Mapping time into Return Period

In mapping time into seismic hazard return period, information regarding spectral intensity corresponding to different return periods is required. In this section a procedure consistent with ASCE7-10 and ASCE41-06 standards has been explained. Adaptation to other standards should be self evident.

Step 1. Design base spectrum: The procedure of mapping time into return period is explained here using ASCE7-10 design spectrum with following parameters:

Ss=1.5g; S1=0.6g; cite class C; TL=8.0s

This is assumed to represent the seismic hazard with return period of 475 years (10/50, i.e. 10% exceedance probability in 50 years). The associated design spectrum is shown in Figure 1.

Step 2. Spectra for other hazard levels: For calculation of design spectrum consistent with other hazard return periods, the procedure of ASCE41-06 will be followed. According to this standard, Ss and S1 for other probabilities of exceedance can be calculated as follows:

Si=S10/50(PR/475)^n

The parameter n turns out to be equal for Ss and S1 for California with a value of n=0.29 for probabilities of exceedance less than 10% in 50 years down to 2% in 50 years, and n=0.44 for probabilities of exceedance greater than 0.44. In this way, the spectrum shape remains constant for all probabilities of exceedance and spectra at all other hazard levels can be correlated to that of 475 years by applying a scale factor. Scale factors corresponding to various PRs are shown in figure 2. In case that the shape of spectrum changes with time, somewhat more elaborate procedure should be followed in order to find appropriate scale factors. It should be noted that scale factors for PRs exceeding 2500 years are extrapolated following same formula.

Step 3. The calculation of PR corresponding to a particular time in ET analysis can be carried out quite efficiently using average spectral intensity from 0.2 to 1.5T (i.e. A215) concept. For example, considering a period of vibration of 1s, at t=1 s, the average spectral intensity turns out to be 0.89g as shown in figure 3.

The 10/50 design base spectrum value at same period is 0.67, as shown in figure 4.

Therefore as scale factor of 0.89/0.67=1.328 matches 10/50 spectrum to ETEF at t=10s and T=1s. Using Figure 2 data, this scale factor corresponds to a return period of 1264. Thus, it can be concluded that t=10s corresponds to PR= years for a structure with T=1s. As shown in Figure 5, the spectrum of ETEF matches with design spectra scaled to represent PR=1264 years.

The ETEFs and Scaled design spectra are compared in Figure 6.

Step 4. This procedure can be repeated for all values of t for a structure and all periodic values of interest. The results of such analysis are presented in Figure 7. The associated matrixes are attached below for convenience.

Example:

As an example, consider a sample ET response history showing maximum interstory drift ratio for a typical three story one bay steel moment frame in Figure Ex1.

The t-PR mapping data for T=1.28 is shown in Figure Ex2. This corresponds to row number 129 (i.e. 1.28*100+1) in 'ETA20inx_Sa_Avr-ASCE7_10_Ss1.5S1_0.6ClassC_TL8-nS0.44nL0.29_PR_A215' matrix.

Now, the Drift ratios can be plotted against PR as shown in Figure Ex4.

A fitting curve can be added to filter out random steps in raw ET response data.

While being quite self evident, this presentation format is very useful for performance based seismic assessment, life cycle cost analysis and value based seismic design applications. Note that yearly exceedance rates can be directly obtained form Figure Ex5 as the inverse of PR.

Direct access: Mapping time into return period sample data