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STRUDL ITALIA srl

STRUDL (UK) Limited

ISC Internacional Ltda.

DYNAMIC ANALYSISTUTORIAL 1

RESPONSE SPECTRAL ANALYSIS

2001

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TUTORIAL ON RESPONSE SPECTRAL ANALYSIS

The data required to perform any dynamic analysis includes:

• Stiffness representation

• Damping representation

• Inertia representation

• Loading data

The inertia representation is made via the specification of geometry, connectivity, boundary

conditions, and mechanical and geometrical element properties. These data, plus the static loading

specification, are the same data required to perform a static analysis, and can be specified, in

GTSTRUDL, via commands, menus or graphics. For instance, a possible model for this type ofanalysis can be the following:

STRUDL 'SPECTRAL' 'RESPONSE ANALYSIS EXAMPLE'$UNITS METERS DEGREESGEN 2 JOINT ID 1,1 X 0 8 Y 22REP 1 TIME ID 2 Z 5GEN 2 JOINT ID 5,1 X 16 Y 10 -10REP 1 ID 2 Z 5GEN 2 JOINTS ID 9,1 X 0 8 Y 10REP 1 ID 2 Y -10REP 2 ID 4 Z DIFF 5 4

JOINT COOR29 4 22 530 0 16 531 4 10 532 8 16 533 0 5 534 4 0 535 8 5 536 12 0 537 16 5 538 12 10 539 4 16 540 4 5 5

41 12 5 5TYPE SPACE FRAMEGEN 2 MEM ID 101,1 FROM 1,1 TO 3,1REP 1 ID 2 FROM 4GEN 2 MEM ID 105,1 FROM 9,1 TO 13,1REP 1 ID 2 FROM 2REP 1 ID 4 FROM 4MEM INC1 3 292 29 43 4 324 32 145 3 30

6 30 137 13 318 31 149 14 35

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10 35 1611 34 1612 15 3413 13 3314 33 1515 14 38

16 38 717 7 3718 37 819 36 820 16 3621 17 1822 18 2023 19 2024 17 19

STATUS SUPPORT 1,2,5,6,9 TO 12MATERIAL STEELUNIT INCMEMBER PROP

1 TO 24 TABLE 'HEA' 'HE400A'101 TO 112 TABLE 'HEA' 'HE600A'UNIT KIPS FTLOAD 1 'WX'JOINT LOAD3 13 15 17 19 FORCE X 10LOAD 2 'WY'JOINT LOAD3 4 7 17 18 FORCE Y -10LOAD 3 'GL'MEM LOAD22 24 17 18 FORCE Z UNIF W -2.023 FORCE Z CONC FR P -15 L 0.5LOAD COMB 4 'ALL' COMBINE 1 1.0 2 1.0 3 1.0DELETIONSJOINTS 39 40 41ADDITIONSSTIFFNESS ANALYSIS$

This structural model is as shown in the following image:

X

YZ

The next step is to define the damping representation. In general terms, damping can be given as

modal damping, useful when applying modal superposition procedures, or proportional to mass and

stiffness, when applying direct integration procedures. In this case it will be assumed that theanalysis to be developed is a response spectral analysis, a modal superposition procedure and

therefore modal damping will be used. The damping data can be given in the “Modeling/Dynamic

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Properties/Specified Damping” function, in the main GTSTRUDL window, using the following

menu:

Equivalently, it can be given for instance through the following command:

$DAMPING RATIOS 0.05 20 0.1 30$

where the damping is given as 5% of the critical damping for the first 20 modes and 10% for the

next 30 modes.

The mass representation can be given in menu form activating the “Analysis/DynamicAnalysis/Eigenvalue” function, leading to the following menu:

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Three different classes of data are given in that menu, including the technique to compute

automatically the mass representation, selected as LUMPED in this example, the specification of

the solution technique to be used for eigenvalue analysis, Lanczos in this case, and the number of

modes to be considered, equal to 50 in this case. Notice also that in the lower part of the menu it is

requested to perform the eigenvalue analysis.

