Response Spectrum Analysis Enhancements GTStrudl Version 30 Response Spectrum Analysis Enhancements Related To NRC Regulatory Guide 1.92, Revision 2 COMBINING MODAL RESPONSES AND SPATIAL COMPONENTS in SEISMIC RESPONSE ANALYSIS Michael H. Swanger, Ph.D. Georgia Tech CASE Center GTSUG 2008 June 23-26, 2008 Las Vegas, NV

Topics Background GTStrudl Enhancements, Version 30 Example NRC Reg Guide 1.92, Rev 1 Positions Response Spectrum Characteristics Response Spectrum Solution Strategy NRC Reg Guide 1.92, Rev 2 Positions Response spectrum Solution Strategy GTStrudl Enhancements, Version 30 The RESPONSE SPECTRUM LOAD/ MODE FACTORS Command The ALGEBRAIC Mode Combination Total Response Example NRC Reg Guide 1.92 Rev 1 vs Rev 2

Background 3

Background

Background NRC Reg Guide 1.92, Rev 1 Positions Response Spectrum Characteristics All modes are assumed to be out-of-phase with the ground acceleration and out-of-phase with each other Acceleration All modes having frequencies ≤ some arbitrary cutoff frequency are deemed “significant” for inclusion in the response spectrum analysis Frequency Note: 1976, the date of Reg 1.92, Rev 1, was prior to many of the significant developments in response spectrum analysis that we take for granted today!

Background NRC Reg Guide 1.92, Rev 1 Positions Response Spectrum Solution Strategy For each ground motion direction, k = 1, 2, 3, the modal maximum responses from all “significant” modes, having no time and phase characteristics, are combined according to a statistical rule, such as SRSS. The total response is computed from the SRSS of the combined modal responses in each ground motion direction

Background NRC Reg Guide 1.92, Rev 1 Positions Response Spectrum Solution Strategy If frequencies are not closely spaced§: SRSS Mode Combination Method § two consecutive modes are defined as closely spaced if their frequencies differ from each other by no more than 10 percent of the lower frequency

Background NRC Reg Guide 1.92, Rev 1 Positions Response Spectrum Solution Strategy If frequencies are closely spaced: NRC Grouping Method NRC Ten Percent Method NRC Double Sum Method td = duration of earthquake

Background NRC Reg Guide 1.92, Rev 2 Positions Response Spectrum Characteristics Frequency Low Frequency Out-of-Phase Response Mid Frequency Transition from Out-of-Phase to In-Phase Response High Frequency In-Phase Rigid Static F1 = frequency at which peak spectral acceleration is observed F2 = frequency above which the SDOF (modal) oscillators are in-phase with the transient acceleration input used to generate the spectrum and in phase with each other FZPA = frequency at which the spectral acceleration returns to the zero period acceleration; maximum base acceleration of transient acceleration input used to generate the spectrum

Background NRC Reg Guide 1.92, Rev 2 Positions Response Spectrum Characteristics Frequency Low Frequency Out-of-Phase Response Mid Frequency Transition from Out-of-Phase to In-Phase Response High Frequency In-Phase Rigid Static fi ≤ F1 Maximum response from periodic or transient response in the modal frequency fi. Maximum modal (oscillator) responses are out-of-phase with one another. 10

Background NRC Reg Guide 1.92, Rev 2 Positions Response Spectrum Characteristics Mid Frequency Transition from Out-of-Phase to In-Phase Response Low Frequency Out-of-Phase Response High Frequency In-Phase Rigid Static Response Frequency fi ≥ F2 Maximum response from steady state response. The maximum modal responses are in phase with one another. 11

Background NRC Reg Guide 1.92, Rev 2 Positions Response Spectrum Characteristics Mid Frequency Transition from Out-of-Phase to In-Phase Response Low Frequency Out-of-Phase Response High Frequency In-Phase Rigid Static Response Frequency F1 < fi < F2 Response is part periodic and part rigid. Maximum modal responses transition from out-of-phase to in phase. 12

Background NRC Reg Guide 1.92, Rev 2 Positions Response Spectrum Solution Strategy For each mode i, in each ground motion direction k, the response is separated into a periodic part and a rigid part: The periodic modal response portions are combined using a double sum rule:

