response spectrum solution strategy

1

GTStrudl Version 30Response Spectrum Analysis Enhancements

Related To

NRC Regulatory Guide 1.92, Revision 2COMBINING MODAL RESPONSES AND SPATIAL COMPONENTS

inSEISMIC RESPONSE ANALYSIS

Michael H. Swanger, Ph.D.Georgia Tech CASE Center

GTSUG 2008June 23-26, 2008

Las Vegas, NV

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Topics1. Background

• NRC Reg Guide 1.92, Rev 1 Positionso Response Spectrum Characteristicso Response Spectrum Solution Strategy

• NRC Reg Guide 1.92, Rev 2 Positionso Response Spectrum Characteristicso 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

1.Background

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4

1.Background

Acceleration vs Time, File ELCENTRO

Time (SEC)

0 5 10 15 20 25 30 35 40 45 50 55

-100

-200

100

200

Tran

slat

ion

Acc

eler

atio

n (IN

/SE

C^2

)

5

1. BackgroundNRC Reg Guide 1.92, Rev 1 Positions

Frequency

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!

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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

1/232

total kk=1

R = R

7



● If frequencies are not closely spaced§:

SRSS Mode Combination Method

1/2n2

k kii=1

R = R , for k = ground motion directions 1, 2, 3

n = number of "significant" modes used in solution

§ 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

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● If frequencies are closely spaced:

− NRC Grouping Method− NRC Ten Percent Method− NRC Double Sum Method

1/2n n

k kij ki kji=1 j=1

12

i jkij

i i j j

1/22

d

R = R R , k = 1, 2, 3

( )1

1

2t

td = duration of earthquake

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Frequency1F 2F ZPAF

Low FrequencyOut-of-Phase

Response

Mid FrequencyTransition fromOut-of-Phase to

In-Phase Response

High FrequencyIn-Phase Rigid Static

Response

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



• 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.

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Frequency1F 2F ZPAF


Response


In-Phase Response


Response



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Frequency1F 2F ZPAF


Response


In-Phase Response


Response

• fi ≥ F2

Maximum response from steady state response. The maximum modal responses are in phase with one another.

• F1 < fi < F2

Response is part periodic and part rigid. Maximum modal responses transition from out-of-phase to in phase.



Frequency1F 2F ZPAF


Response


In-Phase Response


Response

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● For each mode i, in each ground motion direction k, the response is separated into a periodic part and a rigid part:

rki ki ki

2 1/2pki ki ki

ki

2 2 1/2ki rki pki

R = R (rigid modal response)

R = (1 - ) R periodic modal response

where 0 1 and k = 1, 2, 3

R = (R + R )

● The periodic modal response portions are combined using a double sum rule:

1/2n n

pk kij pki pkji=1 j=1

ZPA

R = R R , k = 1, 2, 3,

and where n = number of modes below F

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● The rigid modal responses are combined algebraically,

including the residual rigid contribution from the missing mass:n

rk rki missingmasski=1

ZPA

R = R + R , k = 1,2,3,

and where n = number of modes below F

● The total response in each ground motion direction is computed from the SRSS of the modal combinations of the periodic and rigid responses:

1/22 2k rk pkR = R + R , k = 1, 2, 3

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● Finally, the complete response is computed by performing the SRSS on the total responses in the three ground motion directions:

1/232

total kk=1

R = R

A 100-40-40 rule is also acceptable for combination of the spatial response components

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● Computation of rigid response factor αki ; The Gupta Method:

amax1

vma

ki i 1 ki i

x

2 1 ZPA

a

2

i

ki1ki

max

vma

12

1

x

i 2

SF =

= 0 for f F and

2 SF = (F + 2 F ) / 3S = maximum spectral accelerationS = maximum sp

= 1 for f F

Fln

ectra

0 1F= , F f

l v

FFln F

elocity

Frequency1F 2F ZPAF


Response


In-Phase Response


Response



• Periodic responses are combined using a double sum rule:

1/2n n

pk kij pki pkji=1 j=1

R = R R ,k = 1, 2, 3

εij computed according to the following methods:

− SRSS Method− NRC Double Sum Method (Rosenbleuth correlation coefficient)− CQC method (Der Kiureghian’s correlation coefficient)

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● 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

n

mm i ii=1

K u = ZPA M e -

n

rk rkii=1

R = R + , k = 1,2,3 missingmasskR

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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

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2. GTStrudl Enhancements, Version 30RESPONSE SPECTRUM LOAD/MODE FACTORS Command

F2F1

1 1 2 2 m m

ZPA

F2 vRIG IDCOM PUTE (F1 v )

PE

RESPONSE SPECTRUM LOA DING...

r (i ) r (i )... r (i )MOD E (FACTORS)