The data in that given in that menu is equivalent to the following commands:

$INERTIA OF JOINTS LUMPEDEIGENVALUE PARAMETERSSOLVE USING GTLANCZOSNUMBER OF MODES 50PRINT MAXIMUM

END EIGENVALUE PARAMETERSDYNAMIC ANALYSIS EIGENVALUES$

Having completed the stiffness, damping, and mass representation the next step is to specify the

spectral loading corresponding to an earthquake excitation. This requires first defining a response

spectrum, as a collection of curves relating maximum values of some response measure, such as

displacements, velocity or acceleration, to period or frequency. These data can be given in the

“Modeling/Loads/Dynamic/Response Spectra” function in the GTSTRUDL main window, shown below.

Activating that function the following menu is offered:

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Using that menu, the different curve corresponding to each relevant level of damping consaidered

in the analysis are specified. If you have defined a user data set when starting GTSTRUDL, thespectrum will be permanently saved in that file, for the current run and for future utilization.

The equivalent commands to specify the response spectrum can be the following:

UNITS KIPS INCHES SECONDS CYCLESSTORE RESPONSE SPECTRA VELOCITY VS FREQUENCY 'QUAKE'DAMPING RATIO 1.E-54.401 .01 69.42 .25 52.67 2.5 19.981 9. 1.8635 33.DAMPING RATIO .023.675 .01 54.436 .25 46.945 2.5 14.189 9. 1.836 33.DAMPING RATIO 0.43.347 .01 12.131 .25 10.012 2.5 3.012 9. 1.8636 33.DAMPING RATIO 1.3.347 .01 12.131 .25 10.012 2.5 3.012 9. 1.8636 33.END OF RESPONSE SPECTRA

$

Notice that four curves were defined, relating maximum velocity to frequency.

The next step is to specify the dynamic loading condition, based on that response spectrum. This is

done again in the GTSTRUDL main window, activating the “Modeling/Loads/Dynamics/Response

Spectrum Load” function, as shown below.

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The system will proposed the following menu:

Using that menu it is possible to provide all data related to a response spectra loading.

The equivalente commands in that respect can be the following:

RESPONSE SPECTRA LOADING 1000SUPPORT ACCELERATIONTRANS X FILE 'QUAKE'

END OF RESP$

Once all basic data has been specified, the analysis can be requested, using the “Analysis/Dynamic

Analysis/ Response Spectrum function shown below.

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The equivalent command is the following:

$PERFORM RESPONSE SPECTRUM ANALYSIS$

That analysis command compute the modal results, using the spectral response analysis procedure.

In order to obtain physical results it is necessary to give a compute command, using the

“Results/Dynamic Analysis results/Compute” function in the main GTSTRUDL window, shown

below.

Activating that function brings the following menu:

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In this menu the user selects the type of results desired, in a similar fashion as for the COMPUTE

command.

The equivalent command is the following:

UNITS METERS KNEWTON DEGREESLIST RESPONSE SPECTRUM DISPLACEMENTS FORCES REACTIONS MODE COMBINATION RMS ALL$

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APPENDIX I

THE GTSTRUDL INPUT COMMAND FILE

STRUDL 'SPECTRAL' 'RESPONSE ANALYSIS EXAMPLE'

$UNITS METERS DEGREESGEN 2 JOINT ID 1,1 X 0 8 Y 22REP 1 TIME ID 2 Z 5GEN 2 JOINT ID 5,1 X 16 Y 10 -10REP 1 ID 2 Z 5GEN 2 JOINTS ID 9,1 X 0 8 Y 10REP 1 ID 2 Y -10REP 2 ID 4 Z DIFF 5 4JOINT COOR29 4 22 530 0 16 531 4 10 5

32 8 16 533 0 5 534 4 0 535 8 5 536 12 0 537 16 5 538 12 10 539 4 16 540 4 5 541 12 5 5TYPE SPACE FRAMEGEN 2 MEM ID 101,1 FROM 1,1 TO 3,1REP 1 ID 2 FROM 4

GEN 2 MEM ID 105,1 FROM 9,1 TO 13,1REP 1 ID 2 FROM 2REP 1 ID 4 FROM 4MEM INC1 3 292 29 43 4 324 32 145 3 306 30 137 13 318 31 149 14 35

10 35 1611 34 1612 15 3413 13 3314 33 1515 14 3816 38 717 7 3718 37 819 36 820 16 3621 17 1822 18 2023 19 2024 17 19

STATUS SUPPORT 1,2,5,6,9 TO 12MATERIAL STEEL

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UNIT INCMEMBER PROP1 TO 24 TABLE 'HEA' 'HE400A'101 TO 112 TABLE 'HEA' 'HE600A'UNIT KIPS FTLOAD 1 'WX'

