Statistical evaluation of approximate methods for estimating maximum deformation demands on existing structures

A statistical study is presented to evaluate the accuracy of five approximate methods that have been proposed in the past to estimate the maximum inelastic deformation demand on existing structures. Three are based on equivalent linearization in which the inelastic deformation is approximated by the maximum deformation of an equivalent linear elastic system having lower lateral stiffness and larger viscous damping with respect to the preyielding properties of the inelastic system. In the equivalent linear methods evaluated here the equivalent period and equivalent damping ratio are computed as a function of the maximum deformation through the displacement ductility ratio. The other two methods estimate the maximum inelastic deformation of a system by modifying its maximum elastic deformation through a displacement modification factor. Modification factors depend on the initial period of vibration and its lateral strength. A relatively large number of earthquake ground motions recorded on sites having average shear wave velocities higher than 180 m/s are used to calculate error statistics. For each method mean errors and standard errors, as well as probability of underestimating or overestimating inelastic deformations, are presented and discussed.