This chapter introduces additional numerical integration methods along with their stability and accuracy. These methods are general in that they can be used for irregular loading patterns, such as earthquake ground motion, and for structures whose members change from elastic to inelastic during response. Since maximum structural response is usually needed in structural design, sophisticated response spectra and design spectra are developed. Included are elastic spectra, inelastic spectra, modal combination techniques, and spectra for multicomponent seismic input. An earthquake is an oscillatory, sometimes violent movement of the earth’s surface that follows a release of energy in the earth’s crust. The intensity of an earthquake is based on damage and observed effects on people, buildings, and other objects. Earthquake magnitude is directly measured by instruments called seismograms. Structures subjected to severe earthquake ground motion experience deformations beyond the elastic range. Inelastic deformations depend on load-deformation characteristics of the structure and often result in stiffness deterioration.