JOINT LOAD3 13 15 17 19 FORCE X 10LOAD 2 'WY'JOINT LOAD3 4 7 17 18 FORCE Y -10LOAD 3 'GL'MEM LOAD22 24 17 18 FORCE Z UNIF W -2.023 FORCE Z CONC FR P -15 L 0.5LOAD COMB 4 'ALL' COMBINE 1 1.0 2 1.0 3 1.0DELETIONSJOINTS 39 40 41ADDITIONS

STIFFNESS ANALYSIS$$INERTIA OF JOINTS LUMPED WITH EFFECTIVE MEMBER LENGTH 0.010000 TORSIONAL -INERTIA FACTOR 0.333300EIGENVALUE PARAMETERSSOLVE USING GTLANCZOSNUMBER OF MODES 50PRINT MAXIMUM

END EIGENVALUE PARAMETERSDYNAMIC ANALYSIS EIGENVALUES$DAMPING RATIOS 0.05 20 0.1 30$UNITS KIPS INCHES SECONDS CYCLESSTORE RESPONSE SPECTRA VELOCITY VS FREQUENCY 'QUAKE'DAMPING RATIO 1.E-54.401 .01 69.42 .25 52.67 2.5 19.981 9. 1.8635 33.DAMPING RATIO .023.675 .01 54.436 .25 46.945 2.5 14.189 9. 1.836 33.DAMPING RATIO 0.43.347 .01 12.131 .25 10.012 2.5 3.012 9. 1.8636 33.DAMPING RATIO 1.3.347 .01 12.131 .25 10.012 2.5 3.012 9. 1.8636 33.END OF RESPONSE SPECTRA$RESPONSE SPECTRA LOADING 1000SUPPORT ACCELERATIONTRANS X FILE 'QUAKE'END OF RESP

$$$PERFORM RESPONSE SPECTRUM ANALYSIS$COMPUTE RESPONSE SPECTRUM DISPLACEMENTS FORCES LOADS REACTIONS MODE COMBINATIONRMS ALLUNITS METERS KNEWTON DEGREESLIST RESPONSE SPECTRUM DISPLACEMENTS FORCES LOADS REACTIONS MODE COMBINATION RMSALL$

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APPENDIX I

THE GTSTRUDL OUTPU FILE

Commercial Software Rights Legend

Any use, duplication or disclosure of this software by or for the U.S.Government shall be restricted to the terms of a license agreement inaccordance with the clause at DFARS 227.7202-3.

This computer software is an unpublished work containing valuabletrade secrets owned by the Georgia Tech Research Corporation (GTRC).No access, use, transfer, duplication or disclosure thereof may bemade except under a license agreement executed by GTRC or itsauthorized representatives and no right, title or interest theretois conveyed or granted herein, notwithstanding receipt or possessionhereof. Decompilation of the object code is strictly prohibited.

Georgia Tech Research CorporationGeorgia Institute of TechnologyAtlanta, Georgia 30332 U.S.A.

Copyright (c) 1999 GTRCALL RIGHTS RESERVED.

# Thu Jun 21 14:18:38 2001

1GTICES/C-NP 2.5.0 MD-NT 2.0, January 1995.Proprietary to Georgia Tech Research Corporation, U.S.A.

Reading password file C:\gt2000\25\gtaccess.datCI-i-audfile, Command AUDIT file FILE1418.aud has been activated.

*** G T S T R U D L ***RELEASE DATE VERSION COMPLETION NO.August 30, 2000 25.0 4085

**** ACTIVE UNITS - LENGTH WEIGHT ANGLE TEMPERATURE TIME**** ASSUMED TO BE INCH POUND RADIAN FAHRENHEIT SECOND

Reading global defaults file C:\gt2000\25\defaults.gts{ 1} > UNITS METERS KNEW DEGREES{ 2} > MATERIAL STEEL{ 3} > OUTPUT LONG NAMES

{ 4} > $ ---------------------------------------------------------{ 5} > $ This is the Common Startup Macro; put your company-wide startup commands here.

