Response Spectra Analysis

The MCE_R spectral response acceleration parameters for short periods (S_MS) and at 1 s (S_M1), adjusted for Site Class effects, are calculated from the followings:

S_MS = F_αS_s

(11.4-1)

S_M1 = F_vS₁

(11.4-2)

where

S_s	=	mapped MCE_R spectral response acceleration parameter at short periods
S₁	=	the mapped MCE_R spectral response acceleration parameter at a period of 1 s

Site coefficientsF_α and F_v are given in Table 11.4-1 and 11.4-2, respectively.

Design earthquake spectral response acceleration parameter at short period S_DS and at 1 s period S_D1 are calculated from the following equations:

S_{D S} = \frac{2}{3} S_{M S}

(11.4-3)

S_{D 1} = \frac{2}{3} S_{M 1}

(11.4-4)

The design response spectrum curve is constructed as follows:

S_{a} = {\begin{matrix} S_{D S} (0.4 + 0.6 \frac{T}{T_{0}}) & T < T_{0} \\ S_{D S} & T_{0} \leq T \leq T_{S} \\ \frac{S_{D 1}}{T} & T_{S} < T \leq T_{L} \\ \frac{S_{D 1} T_{L}}{T^{2}} & T \geq T_{L} \end{matrix}

where

S_DS	=	the design spectral response acceleration parameter at short periods, calculated from Eq. (11.4-3)
S_D1	=	the design spectral response acceleration parameter at 1-s period, calculated from Eq. (11.4-4)
T	=	the fundamental period of the structure, $\frac{S_{D 1}}{S_{D S}}$
T_o	=	$0.2 \frac{S_{D 1}}{S_{D S}}$
T_L	=	long-period transition period

RAM Structural System Help

Response Spectra Analysis

ASCE 7-10 Design Spectrum Curve