Background NRC Reg Guide 1.92, Rev 2 Positions Response Spectrum Solution Strategy The rigid modal responses are combined algebraically, including the residual rigid contribution from the missing mass: The total response in each ground motion direction is computed from the SRSS of the modal combinations of the periodic and rigid responses:

Background NRC Reg Guide 1.92, Rev 2 Positions Response Spectrum Solution Strategy Finally, the complete response is computed by performing the SRSS on the total responses in the three ground motion directions: A 100-40-40 rule is also acceptable for combination of the spatial response components

Background NRC Reg Guide 1.92, Rev 2 Positions Response Spectrum Solution Strategy Computation of rigid response factor αki ; The Gupta Method: Mid Frequency Transition from Out-of-Phase to In-Phase Response Low Frequency Out-of-Phase Response High Frequency In-Phase Rigid Static Response Frequency

Background NRC Reg Guide 1.92, Rev 2 Positions Response Spectrum Solution Strategy Periodic responses are combined using a double sum rule: εij computed according to the following methods: SRSS Method NRC Double Sum Method (Rosenbleuth correlation coefficient) CQC method (Der Kiureghian’s correlation coefficient) 17

Background NRC Reg Guide 1.92, Rev 2 Positions Response Spectrum Solution Strategy Computation of the Residual Rigid Response for all fi ≥ FZPA by the Missing Mass Method: The Missing Mass Method is quite accurate and is most important for adequately capturing the high-frequency response near supports

Background NRC Reg Guide 1.92, Rev 2 Positions Response Spectrum Solution Strategy Note: Under Rev 2, the response spectrum solution also may be performed according to Reg 1.92, Rev 1 provided that the residual rigid response due to the missing mass is included 19

GTStrudl Enhancements, Version 30 RESPONSE SPECTRUM LOAD/MODE FACTORS Command Syntax Purpose: To compute α and (1 – α2)1/2 for each active mode for the defined response spectrum load 20

GTStrudl Enhancements, Version 30 RESPONSE SPECTRUM LOAD/MODE FACTORS Command Example UNITS CYCLES SECONDS RESPONSE SPECTRUM LOAD ‘100R’ SUPPORT ACCELERATION TRANSLATION X 1.000000 FILE ‘ELC-RS’ MODE FACTORS COMPUTE RIGID RESPONSE FZPA 40.0 END RESPONSE SPECTRUM LOAD RESPONSE SPECTRUM LOAD ‘100P’ MODE FACTORS COMPUTE PERIODIC RESPONSE FZPA 40.0 Note: FZPA is specified (FZPA 40.0); therefore: F1 = Samax/(2πSvmax) F2 = (F1 + 2FZPA)/3

GTStrudl Enhancements, Version 30 The ALGEBRAIC Mode Combination

GTStrudl Enhancements, Version 30 The ALGEBRAIC Mode Combination Example LOAD LIST ‘100R’ $ Rigid RS Components COMPUTE RESPONSE SPECTRUM DISPLACEMENTS MODE COMBINATION ALGEBRAIC COMPUTE RESPONSE SPECTRUM FORCES MODE COMBINATION ALBEGRAIC CREATE PSEUDO STATIC LOAD ‘PS100R’ FROM ALGEBRAIC OF LOAD ‘100R’ . LOAD LIST ‘100P’ $ Periodic RS Components COMPUTE RESPONSE SPECTRUM DISPLACEMENTS MODE COMBINATION CQC COMPUTE RESPONSE SPECTRUM FORCES MODE COMBINATION CQC CREATE PSEUDO STATIC LOAD ‘PS100P’ FROM CQC OF LOAD ‘100P’

GTStrudl Enhancements, Version 30 Total Rigid, Directional, and Solution Response Example $* ** $* ** Total Rigid Response UNITS CYCLES SECONDS FORM MISSING MASS LOAD ‘100M’ FROM RESPONSE SPECTRUM LOAD ‘100R’ – CUTOFF FREQUENCY 40.0 . STIFFNESS ANALYSIS CREATE LOAD COMBINATION ‘100RTOT’ SPECS ‘PS100R’ 1.0 ‘100M’ 1.0 $* ** Total Directional Response CREATE LOAD COMBINATION ‘100TOT’ TYPE RMS SPECS ‘PS100P’ 1.0 – ‘100RTOT’ 1.0 $* ** Total Solution Response CREATE LOAD COMBINATION ‘EQTOT’ TYPE RMS SPECS - ‘100TOT’ 1.0 ‘200TOT’ 1.0 ‘300TOT’ 1.0