{ 6} > $ You can edit this file from Tools -- Macros. Click "Startup" and then "Edit".{ 7} > $ ---------------------------------------------------------

{ 4} > CINPUT 'C:\Tutorials\DYNAMICS\STRUDL.DAT'{ 5} > STRUDL 'SPECTRAL' 'RESPONSE ANALYSIS EXAMPLE'

********************************************************************* ** ****** G T S T R U D L ** ******** ** ** ** ** ** ***** ****** ***** ** ** ***** ** ** ** ********** ****** ****** ****** ** ** ****** ** ** ** ********** ** ** ** ** ** ** ** ** ** ** ** **** ***** ** ****** ** ** ** ** ** ** ********** ***** ** ***** ** ** ** ** ** ** ****** ** ** ** ** ** ** ** ** ** ** *

* ** ****** ** ** ** ****** ****** ****** ** ** ***** ** ** ** **** ***** ****** ** ** ** ** OWNED BY AND PROPRIETARY TO THE ** ** GEORGIA TECH RESEARCH CORPORATION ** ** RELEASE DATE VERSION COMPLETION NO. ** August 30, 2000 25.0 4085 ** *********************************************************************

**** ACTIVE UNITS - LENGTH WEIGHT ANGLE TEMPERATURE TIME**** ASSUMED TO BE INCH POUND RADIAN FAHRENHEIT SECOND

Reading global defaults file C:\gt2000\25\defaults.gts{ 6} > UNITS METERS KNEW DEGREES

{ 7} > MATERIAL STEEL{ 8} > OUTPUT LONG NAMES{ 9} > ${ 10} > UNITS METERS DEGREES

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{ 32} > TYPE SPACE FRAME{ 33} > GEN 2 MEM ID 101,1 FROM 1,1 TO 3,1

/----------------- MEMBER INCIDENCES -----------------/

MEMBER INCIDENCES

101 1 3102 2 4

{ 34} > REP 1 ID 2 FROM 4


MEMBER INCIDENCES

103 5 7104 6 8

{ 35} > GEN 2 MEM ID 105,1 FROM 9,1 TO 13,1


MEMBER INCIDENCES

105 9 13106 10 14

{ 36} > REP 1 ID 2 FROM 2


MEMBER INCIDENCES

107 11 15108 12 16

{ 37} > REP 1 ID 4 FROM 4


MEMBER INCIDENCES

109 13 17110 14 18

111 15 19

112 16 20

{ 38} > MEM INC{ 39} > 1 3 29{ 40} > 2 29 4{ 41} > 3 4 32{ 42} > 4 32 14{ 43} > 5 3 30{ 44} > 6 30 13{ 45} > 7 13 31{ 46} > 8 31 14{ 47} > 9 14 35{ 48} > 10 35 16{ 49} > 11 34 16{ 50} > 12 15 34{ 51} > 13 13 33{ 52} > 14 33 15{ 53} > 15 14 38

{ 54} > 16 38 7{ 55} > 17 7 37{ 56} > 18 37 8{ 57} > 19 36 8{ 58} > 20 16 36{ 59} > 21 17 18{ 60} > 22 18 20{ 61} > 23 19 20{ 62} > 24 17 19{ 63} > STATUS SUPPORT 1,2,5,6,9 TO 12{ 64} > MATERIAL STEEL{ 65} > UNIT INC{ 66} > MEMBER PROP{ 67} > 1 TO 24 TABLE 'HEA' 'HE400A'{ 68} > 101 TO 112 TABLE 'HEA' 'HE600A'{ 69} > UNIT KIPS FT{ 70} > LOAD 1 'WX'{ 71} > JOINT LOAD{ 72} > 3 13 15 17 19 FORCE X 10

{ 73} > LOAD 2 'WY'{ 74} > JOINT LOAD{ 75} > 3 4 7 17 18 FORCE Y -10{ 76} > LOAD 3 'GL'{ 77} > MEM LOAD{ 78} > 22 24 17 18 FORCE Z UNIF W -2.0

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{ 79} > 23 FORCE Z CONC FR P -15 L 0.5{ 80} > LOAD COMB 4 'ALL' COMBINE 1 1.0 2 1.0 3 1.0{ 81} > DELETIONS{ 82} > JOINTS 39 40 41{ 83} > ADDITIONS{ 84} > STIFFNESS ANALYSIS

BANDWIDTH INFORMATION BEFORE RENUMBERING.

THE MAXIMUM BANDWIDTH IS 19 AND OCCURS AT JOINT 38THE AVERAGE BANDWIDTH IS 7.000THE STANDARD DEVIATION OF THE BANDWIDTH IS 6.640

----------13.640

==========

BANDWIDTH INFORMATION AFTER RENUMBERING.


