Study on Efficacy of Single Set Spectrum Compatible Time History for Linear Seismic Analysis of Structures Anis M.V., Bharti Banshiwal, A.D. Roshan Objective The latest draft version of BIS 1893, Sect 7.6.2 (b), specifies that at-least three sets of ground motions shall be used in linear response history analysis. AERB had commented on the earlier specification of minimum seven time history requirement and opined that for Linear response history analysis, which are often used in generation of input of sub-system design (seismic anchor movement, floor response spectra) single time history or single set of time history is sufficient. An example problem demonstrating efficacy of single spectrum compatible time history in one direction linear analysis was demonstrated using 30 recorded ground motion and single spectrum compatible time history analysis (x-direction). The results were also presented to committee. However, there was an apprehension that, multiple time history requirement is more prudent in the case of simultaneous analysis of lateral directions (X and Y) and the above exercise may not capture this phenomena. The objective of the study to address the above query on efficacy of single set of spectrum compatible history in adequately capturing response of structure while earthquake has occurred in both x and y direction simultaneously. Methodology The series of steps followed in this exercise are briefly described below;
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A thirty one set of recorded ground motions are downloaded from PEER Ground motion database.
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These ground motion are processed and vertical direction ground motions are removed. The complete list ground motion selected for the study are provided in Table 01.
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The complete visualization of these recorded ground motion and its spatial correlations are shown in Annexure 01 and 02.
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The response spectra of above 31 set time histories are extracted using PyRotd library. The average response spectra of 31 time history also calculated.
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A set of spectrum compatible time history (for x-direction average and y direction average) is generated using EARTHQUAKE module of ACS SASSI software. A plot of 31 recorded ground motion, average ground motion and spectrum compatible ground motion is shown below for comparison.
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A stick model of containment and internal structure which is often used in AERB’s pilot/demonstration studies is adopted for linear time history analysis (The structure is assumed to be fixed at bottom. A damping of 0.05 is considered throughout the structure.). A figure of the model is shown below (left- un-deformed, right deformed shape at one of the time instant);
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The modal characteristics of the structure is extracted. Complete modal characteristics is given Table 02. A graph of the same is shown below;
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A linear modal time history analysis of above structure is conducted for 31 recorded time histories obtained from PEER database and one set of spectrum compatible time history.
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The average of peak base shear in both X direction and Y direction for time history analysis using 31 ground motion are extracted.
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Above average is peak base shear is compared with peak bese shear obtained from single set spectrum compatible time history analysis. A comparison plots is give below;
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[Comparison of FRS] – Will be submitted
Conclusion Based on the above study one can infer that single set of spectrum compatible time history is sufficient for linear seismic analysis. This aspect can also be theoretically proven using classical random vibration theory and peak factor formula. It is to be noted that spectrum compatible time history shall have strict compliance with codal requirements (criteria on PSa ratio as well as PSD).
