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
1
Topics
1. Background
•
NRC Reg Guide 1.92, Rev 1 Positions
o
o
•
Response Spectrum Characteristics
Response Spectrum Solution Strategy
NRC Reg Guide 1.92, Rev 2 Positions
o
o
Response Spectrum Characteristics
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
2
1.Background
3
1.Background
Acceleration vs Time, File ELCENTRO
Translation Acceleration (IN/SEC^2)
200
100
0
5
10
15
20
25
30
35
40
45
50
55
-100
-200
Time (SEC)
4
1. Background
NRC Reg Guide 1.92, Rev 1 Positions
Acceleration
Response Spectrum Characteristics
All modes are assumed to
be out-of-phase with the
ground acceleration and
out-of-phase with each
other
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!
5
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
R total
1/2

2
=  R k 
 k=1 
3
6
1. Background
NRC Reg Guide 1.92, Rev 1 Positions
Response Spectrum Solution Strategy
●
If frequencies are not closely spaced§:
SRSS Mode Combination Method
1/2
n 2
R k =  R ki  , for k = ground motion directions 1, 2, 3
 i=1

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
§
7
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
1/2
Rk
 n n

=    kij R ki R kj  , k = 1, 2, 3
 i=1 j=1

 kij

 1 


 (i   j ) 









i
i
j
j


2




1
1/2
    1   2 
   
2
t d
td = duration of earthquake
8
1. 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
F1
F2
High Frequency
In-Phase Rigid Static
Response
FZPA
Frequency
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
9
1. 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
F1
•
F2
High Frequency
In-Phase Rigid Static
Response
FZPA
Frequency
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
1. 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
F1
•
F2
High Frequency
In-Phase Rigid Static
Response
FZPA
Frequency
fi ≥ F2
Maximum response from steady state response. The maximum
modal responses are in phase with one another.
11
1. 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
F1
•
F2
High Frequency
In-Phase Rigid Static
Response
FZPA
Frequency
F1 < fi < F2
Response is part periodic and part rigid. Maximum modal responses
transition from out-of-phase to in phase.
12
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:
R rki =  ki R ki
(rigid modal response)
R pk i = (1 -  ki2 )1/2 R ki
 periodic modal response 
where 0   ki  1 and k = 1, 2, 3
2
R ki = (R rki
+ R 2pki )1/2
●
The periodic modal response portions are combined using a
double sum rule:
1/2
R pk
 n n

=   kij R pki R pkj  , k = 1, 2, 3,
 i=1 j=1

and where n = number of modes below FZPA
13
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:
n
R rk =
R
rki
+ R missingmass k , k = 1, 2,3,
i=1
and where n = number of modes below FZPA
●
The total response in each ground motion direction is
computed from the SRSS of the modal combinations
of the periodic and rigid responses:
1/2
2
 , k = 1, 2, 3
R k =  R rk2 + R pk
14
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:
1/2


R total =  R 2k 
 k=1 
3
A 100-40-40 rule is also acceptable for combination of
the spatial response components
15
1. Background
NRC Reg Guide 1.92, Rev 2 Positions
Response Spectrum Solution Strategy
●
Computation of rigid response factor αki ; The Gupta Method:
 ki = 0 for f i  F1 and  ki = 1 for f i  F2 


F


i


ln 

F


 1 , F  f  F

=
ki
1
i
2


 F2 
ln


 F
 1


Samax
F1 =
2 Svmax
0   ki  1
Mid Frequency
Transition from
Out-of-Phase to
In-Phase Response
Low Frequency
Out-of-Phase
Response
High Frequency
In-Phase Rigid Static
Response
F2 = (F1 + 2 FZPA ) / 3
Samax = maximum spectral acceleration
Svmax = maximum spectral velocity
F1
F2
FZPA
Frequency
16
1. Background
NRC Reg Guide 1.92, Rev 2 Positions
Response Spectrum Solution Strategy
•
Periodic responses are combined using a double sum rule:
R pk
1/2


=   kij R pki R pkj  , k = 1, 2, 3
 i=1 j=1

n
n
εij computed according to the following methods:
−
−
−
SRSS Method
NRC Double Sum Method (Rosenbleuth correlation coefficient)
CQC method (Der Kiureghian’s correlation coefficient)
17
1. 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:
n
R rk =
R
rki
+ R missingmassk , k = 1, 2,3
i=1
 K u mm 

=   ZPA   M  e 
n

i=1

 i i 
The Missing Mass Method is quite accurate and is most important for
adequately capturing the high-frequency response near supports
18
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
19
2. GTStrudl Enhancements, Version 30
RESPONSE SPECTRUM LOAD/MODE FACTORS Command
●
Syntax
RESPONSE SPEC TRUM LOA DING...
r1 (i1 ) r2 (i 2 )... rm (i m )