----------

4.285==========

TIME FOR CONSISTENCY CHECKS FOR 36 MEMBERS 0.00 SECONDSTIME FOR BANDWIDTH REDUCTION 0.00 SECONDSTIME TO GENERATE 36 ELEMENT STIF. MATRICES 0.00 SECONDSTIME TO PROCESS 5 MEMBER LOADS 0.00 SECONDSTIME TO ASSEMBLE THE STIFFNESS MATRIX 0.01 SECONDSTIME TO PROCESS 30 JOINTS 0.00 SECONDSTIME TO SOLVE WITH 4 PARTITIONS 0.01 SECONDSTIME TO PROCESS 30 JOINT DISPLACEMENTS 0.00 SECONDSTIME TO PROCESS 36 ELEMENT DISTORTIONS 0.00 SECONDSTIME FOR STATICS CHECK 0.00 SECONDSTIME TO GENERATE COMBINED RESULTS 0.00 SECONDS{ 85} > ${ 86} > ${ 87} > INERTIA OF JOINTS LUMPED WITH EFFECTIVE MEMBER LENGTH 0.010000 TORSIONAL - INERTIA FACTOR 0.333300**** ERROR_ST1UIP -- TORSIONAL INERTIA FACTOR LESS THAN ZERO - VALUE IGNORED**** STRUDL ERROR - COMMAND FORMAT INCORRECTCI-w-cmdnpro, The following symbols were not processed.

0.333300{ 88} > EIGENVALUE PARAMETERS{ 89} > SOLVE USING GTLANCZOS{ 90} > NUMBER OF MODES 50{ 91} > PRINT MAXIMUM{ 92} > END EIGENVALUE PARAMETERS{ 93} > DYNAMIC ANALYSIS EIGENVALUES

BANDWIDTH INFORMATION BEFORE RENUMBERING.


----------13.640

==========

BANDWIDTH INFORMATION AFTER RENUMBERING.


----------4.285

==========TIME FOR CONSISTENCY CHECKS FOR 36 MEMBERS 0.00 SECONDSTIME FOR BANDWIDTH REDUCTION 0.00 SECONDSTIME TO GENERATE 36 ELEMENT STIF. MATRICES 0.00 SECONDSTIME TO ASSEMBLE THE STIFFNESS MATRIX 0.00 SECONDSTIME TO PROCESS 30 JOINTS 0.00 SECONDSTIME TO GENERATE REDUCED STIFFNESS MATRIX 0.00 SECONDS

TIME TO ASSEMBLE LUMPED MASS MATRIX 0.00 SECONDS

***************************** GT/LANCZOS SOLUTION DATA *****************************

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NUMBER OF DYNAMIC DEGREES-OF-FREEDOM = 132NUMBER OF MODES REQUESTED = 50EIGENVALUE TOLERANCE = 1.00000E-06NUMBER OF TERMS IN SKYLINE = 2609AVERAGE COLUMN HEIGHT OF SKYLINE = 20RANK OF MASS MATRIX = 132IN-CORE EQUATION SOLVER USEDNUMBER OF LANCZOS VECTORS COMPUTED = 93

************************************ END OF GT/LANCZOS SOLUTION DATA ************************************

TIME TO SOLVE EIGENPROBLEM 0.15 SECONDSTIME TO TRANSFORM EIGENVECTORS TO JOINTS 0.00 SECONDS

************************** EIGEN-SOLUTION CHECKS **************************

**** STRUDL MESSAGE - STURM SEQUENCE CHECK WAS SUCCESSFUL - THERE ARE NO MISSING MODES

MODE------EIGENVALUE-------FREQUENCY-------FREQUENCY--------PERIOD--------ESTIMATED---/((RAD/SEC)**2) (RAD/SEC) (CYC/SEC) (SEC/CYC) ACCURACY

