Transcript GTStrudl Modeling and Analysis Using 2-D and 3

GTStrudl Damping Models
for
Dynamic Analysis
Michael H. Swanger, Ph.D.
CASE Center
Georgia Tech
Topics
•
Background
•
Simple Modal Damping
•
Weighted Average Composite Modal Damping
•
Rayleigh Proportional Damping
•
The Viscous Damper Element
•
General Composite Modal Damping
•
New Damping Models/Functions
Background
Equations of Motion
Physical Reference Frame
[ M ]{U }  [C ]{U }  [ K ]{U }  {F (t )}
Modal Reference Frame
i  (2 ii ) i  i 2i  i (t )
2 ii  {i }T [C]{i }
Simple Modal Damping
DAMPING RATIOS 0.05 5 0.03 7 0.02 10
TRANSIENT LOAD ‘TH1’
SUPPORT ACCELERATION
TRANSLATION X FILE ‘ELCENTRO’
INTEGRATE FROM 0.0 TO 55.0 AT 0.01
END
LOAD LIST ‘TH1’
PERFORM TRANSIENT ANALYSIS
RESPONSE SPECTRUM LOAD ‘RS1’
SUPPORT ACCELERATION
TRANSLATION X 1.0 FILE ‘RSCurve1’
END
LOAD LIST ‘RS1’
PERFORM RESPONSE SPECTRUM ANALYSIS
Simple Modal Damping
Frequency-dependent Damping Ratios Per NRC Reg. 1.61,
March 2007
Simple Modal Damping
STORE RESPONSE SPECTRUM …
Design Response Spectrum per FEMA 356
Simple Modal Damping
UNITS
IN LBS CYC SEC StdMASS
CREATE RESPONSE SPECTRUM ACCELERATION LINEAR VS FREQUENCY LINEAR FILE 'RS1‘
FREQUENCY RANGE FROM 0.10000 TO 40.00000 AT 0.10000
DAMPING RATIOS 0.01 0.06 0.15
USE ACCELERATION TIME HISTORY FILES 'ELCENTRO'
INTEGRATE USING DUHAMEL
DIVISOR 20.00000
END OF CREATE RESPONSE SPECTRUM
Weighted Average
Composite Modal Damping
 Ki 
Mi
{i }T [CK ]{i }

2
i
,
{i }T [CM ]{i }

,
1
[CK ] 
[CM ] 
# elements

j 1
 j [k j ]
# elements

j 1
 j [m j ]
 j and  j are appropriate modal damping ratios
 Ri  f K  Ki  f M  Mi
Weighted Average
Composite Modal Damping
Recommended Modal Damping Values per NRC Reg. 1.61,
March 2007
Weighted Average
Composite Modal Damping
UNITS INCHES KIPS
JOINT RELEASES
GROUP 'support' KFX 5.0 DFX 0.04
INERTIA OF JOINTS WEIGHT
EXISTING TRANSL ALL 0.5 DAMPING 0.04
CONSTANTS
MODAL DAMPING PROPORTIONAL TO STIFFNESS 0.04 MEMBERS GROUP 'beams'
MODAL DAMPING PROPORTIONAL TO STIFFNESS 0.04 MEMBERS GROUP 'columns‘
•
•
•
eigenvalue analysis
•
•
•
DYNAMIC PARAMETERS
RESPONSE DAMPING STIFFNESS 1.0 MASS 0.0
END
COMPUTE MODAL DAMPING RATIOS AVERAGE
Weighted Average
Composite Modal Damping
Uniform Damping, Damping Ratios:
All Components 4%
TYPE PLANE FRAME XY
MATERIAL STEEL
OUTPUT LONG NAME
UNITS INCHES KIPS
JOINT COORDINATES
$
Name
X coord
$
-----------------------1
X
0.00000
2
X
120.00000
.
.
.
18
X
240.00000
19
X
360.00000
20
X
480.00000
Y coord
----------------Y
0.00000
Y
0.00000
Y
Y
Y
360.00000
360.00000
360.00000
DEFINE GROUP 'support' ADD JOINTS 1 to 5
STATUS SUPPORT JOINT GROUP 'support'
$* **
$* ** Modal damping ratio for spring support
$* ** stiffnesses
$* **
JOINT RELEASES
GROUP 'support' KFX 5.0 DFX 0.04
Weighted Average
Composite Modal Damping
MEMBER INCIDENCES
$
Name
Start joint
$
--------------$
Columns
1
1
2
6
3
11
4
2
.
.
.
23
14
24
16
25
17
26
18
27
19
End joint
-------6
11
16
7
15
17
18
19
20
DEFINE GROUP 'columns' ADD MEMBERS 1 TO 15
DEFINE GROUP 'beams'
ADD MEMBERS 16 TO 27
MEMBER PROPERTIES
GROUP 'beams'
T 'WBEAM9' 'W18x35'
MEMBER PROPERTIES
GROUP 'columns' T 'WCOLUMN9' 'W14x53'
$* **
$* ** Damping ratios for member structural
$* ** stiffness damping
$* **
CONSTANTS
MODAL DAMPING PROPORTIONAL TO STIFFNESS 0.04 MEMBERS GROUP 'beams'
MODAL DAMPING PROPORTIONAL TO STIFFNESS 0.04 GROUP 'columns'
$* **
$* ** Eigenvalue analysis
$* **
INERTIA OF JOINTS LUMPED
INERTIA OF JOINTS WEIGHT
EXISTING TRANSL ALL 0.5
EIGENVALUE PARAMETERS
SOLVE USING GTLANCZOS
NUMBER OF MODES 20
PRINT MAX
END
DYNAMIC ANALYSIS EIGENVALUE
$* **
$* ** Compute weighted average composite modal
$* ** damping ratios
$* **
DYNAMIC PARAMETERS
RESPONSE DAMPING STIFFNESS 1.0
END
COMPUTE MODAL DAMPING RATIOS AVERAGE
{i} [C]{i}
T
 

