Is Continued Use of the Two-Period Design Spectrum in the Equivalent Lateral Force Procedure of Seismic Design Permitted by ASCE 7-22?

Judging by the number of inquiries received, there appears to be significant confusion as to whether the two-period design response spectrum of ASCE 7-22 Figure 11.4-1 can continue to be used in the equivalent lateral force (ELF) procedure for seismic design, following the introduction of multi-period design response spectra (MPRS) in ASCE 7-22.

As explained below, we interpret ASCE 7-22 to permit the continued use of the two-period design response spectrum in the ELF procedure. It needs to be recognized, however, that the two-period design response spectrum of ASCE 7-22 is not the same as that of ASCE 7-16. This will be the subject of a follow-up article.

Source of Confusion

According to ASCE 7-22 Section 11.4.5, where a design response spectrum is required by ASCE 7, the design response spectrum must be determined in accordance with Section 11.4.5.1, Multi-Period Design Response Spectrum.

There are two exceptions to the above:

1. Where a site-specific ground motion analysis is performed in accordance with Section 11.4.7, the design response spectrum is to be as indicated in Section 21.3.
2. Where the multi-period 5%-damped MCE_R response spectrum is not available from the USGS Seismic Design Geodatabase (this would be true of places outside of the United States and its territories), use of the two-period design response spectrum of Section 11.4.5.2 is permitted. As is well known by now, data from the USGS Seismic Design Geodatabase are typically accessed by the user by utilizing the ASCE Hazard Tool.

In view of the above, many ASCE 7-22 users have concluded that continued use of the two-period design response spectrum in the ELF procedure is permitted only where the multi-period 5%-damped MCE_R response spectrum for a particular site is not available from the ASCE Hazard Tool or where a site-specific ground motion analysis has not been performed.

The above conclusion is not correct because the key words in Section 11.4.5 are “Where a design response spectrum is required by this standard, … .” In the Equivalent Lateral Force procedure of seismic design of ASCE 7, a design response spectrum is not explicitly or specifically required (seismic design forces are obtained from formulas based on the two-period spectrum, that are given in Section 12.8.1.1, without ever requiring the user to construct the full design response spectrum itself).This is made more explicitly clear in ASCE 7-22 Section 12.8.1.1.

Continued Permitted Use of Two-Point Design Response Spectrum in ELF Procedure 

ASCE 7-22 Section 12.8.1.1 clearly indicates that when the multi-period (Section 11.4.5.1) or the site-specific (Chapter 21) design response spectrum for a site is available, either ELF Method 1 or ELF Method 2 can be used. Where Exception 2 of Section 11.4.5.1 applies (see previous section), Method 2 is required to be used. Method 2 is ELF utilizing a two-period design response spectrum (Figure 1). This is clearly allowed irrespective of whether the multi-period response spectrum for a site is available or not.

Errata

Please note that there are errors that matter in Section 12.8 (and elsewhere) in the printed as well as the pdf version of ASCE 7-22. Please download the errata posted on the ASCE website, here.

Conclusion

The following quote from (Soules and Guglielmo 2025) provides an appropriate conclusion to this brief article: “Two response spectra options are incorporated in ASCE 7-22, the Multi-Period Design Response Spectrum and the Two-Period Design Response Spectrum.  Either spectrum is allowed for use with the Equivalent Lateral Force (ELF) procedure.  Only the Multi-Period Design Response Spectrum is allowed to be used with the other analysis methods found in ASCE 7-22.”

Two-Period Spectra of ASCE 7-16 and ASCE 7-22

The constant acceleration plateau of the Two-Period Design Response Spectrum is defined by S_DS. The definition of S_DS has changed from ASCE 7-16 to ASCE 7-22. Through ASCE 7-16, S_DS was defined as the ordinate to the design response spectrum at a period of 0.2 s. However, in ASCE 7-22, S_DS is (2/3) S_MS and S_MS is taken as 90% of the maximum spectral response acceleration, S_a, at any period within the range from 0.2 to 5 s, in accordance with ASCE 7-22 Section 21.4.

The period, T_s​ = S_D1/S_DS, marks the transition from the flat-top or constant-acceleration domain of the two-period design response spectrum to the descending branch or the constant-velocity domain of the spectrum (Figure 1). In this domain, response accelerations are equal to ​S_D1/T.

Through ASCE 7-16, ​ S_D1 was defined as the ordinate to the design response spectrum at a period of 1.0 s. ASCE 7-22 defines S_D1 as in Section 21.4 for site-specific spectra. S_D1 is (2/3) S_M1 and S_M1 is defined as 90% of the maximum value of the product TS_a over periods from 1 to 2 s for sites with shear wave velocity, v_s>1,450 ft/s (stiff to moderately stiff soils), and over periods from 1 to 5 s for sites with v_s≤1,450 ft/s (softer soils). However, S_M1 must not be less than 100% of S_a at a 1-s period.

Other differences between the Two-Period Design Response Spectra of ASCE 7-16 and ASCE 7-22 will be the subject of a follow-up article.