MOD E (FAC TORS) 
RIG ID

COM
PUTE
(F1 v F1 )



PE
R
IODIC





F 2 v F2



FZPA v ZPA 
END OF RESPONSE SPE CTRUM LOA D
Purpose:
To compute α and (1 – α2)1/2 for each active
mode for the defined response spectrum load
20
2. 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’
SUPPORT ACCELERATION
TRANSLATION X 1.000000 FILE ‘ELC-RS’
MODE FACTORS COMPUTE PERIODIC RESPONSE FZPA 40.0
END RESPONSE SPECTRUM LOAD
Note: FZPA is specified (FZPA 40.0); therefore:
F1 = Samax/(2πSvmax)
F2 = (F1 + 2FZPA)/3
21
2. GTStrudl Enhancements, Version 30
The ALGEBRAIC Mode Combination
n
R rk =
R
rki
+ R missingmass k , k = 1, 2,3
i=1
1/2
2
 , k = 1, 2, 3
R k =  R rk2 + R pk
COM PUTE RESPONSE SPE CTRUM ... *
RMS



ABS


PRMS




CQC


MOD AL (COM BINATIONS) (NRC) TPM  ...
(NRC) GPR 


(NRC) TPM 


 ALGEBRAIC
ALL

i 
CRE ATE PSE UDO (STA TIC) LOA DING   ... 'a'