Example 1 Columns: W14X53 Beams (Global X): W18X35 (6 @ 12’) (5 @ 10’) (4 @ 10’) Columns: W14X53 Beams (Global X): W18X35 Beams (Global Z): W18X50 210 Joints, 474 Members Additional Mass: 1 kip, all joints, Global X and Z Seismic Loading: El Centro RS, Global X and Z

El Centro Response Spectrum Example 1 El Centro Response Spectrum UNITS FEET CYCLES SECONDS CREATE RESPONSE SPECTRUM ACCELERATION - LINEAR VS FREQUENCY LINEAR FILE 'ELC-RS' FREQUENCY RANGE FROM 0.10000 TO 60.00000 AT 0.10000 DAMPING RATIOS 0.05 USE ACCELERATION TIME HISTORY FILES 'ELCENTRO' INTEGRATE USING DUHAMEL DIVISOR 20.00000 END OF CREATE RESPONSE SPECTRUM FZPA F1 = 1.9 HZ F2 = 27.3 HZ 26

Example 1 Revision 1 Revision 2 27 UNITS INCHES KIPS DEAD LOAD 'DLX' DIR X ALL MEMBERS DEAD LOAD 'DLZ' DIR Z ALL MEMBERS INERTIA OF JOINTS FROM LOAD 'DLX' SAME DOFS INERTIA OF JOINTS FROM LOAD 'DLZ' SAME DOFS INERTIA OF JOINTS WEIGHT EXISTING TRANSL X 1.0 Z 1.0 UNITS CYCLES SECONDS EIGENVALUE PARAMETERS SOLVE USING GTSEL FREQUENCY SPECS 0.0 TO 40.0 PRINT MAX END DYNAMIC ANALYSIS EIGENVALUE UNITS INCHES KIPS DEAD LOAD 'DLX' DIR X ALL MEMBERS DEAD LOAD 'DLZ' DIR Z ALL MEMBERS INERTIA OF JOINTS FROM LOAD 'DLX' SAME DOFS INERTIA OF JOINTS FROM LOAD 'DLZ' SAME DOFS INERTIA OF JOINTS WEIGHT EXISTING TRANSL X 1.0 Z 1.0 UNITS CYCLES SECONDS EIGENVALUE PARAMETERS SOLVE USING GTSEL FREQUENCY SPECS 0.0 TO 40.0 PRINT MAX END DYNAMIC ANALYSIS EIGENVALUE 27

Example 1 Revision 1 Revision 2 28 $* ** $* ** Define response spectrum loads for response in the $* ** global X and Z directions RESPONSE SPECTRUM LOAD 100 SUPPORT ACCELERATION TRANSLATION X 1.000000 FILE 'ELC-RS' END RESPONSE SPECTRUM LOAD RESPONSE SPECTRUM LOAD 300 TRANSLATION Z 1.000000 FILE 'ELC-RS' UNITS INCHES KIPS CYCLES SEC DAMPING RATIOS 0.05 100 PERFORM RESPONSE SPECTRUM ANALYSIS $* ** $* ** Define response spectrum loads for rigid response in $* ** the global X and Z directions RESPONSE SPECTRUM LOAD ‘100R' SUPPORT ACCELERATION TRANSLATION X 1.000000 FILE 'ELC-RS' MODE FACTORS COMPUTE RIGID RESPONSE FZPA 40.0 END RESPONSE SPECTRUM LOAD RESPONSE SPECTRUM LOAD ‘300R' TRANSLATION Z 1.000000 FILE 'ELC-RS' $* ** Define response spectrum loads for periodic response $* ** in the global X and Z directions RESPONSE SPECTRUM LOAD ‘100P' MODE FACTORS COMPUTE PERIODIC RESPONSE FZPA 40.0 RESPONSE SPECTRUM LOAD ‘300P' UNITS INCHES KIPS CYCLES SEC DAMPING RATIOS 0.05 100 PERFORM RESPONSE SPECTRUM ANALYSIS LOAD LIST ‘100R' ‘300P' PRINT DYNAMIC LOAD DATA 28

