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We should include a link to my paper on spectra
The nonlinear spectrum is an extension of the linear spectrum to sdof systems that behave nonlinearly. Different methods of selecting the yield strength of the systems lead to several types of nonlinear spectra including: “constant strength” and “constant ductility” spectra.
A “constant strength” spectrum is obtained when the system’s strength is constant regardless of the natural period. Different definitions of the strength (absolute or relative to a spectrum or to elastic response), lead to several variations on the “constant strength” spectrum, such as the “constant R” spectra, where R is the force reduction, or the ratio of the linear force demand to the yield strength. The linear demand can be either the linear spectrum of the same earthquake or some idealized linear spectrum (for example, a design spectrum).
The “constant ductility” spectrum is obtained by solving for the yield strength that results in a target ductility demand under the given ground motion. The constant ductility spectrum allows a comparison between systems experiencing the same amount of yielding, as reflected by the ductility demand, which is generally considered a reflection of the damage in the system. An extension of this idea leads to “constant damage” spectra which are computed by solving for the yield strength that results in a target value for a damage index. “Constant ductility” and "constant damage" spectra cannot be obtained directly, but need to be iteratively solved for by iterating over several different strengths, until the correct strength, that which results in the desired ductility (or damage), is found. The associated computational cost is typically many times that of other types of nonlinear spectra such as “constant strength” spectra.
Note: Nonlinear spectra are not currently supported in QuakeManager, but may be supported in the future. In order to calculate nonlinear spectra, you can use Bispec.
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