Engineers can develop two spectra:

1.MCE_R Spectral Response Acceleration Parameters  

2.Design Spectral Acceleration Parameters

1. (MCE_R) Spectral Response Acceleration Parameters

The Risk-Targeted Maximum Considered Earthquake (MCE_R) spectral response acceleration parameters for the short period (S_MS) and at the 1s period (S_M1) varies depending the on the Soil Site Class. QuakeManager computes these parameters according to equations 11.4-1 and 11.4-2 as follows:

•S_MS = F_aS_S .......... Eq. 11.4-1

•S_M1 = F_vS₁ .......... Eq. 11.4-2

QuakeManager refers to 11.4-1 and 11.4-2 to obtain the Site Coefficients F_a and F_v and interpolates automatically in case values fall between a range.

2. Design Spectral Acceleration Parameters

QuakeManager evaluates the design earthquake spectral response acceleration parameters at the short period (S_DS) and at a period of 1s (S_D1) are computed according to equations 11.4-3 and 11.4-4 respectively.

•S_DS = (2÷3) S_MS = (2÷3) F_aS_S .......... Eq. 11.4-3

•S_D1 = (2÷3) S_M1 = (2÷3) F_vS₁ .......... Eq. 11.4-4

Sites Coefficient Fa and Fv

Table: Site Coefficient Fa (ASCE/SEI 7-10)

Table: Site Coefficient Fv (ASCE/SEI 7-10)

Spectrum Development

Figure below illustrates the development of the design spectrum based on the spectral acceleration parameters and periods.

Figure: Spectra Development

The spectral parameter may be computed based on the period conditions as follows:

1.If T<T₀, S_a = S_DS [0.4 + 0.6(T/To)] .......... Eq. 11.4-5

2.If T₀ ≤ T ≤ T_S, S_a = S_DS

3.If T ≤ T ≤ T_L, S_a = (S_D1 ÷ T) .......... Eq. 11.4-6

4.If T ≥ T_L, S_a = (S_D1 ÷ T_L) ÷ T².......... Eq. 11.4-7

where:

•T₀ = 0.2 (S_DS ÷ S_D1)

•T_S = (S_DS ÷ S_D1)

•T_L =  long-period transition period (s)

Note that if the MCE_R response spectrum is required, the design spectrum is multiplied by 1.5.

Copyright © 2022 Earthquake Solutions