Journal of Applied Sciences1812-56541812-5662Asian Network for Scientific Information10.3923/jas.2010.45.51Haddad SharghFarzanHosseiniMahmood12010101In the Energy Based Design (EBD) of structures Housner's assumption has a primary importance. Based on this assumption the average input energy from earthquakes to a building, modeled as a SDOF system, is related mainly to total mass of the building, having the damping ratio of the building as small as 0.03 and its period of vibration more than 0.4 sec (For smaller periods input energy is function of period also). For higher damping ratios, the maximum energy attained decreases as the damping ratio increases. Thus, mainly the seismic input energy per unit mass of the system is only related to the ground motion characteristics. Housner and Akiyama assumed that the seismic input energy to multistory structures can be estimated by input energy to an equivalent single degree of freedom system. The validity of this assumption was demonstrated experimentally. This study attempts to show analytically the range of validity of these assumptions in linear systems and the possibility of existence of an optimal stiffness distribution over the height of high rise buildings to minimize the seismic input energy. For this purpose it will be shown that from the spectral standpoint, input energy spectra generally is a function of natural period of vibration and if so, input energy is related also to the stiffness of structure, as to the mass, damping ratio and ground motion characteristics.]]>Akiyama, M.,1985Fajfar, P., T. Vidic and M. Fischinger,1989Housner, G.W.,1956Kuwamura, H. and T.V. Galambos,1989Kuwamura, H., Y. Kirino and H. Akiyama,1994Khashaee, P.,2003Park, Y.J. and A.H.S. Ang, 1985Uang, C.M. and V.V. Bertero,1990Climent, A.V., L.G. Pujades and F.L. Almansa,2002