# On the Seismic Design of Structures with Tilting Located within a Seismic Region
## 7 Conclusions  
A reliability-based methodology to estimate the additional strength requirement for structures exhibiting asymmetric yielding caused by different reasons was proposed and properly applied. Simplified mathematical expressions to estimate strength amplification factors were obtained for different soil conditions, and the methodology was applied to the valley of Mexico; however, the proposed steps can be applied to structural systems located in other seismic regions. The objective of amplifying the lateral strength of structures with asymmetric yielding with the expressions proposed in this study is that they achieve a seismic performance, in terms of the expected ductility demand, equivalent to that of their symmetric yielding counterparts; that is, they have similar reliability levels. The resulting expressions were compared with that recommended in the current Mexico City Building Code (MCBC-2004) and their advantages and disadvantages were discussed. The main conclusions of this study are listed as follows:  
1. Results indicate that the additional lateral strength requirement of structures with asymmetric yielding is higher for those with fundamental vibration periods close to the dominant period of the soil where they are located; this requirement is even higher for structures located on soft soils.
2. Simplified mathematical expressions were proposed for the estimation of strength amplification factors for structures with asymmetric yielding, considering different soil conditions. The expressions correspond to the valley of Mexico and depend on factors such as the ductility of the structure, the level of asymmetric yielding, and the ratio between the fundamental vibration period of the structure and that of the dominant period of the soil.
3. The proposed mathematical expressions are more conservative than that recommended in the current Mexico City Building Code (MCBC-2004) for intermediate and soft soils, especially for structures whose vibration period is close to the dominant period of the soil where they are located. Although the expression proposed in the MCBC-2004 leads to conservative results for firm ground, results indicate that the effect of asymmetric yielding is much more detrimental on intermediate and soft soils than on firm ground. The expressions developed in this study have been approved by the Technical Committee for Seismic Design of the MCBC, and will be incorporated in the new version of the Mexico City Building Code.
4. It was verified that the value of the expected ductility demand of asymmetric yielding MDOF systems, associated with a given return period, is almost equal to that corresponding to their equivalent simplified systems. The implication of this is that the use of simplified structural systems to estimate strength amplification factors for MDOF structures with asymmetric yielding is appropriate.  
The authors thank the three anonymous reviewers whose comments improved the quality of this work. The valuable comments made by [PERSON], [PERSON] and [PERSON] are greatly appreciated, as well as the support given by UNAM (under project PAPIIT-IN103517) and by Instituto para la Seguridad de las Construcciones en el Distrito Federal. The first author acknowledges the scholarship given by Consejo Nacional de Ciencia y Tecnologia (CONACyT) for his Ph.D. studies. The seismic records used were obtained from the database of the Institute of Engineering, UNAM. [PERSON] and [PERSON] performed the nonlinear time history analyses of the structural models and estimated the ductility transformation factors for actual MDOF structural systems; [PERSON] and [PERSON] performed the reliability analysis, fitted the mathematical expressions to the data and wrote the paper.