Document: NUREG-0800
Document ID: 94da2f11-6df6-47d0-a25e-edeb21a4d649
Document Type: srp
Title: 3.7.1-12
Source: NUREG-0800
Source URL: https://www.nrc.gov/docs/ML1419/ML14198A460.pdf
Revision Date: 2023-06
Chapter: 3
Section ID: 3.0
CFR Part: 
CFR Title: 

Content:
ch ܨሺ߱ሻ is evaluated; ߱ represents the circular frequency (in rad/s) and is defined as: ߱ൌ2ߨ݂, where ݂ is the natural frequency (in Hz). The duration ܶ஽ represents the duration of near maximum and nearly stationary power of an acceleration time history record. Additional guidance on estimating ܶ஽ for artificial time history or actual earthquake time history is provided in Appendix B of NUREG/CR-5347. Fourier amplitude |ܨሺ߱ሻ| in Equation (1) (also for Appendix A) is defined at each circular frequency ߱௡ as: |ܨሺ߱௡ሻ| ൌΔݐቤ෍ ܽሺݐ௝ሻ݁ିଶగ௜ቀ௡௝ ேቁ ேିଵ ௝ୀ଴ ቤ (2) where, ܽሺݐ௝ሻ is the strong motion portion of the acceleration time history (after proper tapering at both ends), ݐ௝ൌ݆ Δݐ, ݆ൌ0, 1, … ܰെ1, and ݊ൌ0, 1, … ܰ/2. For ܰ/2 ൏݊൑ ܰെ1, ߱௡ represents the negative frequencies and does not appear in the one-sided PSD calculation. At any frequency ݂ (where, ݂ൌ߱/2ߨ), the average one-sided PSD is computed over a frequency band width of ±20%, centered on the frequency ݂ (e.g., 4 Hz to 6 Hz band width for ݂ = 5 Hz). In NUREG/CR-6728, the horizontal design response spectra (RS) for rock site conditions appropriate for the Central and Eastern United States (CEUS) are defined as a function of the earthquake moment magnitude M and the fault distance R (in km) by the following equation: ln ቆܵܣሺ݂ሻ ܲܩܣቇൌ ܥଵ cosh ሺܥଶ݂஼యሻ൅ܥସቆexpሺܥହ݂ሻ ݂஼ల ൅ܥ଻expሺܥ଼݂ሻ ݂஼వ ቇ ଵ/ଶ (3) 3.7.1-28 Revision 4 – December 2014 where SA and PGA represent the spectral amplitude and peak ground acceleration, respectively, and the parameters C1 through C9 are defined as (for the single corner frequency model): ܥଵൌ0.88657 ܥଶൌexpሺെ10.411ሻ ܥଷൌ2.5099 ܥସൌെ7.4408 ൅ܯሾ1.5220 െ0.088588ܯ൅0.0073069 lnሺ0.12639ܴ൅1ሻሿ ܥହൌെ0.34965 ܿ଺ൌെ0.31162 ൅0.0019646ܴ ܿ଻ൌ3.7841