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Multi-Period Spectrum
The multi-period design response spectrum may be developed as follows:
•At discrete values of period, T, equal to 0.0 s, 0.01 s, 0.02 s, 0.03 s, 0.05 s, 0.075 s, 0.1 s, 0.15 s, 0.2 s, 0.25 s, 0.3 s, 0.4 s, 0.5 s, 0.75 s, 1.0 s, 1.5 s, 2.0 s, 3.0 s, 4.0 s, 5.0 s, 7.5 s and 10 s, the 5%-damped design spectral response acceleration parameter, Sa, shall be taken as 2/3 of the multi-period 5%-damped MCER response spectrum of the USGS Seismic Design Geodatabase for ASCE 7-22. Values of these parameters are provided by the USGS Seismic Design Web Service for ASCE 7-22, for the site class determined in accordance with Section 11.4.2.
•At each response period, T, less than 10 s and not equal to one of the discrete values of period, T, listed in Item 1 above, Sa, shall be determined by linear interpolation between values of Sa, of Item 1 above.
•At each response period, T, greater than 10 s, Sa, shall be taken as the value of Sa at the period of 10 s of Item 1 above, factored by 10/T, where the value of T is less than or equal to that of the long-period transition period, TL, and shall be taken as the value of Sa at the period of 10 s factored by 10TL/T2, where the value of T is greater than that of the long-period transition period, TL.
Two-Period Spectrum
The two-period design response spectrum may be developed as follows:
1.If T<T0, Sa = SDS [0.4 + 0.6 (T ÷ To)] .......... Eq. 11.4-5
2.If T0 ≤ T ≤ TS, Sa = SDS
3.If T ≤ T ≤ TL, Sa = (SD1 ÷ T) .......... Eq. 11.4-6
4.If T ≥ TL, Sa = (SD1 ÷ TL) ÷ T2.......... Eq. 11.4-7
where:
•SDS = design spectral response acceleration parameter at short periods
•SD1 = design spectral response acceleration parameter at a 1-s period
•T0 = 0.2 (SDS ÷ SD1)
•TS = (SDS ÷ SD1)
•TL = long-period transition period (s)
Vertical Response Spectrum
QuakeManager is capable of developing a vertical response spectrum according to the regulations of ASCE 7-22. The requirements may only apply to structures in Seismic Design Categories C, D, E, and F at sites in the conterminous United States west of -105 degrees longitude. For all other sites, a site-specific study may be conducted to determine vertical design earthquake ground motions.
QuakeManager evaluates the following expressions:
•If Tv < 0.025 s, SaMv = 0.3CvSMS ......... Eq. 11.9-1
•If 0.025 s < Tv < 0.05 s, SaMv = 20CvSMS(Tv-0.025) + 0.3CvSMS ......... Eq. 11.9-2
•If 0.05 s < Tv < 0.15 s, SaMv = 0.8CvSMS ......... Eq. 11.9-3
•If 0.15 s < Tv < 2.0 s, SaMv = 0.8CvSMS [(0.15/Tv)0.75] ......... Eq. 11.9-3
The vertical coefficient values may be obtained from the table below.
Table: Values of Vertical Coefficient Cv (ASCE 7-22)
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MCER Spectral Response Parameter at Short Periods
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Site Class A, B
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Site Class BC
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Site Class C
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Site Class CD
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Site Class D, DE, E, F
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Ss ≥ 2.0
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0.9
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1.1
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1.3
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1.4
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1.5
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Ss = 1.0
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0.9
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1.0
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1.1
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1.2
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1.3
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Ss = 0.6
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0.9
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0.95
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1.0
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1.05
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1.1
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Ss = 0.3
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0.8
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0.8
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0.8
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0.85
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0.9
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Ss ≤ 0.2
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0.7
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0.7
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0.7
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0.7
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0.7
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