# G.17.4.2.1.7 Define Input for Demand Spectrum

Demand Spectrum is generated according to the method described in Section 1.6.1.5 of FEMA 356 : 2000.

The program generates Demand Spectrum for the purpose of finding Ts and Sa (corresponding to Te for the purpose of calculating target displacement).

## Generation of Demand Spectrum

The following criteria is used to develop the demand spectrum for a pushover analysis.

### Site Classes

1. Hard rock with average shear wave velocity, vs > 5,000 ft/sec
2. Rock with 2,500 ft/sec < vs < 5,000 ft/sec
3. Very dense soil and soft rock with 1,200 ft/sec < vs ≤ 2,500 ft/sec or with either standard blow count N > 50 or undrained shear strength su > 2,000 psf
4. Stiff soil with 600-ft/sec< vs ≤ 1,200 ft/sec, with 15< N ≤ 50, or 1,000 psf ≤ su < 2,000 psf
5. Any profile with more than 10 feet of soft clay defined as soil with plasticity index PI > 20, or water content w > 40 percent, and su < 500 psf or a soil profile with vs < 600 ft/sec.
6. Soils requiring site specific evaluations

The design short period spectral response acceleration parameter, SXS, and the design spectral response acceleration parameter at one second, SX1, shall be obtained from equations (2-7-1) and (2-7-2), respectively, as follows:

 SXS = FaSS (2-7-1)

 SX1 = FvS1 (2-7-2)

where
 Fa and Fv = site coefficients determined respectively from Tables 1-4 and 10-5 in FEMA 365, based on the site class and the values of the response acceleration parameters SS and S1 for the selected return period.

### General Horizontal Response Spectrum

A general response spectrum as shown in Figure 1-1 of FEMA 365 shall be developed using equations (2-6-3), (2-6-4) and (2-6-5) for spectral response acceleration, Sa, versus structural period, T, in the horizontal direction.

For 0 < T < Ts,

 $S a = S x s [ ( 5 B s − 2 ) T T s + 0.4 ]$ (2-7-3)

for T < Ts

 Sa = SXS/BS (2-7-4)

for T > TS

 Sa = SX1/(B1T) (2-7-5)

where
TS
=

 SX1BS/(SXSBS) (2-7-6)

T0
=

 0.2·TS (2-7-7)

Now this response spectrum with Sa vs T is converted to demand spectrum with Sa vs Sd. (in case of Capacity Spectrum method)

Note: The program generates Demand Spectrum for the purpose of finding TS and Sa (corresponding to Te for the purpose of calculating target displacement).