Example 1 Revision 2 29 { 790} > PRINT DYNAMIC LOAD DATA . --------------------------------------------------------------------------------------------------------------------- LOADING - 100R STATUS - ACTIVE RIGID Response Modal Scaling (NRC Guide 1.92, Rev. 2, Combination Method A) =========================================================================== F1 = 1.8609530 F2 = 27.2869854 FZPA = 40.0000000 MODE FACTOR MODE FACTOR MODE FACTOR MODE FACTOR MODE FACTOR MODE FACTOR 1 0.0000000E+00 2 0.7675107E-02 3 0.1194761 4 0.2027510 5 0.2507934 6 0.2800766 7 0.2969909 8 0.3068923 9 0.3864122 10 0.4034464 11 0.4294790 12 0.4493059 49 0.8701187 50 0.8760816 51 0.8862190 52 0.8957242 53 0.9050707 54 0.9183331 55 0.9600146 56 0.9641243 57 0.9722605 58 0.9814596 59 0.9869605 60 0.9920438 61 1.000000 62 1.000000 63 1.000000 64 1.000000 65 1.000000 66 1.000000 --------------------------------------------------------------------------------------------------------------------- LOADING - 100P STATUS - ACTIVE PERIODIC Response Modal Scaling (NRC Guide 1.92, Rev. 2, Combination Method A) ============================================================================== F1 = 1.8609530 F2 = 27.2869854 FZPA = 40.0000000 MODE FACTOR MODE FACTOR MODE FACTOR MODE FACTOR MODE FACTOR MODE FACTOR 1 1.000000 2 0.9999706 3 0.9928371 4 0.9792303 5 0.9680406 6 0.9599776 7 0.9548803 8 0.9517443 9 0.9223262 10 0.9150033 11 0.9030768 12 0.8933780 . 49 0.4928423 50 0.4821628 51 0.4632666 52 0.4446102 53 0.4252612 54 0.3958085 55 0.2799498 56 0.2654511 57 0.2339008 58 0.1916690 59 0.1609628 60 0.1258933 61 0.0000000E+00 62 0.0000000E+00 63 0.0000000E+00 64 0.0000000E+00 65 0.0000000E+00 66 0.0000000E+00 29

Response Spectrum Loadings 100R and 100P Example 1 Revision 2 Response Spectrum Loadings 100R and 100P Mode # X mass % Freq (HZ) α (1-α2)1/2 ------ -------- --------- ------- ------- 3 83.0052 2.56 0.119 0.993 19 10.0467 7.84 0.536 0.844 24 0.4465 8.69 0.574 0.819 43 3.0879 13.54 0.739 0.674 45 0.5408 14.34 0.760 0.649 49 1.3443 19.25 0.870 0.493 51 0.3270 20.10 0.886 0.463 55 0.5741 24.51 0.960 0.280 57 0.1194 25.32 0.972 0.234 59 0.1003 26.35 0.987 0.161 61 0.1519 28.32 1.000 0.000 Total %100.0000 Active %100.0000 (Modes having X mass participation ≥ 0.05% listed) F2 = 27.29 HZ F1 = 1.86 HZ 30

Example 1 Revision 1 Revision 2 31 $* ** $* ** Compute modal and combined modal results LOAD LIST 100 300 COMPUTE RESPONSE SPECTRUM DISPL MODE COMBINATION CQC COMPUTE RESPONSE SPECTRUM FORCES MODE COMBINATION CQC COMPUTE RESPONSE SPECTRUM REACTIONS MODE COMBINATION CQC CREATE PSEUDO STATIC LOAD 'PS100' FROM CQC OF LOAD ‘100’ CREATE PSEUDO STATIC LOAD 'PS300' FROM CQC OF LOAD ‘300’ $* ** $* ** Compute rigid modal and combined rigid modal results LOAD LIST ‘100R’ ‘300R’ COMPUTE RESPONSE SPECTRUM DISPL MODE COMBINATION ALG COMPUTE RESPONSE SPECTRUM FORCES MODE COMBINATION ALG COMPUTE RESPONSE SPECTRUM REACTIONS MODE COMBINATION ALG CREATE PSEUDO STATIC LOAD ‘PS100R’ FROM ALG OF LOAD ‘100R' CREATE PSEUDO STATIC LOAD ‘PS300R’ FROM ALG OF LOAD ‘300R' $* ** Compute Periodic modal and combined periodic modal $* ** results LOAD LIST ‘100P’ ‘100P’ COMPUTE RESPONSE SPECTRUM DISPL MODE COMBINATION CQC COMPUTE RESPONSE SPECTRUM FORCES MODE COMBINATION CQC COMPUTE RESPONSE SPECTRUM REACTIONS MODE COMBINATION CQC CREATE PSEUDO STATIC LOAD ‘PS100P’ FROM CQC OF LOAD ‘100P’ CREATE PSEUDO STATIC LOAD ‘PS300P’ FROM CQC OF LOAD ‘300P’ 31

