The structural properties of a structure deteriorate when deformations reach the range of inelastic behavior. A possible consequence of deterioration of the hysteretic behavior of a structure is failure of critical elements at deformation levels that are significantly smaller than its ultimate deformation capacity. Seismic design methodologies that account for low cycle fatigue can be formulated using the concept of target ductility. The practical use of one such methodology requires the consideration of simple low cycle fatigue models that consider the severity of repeated loading through a normalized plastic energy parameter. The inconsistencies inherent to the use of such indices can be corrected through simple empirical rules derived from an understanding of the effect of the history of energy dissipation in the assessment of the level of structural damage.

A seismic design procedure that does not take into account the maximum and cumulative plastic deformation demands that a structure is likely to undergo during severe ground motion could lead to unsatisfactory performance. In spite of this, current design procedures do not take into account explicitly the effect of low-cycle fatigue. Based on the high correlation that exists between the strength reduction factor and the energy demand in earthquake-resistant structures, simple procedures can be formulated to estimate the cumulative plastic deformation demands for design purposes. Several issues should be addressed during the use of plastic energy within a practical performance-based seismic design methodology.The results in this paper were obtained from the dynamic response of single-degree-of-freedom (SDOF) systems having elastic-perfectly-plastic behaviour and 5% critical damping. The conclusions and design expressions offered have been established by considering systems with period of vibration (T ) ranging from 0.2 to 5.0 s. The dynamic response of these systems was established using Newmark's integration method with constant acceleration.Four sets of ground motions are considered, three of them corresponding to the Los Angeles (LA) urban area and one corresponding to Mexico City. The ground motions for LA, established for the FEMA/SAC Steel Project [11], were grouped in sets of 20 motions as follows: design earthquake for firm soil with 10% exceedance in 50 years (LA 10in50), design earthquake for ENERGY DEMANDS FOR SEISMIC DESIGN Assume max = f (judgement), and b = f (detailing) 2Determine T Determine T 3Estimate max = f (T, u , b) Estimate u = f (T, max , b) 4Estimate

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The structural reliability in terms of maximum interstory drift-and, alternatively, in terms of plastic hysteretic energy-is evaluated for six regular momentresisting steel frames designed according to the Mexico City Building Code, and located in the Lake Zone of that city. While the maximum interstory drift was used because of its relevance within the format of current seismic design codes, the plastic hysteretic energy was considered due to its importance for the performance of structures when subjected to severe cumulative plastic deformation demands. The demand hazard curves of the frames in terms of drift and energy are compared to provide a general idea of the reliability levels associated to the models, and to provide insights into which response parameter dominates their dynamic behavior and structural performance. In some cases, large differences are observed in the reliabilities computed by measure of the two different response parameters under consideration.