i
$* **
2
$* ** Response spectrum analsis
i
$* **
UNITS INCHES CYCLES
CREATE RESPONSE SPECTRUM ACCELERATION LIN VS FREQUENCY LIN FILE 'RS'
FREQUENCY RANGE FROM 1.00000 TO 40.00000 AT 1.00000
DAMPING RATIOS 0.04
USE ACCELERATION TIME HISTORY FILES 'ELCENTRO'
INTEGRATE USING DUHAMEL
DIVISOR 20.00000
END OF CREATE RESPONSE SPECTRUM
Weighted Average
Composite Modal Damping
RESPONSE SPECTRUM LOAD 'RS1'
SUPPORT ACCELERATION
TRANSLATION X 1.0 FILE 'RS'
END
RS Analysis, 4% Uniform
PERFORM RESPONSE SPECTRUM ANALYSIS
COMPUTE RESPONSE SPECTRUM DISPLACEMENTS
OUTPUT MODAL CONTRIBUTIONS ON
LIST RESPONSE SPECTRUM DISPL JOINT 16
$* **
$* ** Mode superposition transient analysis
$* **
TRANSIENT LOAD ‘TH1’
SUPPORT ACCELERATION
TRANSLATION X FILE ‘ELCENTRO’
INTEGRATE FROM 0.0 TO 10.0 AT 0.01
END
PERFORM TRANSIENT ANALYSIS
LIST TRANSIENT MAX DISPL JOINT 16
TH Analysis, 4% Uniform
TH Analysis, No Damping
Weighted Average
Composite Modal Damping
Damping Ratios (non-uniform):
Beams 5%, Columns 3%, Foundation 10%
TYPE PLANE FRAME XY
MATERIAL STEEL
OUTPUT LONG NAME
UNITS INCHES KIPS
JOINT COORDINATES
$
Name
X coord
$
-----------------------1
X
0.00000
2
X
120.00000
.
.
.
18
X
240.00000
19
X
360.00000
20
X
480.00000
Y coord
----------------Y
0.00000
Y
0.00000
Y
Y
Y
360.00000
360.00000
360.00000
DEFINE GROUP 'support' ADD JOINTS 1 to 5
STATUS SUPPORT JOINT GROUP 'support'
$* **
$* ** Modal damping ratio for spring support
$* ** stiffnesses
$* **
JOINT RELEASES
GROUP 'support' KFX 5.0 DFX 0.10
Weighted Average
Composite Modal Damping
MEMBER INCIDENCES
$
Name
Start joint
$
--------------$
Columns
1
1
2
6
3
11
4
2
.
.
.
23
14
24
16
25
17
26
18
27
19
End joint
-------6
11
16
7
15
17
18
19
20
DEFINE GROUP 'columns' ADD MEMBERS 1 TO 15
DEFINE GROUP 'beams'
ADD MEMBERS 16 TO 27
MEMBER PROPERTIES
GROUP 'beams'
T 'WBEAM9' 'W18x35'
MEMBER PROPERTIES
GROUP 'columns' T 'WCOLUMN9' 'W14x53'
$* **
$* ** Damping ratios for member structural
$* ** stiffness damping
$* **
CONSTANTS
MODAL DAMPING PROPORTIONAL TO STIFFNESS 0.05 MEMBERS GROUP 'beams'
MODAL DAMPING PROPORTIONAL TO STIFFNESS 0.03 GROUP 'columns'
$* **
$* ** Eigenvalue analysis
$* **
INERTIA OF JOINTS LUMPED
INERTIA OF JOINTS WEIGHT
EXISTING TRANSL ALL 0.5
EIGENVALUE PARAMETERS
SOLVE USING GTLANCZOS
NUMBER OF MODES 20
PRINT MAX
END
DYNAMIC ANALYSIS EIGENVALUE
$* **
$* ** Compute weighted average composite modal
$* ** damping ratios
$* **
DYNAMIC PARAMETERS
RESPONSE DAMPING STIFFNESS 1.0
END
COMPUTE MODAL DAMPING RATIOS AVERAGE
{i} [C]{i}
T
 

