Inverse damping perturbation for stiffness design of shear buildings

The problem in this paper is to find the set of story stiffnesses of an elastic shear building with added viscous dampers such that each mean maximum interstory drift due to spectrum-compatible design earthquakes would coincide with the specified value. Two simple stiffness formulas have been derived by means of the proposed inverse perturbation procedure of damping level, referred to as the ″inverse damping perturbation″. The first formula enables one to evaluate the primary effect of heavy damping for stiffness design, and the second formula enables one to evaluate the effect of off-diagonal terms of the modal damping matrix that is neglected in the first formula. A storywise criterion is derived by use of the second formula as to whether the effect can be negligible or not.