D

0.20g < Sd1

Da

Da

Da

aSUG I and II structures located on sites with mapped maximum considered earthquake spectral response acceleration at 1-second period, S1, equal to or greater than 0.75g shall be assigned to SDC E, and SUG III structures located on such sites shall be assigned to SDC F. (From ASCE 7-02, Table 9.4.2.1b.)

aSUG I and II structures located on sites with mapped maximum considered earthquake spectral response acceleration at 1-second period, S1, equal to or greater than 0.75g shall be assigned to SDC E, and SUG III structures located on such sites shall be assigned to SDC F. (From ASCE 7-02, Table 9.4.2.1b.)

SDC C includes SUG III structures in regions where moderately destructive ground shaking may occur as well as SUG I and II structures in regions with somewhat more severe ground shaking potential. In SDC C, the use of some structural systems is limited and some nonstructural components must be specifically designed for seismic resistance.

SDC D includes structures of SUG I, II, or III located in regions expected to experience destructive ground shaking, but not located very near major active faults. In SDC D, severe limits are placed on the use of some structural systems and irregular structures must be subjected to dynamic analysis techniques as part of the design process.

SDC E includes SUG I and II structures in regions located very close to major active faults and SDC F includes Seismic Use Group III structures in these locations. Very severe limitations on systems, irregularities, and design methods are specified for SDC E and F. For the purpose of determining if a structure is located in a region that is very close to a major active fault, ASCE-7 uses a trigger of mapped MCE spectral response acceleration at 1-second periods, S1 of 0.75 g or more regardless of the structure's fundamental period. The mapped short-period acceleration, Ss, is not used for this purpose because short-period response accelerations do not tend to be affected by near-source conditions as strongly as do response accelerations at longer periods.

2.4.2.8. Development of Response Spectrum

To proceed with an equivalent static analysis of a structure, we need to determine only the two values of the design acceleration response parameters, SD1 and SDs. This is because the base shear equations, discussed presently, are directly related to these parameters. However, for buildings and structures requiring modal analysis procedures, it is necessary to develop an acceleration graph, commonly referred to as an acceleration spectrum, because design acceleration values are required for an entire range of building periods. In a modal analysis, we attempt to capture the multimodal response of a building by statistically combining its individual modal responses. Therefore, accelerations corresponding to an entire range of building periods are typically required in performing the dynamic analysis.

The characteristic features of an acceleration response spectrum are as follows:

1. For very stiff buildings, the acceleration response approaches the maximum ground acceleration. Buildings in this period, with a range of 0.3 seconds or less, behave as rigid bodies attached to the ground.

2. For moderately short periods of the order of 0.1 to 0.3 seconds, the maximum response accelerations are about two to three times the maximum ground acceleration, and remain constant over this period range.

3. For long-period buildings, the maximum response velocity is the same as the maximum ground velocity.

4. For the very long-period buildings, the maximum displacement response is the same as the maximum ground displacement.

However, in the development of a generalized acceleration response curve, the constant displacement domain is not included because relatively few buildings have a period long enough to fall into this range. Thus, a generalized response curve for all practical purposes may be developed by three curves. The procedure is as follows:

1. Determine the period T = SD1/SDS, which defines the period at which the constant spectral acceleration and constant velocity portions of the spectra meet.

2. Determine the spectral acceleration at zero period, T0, by the relation: T0 = 0.4 SD1, i.e., the spectral acceleration at zero period is equal to 40% of the spectral acceleration corresponding to the flat top, SDS.

3. For periods greater than or equal to T0 and less than or equal to Ts, determine

4. For periods less than or equal to T0, determine the spectral response acceleration, Sa, by: Sa = SDS(0.6 T/T0 + 0.4). This region, referred to as the upramp, is used in computer analyses to capture the modal response in the very short-period range of the building.

5. For periods greater than Ts, determine Sa by: Sa = SDS/T, where Tis the desired range of building periods corresponding to the acceleration input in the computer analysis.

Design Example

Given. A building on site class D, near the city of Memphis, which is close to the New Madrid fault. Partial regionalization maps of the MCE ground motion contours for 0.2-sec and 1.0-sec spectral response accelerations, Ss and S1, are given in terms of percentage of g in Figs. 2.45a and 2.45b. The maps are for site class B. A site-specific response spectrum is not required for the building.

Required. Develop a general design response spectra for the building site. Solution.

1. Read the maximum considered earthquake spectral response accelerations SS and S1, from the given maps (Fig. 2.45a and b). It is perhaps obvious that Figs. 2.45a and b are too small to read the values of SS and S1. In practice, the designer would be using the large maps developed by USGS. However, for purposes of this example, we will assign the following values for SS and S1:

Figure 2.45a. Maximum considered earthquake ground motion map of 0.2 sec (short-period) spectral response acceleration SS (5% of critical damping), site class B.

2. Find site coefficients Fa and Fv from Tables 2.15 and 2.16.

For the given site class D, and SS _ 1.5g Fa _ 1.0 For the given site class D, and S1 _ 0.4, Fv _ 1.6

3. Calculate adjusted MCE spectral response accelerations for short period as SMS _ FaSS, and for 1-sec period as SM1 _ FvS1.

4. Determine design spectral response accelerations as

Sds _ 2/3 x Sms _ 2/3 x 1.5 _ 1.0 SD1 _ 2/3 x SM _ 2/3 x 0.64 _ 0.43

Figure 2.45 b. Maximum considered earthquake ground motion map of 1-sec spectral response acceleration, S1 (5% of critical damping), site class B.

5. Formulate the general design acceleration response spectrum, Sa. Use the following relations:

For the example, S

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