1 3.030824D+02 1.740926D+01 2.770770D+00 3.609105D-01 7.423844D-132 6.717253D+02 2.591766D+01 4.124924D+00 2.424287D-01 4.400210D-133 1.109309D+03 3.330630D+01 5.300862D+00 1.886486D-01 4.168984D-134 1.124616D+03 3.353529D+01 5.337307D+00 1.873604D-01 4.024382D-135 2.216648D+03 4.708129D+01 7.493220D+00 1.334540D-01 2.465583D-136 2.409939D+03 4.909113D+01 7.813096D+00 1.279902D-01 1.339315D-137 2.420696D+03 4.920057D+01 7.830514D+00 1.277055D-01 1.291233D-138 2.481817D+03 4.981784D+01 7.928755D+00 1.261232D-01 1.861595D-139 2.852634D+03 5.341006D+01 8.500474D+00 1.176405D-01 2.011254D-1410 2.853969D+03 5.342255D+01 8.502463D+00 1.176130D-01 2.305934D-1411 3.465386D+03 5.886753D+01 9.369058D+00 1.067343D-01 1.138669D-1312 4.106648D+03 6.408313D+01 1.019915D+01 9.804741D-02 5.688446D-1413 4.108627D+03 6.409857D+01 1.020160D+01 9.802380D-02 5.520044D-1414 4.109871D+03 6.410828D+01 1.020315D+01 9.800896D-02 5.390011D-1415 4.926282D+03 7.018748D+01 1.117068D+01 8.952003D-02 9.820313D-1416 5.056715D+03 7.111058D+01 1.131760D+01 8.835795D-02 1.416179D-1317 5.056838D+03 7.111145D+01 1.131774D+01 8.835688D-02 1.284174D-1318 5.602840D+03 7.485212D+01 1.191308D+01 8.394132D-02 1.099562D-1319 6.212172D+03 7.881734D+01 1.254417D+01 7.971832D-02 1.344368D-13

20 6.423235D+03 8.014509D+01 1.275549D+01 7.839763D-02 6.756807D-1421 6.423710D+03 8.014805D+01 1.275596D+01 7.839474D-02 2.902787D-1422 6.424274D+03 8.015157D+01 1.275652D+01 7.839130D-02 5.728680D-1423 6.424425D+03 8.015251D+01 1.275667D+01 7.839038D-02 1.775347D-1424 6.432187D+03 8.020092D+01 1.276437D+01 7.834306D-02 7.857863D-1425 8.002345D+03 8.945583D+01 1.423734D+01 7.023786D-02 1.320872D-1326 8.353340D+03 9.139661D+01 1.454622D+01 6.874637D-02 1.490897D-1327 8.374609D+03 9.151289D+01 1.456473D+01 6.865902D-02 1.606713D-1328 9.969825D+03 9.984901D+01 1.589146D+01 6.292687D-02 1.811659D-1329 1.064056D+04 1.031531D+02 1.641733D+01 6.091125D-02 1.238689D-1330 1.066424D+04 1.032678D+02 1.643558D+01 6.084361D-02 1.782943D-1331 1.153183D+04 1.073863D+02 1.709107D+01 5.851010D-02 1.815824D-1332 1.403590D+04 1.184732D+02 1.885560D+01 5.303465D-02 1.738611D-1333 1.426983D+04 1.194564D+02 1.901207D+01 5.259815D-02 1.891608D-1334 1.763903D+04 1.328120D+02 2.113769D+01 4.730886D-02 8.394041D-1435 2.174752D+04 1.474704D+02 2.347064D+01 4.260641D-02 1.684155D-1336 3.355944D+04 1.831924D+02 2.915597D+01 3.429830D-02 1.810761D-1337 3.431389D+04 1.852401D+02 2.948188D+01 3.391914D-02 1.665512D-13

38 3.929160D+04 1.982211D+02 3.154786D+01 3.169787D-02 2.030186D-1339 4.571318D+04 2.138064D+02 3.402835D+01 2.938726D-02 9.904575D-1440 5.263243D+04 2.294176D+02 3.651294D+01 2.738755D-02 2.741982D-1341 2.116284D+05 4.600309D+02 7.321618D+01 1.365818D-02 1.087107D-1242 2.236917D+05 4.729606D+02 7.527401D+01 1.328480D-02 1.377854D-1343 2.245652D+05 4.738831D+02 7.542084D+01 1.325894D-02 8.527452D-1344 2.349823D+05 4.847497D+02 7.715031D+01 1.296171D-02 2.633913D-1445 2.415363D+05 4.914634D+02 7.821883D+01 1.278465D-02 1.633096D-1246 2.541804D+05 5.041630D+02 8.024004D+01 1.246261D-02 4.768680D-1347 2.723276D+05 5.218502D+02 8.305503D+01 1.204021D-02 1.788867D-1248 3.067225D+05 5.538253D+02 8.814403D+01 1.134507D-02 4.342357D-1349 4.344448D+05 6.591243D+02 1.049029D+02 9.532626D-03 2.177232D-1250 4.348458D+05 6.594284D+02 1.049513D+02 9.528230D-03 2.619295D-12

