GTStrudl Damping Models for Dynamic Analysis

1
GTStrudl Damping ModelsforDynamic Analysis
Michael H. Swanger, Ph.D. CASE Center Georgia Tech
2
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

3
Background
4
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
5
Simple Modal DampingFrequency-dependent Damping
Ratios Per NRC Reg. 1.61,March 2007
6
Simple Modal Damping
STORE RESPONSE SPECTRUM
Design Response Spectrum per FEMA 356
7
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
8
Weighted AverageComposite Modal Damping
9
Weighted AverageComposite Modal
DampingRecommended Modal Damping Values per NRC
Reg. 1.61, March 2007
10
Weighted AverageComposite 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

11
Weighted AverageComposite 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 Y coord
-------- -----------------
----------------- 1 X
0.00000 Y 0.00000 2 X
120.00000 Y 0.00000 . . .
18 X 240.00000 Y 360.00000
19 X 360.00000 Y 360.00000
20 X 480.00000 Y
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
12
Weighted AverageComposite Modal Damping
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 Response
spectrum analsis 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
MEMBER INCIDENCES Name Start joint
End joint -------- --------
-------- Columns 1
1 6 2 6
11 3 11 16
4 2
7 . . . 23 14
15 24 16 17
25 17 18
26 18 19 27
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'
13
Weighted AverageComposite 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
RS Analysis, 4 Uniform
TH Analysis, 4 Uniform
TH Analysis, No Damping
14
Weighted AverageComposite 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 Y coord
-------- -----------------
----------------- 1 X
0.00000 Y 0.00000 2 X
120.00000 Y 0.00000 . . .
18 X 240.00000 Y 360.00000
19 X 360.00000 Y 360.00000
20 X 480.00000 Y
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
15
Weighted AverageComposite Modal Damping
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 Response
spectrum analsis 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
MEMBER INCIDENCES Name Start joint
End joint -------- --------
-------- Columns 1
1 6 2 6
11 3 11 16
4 2
7 . . . 23 14
15 24 16 17
25 17 18
26 18 19 27
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'
16
Weighted AverageComposite 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
17
Rayleigh Proportional Damping
18
Rayleigh Proportional Damping
Classical Damping 5 at ? 3.16 Hz and 100 Hz
DAMPING PROPORTIONAL TO STIFFNESS 1.5271E-4 MASS
1.9238
Non-classical
Damping at ? 3.16 Hz and 100 Hz Beams and
columns 5 Supports
15
CONSTANTS RAYLEIGH DAMPING PROPORTIONAL TO
STIFFNESS 1.5271E-4 - MEMBERS GROUP LIST
'beams columns RAYLEIGH DAMPING
PROPORTIONAL TO MASS 1.9238 MEMBERS 6 TO 20
GROUP beams RAYLEIGH DAMPING PROPORTIONAL
TO MASS 5.7714 MEMBERS 1 TO 5 UNITS INCHES
KIPS JOINT RELEASES 1 TO 5 KFX 5.0 DFX
4.5813E-4
19
Rayleigh Proportional Damping
Classical Damping
TYPE PLANE FRAME XY MATERIAL STEEL OUTPUT LONG
NAME UNITS INCHES KIPS JOINT COORDINATES
Name X coord Y coord
-------- -----------------
----------------- 1 X
0.00000 Y 0.00000 2 X
120.00000 Y 0.00000 . . .
18 X 240.00000 Y 360.00000
19 X 360.00000 Y 360.00000
20 X 480.00000 Y
360.00000 DEFINE GROUP 'support' ADD JOINTS 1
to 5 STATUS SUPPORT JOINT GROUP 'support JOINT
RELEASES GROUP 'support' KFX 5.0
20
Rayleigh Proportional Damping
Classical Damping
MEMBER INCIDENCES Name Start joint
End joint -------- --------
-------- Columns 1
1 6 2 6
11 3 11 16
4 2
7 . . . 23 14
15 24 16 17
25 17 18
26 18 19 27
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 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
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
Rayleigh Damping, Classical, Physical Analysis
No Rayleigh Damping, Physical Analysis
Modal TH Analysis, 5 Uniform Damping
21
Rayleigh Proportional Damping
Non-classical Damping
TYPE PLANE FRAME XY MATERIAL STEEL OUTPUT LONG
NAME UNITS INCHES KIPS JOINT COORDINATES
Name X coord Y coord
-------- -----------------
----------------- 1 X
0.00000 Y 0.00000 2 X
120.00000 Y 0.00000 . . .
18 X 240.00000 Y 360.00000
19 X 360.00000 Y 360.00000
20 X 480.00000 Y
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
22
Rayleigh Proportional Damping
Non-classical Damping
MEMBER INCIDENCES Name Start joint
End joint -------- --------
-------- Columns 1
1 6 2 6
11 3 11 16
4 2
7 . . . 23 14
15 24 16 17
25 17 18
26 18 19 27
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 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
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'
23
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
24
The Viscous Damper Element
25
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)

26
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
27
General Composite Modal Damping
28
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 End
joint -------- -------- --------
Columns 1 1
6 2 6
11 . . . MEMBER PROPERTIES GROUP 'beams'
T 'WBEAM9' 'W18x35' MEMBER PROPERTIES GROUP
'columns' T 'WCOLUMN9' 'W14x53'
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
29
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 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
30
General Composite Modal Damping
DAMPING PROPORTIONAL TO STIFFN 1.5271E-4 MASS
1.9238 COMPUTE MODAL DAMPING RATIOS PROPORTIONAL
31
New Damping Models/Functions

• Direct Computation of Rayleigh Damping Ratios
• Caughey Damping

32
New Damping Models/Functions

• Superposition of Modal Damping Matrices