Example 1 Revision 1 Revision 2 $* ** $* ** Compute total combined modal results, including missing $* ** mass,in the global X and Z directions FORM MISSING MASS LOAD ‘100M’ FROM RESPONSE SPECTRUM LOAD 100 - DAMPING RATIO 0.05 CUTOFF FREQUENCY 28.77 FORM MISSING MASS LOAD ‘300M’ FROM RESPONSE SPECTRUM LOAD 300 - LOAD LIST ‘100M’ ‘300M’ STIFFN ANALYSIS GTSES $* ** Compute total response in the global X direction LOAD LIST ALL CREATE LOAD COMBINATION ‘100TOT’ TYPE RMS - SPECS ‘PS100’ 1.0 ‘100M’ 1.0 $* ** Compute total response in the global Z direction CREATE LOAD COMBINATION ‘300TOT’ TYPE RMS - SPECS ‘PS300’ 1.0 ‘300M’ 1.0 $* ** Compute total solution CREATE LOAD COMBINATION 'EQTOT' TYPE RMS - SPECS ‘100TOT’ 1.0 ‘300TOT’ 1.0 $* ** $* ** Compute total combined rigid results, including missing $* ** mass, in the global X and Z directions FORM MISSING MASS LOAD ‘100M’ FROM RESPONSE SPECTRUM LOAD ‘100P’ - DAMPING RATIO 0.05 CUTOFF FREQUENCY 28.77 FORM MISSING MASS LOAD ‘300M’ FROM RESPONSE SPECTRUM LOAD ‘300P’ - LOAD LIST ‘100M’ ‘300M’ STIFFN ANALYSIS GTSES CREATE LOAD COMBINATION ‘100RTOT’ SPECS ‘PS100R’ 1.0 ‘100M’ 1.0 CREATE LOAD COMBINATION ‘300RTOT’ SPECS ‘PS300R’ 1.0 ‘300M’ 1.0 $* ** Compute total response in the global X direction LOAD LIST ALL CREATE LOAD COMBINATION ‘100TOT’ TYPE RMS - SPECS ‘100RTOT’ 1.0 ‘PS100P’ 1.0 $* ** Compute total response in the global Z direction CREATE LOAD COMBINATION ‘300TOT’ TYPE RMS - SPECS ‘300RTOT’ 1.0 ‘PS300P’ 1.0 $* ** Compute total solution CREATE LOAD COMBINATION ‘EQTOT’ TYPE RMS - SPECS ‘300TOT 1.0 ‘300TOT’ 1.0

Example 1 Revision 1 Revision 2 { 804} > LOAD LIST 'PS100' '100M' '100TOT' { 805} > OUTPUT BY MEMBER { 806} > LIST REACTION JOINT 7 ACTIVE UNITS INCH KIP CYC DEGF SEC RESULTANT JOINT LOADS SUPPORTS JOINT LOADING /---------------------FORCE---------------------//--------------------MOMENT--------------------/ X FORCE Y FORCE Z FORCE X MOMENT Y MOMENT Z MOMENT 7 GLOBAL PS100 7.9233351 0.8505948 0.0001352 0.0067266 0.0101057 663.6497192 100M -0.0000028 0.0000031 0.0000000 -0.0000005 0.0000000 0.0001812 100TOT 7.9233351 0.8505948 0.0001352 0.0067266 0.0101057 663.6497192 Revision 2 { 848} > LOAD LIST 'PS100P' 'PS100R' '100M' '100RTOT' '100TOT' { 849} > OUTPUT BY MEMBER { 850} > LIST REACTION JOINT 7 ACTIVE UNITS INCH KIP CYC DEGF SEC RESULTANT JOINT LOADS SUPPORTS JOINT LOADING /---------------------FORCE---------------------//--------------------MOMENT--------------------/ X FORCE Y FORCE Z FORCE X MOMENT Y MOMENT Z MOMENT 7 GLOBAL PS100R 1.9317409 -0.1624137 -0.0000177 -0.0008941 0.0009135 -156.4043427 100M -0.0000028 0.0000031 0.0000000 -0.0000005 0.0000000 0.0001812 100RTOT 1.9317381 -0.1624106 -0.0000177 -0.0008946 0.0009135 -156.4041443 PS100P 7.8353539 0.8071265 0.0001135 0.0056487 0.0092773 656.5211792 100TOT 8.0699682 0.8233045 0.0001148 0.0057191 0.0093221 674.8942871

