancy level, more in detail, the inter-story drift limitation suggested by EC8 for buildings having ductile non-structural elements was taken into account (see SS 4.4.3.2(b) in [13]), thus corresponding to 0.75%. For the Life Safety level, the 2.5% limit suggested in SS12 of ASCE 7-16 [5] was considered. The latter applies to \"other than masonry\" structures, with four of less stories and a risk category I or II that properly represent the system of Figure 4. Risk category I contains structures that are mainly unoccupied and would result in negligible risk for people, in the case of failure. At the same time, risk category II refers to buildings and structures not specifically  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{2}{c}{**Performance Expectations**} & \multicolumn{2}{c}{**Drift Limit**} \\  & & **(\%)** \\ \hline \multirow{2}{*}{**Level**} & **Exceedance Probability** & **Values from [5] for** & **Proposal for Blockhaus** \\  & **(\%/50 years)** & **“Other than Masonry”** & **Systems** \\ \hline \hline IO & 50 & 0.5 & 0.75 \\ LS & 10 & 1 & 2.5 \\ CP & 2 & 2 & 4 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Allowable inter-story drift for structures “other than masonry”, according to ASCE/SEI-7 provisions [5], or herein proposed for Blockhaus systems.  
classified as conforming to other categories such as the majority of structures (residential, commercial and industrial buildings).  
Based on literature values of collapse displacements for Blockhouse structures, finally, experimental and numerical outcomes from past literature projects on single log-walls under in-plane lateral loads were taken into account (i.e., [24]). Accordingly, the conventional 3% drift in use for the CP level was incremented to a more realistic 4%. It was in fact demonstrated by the experimental evidences in [20] that typical log-walls under in-plane seismic loads can accommodate large drift ratios (up to 2%) before local damage in carpentry joints and logs could manifest.