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The spectral response acceleration for short periods (SS), adjusted for the target risk of collapse, shall be determined as the lesser value of Equations 11.4-1 and 11.4-2:
•SS = CRS * SSUH……. Eq. 11.4-1
•SS = SSD…….. Eq. 11.4-2
and the spectral response acceleration at a period of 1 second (S1), adjusted for the target risk of collapse, shall be determined as the lesser value of Equations 11.4-3 and 11.4-4:
•S1 = CR1 * S1UH ……. Eq. 11.4-3
•S1 = S1D ……. Eq. 11.4-4
Where:
•SSD = mapped deterministic, 5 percent damped, spectral response acceleration parameter at short periods as defined in Section 11.4.1
•SSUH = mapped uniform-hazard, 5 percent damped, spectral response acceleration parameter at short periods as defined in Section 11.4.1
•CRS = mapped value of the risk coefficient at short periods as defined in Section 11.4.1
•S1D = mapped deterministic, 5 percent damped, spectral response acceleration parameter at a period of 1 second as defined in Section 11.4.1
•S1UH = mapped uniform-hazard, 5 percent damped, spectral response acceleration parameter at a period of 1 second as defined in Section 11.4.1
•CR1 = mapped value of the risk coefficient at a period of 1 second as defined in Section 11.4.1
The MCER spectral response acceleration for short periods (SMS) and at 1 second (SM1), adjusted for Site Class effects and the target risk of collapse, may be evaluated using the Equations 11.4-5 and 11.4-6, respectively.
•SMS = FaSs …… Eq. 11.4-5
•SM1 = FvS1 …… Eq. 11.4-6
Site Coefficients Fa and Fv
Site coefficients Fa and Fv are defined in Tables 11.4-1 and 11.4-2 (check tables below), respectively.
When the simplified design procedure of Section 12.14 is used, the value Fa shall be determined in accordance with Section 12.14.8.1, and the values of Fv, S1, SMS, and SM1 need not be determined.
Table: Site Coefficient Fa (NEHRP 2009)
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Table: Site Coefficient Fv (NEHRP 2009)
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Spectrum Development
Design earthquake spectral response acceleration parameter at short periods, SDS, and at a 1-second period, SD1, may be evaluated using the following equations:
•SDS = (2/3) SMS….. Eq. 11.4-7
•SD1 = (2/3) SM1….. Eq. 11.4-8
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Figure: NEHRP 2009 Spectrum Development
The spectral parameter may be computed based on the period conditions as follows:
•If T<T0, Sa = SDS [0.4 + 0.6 (T ÷ To)] .......... Eq. 11.4-9
•If T0 ≤ T ≤ TS, Sa = SDS
•If Ts ≤ T ≤ TL, Sa = (SD1 ÷ T) .......... Eq. 11.4-10
•If T ≥ TL, Sa = (SD1 × TL) ÷ T2.......... Eq. 11.4-11
where:
•T0 = 0.2 (SD1 ÷ SDS)
•TS = (SD1 ÷ SDS)
•TL = long-period transition period (s)
Note that if the MCER response spectrum is required, the design spectrum is multiplied by 1.5.
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