END OF RESPONSE SPE CTRU

R IODIC FZ

M D

PA v

LOA

Purpose: To compute α and (1 – α2)1/2 for each active mode for the defined response

spectrum load

● Syntax

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2. GTStrudl Enhancements, Version 30RESPONSE SPECTRUM LOAD/MODE FACTORS Command

● ExampleUNITS CYCLES SECONDSRESPONSE SPECTRUM LOAD ‘100R’SUPPORT ACCELERATION TRANSLATION X 1.000000 FILE ‘ELC-RS’ MODE FACTORS COMPUTE RIGID RESPONSE FZPA 40.0END RESPONSE SPECTRUM LOAD

RESPONSE SPECTRUM LOAD ‘100P’SUPPORT ACCELERATION TRANSLATION X 1.000000 FILE ‘ELC-RS’ MODE FACTORS COMPUTE PERIODIC RESPONSE FZPA 40.0END RESPONSE SPECTRUM LOAD

Note: FZPA is specified (FZPA 40.0); therefore:

F1 = Samax/(2πSvmax) F2 = (F1 + 2FZPA)/3

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2. GTStrudl Enhancements, Version 30The ALGEBRAIC Mode Combination

*COM PUTE RESPONSE SPE CTRUM ... -

RMSABSPRMSCQC

MOD AL (COM BINATIONS) ...(NRC) TPM(NRC) GPR(NRC) TPM

ALL

ALGEBRAIC

iCRE ATE PSE UDO (STA TIC) LOA DING ... -

'a'

CQC

(NRC) TPM(NRC) GPR

(FRO M) (OF) LOA DING ...(NRC) TPM

MOD E j

ALGEBRAIC

rk missingm

n

i=1assk+ ,R = R k = 1,2,3 rkiR

1/22 2k rk pkR = R + R , k = 1, 2, 3

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2. GTStrudl Enhancements, Version 30The ALGEBRAIC Mode Combination

● Example

LOAD LIST ‘100R’ $ Rigid RS ComponentsCOMPUTE RESPONSE SPECTRUM DISPLACEMENTS MODE COMBINATION ALGEBRAICCOMPUTE RESPONSE SPECTRUM FORCES MODE COMBINATION ALBEGRAICCREATE PSEUDO STATIC LOAD ‘PS100R’ FROM ALGEBRAIC OF LOAD ‘100R’

.

.

.

LOAD LIST ‘100P’ $ Periodic RS ComponentsCOMPUTE RESPONSE SPECTRUM DISPLACEMENTS MODE COMBINATION CQCCOMPUTE RESPONSE SPECTRUM FORCES MODE COMBINATION CQCCREATE PSEUDO STATIC LOAD ‘PS100P’ FROM CQC OF LOAD ‘100P’

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2. GTStrudl Enhancements, Version 30Total Rigid, Directional, and Solution Response

● Example$* **$* ** Total Rigid Response$* **UNITS CYCLES SECONDSFORM 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

X

Y

Z

XXXX

XXXX 50.00 FTXXXX

XXXX

40.00 FT

XXXX

XXXX

72.00 FT

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3. Example 1

(4 @ 10’) (5 @ 10’)

(6 @ 12’)

Columns: W14X53Beams (Global X): W18X35Beams (Global Z): W18X50210 Joints, 474 Members

Additional Mass: 1 kip, all joints, Global X and Z

Seismic Loading: El Centro RS, Global X and Z

3. Example 1El Centro Response Spectrum

UNITS FEET CYCLES SECONDSCREATE 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 20.00000END OF CREATE RESPONSE SPECTRUM

F1 = 1.9 HZ F2 = 27.3 HZ

FZPA

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3. Example 1Revision 1 Revision 2

UNITS INCHES KIPSDEAD LOAD 'DLX' DIR X ALL MEMBERSDEAD LOAD 'DLZ' DIR Z ALL MEMBERSINERTIA OF JOINTS FROM LOAD 'DLX' SAME DOFSINERTIA OF JOINTS FROM LOAD 'DLZ' SAME DOFSINERTIA OF JOINTS WEIGHT EXISTING TRANSL X 1.0 Z 1.0

UNITS CYCLES SECONDSEIGENVALUE PARAMETERS SOLVE USING GTSEL FREQUENCY SPECS 0.0 TO 40.0 PRINT MAXEND

DYNAMIC ANALYSIS EIGENVALUE

UNITS INCHES KIPSDEAD LOAD 'DLX' DIR X ALL MEMBERSDEAD LOAD 'DLZ' DIR Z ALL MEMBERSINERTIA OF JOINTS FROM LOAD 'DLX' SAME DOFSINERTIA OF JOINTS FROM LOAD 'DLZ' SAME DOFSINERTIA OF JOINTS WEIGHT EXISTING TRANSL X 1.0 Z 1.0