Example 1 Revision 1 Revision 2 { 808} > LOAD LIST '100TOT' '300TOT' 'EQTOT' { 809} > OUTPUT BY MEMBER { 810} > LIST REACT JOINT 7 ACTIVE UNITS INCH KIP CYC DEGF SEC RESULTANT JOINT LOADS SUPPORTS JOINT LOADING /---------------------FORCE---------------------//--------------------MOMENT--------------------/ X FORCE Y FORCE Z FORCE X MOMENT Y MOMENT Z MOMENT 7 GLOBAL 100TOT 7.9233351 0.8505948 0.0001352 0.0067266 0.0101057 663.6497192 300TOT 0.0004739 8.5615606 7.4463096 541.7026978 0.0030473 0.0303222 EQTOT 7.9233351 8.6037102 7.4463096 541.7026978 0.0105552 663.6497192 Revision 2 { 852} > LOAD LIST '100TOT' '300TOT' 'EQTOT' { 853} > OUTPUT BY MEMBER { 854} > LIST REACT JOINT 7 ACTIVE UNITS INCH KIP CYC DEGF SEC RESULTANT JOINT LOADS SUPPORTS JOINT LOADING /---------------------FORCE---------------------//--------------------MOMENT--------------------/ X FORCE Y FORCE Z FORCE X MOMENT Y MOMENT Z MOMENT 7 GLOBAL 100TOT 8.0699682 0.8233045 0.0001148 0.0057191 0.0093221 674.8942871 300TOT 0.0004690 8.5616188 7.4547424 542.3069458 0.0029606 0.0298751 EQTOT 8.0699682 8.6011124 7.4547424 542.3069458 0.0097810 674.8942871

Example 2 Material Concrete Columns: 18”x18” 50.0 FT (5 @ 10’) (20 @ 10’) (19 @ 10’) Material Concrete Columns: 18”x18” Floor and Wall Panel Thicknesses: 12” 2520 Joints, 342 Members, 2670 Plate FEs

Response Spectrum Loadings 100R and 100P Example 2 Revision 2 Response Spectrum Loadings 100R and 100P Mode # X mass % Freq (HZ) α (1-α2)1/2 ------ -------- --------- -------- --------- . . (Total X mass particpation, modes 1-24 = 0.06%!) 25 1.4600 1.97 0.021 1.000 26 1.1638 2.01 0.028 1.000 34 13.5330 2.35 0.087 0.996 48 14.1142 2.96 0.172 0.985 67 0.9038 3.84 0.270 0.963 74 1.7794 4.19 0.302 0.953 96 22.5149 5.19 0.382 0.924 111 1.7086 5.88 0.428 0.904 112 1.3514 5.92 0.431 0.902 245 2.2235 10.80 0.655 0.756 255 1.8683 11.37 0.674 0.739 263 0.5092 11.67 0.684 0.729 266 0.8349 11.73 0.686 0.728 268 0.9019 11.79 0.687 0.727 389 1.0395 15.86 0.798 0.603 419 0.8794 16.91 0.822 0.569 836 0.7776 28.18 1.000 0.000 850 0.5940 28.44 1.000 0.000 851 0.7370 28.46 1.000 0.000 Total % 99.9411 99.9997 99.9486 (f ≤ 40 HZ) Active % 99.9175 99.9889 99.9286 (mass participation ≥ 0.001%) F2 = 27.29 HZ F1 = 1.86 HZ 36