CQC



(NRC) TPM 


(NRC) GPR 
(FRO M) 
 (OF) LOA DING ...
(NRC) TPM 
 ALGEBRAIC 


MOD E j





22
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’
23
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 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
24
3. Example 1
X
72.00 FT
(6 @ 12’)
X
Y
X
Z
X
40.00 FT
X
50.00 FT
(4 @ 10’)
(5 @ 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
25
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 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
3. Example 1
Revision 1
Revision 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 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
UNITS CYCLES SECONDS
EIGENVALUE PARAMETERS
SOLVE USING GTSEL
FREQUENCY SPECS 0.0 TO 40.0
PRINT MAX
END
DYNAMIC ANALYSIS EIGENVALUE
DYNAMIC ANALYSIS EIGENVALUE
27
3. Example 1
Revision 1
$* **
$* ** 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
Revision 2
$* **
$* ** 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'
SUPPORT ACCELERATION
TRANSLATION Z 1.000000 FILE 'ELC-RS'
MODE FACTORS COMPUTE RIGID RESPONSE FZPA 40.0
END RESPONSE SPECTRUM LOAD
RESPONSE SPECTRUM LOAD 300
SUPPORT ACCELERATION
TRANSLATION Z 1.000000 FILE 'ELC-RS'
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 1.000000 FILE 'ELC-RS'
MODE FACTORS COMPUTE PERIODIC RESPONSE FZPA 40.0
END RESPONSE SPECTRUM LOAD
RESPONSE SPECTRUM LOAD ‘300P'
SUPPORT ACCELERATION
TRANSLATION Z 1.000000 FILE 'ELC-RS'
MODE FACTORS COMPUTE PERIODIC RESPONSE FZPA 40.0
END RESPONSE SPECTRUM LOAD
UNITS INCHES KIPS CYCLES
DAMPING RATIOS 0.05 100
SEC
PERFORM RESPONSE SPECTRUM ANALYSIS
UNITS INCHES KIPS CYCLES
DAMPING RATIOS 0.05 100
SEC
PERFORM RESPONSE SPECTRUM ANALYSIS
LOAD LIST ‘100R' ‘300P'
PRINT DYNAMIC LOAD DATA
28
3. Example 1
Revision 2
{
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
MODE
FACTOR
1
7
0.0000000E+00
0.2969909
.
.
.
0.8701187
0.9600146
1.000000
49
55
61
F2 =
MODE
2
8
50
56
62
27.2869854
FZPA =
FACTOR
MODE
0.7675107E-02
0.3068923
3
9
0.1194761
0.3864122
4
10
0.2027510
0.4034464
5
11
0.2507934
0.4294790
6
12
0.2800766
0.4493059
51
57
63
0.8862190
0.9722605
1.000000
52
58
64
0.8957242
0.9814596
1.000000
53
59
65
0.9050707
0.9869605
1.000000
54
60
66
0.9183331
0.9920438
1.000000
0.8760816
0.9641243
1.000000
FACTOR
40.0000000
MODE
FACTOR
MODE
FACTOR
MODE
FACTOR
--------------------------------------------------------------------------------------------------------------------LOADING - 100P
STATUS - ACTIVE
--------------------------------------------------------------------------------------------------------------------PERIODIC Response Modal Scaling (NRC Guide 1.92, Rev. 2, Combination Method A)
==============================================================================
F1 =
1.8609530
MODE
FACTOR
1
7
1.000000
0.9548803
.
.
.
0.4928423
0.2799498
0.0000000E+00
49
55
61
F2 =
MODE
2
8
50
56
62
27.2869854
FACTOR
0.9999706
0.9517443
0.4821628
0.2654511
0.0000000E+00
MODE
3
9
51
57
63
FZPA =
FACTOR
40.0000000
MODE
FACTOR
MODE
FACTOR
MODE
FACTOR
0.9928371
0.9223262
4
10
0.9792303
0.9150033
5
11
0.9680406
0.9030768
6
12
0.9599776
0.8933780
0.4632666
0.2339008
0.0000000E+00
52
58
64
0.4446102
0.1916690
0.0000000E+00
53
59
65
0.4252612
0.1609628
0.0000000E+00
54
60
66
0.3958085
0.1258933
0.0000000E+00
29
3. Example 1
Revision 2
Response Spectrum Loadings 100R and 100P
Mode # X mass %
------ -------3
83.0052
19
10.0467
24
0.4465
43
3.0879
45
0.5408
49
1.3443
51
0.3270
55
0.5741
57
0.1194
59
0.1003
61
0.1519
Total %100.0000
Active %100.0000
Freq (HZ)
--------2.56
7.84
8.69
13.54
14.34
19.25
20.10
24.51
25.32
26.35
28.32
α
------0.119
0.536
0.574
0.739
0.760
0.870
0.886
0.960
0.972
0.987
1.000
(1-α2)1/2
------0.993
0.844
0.819
0.674
0.649
0.493
0.463
0.280
0.234
0.161
0.000
F1 = 1.86 HZ
F2 = 27.29 HZ
(Modes having X mass participation ≥ 0.05% listed)
30
3. Example 1
Revision 1
Revision 2
$* **
$* ** 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
$* **
$* ** Compute rigid modal
$* **
LOAD LIST ‘100R’ ‘300R’
COMPUTE RESPONSE SPECTRUM
COMPUTE RESPONSE SPECTRUM
COMPUTE RESPONSE SPECTRUM
CREATE PSEUDO STATIC LOAD 'PS100' FROM CQC OF LOAD ‘100’
CREATE PSEUDO STATIC LOAD 'PS300' FROM CQC OF LOAD ‘300’
CREATE PSEUDO STATIC LOAD ‘PS100R’ FROM ALG OF LOAD ‘100R'
CREATE PSEUDO STATIC LOAD ‘PS300R’ FROM ALG OF LOAD ‘300R'
and combined rigid modal results
DISPL MODE COMBINATION ALG
FORCES MODE COMBINATION ALG
REACTIONS MODE COMBINATION ALG
$* **
$* ** 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
3. 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
$* **
$* ** 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 300 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
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 ‘PS100’ 1.0 ‘100M’ 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 ‘PS300’ 1.0 ‘300M’ 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 ‘100TOT’ 1.0 ‘300TOT’ 1.0