i
$* **
2
$* ** Response spectrum analsis
i
$* **
UNITS INCHES CYCLES
CREATE RESPONSE SPECTRUM ACCELERATION LIN VS FREQUENCY LIN FILE 'RS'
FREQUENCY RANGE FROM 1.00000 TO 40.00000 AT 1.00000
DAMPING RATIOS 0.01 0.07 0.15
USE ACCELERATION TIME HISTORY FILES 'ELCENTRO'
INTEGRATE USING DUHAMEL
DIVISOR 20.00000
END OF CREATE RESPONSE SPECTRUM
Weighted Average
Composite Modal Damping
RESPONSE SPECTRUM LOAD 'RS1'
SUPPORT ACCELERATION
TRANSLATION X 1.0 FILE 'RS'
END
PERFORM RESPONSE SPECTRUM ANALYSIS
COMPUTE RESPONSE SPECTRUM DISPLACEMENTS
OUTPUT MODAL CONTRIBUTIONS ON
LIST RESPONSE SPECTRUM DISPL JOINT 16
$* **
$* ** Mode superposition transient analysis
$* **
TRANSIENT LOAD ‘TH1’
SUPPORT ACCELERATION
TRANSLATION X FILE ‘ELCENTRO’
INTEGRATE FROM 0.0 TO 10.0 AT 0.01
END
PERFORM TRANSIENT ANALYSIS
LIST TRANSIENT MAX DISPL JOINT 16
WtAvgCMD, Non-Uniform, KFX = 50 k
WtAvgCMD, Non-Uniform, KFX = 1 k
Rayleigh Proportional Damping
[ M ]{U }  [C ]{U }  [ K ]{U }  {F (t )}
[C ]  a0 [ M ]  b0 [ K ]
n 
a0 1
b
 0 n
2 n
2
 i 
1 1 i i  a0 
1        
2 j
j   b0 
 j
a0  
2i j
i   j
b0  
2
i   j
Rayleigh Proportional Damping
Classical Damping = 5% at ω = 3.16 Hz and 100 Hz
DAMPING PROPORTIONAL TO STIFFNESS 1.5271E-4 MASS 1.9238
Non-classical
Damping at ω =3.16 Hz and 100 Hz
Beams and columns
5%
Supports
15%
CONSTANTS
RAYLEIGH DAMPING PROPORTIONAL TO
MEMBERS GROUP LIST 'beams‘
RAYLEIGH DAMPING PROPORTIONAL TO
RAYLEIGH DAMPING PROPORTIONAL TO
UNITS INCHES KIPS
JOINT RELEASES
1 TO 5 KFX 5.0 DFX 4.5813E-4
STIFFNESS 1.5271E-4 ‘columns’
MASS 1.9238 MEMBERS 6 TO 20 GROUP ‘ beams’
MASS 5.7714 MEMBERS 1 TO 5
Rayleigh Proportional Damping
Classical Damping
TYPE PLANE FRAME XY
MATERIAL STEEL
OUTPUT LONG NAME
UNITS INCHES KIPS
JOINT COORDINATES
$
Name
X coord
$
-----------------------1
X
0.00000
2
X
120.00000
.
.
.
18
X
240.00000
19
X
360.00000
20
X
480.00000
Y coord
----------------Y
0.00000
Y
0.00000
Y
Y
Y
DEFINE GROUP 'support' ADD JOINTS 1 to 5
STATUS SUPPORT JOINT GROUP 'support‘
JOINT RELEASES
GROUP 'support' KFX 5.0
360.00000
360.00000
360.00000
Rayleigh Proportional Damping
Classical Damping
MEMBER INCIDENCES
$
Name
Start joint
$
--------------$
Columns
1
1
2
6
3
11
4
2
.
.
.
23
14
24
16
25
17
26
18
27
19
End joint
-------6
11
16
7
15
17
18
19
20
$* **
$* ** Perform direct integration time history
$* ** analysis
$* **
UNITS INCHES CYCLES
TRANSIENT LOAD 'T1'
SUPPORT ACCELERATION
TRANSLATION X FILE ‘ELCENTRO’
INTEGRATE FROM 0.0 TO 10.0 AT 0.01
END
DYNAMIC ANALYSIS PHYSICAL NEWMARK BETA 0.25
LIST TRANSIENT MAX DISPL JOINTS 1 16
DEFINE GROUP 'columns' ADD MEMBERS 1 TO 15
DEFINE GROUP 'beams'
ADD MEMBERS 16 TO 27
MEMBER PROPERTIES
GROUP 'beams'
T 'WBEAM9' 'W18x35'
MEMBER PROPERTIES
GROUP 'columns' T 'WCOLUMN9' 'W14x53‘
INERTIA OF JOINTS LUMPED
