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The seismic response of structures to strong ground motions is a complex problem that has been studied for decades. However, current seismic regulations do not assess the potential level of damage that a structure may undergo during a given seismic event. This will happen in spite that the design objectives for any structural system are formulated in terms of acceptable levels of damage. This paper develops simple expressions to estimate plastic energy demands for soft soil sites (particularly, those located in Mexico City) capable of generating long duration narrow-banded ground motions. To overcome the limited scope of previous studies, about 35,000 seismic simulations were performed using two scaling methodologies: linear and seismological. A new simplified relation between plastic hysteretic energy and maximum ductility demands is presented, and also, a discussion offered on how this relation can be used to allow for an energy-based design aimed at controlling structural damage under the explicit consideration of low cycle fatigue. [ABSTRACT FROM AUTHOR]