An Optimal Distribution of Stiffness Over the Height of Shear Buildings to Minimize the Seismic Input Energy

Based on Housnerʹs assumption, the average input energy from earthquakes to a building modeled as a single degree of freedom (SDOF) system, is related mainly to total mass of the building. Thus, based on the above premise for low damping and relatively long period systems, the seismic input energy per unit mass of the system (SDOF or MDOF) is mainly related to the ground motion features. The present study attempts to analytically reveal the range of validity of these assumptions in linear systems and to find an optimal stiffness distribution over the height of high-rise shear linear buildings to minimize the seismic input energy. To accomplish this objective, it is shown from the spectral standpoint that input energy spectra generally is a function of the natural period of vibration, so the input energy is further related to the stiffness of structure, the mass, damping ratio and ground motion characteristics. Subsequently, it is demonstrated that for low to moderate height (up to 20 stories) shear type structures, the optimal distribution of stiffness obeys a parabolic form, while for taller structures, this form is a bell-shaped function.