INERTIA OF JOINTS WEIGHT
EXISTING TRANSL ALL 0.5
$* **
$* ** Rayleigh proportional damping for
$* ** structural damping at 0.05 for
$* ** w = 19.84 rad/sec (3.16 Hz) and
$* ** 635 rad/sec (100 Hz)
$* **
DAMPING PROPORTIONAL TO STIFFNESS 1.5271E-4
MASS 1.9238
Rayleigh Damping, Classical, Physical Analysis
No Rayleigh Damping, Physical Analysis
Modal TH Analysis, 5% Uniform Damping
Rayleigh Proportional Damping
Non-classical Damping
TYPE PLANE FRAME XY
MATERIAL STEEL
OUTPUT LONG NAME
UNITS INCHES KIPS
JOINT COORDINATES
$
Name
X coord
$
-----------------------1
X
0.00000
2
X
120.00000
.
.
.
18
X
240.00000
19
X
360.00000
20
X
480.00000
Y coord
----------------Y
0.00000
Y
0.00000
Y
Y
Y
360.00000
360.00000
360.00000
DEFINE GROUP 'support' ADD JOINTS 1 to 5
STATUS SUPPORT JOINT GROUP 'support‘
$* **
$* ** Rayleigh damping factor for spring support
$* ** stiffnesses corresponding to 15% damping in
$* ** the support for w = 19.84 rad/sec (3.16 Hz) and
$* ** 635 rad/sec (100 Hz)
$* **
JOINT RELEASES
GROUP 'support' KFX 5.0 DFX 4.5813E-4
Rayleigh Proportional Damping
Non-classical Damping
MEMBER INCIDENCES
$
Name
Start joint
$
--------------$
Columns
1
1
2
6
3
11
4
2
.
.
.
23
14
24
16
25
17
26
18
27
19
End joint
-------6
11
16
7
15
17
18
19
20
DEFINE GROUP 'columns' ADD MEMBERS 1 TO 15
DEFINE GROUP 'beams'
ADD MEMBERS 16 TO 27
MEMBER PROPERTIES
GROUP 'beams'
T 'WBEAM9' 'W18x35'
MEMBER PROPERTIES
GROUP 'columns' T 'WCOLUMN9' 'W14x53‘
CONSTANTS
RAYLEIGH DAMPING PROPORTIONAL TO MASS 5.7714
MEMBERS 1 TO 5
RAYLEIGH DAMPING PROPORTIONAL TO MASS 1.9238
MEMBERS 6 TO 15 GROUP 'beams'
-
$* **
$* ** Rayleigh damping for member stiffnesses at 5%
$* ** for w = 19.84 rad/sec (3.16 Hz) and
$* ** 635 rad/sec (100 Hz)
$* **
CONSTANTS
RAYLEIGH DAMPING PROPORTIONAL TO STIFFNESS 1.5271E-4 GROUP LIST 'beams' 'columns'
INERTIA OF JOINTS LUMPED
INERTIA OF JOINTS WEIGHT
EXISTING TRANSL ALL 0.5
$* **
$* ** Rayleigh damping factors for joint and member
$* ** inertias corresponding to 15% damping in the
$* ** support and 5% elsewhere for w = 19.84 rad/sec
$* ** (3.16 Hz) and 635 rad/sec (100 Hz)
$* **
INERTIA OF JOINTS WEIGHT
1 to 5 TRANSL ALL 0.5 DAMPING 5.7714
6 TO 20 TRANSL ALL 0.5 DAMPING 1.9238
Rayleigh Proportional Damping
Non-classical Damping
$* **
$* ** Perform direct integration time history
$* ** analysis
$* **
UNITS INCHES CYCLES
TRANSIENT LOAD 'TH1'
SUPPORT ACCELERATION
TRANSLATION X FILE 'ELCENTRO'
INTEGRATE FROM 0.0 TO 10.0 AT 0.01
END
DYNAMIC ANALYSIS PHYSICAL NEWMARK BETA 0.25
LIST TRANS MAX DISPL JOINT 1 16
Rayleigh Damping, Non-Classical, Physical Analysis
Rayleigh Damping, Classical, Physical Analysis
The Viscous Damper Element
DAMPER ELEMENT (DATA)
iD 
iS 
  INCIDENCES  
' aD'
' aS'
[CTX] vCTX [CTY]
iE    GLOBAL 
(  ) 
 