$* **
$* ** Compute total solution
$* **
CREATE LOAD COMBINATION ‘EQTOT’ TYPE RMS
SPECS ‘300TOT 1.0 ‘300TOT’ 1.0
-
-
32
3. Example 1
Revision 1
{
{
{
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
7
LOADING
/---------------------FORCE---------------------//--------------------MOMENT--------------------/
X FORCE
Y FORCE
Z FORCE
X MOMENT
Y MOMENT
Z MOMENT
GLOBAL
PS100
100M
100TOT
7.9233351
-0.0000028
7.9233351
0.8505948
0.0000031
0.8505948
0.0001352
0.0000000
0.0001352
0.0067266
-0.0000005
0.0067266
0.0101057
0.0000000
0.0101057
663.6497192
0.0001812
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
7
LOADING
/---------------------FORCE---------------------//--------------------MOMENT--------------------/
X FORCE
Y FORCE
Z FORCE
X MOMENT
Y MOMENT
Z MOMENT
GLOBAL
PS100R
100M
100RTOT
1.9317409
-0.0000028
1.9317381
-0.1624137
0.0000031
-0.1624106
-0.0000177
0.0000000
-0.0000177
-0.0008941
-0.0000005
-0.0008946
0.0009135
0.0000000
0.0009135
-156.4043427
0.0001812
-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
33
3. Example 1
Revision 1
{
{
{
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
7
LOADING
/---------------------FORCE---------------------//--------------------MOMENT--------------------/
X FORCE
Y FORCE
Z FORCE
X MOMENT
Y MOMENT
Z MOMENT
GLOBAL
100TOT
300TOT
EQTOT
7.9233351
0.0004739
7.9233351
0.8505948
8.5615606
8.6037102
0.0001352
7.4463096
7.4463096
0.0067266
541.7026978
541.7026978
0.0101057
0.0030473
0.0105552
663.6497192
0.0303222
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
7
LOADING
/---------------------FORCE---------------------//--------------------MOMENT--------------------/
X FORCE
Y FORCE
Z FORCE
X MOMENT
Y MOMENT
Z MOMENT
GLOBAL
100TOT
300TOT
EQTOT
8.0699682
0.0004690
8.0699682
0.8233045
8.5616188
8.6011124
0.0001148
7.4547424
7.4547424
0.0057191
542.3069458
542.3069458
0.0093221
0.0029606
0.0097810
674.8942871
0.0298751
674.8942871
34
3. Example 2
50.0 FT
(5 @ 10’)
X
X
190.0 FT
X
190.0 FT
(19 @ 10’)
(20 @ 10’)
Y
Z
X
Material Concrete
Columns: 18”x18”
Floor and Wall Panel Thicknesses: 12”
2520 Joints, 342 Members, 2670 Plate FEs
35
3. Example 2
Revision 2
Response Spectrum Loadings 100R and 100P
Mode #
-----.
.
.
25
26
34
48
67
74
96
111
112
.
.
.
245
255
263
266
268
389
419
836
850
851
X mass %
--------
Freq (HZ)
---------
α
--------
(1-α2)1/2
---------
(Total X mass particpation, modes 1-24 = 0.06%!)
1.4600
1.1638
13.5330
14.1142
0.9038
1.7794
22.5149
1.7086
1.3514
1.97
2.01
2.35
2.96
3.84
4.19
5.19
5.88
5.92
0.021
0.028
0.087
0.172
0.270
0.302
0.382
0.428
0.431
1.000
1.000
0.996
0.985
0.963
0.953
0.924
0.904
0.902
2.2235
1.8683
0.5092
0.8349
0.9019
1.0395
0.8794
0.7776
0.5940
0.7370
10.80
11.37
11.67
11.73
11.79
15.86
16.91
28.18
28.44
28.46
0.655
0.674
0.684
0.686
0.687
0.798
0.822
1.000
1.000
1.000
0.756
0.739
0.729
0.728
0.727
0.603
0.569
0.000
0.000
0.000
Total % 99.9411
Active % 99.9175
99.9997
99.9889
99.9486
99.9286
F1 = 1.86 HZ
F2 = 27.29 HZ
(f ≤ 40 HZ)
(mass participation ≥ 0.001%)
36
3. Example 2
Revision 1
{
{
{
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
21
LOADING
/---------------------FORCE---------------------//--------------------MOMENT--------------------/
X FORCE
Y FORCE
Z FORCE
X MOMENT
Y MOMENT
Z MOMENT
GLOBAL
PS100
100M
100TOT
55.4891853
0.0611252
55.4892197
51.0420609
-0.0009288
51.0420609
35.3468590
0.0170936
35.3468628
445.2986755
0.1989509
445.2987061
151.3651123
-0.1460913
151.3651733
903.9607544
0.5150789
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
21
LOADING
/---------------------FORCE---------------------//--------------------MOMENT--------------------/
X FORCE
Y FORCE
Z FORCE
X MOMENT
Y MOMENT
Z MOMENT
GLOBAL
PS100R
100M
100RTOT
35.0519829
0.0611252
35.1131058
7.9105206
-0.0009288
7.9095917
13.9957037
0.0170936
14.0127974
-163.2551575
0.1989509
-163.0562134
62.1802177
-0.1460913
62.0341263
-169.3596344
0.5150789
-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
3. Example 2
Revision 1
{
{
{
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
21
LOADING
/---------------------FORCE---------------------//--------------------MOMENT--------------------/
X FORCE
Y FORCE
Z FORCE
X MOMENT
Y MOMENT
Z MOMENT
GLOBAL
100TOT
300TOT
EQTOT
55.4892197
31.8329468
63.9717903
51.0420609
48.5689278
70.4573059
35.3468628
53.4435310
64.0750427
445.2987061
822.1765137
935.0214844
151.3651733
139.6783752
205.9647064
903.9608765
410.5592957
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
7
LOADING
/---------------------FORCE---------------------//--------------------MOMENT--------------------/
X FORCE
Y FORCE
Z FORCE
X MOMENT
Y MOMENT
Z MOMENT
GLOBAL
100TOT
300TOT
EQTOT
62.6293793
32.4566460
70.5398712
50.6817245
48.1798668
69.9280777
35.6329117
61.0580063
70.6950150
456.2272339
823.7388916
941.6416626
150.3090363
139.6220093
205.1514282
903.4033813
424.5520935
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.
40