# On the Seismic Design of Structures with Tilting Located within a Seismic Region
## 1 Introduction
In addition, in order to verify the applicability of the mathematical expressions to multi-degree of freedom (MDOF) structural systems, ductility transformation factors (DTF) between MDOF asymmetric yielding structural systems and simplified (one-story one-bay) 3D asymmetric yielding systems, are estimated. Figure 1: Some examples of structures with asymmetric yielding: (**a**) asymmetry in vertical loads; (**b**) structures with sloping facades; (**c**) tilting. There are several studies in the literature in which modification factors of the seismic design spectrum are proposed. The factors are intended to reduce linear elastic design spectra due to different reasons. For example, different methods to calculate strength reduction factors that allow estimating inelastic strength demands from elastic strength demands for structures located in different soil conditions have been proposed [7; 8; 9]. Other authors have proposed factors to reduce elastic seismic design spectra due to damping [10; 11; 12; 13; 14; 15]; however, none of the mentioned studies consider the influence of asymmetric yielding on the seismic structural response. Although there are several studies related to strength modification factors of the seismic design spectra, there are only a few studies in the literature focused on proposing strength amplification factors of the design spectrum that consider the yielding asymmetry of structural systems. Most of them analyze asymmetric yielding structural systems located in Mexico City (this is mainly due to the particular characteristics of the soft soil in this region). Some of these studies are focused on estimating the increment of the seismic response of systems with asymmetric yielding with respect to that of symmetric systems, and in developing mathematical expressions for that purpose [16; 17]. Other studies are addressed on identifying some of the characteristics of both the structure and the soil involved in the seismic response of asymmetric yielding structures [18]. There are studies that evaluate the seismic response of tilted structures subjected to different scenarios. [PERSON] [19] studied the performance of tilted tall buildings designed with different structural systems such as braced tubes, diagrids, and outrigger systems, identifying several factors that affect the structural performance of tilted buildings. [PERSON] et al. [20] assessed the behavior of an eighth-century masonry tower called \"Torre Sineo\", located in Italy. The tower has been damaged due to seismic events during the last few years and presents a deviation from verticality. The study deals with the possible scenario of an increase in the tilt mechanism of the tower and performs some numerical simulations to predict the possible damages. The results present a valuable picture of possible damage evolution and provide some advices for structural monitoring of the tower. Recent studies regarding the asymmetric yielding behavior propose amplification factors for the lateral seismic design forces for either reinforcement or design of new structures. [PERSON] and [PERSON] [21] proposed mathematical expressions of strength amplification factors for structures with asymmetric yielding located on soft and firm soils of Mexico City. They analyzed single degree of freedom systems (SDOF) with different hysteretic behavior. The obtained expressions were similar for all the hysteretic rules considered. In general, these expressions came out to be more conservative than those recommended by the Mexico City Building Code (MCBC-2004) [3]. [PERSON] et al. [22] proposed a reliability-based methodology to estimate strength amplification factors for structures with asymmetric yielding by means of ductility uniform exceedance rate spectra corresponding to narrow-band seismic ground motions.