Please note that the complete computer codes used in this exercise can be downloaded from HERE for verification. Table 1 List of Ground Motions Considered for the Present Study PEER EQ ID Name Station Date PGAx (g) PGAy (g) RSN1083 Northridge-01 Sunland - Mt Gleason Ave 1/17/1994 0.133 0.157 RSN1614 Duzce Turkey Lamont 1061 11-12-1999 0.114 0.101 RSN1616 Duzce Turkey Lamont 362 11-12-1999 0.025 0.044 RSN1633 Manjil Iran Abbar 6/20/1990 0.515 0.462 RSN164 Imperial Valley-06 Cerro Prieto 10/15/1979 0.160 0.148 RSN286 Irpinia Italy-01 Bisaccia 11/23/1980 0.065 0.049 RSN289 Irpinia Italy-01 Calitri 11/23/1980 0.126 0.136 RSN290 Irpinia Italy-01 Mercato San Severino 11/23/1980 0.108 0.140 RSN313 Corinth Greece Corinth 2/24/1981 0.237 0.296 RSN3750 Cape Mendocino Loleta Fire Station 4/25/1992 0.205 0.222 RSN3753 Landers Fun Valley 6/28/1992 0.146 0.206 RSN3757 Landers North Palm Springs Fire Sta #36 6/28/1992 0.105 0.139 RSN3759 Landers Whitewater Trout Farm 6/28/1992 0.123 0.124 RSN3907 Tottori Japan OKY004 10-06-2000 0.825 0.539 RSN3926 Tottori Japan OKYH08 10-06-2000 0.241 0.228 RSN3927 Tottori Japan OKYH09 10-06-2000 0.290 0.163 RSN3932 Tottori Japan OKYH14 10-06-2000 0.453 0.264 RSN3948 Tottori Japan SMNH02 10-06-2000 0.282 0.576 RSN4013 San Simeon CA San Antonio Dam - Toe 12/22/2003 0.093 0.103 RSN4841 Chuetsu-oki Joetsu Yasuzukaku Yasuzuka 7/16/2007 0.223 0.154 RSN4843 Chuetsu-oki Matsushiro Tokamachi 7/16/2007 0.193 0.185 RSN57 San Fernando Castaic - Old Ridge Route 02-09-1971 0.320 0.275 RSN70 San Fernando Lake Hughes #1 02-09-1971 0.151 0.094 RSN740 Loma Prieta Anderson Dam (L Abut) 10/18/1989 0.064 0.061 RSN755 Loma Prieta Coyote Lake Dam - Southwest Abutment 10/18/1989 0.132 0.280 RSN78 San Fernando Palmdale Fire Station 02-09-1971 0.103 0.098 RSN827 Cape Mendocino Fortuna - Fortuna Blvd 4/25/1992 0.106 0.114 RSN830 Cape Mendocino Shelter Cove Airport 4/25/1992 0.229 0.184 RSN864 Landers Joshua Tree 6/28/1992 0.274 0.284 RSN881 Landers Morongo Valley Fire Station 6/28/1992 0.223 0.164 RSN88 San Fernando Santa Felita Dam (Outlet) 02-09-1971 0.155 0.155
Table 2 Modal Characteristics of RB Stick Model Modal Mass Cum. Modal Mass Mode NO Freq (Hz) X-Dir Y-Dir Z-Dir X-Dir Y-Dir Z-Dir 1 1.68 16904.00 112611.00 0.00 16904.00 112611.00 0.00 2 1.68 112611.00 16904.00 0.00 129515.00 129515.00 0.00 3 3.65 4782.70 16772.00 0.00 134297.70 146287.00 0.00 4 3.65 16772.00 4782.70 0.00 151069.70 151069.70 0.00 5 4.99 0.00 0.00 144208.00 151069.70 151069.70 144208.00 6 5.20 23454.00 4310.90 0.00 174523.70 155380.60 144208.00 7 5.20 4310.90 23454.00 0.00 178834.60 178834.60 144208.00 8 5.50 45959.00 18231.00 0.00 224793.60 197065.60 144208.00 9 5.50 18231.00 45959.00 0.00 243024.60 243024.60 144208.00 10 9.34 1240.20 5644.90 0.00 244264.80 248669.50 144208.00 11 9.34 5644.90 1240.20 0.00 249909.70 249909.70 144208.00 12 12.55 0.00 0.00 92101.00 249909.70 249909.70 236309.00 13 13.36 2100.10 888.09 0.00 252009.80 250797.79 236309.00 14 13.36 888.09 2100.10 0.00 252897.89 252897.89 236309.00 15 14.05 0.00 0.00 14724.00 252897.89 252897.89 251033.00 16 14.83 22039.00 1713.80 0.00 274936.89 254611.69 251033.00 17 14.83 1713.80 22039.00 0.00 276650.69 276650.69 251033.00 18 17.16 789.22 331.31 0.00 277439.91 276982.00 251033.00 19 17.16 331.31 789.22 0.00 277771.22 277771.22 251033.00 20 19.79 0.64 414.18 0.00 277771.86 278185.40 251033.00 21 19.79 414.18 0.64 0.00 278186.04 278186.04 251033.00 22 20.51 0.00 0.00 6203.50 278186.04 278186.04 257236.50 23 22.02 0.00 0.00 5645.90 278186.04 278186.04 262882.40 24 22.29 139.40 131.77 0.00 278325.44 278317.81 262882.40 25 22.29 131.77 139.40 0.00 278457.21 278457.21 262882.40 26 24.47 439.78 28.39 0.00 278896.99 278485.60 262882.40 27 24.47 28.39 439.78 0.00 278925.38 278925.38 262882.40 28 24.93 88.15 9.22 0.00 279013.53 278934.61 262882.40 29 24.93 9.22 88.15 0.00 279022.76 279022.76 262882.40 30 26.77 18.23 0.70 0.00 279040.99 279023.45 262882.40 31 26.77 0.70 18.23 0.00 279041.68 279041.68 262882.40 32 27.85 20.38 1982.60 0.00 279062.07 281024.28 262882.40 33 27.85 1982.60 20.38 0.00 281044.67 281044.67 262882.40 34 29.06 0.01 0.00 0.00 281044.67 281044.67 262882.40 35 29.06 0.00 0.01 0.00 281044.67 281044.67 262882.40 36 30.75 0.00 0.00 2703.80 281044.67 281044.67 265586.20 37 35.77 0.00 0.00 12637.00 281044.67 281044.67 278223.20 38 39.22 0.00 0.00 1068.20 281044.67 281044.67 279291.40 39 41.72 1007.10 2196.00 0.00 282051.77 283240.67 279291.40 40 41.72 2196.00 1007.10 0.00 284247.77 284247.77 279291.40 41 45.27 0.00 0.00 368.42 284247.77 284247.77 279659.82 42 50.51 0.00 0.00 246.83 284247.77 284247.77 279906.65 43 56.27 0.00 0.00 92.42 284247.77 284247.77 279999.07 44 60.35 0.00 0.00 18.29 284247.77 284247.77 280017.36 45 61.30 0.00 0.00 318.42 284247.77 284247.77 280335.78 46 66.24 0.00 0.00 0.00 284247.77 284247.77 280335.78 47 70.53 0.00 0.00 2194.50 284247.77 284247.77 282530.28 48 82.03 210.73 4.80 0.00 284458.50 284252.58 282530.28 49 82.03 4.80 210.73 0.00 284463.31 284463.31 282530.28 50 83.07 0.00 0.00 0.00 284463.31 284463.31 282530.28 51 83.07 0.00 0.00 0.00 284463.31 284463.31 282530.28 52 86.57 0.00 0.00 1745.60 284463.31 284463.31 284275.88 53 94.21 0.00 0.00 0.00 284463.31 284463.31 284275.88 54 97.32 0.00 0.00 0.00 284463.31 284463.31 284275.88 55 97.32 0.00 0.00 0.00 284463.31 284463.31 284275.88