Example 2 Revision 1 Revision 2 37 37 { 804} > LOAD LIST 'PS100' '100M' '100TOT' { 805} > OUTPUT BY MEMBER { 806} > LIST REACTION JOINT 21 ACTIVE UNITS INCH KIP CYC DEGF SEC RESULTANT JOINT LOADS SUPPORTS JOINT LOADING /---------------------FORCE---------------------//--------------------MOMENT--------------------/ X FORCE Y FORCE Z FORCE X MOMENT Y MOMENT Z MOMENT 21 GLOBAL PS100 55.4891853 51.0420609 35.3468590 445.2986755 151.3651123 903.9607544 100M 0.0611252 -0.0009288 0.0170936 0.1989509 -0.1460913 0.5150789 100TOT 55.4892197 51.0420609 35.3468628 445.2987061 151.3651733 903.9608765 Revision 2 { 848} > LOAD LIST 'PS100P' 'PS100R' '100M' '100RTOT' '100TOT' { 849} > OUTPUT BY MEMBER { 850} > LIST REACTION JOINT 21 ACTIVE UNITS INCH KIP CYC DEGF SEC RESULTANT JOINT LOADS SUPPORTS JOINT LOADING /---------------------FORCE---------------------//--------------------MOMENT--------------------/ X FORCE Y FORCE Z FORCE X MOMENT Y MOMENT Z MOMENT 21 GLOBAL PS100R 35.0519829 7.9105206 13.9957037 -163.2551575 62.1802177 -169.3596344 100M 0.0611252 -0.0009288 0.0170936 0.1989509 -0.1460913 0.5150789 100RTOT 35.1131058 7.9095917 14.0127974 -163.0562134 62.0341263 -168.8445587 PS100P 52.1882515 50.7435150 33.4411621 431.6027832 140.1225433 898.0291748 100TOT 62.9010658 51.3562660 36.2583771 461.3764954 153.2401886 913.7640991 37 37

Example 2 Revision 1 Revision 2 38 { 808} > LOAD LIST '100TOT' '300TOT' 'EQTOT' { 809} > OUTPUT BY MEMBER { 810} > LIST REACT JOINT 21 ACTIVE UNITS INCH KIP CYC DEGF SEC RESULTANT JOINT LOADS SUPPORTS JOINT LOADING /---------------------FORCE---------------------//--------------------MOMENT--------------------/ X FORCE Y FORCE Z FORCE X MOMENT Y MOMENT Z MOMENT 21 GLOBAL 100TOT 55.4892197 51.0420609 35.3468628 445.2987061 151.3651733 903.9608765 300TOT 31.8329468 48.5689278 53.4435310 822.1765137 139.6783752 410.5592957 EQTOT 63.9717903 70.4573059 64.0750427 935.0214844 205.9647064 992.8263550 Revision 2 { 852} > LOAD LIST '100TOT' '300TOT' 'EQTOT' { 853} > OUTPUT BY MEMBER { 854} > LIST REACT JOINT 7 ACTIVE UNITS INCH KIP CYC DEGF SEC RESULTANT JOINT LOADS SUPPORTS JOINT LOADING /---------------------FORCE---------------------//--------------------MOMENT--------------------/ X FORCE Y FORCE Z FORCE X MOMENT Y MOMENT Z MOMENT 7 GLOBAL 100TOT 62.6293793 50.6817245 35.6329117 456.2272339 150.3090363 903.4033813 300TOT 32.4566460 48.1798668 61.0580063 823.7388916 139.6220093 424.5520935 EQTOT 70.5398712 69.9280777 70.6950150 941.6416626 205.1514282 998.1893921 38

Concluding Remarks The Rev 2 response spectrum solution methodology appears to be a reasonably rational way to incorporate more recent knowledge about periodic and rigid response characteristics. The effect of the Rev 2 rigid response modifications may increase or decrease the magnitude of response predictions, depending on where the modal frequencies are distributed on the response spectrum curves with respect to F1, F2, and FZPA. The more concise way in which rigid response is treated in the Rev 2 solution may reign in the trend toward higher and higher cutoff frequencies. The Rev 2 solution does require additional dynamic loading conditions, longer compute times, and more results data to manage. Are differences in results worth the extra effort?

Concluding Remarks Practical Issues: It may take a very large number of modes to encompass all frequencies ≤ FZPA . Computer resources are still finite! No specified role for mass participation percentage under RG 1.92.