# 1615.1.3 Design spectral response acceleration parameters

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Within the International Code Council’s 2003 International Building Code (IBC), the five-percent damped design spectral response accelerations at short periods, SDS, and at 1-second period, SD1, are used to determine the seismic design base shear. These parameters, which are a function of the site’s seismicity and soil, are also used as parts of triggers for other code requirements. There are four steps involved in determining the value of SDS and SD1. They are as follows:

Step 1: Determine the mapped maximum considered earthquake spectral response accelerations at short periods, SDS, and 1-second period, SD1. These values can be determined either by using the 2003 IBC Figures 1615(1) through 1615(10) or by using the Seismic Design Parameters Version 3.10 CD-ROM, which also is published by the ICC.

Step 2: Determine the site’s soil classification in accordance with IBC Section 1615.1.1.

Step 3: Determine the site coefficients Fa and Fv using IBC Tables 1615.1.2 (1) and 1615.1.2(2). Fa is a function of the site’s soil classification and SS. And, Fv is a function of the site’s soil classification and S1.

Step 4: Calculate SDS = (2/3)(Fa)(SS) and SD1 = (2/3)(Fv)(S1).

Answers to FAQ’s

Q: 2003 IBC Figures 1615(1) through 1615(10) provide mapping values for the maximum considered earthquake ground motion. What does maximum considered earthquake (MCE) mean? Can a Richter magnitude be associated with the MCE?

A: In coastal California, the MCE is the largest earthquake that can be delivered by the known seismic sources—it is also referred to as the deterministic earthquake. Elsewhere in the country, the MCE is an earthquake that is expected to occur once in approximately 2,500 years, which has a 2-percent probability of exceedance in 50 years.

No, a Richter magnitude cannot be associated with the MCE. The Richter magnitude provides a measure of the energy released at the source of an earthquake. The mapped values, on the other hand, are indicative of the intensity of earthquake ground motions expected at a site and are associated with the probability indicated above. They depend on the estimated energy released at source (magnitude) considering known seismic sources that may cause earthquake ground motions at the site, the source-to-site transmission path (including, very importantly, the distance from source to site), and the site soil characteristics.

Q: I understand that the mapped spectral response accelerations SS and S1 relate to the MCE, which has a 2-percent probability of being exceeded in 50 years. Also, I understand that the mapped spectral response accelerations need to be adjusted for site class effects. However, I don’t understand the extra step of multiplying by 2/3, as prescribed in 2003 IBC Section 1615.1.3. What earthquake are we designing for when we do this? Does it still represent the 2 percent in 50-year earthquake? (This question and the following response is reprinted with permission from the 2003 IBC Structural Q&A Application Guide.)

A: You are still designing for an earthquake with the 2-percent probability of being exceeded in 50 years. It’s just that you are designing for collapse prevention in this earthquake, rather than life safety. The 2/3 factor reduces the mapped spectral response accelerations to correspond to a collapse prevention goal by offsetting the factor of safety of 1.5 which is consistent with the life-safety goal and is inherent in the R factor. (Refer to the sidebar for term definitions and more explanations.)

Collapse prevention versus life safety

The Federal Emergency Management Agency defines collapse prevention and life safety within The National Earthquake Hazards Reduction Program’s Guidelines for the Seismic Rehabilitation of Buildings.

Collapse prevention: The building remains standing, but only barely; any other damage or loss is acceptable.

Life safety: The structure remains stable and has significant reserve capacity; hazardous nonstructural damage is controlled.

Why are the spectral response accelerations corresponding to the MCE multiplied by 2/3? In prior building codes, the intent was to design structures for life safety in an earthquake with a 10-percent probability of being exceeded in 50 years (also referred to as the 500-year event). However, with the development of the new spectral response acceleration maps, it was recognized that this design basis was not adequate for the infrequent, but very large earthquake events that could occur in the eastern United States. Therefore the design philosophy changed so that structures were designed for collapse prevention in an earthquake with the 2-percent probability of being exceeded in 50 years (2,500- year event), except for portions of California, where the seismic sources are better known.

The switch from the 500-year event to the 2,500-year event was incorporated into the new seismic maps. However, the R coefficients used in the base shear formula are based on the life safety goal. Rather than revising the R values, the code writers opted to reduce mapped spectral response accelerations by the factor of safety of 1.5, which explains the 2/3 factor (2/3 is the reciprocal of 1.5).