The steel structural system with the optimum distribution of the yield shear coefficients subjected to any nonstati'onary random earthquakes, is constructed by simply averaging the optimum yield shear coefficients for .each sample of the random earthquakes population. Whatever the statistical properties of random earthquakes may be, the damage distribution of each story of the system is always almost constant, even if the statistical properties are given to the structural characteristic of the system and the soil. The above fact is examined using two damage indices (cumulative plastic deformation ratio & hysteretic discipated energy).
