## 3 Design Response Spectra for Lebanon  
The first Lebanese seismic design rules were introduced in the early 1990s. Governmental decreres N. 646, N. 14293, and N. 7964, issued in 2004, 2005 and 2012, respectively, provided the seismic design rules which are currently adopted in Lebanon. Based on such decrees, the Lebanese Standards Institution (LIBNOR) issued the Standard NL135 [31]. The latter assumes the same seismic hazard for the whole Lebanese territory, classifying it as a 2\(c\) seismic zone. NL135 also instructs the designer to refer to (i) the French Norm PS92 [32], (ii) the Uniform Building Code (UBC) [33] or (iii) the International Building Code (IBC) [34], while announcing the adoption of (iv) the Eurocode 8 (EC8) [35] as the only seismic code in Lebanon. To sum up, three different seismic design lines are currently allowed by Lebanese NL135, while a fourth one is mentioned as the future unique reference code. It is worth noting that some of the codes referred to by Lebanese NL135 are obsolete in their countries. This is the case of PS92, which is not in force anymore in France, where presently EC8 is the reference code. On the other hand, IBC is a recent code which incorporates other previous USA codes, including UBC. The latter is, however, still widely used in some developing countries such as Lebanon. To get a complete picture of the seismic design tools allowed in Lebanon, the DRS relevant to PS92, UBC, IBC are derived in the following Sections 3.1-3.3. In addition, the DRS obtained from EC8 are provided in Section 3.4. All the DRS meet the Lebanese NL135 and LIBNOR recommendations and have been built under the assumptions listed below. **Assumption 1**. : _Only the elastic design response spectra are considered._  
**Assumption 2**. : _The reference peak ground acceleration (PGA) is taken as equal to \(2.5\ m/s^{2}\)._  
**Assumption 3**. : _A period range \(0\ s\)-\(4\ s\) will be considered here in the spectra._  
**Assumption 4**. : _A damping ratio of \(5\%\) is considered._  
**Assumption 5**. : _The vertical seismic action is neglected._  
It is worth noting that Assumption 1 and Assumption 2 are mandatory. The first one, in fact, derives from the final purpose of this study which is obtaining SCEs for transient dynamic analyses. The acceleration records must in fact be obtained by referring to the elastic (and not to the reduced). On the other hand, Assumption 2 meets the Lebanese code recommendations which assume a seismic zone factor \(Z=0.25\) and thus \(\text{PGA}=2.5\ \text{m}/\text{s}^{2}\). Regarding Assumption 3, it should be noted that \(0\ s\)-\(4\ s\) is the range where the fundamental \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Date** & **Location** & **Magnitude** \\ \hline
1 & 9 July 551 A.D. & Phoenicia (Roman Province), Byzantine Empire (now Lebanon) & 7.5 \\ \hline
2 & 15 August 1157 & Hama, West central Syria & \textgreater{}7.0 \\ \hline
3 & 29 June 1170 & Idlib, Northwestern Syria & \textgreater{}7.0 \\ \hline
4 & 20 May 1202 & Southwestern Syria & 7.6 \\ \hline
5 & 30 October 1759 & Ottoman Syria part known today as Lebanon & 6.7 \\ \hline
6 & 25 November 1759 & Ottoman Syria part known today as Lebanon & 7.4 \\ \hline
7 & 26 April 1796 & Ladhikiya, Southwestern Syria & 6.6 \\ \hline
8 & 13 April 1822 & Aafarine, Beqaa, Lebanon & 7.4 \\ \hline
9 & 3 April 1872 & Amik golu, Beqaa, Lebanon & 7.2 \\ \hline
10 & 29 September 1918 & Northwest of Tartus, Syria & 6.6 \\ \hline  & 16 March 1956 & Southeast of Baabda, Mohafazat Mont-Liban, Lebanon & 5.3 \\ \hline
11 & 16 March 1956 & Southwest of Zahle, Mohafazat Béqaa, Lebanon & 5.5 \\ \hline
12 & 26 March 1997 & Nabatye et Tahta, Mohafazat Nabatityé, Lebanon & 5.0 \\ \hline
13 & 15 February 2008 & Tyros, South Governorate, Lebanon & 5.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Some of the strongest Lebanese earthquakes. period of buildings typically falls, and in fact some codes, like the EC8 (see Section 3.4), confine the use of the design response spectra to this range.