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1 GTStrudl Version 30 Response Spectrum Analysis Enhancements Related To NRC Regulatory Guide 1.92, Revision 2 COMBINING MODAL RESPONSES AND SPATIAL COMPONENTS.

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Presentation on theme: "1 GTStrudl Version 30 Response Spectrum Analysis Enhancements Related To NRC Regulatory Guide 1.92, Revision 2 COMBINING MODAL RESPONSES AND SPATIAL COMPONENTS."— Presentation transcript:

1 1 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

2 2 Topics 1.Background NRC Reg Guide 1.92, Rev 1 Positions o Response Spectrum Characteristics o Response Spectrum Solution Strategy NRC Reg Guide 1.92, Rev 2 Positions o Response Spectrum Characteristics o Response spectrum Solution Strategy 2.GTStrudl Enhancements, Version 30 The RESPONSE SPECTRUM LOAD/ MODE FACTORS Command The ALGEBRAIC Mode Combination Total Response 3.Example NRC Reg Guide 1.92 Rev 1 vs Rev 2

3 1.Background 3

4 4

5 5 NRC Reg Guide 1.92, Rev 1 Positions Frequency Acceleration All modes are assumed to be out-of-phase with the ground acceleration and out-of-phase with each other Response Spectrum Characteristics All modes having frequencies ≤ some arbitrary cutoff frequency are deemed “significant” for inclusion in the response spectrum analysis 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!

6 6 1.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

7 7 1.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

8 8 1.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 t d = duration of earthquake

9 9 1.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 Response F 1 =frequency at which peak spectral acceleration is observed F 2 = 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 F ZPA =frequency at which the spectral acceleration returns to the zero period acceleration; maximum base acceleration of transient acceleration input used to generate the spectrum

10 1.Background NRC Reg Guide 1.92, Rev 2 Positions Response Spectrum Characteristics f i ≤ F 1 Maximum response from periodic or transient response in the modal frequency f i. Maximum modal (oscillator) responses are out-of-phase with one another. 10 Frequency Low Frequency Out-of-Phase Response Mid Frequency Transition from Out-of-Phase to In-Phase Response High Frequency In-Phase Rigid Static Response

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

12 F 1 < f i < F 2 Response is part periodic and part rigid. Maximum modal responses transition from out-of-phase to in phase. 1.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 Response 12

13 13 1.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:

14 14 1.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:

15 15 1.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 rule is also acceptable for combination of the spatial response components

16 16 1.Background NRC Reg Guide 1.92, Rev 2 Positions Response Spectrum Solution Strategy ● Computation of rigid response factor α ki ; The Gupta Method: Frequency Low Frequency Out-of-Phase Response Mid Frequency Transition from Out-of-Phase to In-Phase Response High Frequency In-Phase Rigid Static Response

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

18 18 1.Background NRC Reg Guide 1.92, Rev 2 Positions Response Spectrum Solution Strategy ● Computation of the Residual Rigid Response for all f i ≥ F ZPA 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

19 19 1.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

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

21 21 2.GTStrudl Enhancements, Version 30 RESPONSE SPECTRUM LOAD/MODE FACTORS Command ● Example UNITS CYCLES SECONDS RESPONSE SPECTRUM LOAD ‘100R’ SUPPORT ACCELERATION TRANSLATION X FILE ‘ELC-RS’ MODE FACTORS COMPUTE RIGID RESPONSE FZPA 40.0 END RESPONSE SPECTRUM LOAD RESPONSE SPECTRUM LOAD ‘100P’ SUPPORT ACCELERATION TRANSLATION X FILE ‘ELC-RS’ MODE FACTORS COMPUTE PERIODIC RESPONSE FZPA 40.0 END RESPONSE SPECTRUM LOAD Note: F ZPA is specified (FZPA 40.0); therefore: F 1 = S amax /(2 π S vmax ) F 2 = (F 1 + 2F ZPA )/3

22 22 2.GTStrudl Enhancements, Version 30 The ALGEBRAIC Mode Combination

23 23 2.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’

24 24 2.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 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

25 25 3.Example 1 10’) 10’) 12’) Columns: W14X53 Beams (Global X): W18X35 Beams (Global Z): W18X Joints, 474 Members Additional Mass: 1 kip, all joints, Global X and Z Seismic Loading: El Centro RS, Global X and Z

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

27 3.Example 1 Revision 1Revision 2 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

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

29 { 790} > PRINT DYNAMIC LOAD DATA LOADING - 100R STATUS - ACTIVE RIGID Response Modal Scaling (NRC Guide 1.92, Rev. 2, Combination Method A) =========================================================================== F1 = F2 = FZPA = MODE FACTOR MODE FACTOR MODE FACTOR MODE FACTOR MODE FACTOR MODE FACTOR E E Example 1 29 Revision LOADING - 100P STATUS - ACTIVE PERIODIC Response Modal Scaling (NRC Guide 1.92, Rev. 2, Combination Method A) ============================================================================== F1 = F2 = FZPA = MODE FACTOR MODE FACTOR MODE FACTOR MODE FACTOR MODE FACTOR MODE FACTOR E E E E E E+00

30 3.Example 1 Revision 2 Mode # X mass % Freq (HZ) α (1-α 2 ) 1/ Total % Active % (Modes having X mass participation ≥ 0.05% listed) F2 = HZ F1 = 1.86 HZ Response Spectrum Loadings 100R and 100P 30

31 3.Example 1 Revision 1Revision 2 $* ** $* ** Compute modal and combined modal results $* ** LOAD LIST 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

32 3.Example 1 Revision 1Revision 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 DAMPING RATIO 0.05 CUTOFF FREQUENCY FORM MISSING MASS LOAD ‘300M’ FROM RESPONSE SPECTRUM LOAD DAMPING RATIO 0.05 CUTOFF FREQUENCY 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 FORM MISSING MASS LOAD ‘300M’ FROM RESPONSE SPECTRUM LOAD ‘300P’ - DAMPING RATIO 0.05 CUTOFF FREQUENCY 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’

33 33 3.Example 1 Revision 1 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 M RTOT PS100P TOT { 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 PS M TOT

34 34 3.Example 1 Revision 1 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 TOT EQTOT { 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 TOT EQTOT

35 35 3.Example 2 Material Concrete Columns: 18”x18” Floor and Wall Panel Thicknesses: 12” 2520 Joints, 342 Members, 2670 Plate FEs 10’) 10’) 50.0 FT 10’)

36 3.Example 2 Revision 2 Mode # X mass % Freq (HZ) α (1-α 2 ) 1/ (Total X mass particpation, modes 1-24 = 0.06%!) Total % (f ≤ 40 HZ) Active % (mass participation ≥ 0.001%) F2 = HZ F1 = 1.86 HZ Response Spectrum Loadings 100R and 100P 36

37 37 3.Example 2 37 Revision 1 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 M RTOT PS100P TOT { 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 PS M TOT

38 38 3.Example 2 Revision 1 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 TOT EQTOT { 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 TOT EQTOT

39 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 F 1, F 2, and F ZPA. ● 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?

40 40 Concluding Remarks ● Practical Issues:  It may take a very large number of modes to encompass all frequencies ≤ F ZPA. Computer resources are still finite!  No specified role for mass participation percentage under RG 1.92.


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