This chapter addresses the equation of motion for the response of nonlinear single-degree-of-freedom (SDOF) oscillators, its solution, common hysteretic models, inelastic response trends and estimates, inelastic spectra, and the influence of P-Δ effects on response. Nonlinear SDOF oscillators provide an excellent basis for estimating the displacement response of multi-degree-of-freedom (MDOF) systems. ElaΔstic systems are conservative or non-dissipating systems and do not dissipate energy during any quasi-static complete cycle of loading. Linear elastic response implies that there is no damage to the structural system. Various hysteretic models are available to represent in an idealized, approximate manner the response observed in experimental tests. Superposition relies upon linearity, and is implicit in the use of other mathematical approaches such as frequency domain solutions. Different strategies exist for the solution of nonlinear systems. The peak displacement response of a yielding oscillator may be higher or lower than the response of an elastic oscillator of the same period and viscous damping for any individual record.
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