# On the Seismic Design of Structures with Tilting Located within a Seismic Region
## 6 Ductility Transformation Factors between Simplified and MDOF Systems
### Characteristics of the Buildings Analyzed  
The buildings analyzed in this study were designed in a conventional way, following the recommendations of the MCBC-2004. The plan and elevation of the buildings are illustrated in Figure 11. The occupancy of the buildings is considered to be residential. The nominal design compression stress is f'c = 29.4 MPa for concrete, and fy = 411.9 MPa in tension and compression for the reinforcing steel. The design of the buildings was carried out by using the software ETABS (2016, Computers and Structures Inc., Berkeley, CA, USA) [50]. The buildings are assumed to be located in a zone in the valley of Mexico with a soil dominant period Ts = 1.8 s (which falls in the intermediate zone as considered in the present study), with a seismic behavior coefficient, Q = 3 (which implies that the detailing requirements for their structural members are similar to those established by the Uniform Building Code [51] for reinforced concrete special moment-resisting frames). The design of the buildings was based on a modal spectral dynamic analysis. The lateral stiffness was selected so that the maximum inter-story drift does not exceed 0.030, which is the limit specified by MCBC-2004 for the design of ductile moment-resisting concrete frames.  
The nonlinear idealization of the buildings was carried out with the Ruaumoko3D (2007, Athol Carr., Canterbury, Christchurch, New Zealand) [52] software. The modeling of the buildings includes the nonlinear behavior of their structural members. In this study, the modeling of the beams considers a plastic hinge length equal to half of their height, to estimate the rotational capacity. The yield moment in each of the principal axes of the beams is obtained from the corresponding moment-curvature diagram of the cross sections located at their ends, and it is associated with the smallest of the curvatures corresponding to: (1) fracture of the tension longitudinal steel, (2) buckling of the compression longitudinal steel, and (3) crushing of the compression concrete block. An interaction diagram is developed for each column. The rigid end-block lengths of the beams and columns are taken equal to half of the height of the members with which they intersect. Rigid diaphragms are considered in all building levels, and the corresponding mass of a given story is considered to be lumped in its center of mass. The Tangent Stiffness Rayleigh Damping model was used in the analysis. The hysteretic behavior of the structural members is idealized as bi-linear, with 1% of post-elastic stiffness (to be consistent with the results presented before for simplified models), and therefore, P-\(\Delta\) effects are implicitly considered.  
Figure 11: Plan, elevation, and characterization of asymmetric yielding of the buildings. (**a**) plan; (**b**) elevation; (**c**) asymmetric yielding building.  
Table 3 summarizes the main dynamic characteristics of the buildings such as their fundamental vibration period (T\({}_{1}\)), the resistant base shear (V\({}_{\text{b}}\)), the resistant base shear coefficient (c), the yield displacement (d\({}_{\text{y}}\)), and the ultimate displacement (d\({}_{\text{u}}\)), the latter two were obtained through nonlinear static (pushover) analyses.