' aE'  LOCAL 
vCTY [CTZ] vCTZ [CRX] vCRX [CRY] vCRY [CRZ] vCRZ



iD 
iS  iE    GLOBAL 
  INCIDENCES   (  ) 
 
' aD'
' aS' ' aE'  LOCAL 
[CTX] vCTX [CTY] vCTY [CTZ] vCTZ [CRX] vCRX [CRY] vCRY [CRZ] vCRZ
END (OF DAMPER ELEMENT DATA)
PRINT DAMPER (ELEMENT DATA)
iD 
DELETE DAMPER (ELEMENT DATA)  ...
' aD'
iD 
 
' aD'
The Viscous Damper Element
•
•
•
MEMBER PROPERTIES
GROUP 'beams'
T 'WBEAM9' 'W18x35'
MEMBER PROPERTIES
GROUP 'columns' T 'WCOLUMN9' 'W14x53‘
INERTIA OF JOINTS LUMPED
INERTIA OF JOINTS WEIGHT
EXISTING TRANSL ALL 0.5
$* **
$* ** Rayleigh proportional damping for
$* ** structural damping at 0.05 for
$* ** w = 19.84 rad/sec (3.16 Hz) and
$* ** 635 rad/sec (100 Hz)
$* **
DAMPING PROPORTIONAL TO STIFFNESS 1.5271E-4
MASS 1.9238
$* **
$* ** Viscous damper
$* **
DAMPING ELEMENT DATA
'DE1' INC 1 GLOBAL
'DE2' INC 2 GLOBAL
'DE3' INC 3 GLOBAL
'DE4' INC 4 GLOBAL
'DE5' INC 5 GLOBAL
END
elements at supports
CTX
CTX
CTX
CTX
CTX
1.E4
1.E4
1.E4
1.E4
1.E4
-
The Viscous Damper Element
$* **
$* ** Perform direct integration time history
$* ** analysis
$* **
UNITS INCHES CYCLES
TRANSIENT LOAD 'TH1'
SUPPORT ACCELERATION
TRANSLATION X FILE 'ELCENTRO'
INTEGRATE FROM 0.0 TO 10.0 AT 0.01
END
DYNAMIC ANALYSIS PHYSICAL NEWMARK BETA 0.25
LIST TRANS MAX DISPL JOINT 16
Viscous Damping, CTX = 1.e7 lb
Viscous Damping, CTX = 100 lb
General Composite Modal Damping
[ M ]{U }  [C ]{U }  [ K ]{U }  {F (t )}
i  (2 ii ) i  i 2i  i (t )
2 ii  {i }T C {i }
i 
{i }T C {i }
2i i
General Composite Modal Damping
.
.
.
DEFINE GROUP 'support' ADD JOINTS 1 to 5
STATUS SUPPORT JOINT GROUP 'support'
JOINT RELEASES
GROUP 'support' KFX 5.0
MEMBER INCIDENCES
$
Name
Start joint
$
--------------$
Columns
1
1
2
6
.
.
.
End joint
--------
MEMBER PROPERTIES
GROUP 'beams'
T 'WBEAM9' 'W18x35'
MEMBER PROPERTIES
GROUP 'columns' T 'WCOLUMN9' 'W14x53'
6
11
$* **
$* ** Define damping properties for modal
$* ** damping ratio computation:
$* ** Rayleigh damping factors for structural
