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.  The parameters are computed 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

2. Design Spectral Acceleration Parameters

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

Site Coefficients (Fa and Fv)

The evaluation of the short-period site coefficient (F_a) and long-period site coefficient (Fv) depends on the Soil Site Class. The Site Coefficients F_a and F_v are obtained from tables 11.4-1 and 11.4-2. See tables below. QuakeManager refers to the tables below to evaluate site coefficients. Additionally, QuakeManager have the ability to compute the site coefficient (F_a) indicated per code regulations in the following cases:

Case 1: If the user selected the Default Site Class "D", F_a must be greater than 1.2.

Case 2: If users follows the Simplified Procedure (section 12.14), the following short-period site coefficients applies:

•F_a = 1.0 for Rock Sites

•F_a = 1.4 for Soil Classes

Note that in Simplified Procedure, there is no need to assess the long-period site coefficient (F_v) and the (MCE_R) Spectral Response Acceleration Parameters (S_MS & S_M1). 

For Site Classes E and F, engineers may perform a site response analysis according to section 21.1.

The ground motion hazard analysis may be performed for the following cases:

1.Seismic Isolated structures and structures with damping systems on sites with S1 ≥ 0.6

2.Structures on Site Class "E" with SS ≥ 0.1

3.Structures on Site Class "D" and "E" with S1 ≥ 0.2

However, the ground motion hazard analysis is not required for the following cases:

1.Structures on Site Class E sites with S_S ≥ 1.0, provided the site coefficient Fa is taken as equal to that of Site Class C.

2.Structures on Site Class D sites with S₁ greater than or equal to 0.2, provided the value of the seismic response coefficient Cs is determined by Eq. (12.8-2) for values of T ≤ 1.5Ts and taken as equal to 1.5 times the value computed in accordance with either Eq. (12.8-3) for TL ≥ T > 1.5Ts or Eq. (12.8-4) for T > T_L.

3.Structures on Site Class E sites with S₁ ≥ 0.2, provided that T is less than or equal to Ts and the equivalent static force procedure is used for design.

Table: Site Coefficient Fa (ASCE/SEI 7-16)

Table: Site Coefficient Fv (ASCE/SEI 7-16)

Horizontal Spectrum Development

Figure below illustrates the development of the design spectrum based on the spectral acceleration parameters and periods. QuakeManager develops the spectra based on the provisions of Chapter 11 (ASCE 7-16) as illustrated in the figure below:

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.

Vertical Response Spectrum

QuakeManager is capable of developing a vertical response spectrum according to the regulations of ASCE 7-16. The requirements of such spectrum are applicable only for structures under the seismic design categories C, D, E and F.

QuakeManager evaluates the following expressions:

•If T_v < 0.025 s, SaMv = 0.3C_vS_MS ......... Eq. 11.9-1

•If 0.025 s < T_v < 0.05 s, S_aMv = 20C_vS_MS(T_v-0.025) + 0.3C_vS_MS ......... Eq. 11.9-2

•If 0.05 s < T_v < 0.15 s, S_aMv = 0.8C_vS_MS ......... Eq. 11.9-3

•If 0.15 s < T_v < 2.0 s, S_aMv = 0.8C_vS_MS [(0.15/T_v)^0.75] ......... Eq. 11.9-3

The vertical coefficient values may be obtained from the table below.

Table: Values of Vertical Coefficient C_v (ASCE 7-16)

Where:

•T_v = the vertical period of vibration

•C_v = is defined in terms of S_S in Table 11.9-1

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