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PGA is a familiar indicator of seismic intensity. However, it is not a very good predictor of structural response. Spectral intensity correlates to structural response much more reliably. Usually, the spectral intensity in the vicinity of the fundamental period of vibration of the structure is used in order scale ground motions into appropriate intensities. In this section, a procedure for mapping time into PGA based on matching spectral intensities in the range of 0.2T to 1.5T as recommended by various seismic design codes is explained.
Step 1. Start with an appropriate acceleration spectrum scaled to PGA of 1g. For matter of explanation, we will consider the set of 44 far field ground motions introduced in FEMA p695. This set of records fits various design and assessment problems consistent with ASCE7-10 site classes C and D. All records are scaled to PGA of 1g and then averaged to produce the template spectra shown in figure 1. The average spectral intensity in the range of 0.2T to 1.5T is also shown in the Figure 1.
Figure 1. Acceleration spectrum of GMs scaled to 1g.
Step 2 : Find average spectral intensity from 0.2T to 1.5T (i.e. A215 value) where T is the fundamental period of vibration for the structure being investigated . For T=1s, the A215 value for GMs turns out to be 1.51 as shown on Figure 2.
Figure 2. Average spectral intensity at T=1s
Step 3: At each particular time, find average Sa from 0.2T to 1.5T for considered ETEF records. This can be done using the average spectral intensity of ETEFs or more conveniently by using the A215 data. For example, considering ETA20inx series, at t=10 seconds, the A215 vale is 0.89 as shown in Figure 3.
Figure 3. Average ETEFs spectral intensity at t=10s and T=1s
Step 4. The equivalent PGA corresponding can simply be worked out by dividing A215 value from ETEF to that of GM i.e.:
EqPGA=A215ET/A215GM=0.89/1.51=0.59
The response spectra of ETA20inx at t=10s is depicted along with GM response spectra scaled to 0.59g in Figure 4 for comparison.
Figure 4. ETEFs spectrum at t=10s compared with GMs
As can be seen in Figure 4, the GM spectrum scaled to PGA of 0.59g matches well with that of ETA20inx at t=10 seconds. This procedure can be repeated for the entire time and periodic span of interest, producing equivalent PGA as a function of t and T. A contour plot of PGA for above case is shown in figure 5.
Figure 5. Equivalent PGA for ETA20inx series considering FEMA p695 44 far field GMs
The matrix presenting this data is provided in attached files bellow 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 subjected to ETA20inx ETEFs in Figure Ex1.
Figure Ex1. Sample ET analysis output
Period of vibration of this frame is 1.28s. Using 'ETA20inx_Sa_Avr-FEMAp695All44_SaA1g_S215' matrix (row 129=1.28*100+1), the t-PGA mapping function is as shown in Fig Ex2.
Figure Ex2. t-PGA mapping data for T=1.28s
Using this data, the Drift Ratio can be plotted against PGA as shown in Fig Ex3.
Figure Ex3. Maximum Interstory Drift as a function of PGA
A fitting curve can also be used in order to filter out the random steps in the raw analysis data as shown in figure Ex4.
Figure Ex4. Smoothed maximum drift response
Direct access: Mapping time to PGA sample data
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