UNITS CYCLES SECONDSEIGENVALUE PARAMETERS SOLVE USING GTSEL FREQUENCY SPECS 0.0 TO 40.0 PRINT MAXEND

DYNAMIC ANALYSIS EIGENVALUE

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$* **$* ** 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 40.0END RESPONSE SPECTRUM LOAD

RESPONSE SPECTRUM LOAD ‘300R'SUPPORT ACCELERATION TRANSLATION Z 1.000000 FILE 'ELC-RS' MODE FACTORS COMPUTE RIGID RESPONSE FZPA 40.0END 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 1.000000 FILE 'ELC-RS' MODE FACTORS COMPUTE PERIODIC RESPONSE FZPA 40.0END RESPONSE SPECTRUM LOAD

RESPONSE SPECTRUM LOAD ‘300P'SUPPORT ACCELERATION TRANSLATION Z 1.000000 FILE 'ELC-RS' MODE FACTORS COMPUTE PERIODIC RESPONSE FZPA 40.0END RESPONSE SPECTRUM LOAD

UNITS INCHES KIPS CYCLES SECDAMPING RATIOS 0.05 100

PERFORM RESPONSE SPECTRUM ANALYSIS

LOAD LIST ‘100R' ‘300P'PRINT DYNAMIC LOAD DATA

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$* **$* ** Define response spectrum loads for response in the$* ** global X and Z directions$* **RESPONSE SPECTRUM LOAD 100SUPPORT ACCELERATION TRANSLATION X 1.000000 FILE 'ELC-RS'END RESPONSE SPECTRUM LOAD

RESPONSE SPECTRUM LOAD 300SUPPORT ACCELERATION TRANSLATION Z 1.000000 FILE 'ELC-RS'END RESPONSE SPECTRUM LOAD

UNITS INCHES KIPS CYCLES SECDAMPING RATIOS 0.05 100

PERFORM RESPONSE SPECTRUM ANALYSIS

{ 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

3. Example 1

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Revision 2

--------------------------------------------------------------------------------------------------------------------- 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

3. Example 1

Revision 2

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

Response Spectrum Loadings 100R and 100P

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$* **$* ** Compute modal and combined modal results$* **LOAD LIST 100 300COMPUTE RESPONSE SPECTRUM DISPL MODE COMBINATION CQCCOMPUTE RESPONSE SPECTRUM FORCES MODE COMBINATION CQCCOMPUTE 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 ALGCOMPUTE RESPONSE SPECTRUM FORCES MODE COMBINATION ALGCOMPUTE 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 CQCCOMPUTE RESPONSE SPECTRUM FORCES MODE COMBINATION CQCCOMPUTE 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’

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$* **$* ** 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 - DAMPING RATIO 0.05 CUTOFF FREQUENCY 28.77

LOAD LIST ‘100M’ ‘300M’STIFFN ANALYSIS GTSES

$* **$* ** Compute total response in the global X direction$* **LOAD LIST ALLCREATE 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’ - DAMPING RATIO 0.05 CUTOFF FREQUENCY 28.77

LOAD LIST ‘100M’ ‘300M’STIFFN ANALYSIS GTSES

CREATE LOAD COMBINATION ‘100RTOT’ SPECS ‘PS100R’ 1.0 ‘100M’ 1.0CREATE LOAD COMBINATION ‘300RTOT’ SPECS ‘PS300R’ 1.0 ‘300M’ 1.0

$* **$* ** Compute total response in the global X direction$* **LOAD LIST ALLCREATE 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

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3. Example 1Revision 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 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

{ 804} > LOAD LIST 'PS100' '100M' '100TOT' { 805} > OUTPUT BY MEMBER { 806} > LIST REACTION JOINT 7



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

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Revision 2

{ 852} > LOAD LIST '100TOT' '300TOT' 'EQTOT' { 853} > OUTPUT BY MEMBER { 854} > LIST REACT JOINT 7 ACTIVE UNITS INCH KIP CYC DEGF SEC


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




35

X

Y

Z

XXXX

XXXX

190.0 FT

XXXX

XXXX190.0 FT

3. Example 2

Material ConcreteColumns: 18”x18”

Floor and Wall Panel Thicknesses: 12”2520 Joints, 342 Members, 2670 Plate FEs

(20 @ 10’)(19 @ 10’)

50.0 FT(5 @ 10’)


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

Response Spectrum Loadings 100R and 100P

36

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



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

{ 804} > LOAD LIST 'PS100' '100M' '100TOT' { 805} > OUTPUT BY MEMBER { 806} > LIST REACTION JOINT 21



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

38


Revision 2







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?

40

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.

response spectrum solution strategy

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