Design Spectrum for Elastic Analysis (Section 3.2.2.5)

The following spectra definition S_d(T) is used for equivalent lateral force method. This part is used in calculation of lateral seismic loads per Section 4.3.3.2.

For the horizontal components of the seismic action the design spectrum, S_d(T), shall be defined by the following expressions:

\begin{matrix} For 0 \leq T \leq T_{B}, & S_{d} (T) = a_{g} S [\frac{2}{3} + \frac{T}{T_{B}} (\frac{2.5}{q} - \frac{2}{3})] \end{matrix}

(3.13)

\begin{matrix} For T_{B} \leq T \leq T_{C}, & S_{d} (T) = a_{g} S \frac{2.5}{q} \end{matrix}

(3.14)

\begin{matrix} For T_{C} \leq T \leq T_{D}, & S_{d} (T) \{\begin{matrix} = & a_{g} S \frac{2.5}{q} (\frac{T_{C}}{T}) \\ \geq & β a_{g} \end{matrix} \end{matrix}

(3.15)

\begin{matrix} For T_{D} \leq T, & S_{d} (T) \{\begin{matrix} = & a_{g} S \frac{2.5}{q} (\frac{T_{C} T_{D}}{T^{2}}) \\ \geq & β a_{g} \end{matrix} \end{matrix}

(3.16)

where

S_d(T)	=	the design spectrum
T	=	Fundamental period of vibration of the building for lateral motion in the direction considered (calculated or user input)
a_g	=	the design ground acceleration on type A ground
S	=	the soil factor
T_B	=	the lower limit of the period of the constant spectral acceleration branch
T_C	=	the upper limit of the period of the constant spectral acceleration branch
T_D	=	the value defining the beginning of the constant displacement response range of the spectrum
q	=	the behavior factor
β	=	the lower bound factor for the horizontal design spectrum. The value to be ascribed to β for use in a country can be found in its National Annex. The recommended value for β is 0.2

The terms a_g, q, and β are user-specified values. In addition, q and β should be defined separately for each direction.

For the vertical component of the seismic action, the design spectrum given by expressions (3.13) to (3.16) is not implemented and hence, dynamic analysis for vertical direction is not supported. The terms calculated for Se(T) (Equations (3.2) – (3.5)) and Sd(T) (Equations (3.13) – (3.16)) are further amplified if topographic effects are optionally considered.