# Reduced Design Response Spectrum for Modal Analysis per ASCE 7-16 §12.9.1.2

**Symbols**

* C_{d} = *Deflection amplification factor

*Seismic importance factor*

**I**_{e}=*Response modification coefficient*

**R =**### Modal Response Parameters

The seismic force-related design parameters, such as story drift values, support forces, and individual member forces for each mode of response are calculated using each mode's properties and the response spectra divided by the quantity R ∕ I_{e}. The value for displacement and drift quantities is multiplied by the quantity **C _{d }∕ I_{e}**.

The design response spectrum is simulated of linear elastic structures. The inelastic behavior of the structure is explained by dividing the spectral coordinates by the response modification coefficient, R. Multiplying the spectral coordinates by the Importance Factor, Ie, provides the additional power needed to improve the performance of important structures. The displacements that are calculated using the response spectrum must be amplified by C_{d} and reduced by I_{e} to produce the expected inelastic displacements.