Design Example 1 Design Spectral Response Acceleration Parameters 11.4

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1 Design Example 1 Design Spectral Response Acceleration Parameters 11.4 OVERVIEW For a given building site, the risk-targeted maximum considered earthquake spectral response accelerations S S, at short periods, and S 1, at a 1-second period, are given by the acceleration contour maps in Chapter 22 in Figures 22-1 through This example illustrates the general procedure for determining the design spectral response acceleration parameters S DS and S D1 from the mapped values of S S and S 1. The parameters S DS and S D1 are used to calculate the design response spectrum in Section and the design base shear in Section The easiest and most accurate way to obtain the spectral values is to use the U.S. Seismic Design Maps application from the USGS website ( The USGS application allows for values of S S and S 1 to be provided based on the address or the longitude and latitude of the site being entered. PROBLEM STATEMENT A building site in California is located at North (Latitude ) and West (Longitude ). The soil profile is Site Class D. DETERMINE THE FOLLOWING: 1. Mapped risk-targeted maximum considered earthquake (MCE R ) spectral response acceleration parameters S S and S Site coefficients F a and F v and MCE R spectral response acceleration parameters S MS and S M1 adjusted for Site Class effects. 3. Design spectral response acceleration parameters S DS and S D1. 1. Mapped MCE R Spectral Response Acceleration Parameters S s and S For the given site at North (Latitude ) and West (Longitude ), the USGS U.S. Seismic Design Maps application provides the values of S S = 0.634g S 1 = 0.272g IBC SEAOC Structural/Seismic Design Manual, Vol. 1 1

acceleration contour maps in Chapter 22 in Figures 22-1 through 22-6.

2 11.4 Design Example 1 n Design Spectral Response Acceleration Parameters 2. Site Coefficients F a and F v and MCE R Spectral Response Acceleration Parameters S MS and S M1 Adjusted for Site Class Effects For the given Site Class D and the values of S S and S 1 determined above, the site coefficients are F a = F v = T T The MCE R spectral response acceleration parameters adjusted for Site Class effects are S MS = F a S S = 1.292(0.634g) = 0.819g Eq S M1 = F v S 1 = 1.857(0.272g) = 0.505g Eq Design Spectral Response Acceleration Parameters S DS and S D S DS = (2/3) S MS = (2/3)(0.819g) = 0.546g Eq S D1 = (2/3) S M1 = (2/3)(0.505g) = 0.337g Eq Commentary The USGS application U.S. Seismic Design Maps requires the risk category to be specified, even though that category is not necessary for determining S DS and S D IBC SEAOC Structural/Seismic Design Manual, Vol. 1

3 For the given Site Class D and the values of S S and S 1 determined above, the site coefficients are F a = 1.293 F v = 1.856. T11.4-1 T11.

3 Design Example 2 n Design Response Spectrum Design Example 2 Design Response Spectrum PROBLEM STATEMENT A building site in California has the following design spectral response acceleration parameters determined in accordance with Section and mapped long-period transition period evaluated from Figure 22-12: S DS = 0.55g S D1 = 0.34g T L = 8 sec. DETERMINE THE FOLLOWING: 1. Design response spectrum. 1. Design Response Spectrum Section provides the equations for the 5 percent damped spectral response acceleration, S a, relative to period, T, in the following ranges: 0 T < T 0, T 0 T T S, T S < T T L, and T L < T where: T 0 = 0.2 S D1 / S DS, T S = S D1 / S DS, and T L = long-period transition period from Figures through Given the values above for this example, T 0 = 0.2 S D1 / S DS = 0.2(0.34g / 0.55g) = 0.12 sec T S = S D1 / S DS = (0.34g / 0.55g) = 0.62 sec, and T L = 8 sec IBC SEAOC Structural/Seismic Design Manual, Vol. 1 3

5 PROBLEM STATEMENT A building site in California has the following design spectral response acceleration parameters determined in accordance with Section 11.4.

4 Design Example 2 n Design Response Spectrum The spectral response acceleration, S a, is calculated as follows: 1. For the interval 0 T < T 0 (0 T < 0.12 s), S a = S DS ( T/T 0 ) Eq S a = 0.55g( T/0.12) = ( T)g. 2. For the interval T 0 T T S (0.12 s T 0.62 s), S a = S DS = 0.55g. 3. For the interval T S < T T L (0.62 s < T 8 s), S a = S D1 /T Eq S a = (0.34/T)g. 4. For the interval T L < T (8 s < T), S a = S D1 T L /T 2 Eq S a = 0.34g(8)/T 2 = (2.72/T 2 )g. From this information, the elastic design response spectrum for this site can be drawn, as shown below, in accordance with Figure : T (sec) S a (g) IBC SEAOC Structural/Seismic Design Manual, Vol. 1

4-6 S a = (0.34/T)g. 4. For the interval T L < T (8 s < T), S a = S D1 T L /T 2 Eq 11.4-7 S a = 0.34g(8)/T 2 = (2.72/T 2 )g.

5 Design Example 2 n Design Response Spectrum Figure 2-1. Design response spectrum per Section IBC SEAOC Structural/Seismic Design Manual, Vol. 1 5

Design response spectrum per Section 11.

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