-------------------ORTHOGONALITY CHECK-------------------

WITH RESPECT TO MASS--------------------

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OFF DIAGONALS: MAXIMUM = 0.1160E-13MINIMUM = 0.1969E-18

MEAN = 0.3014E-15

DIAGONALS: MAXIMUM = 0.1000E+01MINIMUM = 0.1000E+01

MEAN = 0.1000E+01

WITH RESPECT TO STIFFNESS-------------------------

OFF DIAGONALS: MAXIMUM = 0.2948E-08MINIMUM = 0.1429E-14

MEAN = 0.1646E-10

DIAGONALS: MAXIMUM = 0.4348E+06MINIMUM = 0.3031E+03

MEAN = 0.6546E+05

********************************* END OF EIGEN-SOLUTION CHECKS *********************************

TIME TO CHECK EIGENSOLUTION 0.04 SECONDS{ 94} > ${ 95} > DAMPING RATIOS 0.05 20 0.1 30{ 96} > ${ 97} > UNITS KIPS INCHES SECONDS CYCLES{ 98} > STORE RESPONSE SPECTRA VELOCITY VS FREQUENCY 'QUAKE'{ 99} > DAMPING RATIO 1.E-5{ 100} > 4.401 .01 69.42 .25 52.67 2.5 19.981 9. 1.8635 33.{ 101} > DAMPING RATIO .02{ 102} > 3.675 .01 54.436 .25 46.945 2.5 14.189 9. 1.836 33.{ 103} > DAMPING RATIO 0.4{ 104} > 3.347 .01 12.131 .25 10.012 2.5 3.012 9. 1.8636 33.{ 105} > DAMPING RATIO 1.{ 106} > 3.347 .01 12.131 .25 10.012 2.5 3.012 9. 1.8636 33.{ 107} > END OF RESPONSE SPECTRA{ 108} > ${ 109} > RESPONSE SPECTRA LOADING 1000{ 110} > SUPPORT ACCELERATION

{ 111} > TRANS X FILE 'QUAKE'{ 112} > END OF RESP{ 113} > $${ 114} > ${ 115} > PERFORM RESPONSE SPECTRUM ANALYSISTIME TO COMPUTE RESPONSE SPECTRA RESULTS 0.00 SECONDS{ 116} > ${ 117} > COMPUTE RESPONSE SPECTRUM DISPLACEMENTS FORCES LOADS REACTIONS MODE COMBINATION RMS ALLTIME FOR RESPONSE SPECTRA COMPUTATION 0.27 SECONDS{ 118} > UNITS METERS KNEWTON DEGREES{ 119} > LIST RESPONSE SPECTRUM DISPLACEMENTS FORCES LOADS REACTIONS MODE COMBINATION RMS ALL1

*****************************RESULTS OF LATEST ANALYSES*****************************

PROBLEM - SPECTRAL TITLE - RESPONSE ANALYSIS EXAMPLE

ACTIVE UNITS M KN DEG DEGF SEC

==============================================================================================================================LOADING - 1000

==============================================================================================================================

MEMBER FORCES

MEMBER JOINT RESPONSE /---------------------FORCE--------------------//--------------------MOMENT--------------------/TYPE AXIAL SHEAR-Y SHEAR-Z TORSIONAL BENDING-Y BENDING-Z

101 1 RMS 11.00768 18.67241 22.17477 0.7253978E-01 69.93507 86.50341

ABS SUM 20.33370 42.55411 38.56872 0.1130479 121.6257 196.2222PRMS 15.30750 26.06577 30.66450 0.9005818E-01 96.70601 120.6685CQC 11.51805 13.14859 24.08426 0.7156673E-01 75.95378 61.05474

NRC GRP 11.55224 22.77757 23.25706 0.7396144E-01 73.34601 105.1659NRC TPM 11.55248 22.77770 23.25708 0.7396247E-01 73.34606 105.1665NRC DSM 12.18228 24.97740 24.58894 0.7594500E-01 77.54518 115.2757

8/18/2019 GTMTUT11

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GTMTUT11