$* ** damping at 0.05 for w = 19.4 rad/sec (3.16 Hz)
$* ** and 635 rad/sec (100 Hz)
$* **
DAMPING PROPORTIONAL TO STIFFN 1.5271E-4 MASS 1.9238
$* **
$* ** Viscous damper elements at supports
$* **
DAMPING ELEMENT DATA
'DE1' INC 1 GLOBAL CTX 1.E4
'DE2' INC 2 GLOBAL CTX 1.E4
'DE3' INC 3 GLOBAL CTX 1.E4
'DE4' INC 4 GLOBAL CTX 1.E4
'DE5' INC 5 GLOBAL CTX 1.E4
END
PRINT DAMPING ELEMENT DATA
$* **
$* ** Eigenvalue analysis
$* **
INERTIA OF JOINTS LUMPED
INERTIA OF JOINTS WEIGHT
EXISTING TRANSL ALL 0.5
EIGENVALUE PARAMETERS
SOLVE USING GTLANCZOS
NUMBER OF MODES 20
PRINT MAX
END
DYNAMIC ANALYSIS EIGENVALUE
General Composite Modal Damping
$* **
$* ** Compute modal damping ratios assuming
$* ** classical proportional damping
$* **
COMPUTE MODAL DAMPING RATIOS PROPORTIONAL INCLUDE COUPLING ALL
$* **
$* ** Mode superposition transient analysis
$* **
UNITS INCHES CYCLES
TRANSIENT LOAD 'TH1'
SUPPORT ACCELERATION
TRANSLATION X FILE 'ELCENTRO'
INTEGRATE FROM 0.0 TO 10.0 AT 0.01
END
{i} [C]{i}
i 
2i
T
PERFORM TRANSIENT ANALYSIS
LIST TRANSIENT MAX DISPL JOINT 16
DYNAMIC ANALYSIS PHYSICAL NEWMARK BETA 0.25
LIST TRANS MAX DISPL JOINT 16
General Composite modal damping, No CTX
General Composite modal damping, CTX = 1.e7 lb
General Composite modal damping, CTX = 100 lb
General Composite Modal Damping
DAMPING PROPORTIONAL TO STIFFN 1.5271E-4 MASS 1.9238
COMPUTE MODAL DAMPING RATIOS PROPORTIONAL
i 
{i }T [C ]{i }
2i
i 
1.5271e4i
1.9238

2i
2
Damping Ratio vs Frequency (Hz)
0.120
Damping Ratio
0.100
0.080
0.060
0.040
0.020
0.000
0.0
50.0
100.0
150.0
Frequency (Hz)
200.0
250.0
New Damping Models/Functions
1. Direct Computation of “Rayleigh” Damping Ratios
i 
a0
a
 1 i
2i
2
2. Caughey Damping
N 1
j
[C ]  [ M ] a j [ M ]1[ K ] , N  # of DOFs
j 0
1 J 1
 i   ali2l 1 , J  # of modes in some selection of modes
2 l 1
New Damping Models/Functions
3. Superposition of Modal Damping Matrices
 N 2 ii

[C ]  [M ]  
{i }{i }T  [M ], N  # of modes
 i 1 1
