adaptive nonlinear analysis as applied to performance based earthquake engineering dr. erol kalkan,...
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Adaptive Nonlinear Analysis as Applied to Performance based Earthquake Engineering
Dr. Erol Kalkan, P.E. United States Geological SurveyTUFTS, 2008
Dr. E. Kalkan Slide: 2/53
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This study is based on a paper published in theJournal of Structural Engineering,
and winner of the 2008 ASCE Raymond Reese Research
Award
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Outline
• Seismic Analysis Methods of Structures• Nonlinear Static Analysis
– Fundamental Theory– Conventional Methods (FEMA and ATC)– Limitations
• Adaptive Nonlinear Static Analysis– Methodology Developed– Comparative Results
• Summary & Conclusions
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• Linear static procedures• Equivalent static analysis
• Linear dynamic procedures• Modal analysis • Direct time-history analysis
• Nonlinear static analysis - Nonlinear static procedures (NSPs)
• Capacity spectrum analysis (ATC-40, FEMA-440)• Displacement coefficients method (FEMA-273-274,356,440)
- Improved NSPs• Modal pushover analysis (MPA) (Chopra & Goel, 2002)• Adaptive Modal Combination (AMC) (Kalkan & Kunnath, 2006)
• Nonlinear dynamic analysis
Seismic Analysis Methods of Structures
Most common in routine applications
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Nonlinear Static Analysis
Conceptual Theory&
Current Practice
Dr. E. Kalkan Slide: 6/55
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g. Multi-degree-of-freedom (MDF) system
seismic behavior can be approximated with certain accuracy
by equivalent SDF systems.
Equivalent SDF (ESDF) system properties are computed by conducting pushover analyses…
Dr. E. Kalkan Slide: 7/53
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Conventional Nonlinear Static (Pushover) Analysis Choose height-wise distribution of lateral forces Monotonically increase lateral forces till the “control node” reaches a
“target displacement” i.e., increasing load factor while fixing load pattern.
Develop pushover (capacity) curve: Plot of base shear vs. roof displacement
ur
Vb
Dr. E. Kalkan Slide: 8/55
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g. Summary of Nonlinear Static Analysis
VV
V
InelasticInelasticSDF SystemSDF System
Target Displacementof MDF System ut
ut
uj
j
Capacity estimation at Capacity estimation at target displacementtarget displacement
Pushover AnalysisPushover Analysis
Participation Participation Factor, Factor, nn
Dn
Fsn/Ln
ESD System ESD System Force-Deformation RelationForce-Deformation Relation
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Fundamental Assumptions:
• The response of the multi-degree-of-freedom (MDF) structure can be related to the response of an equivalent SDF system, implying that the response is controlled by a single mode and this mode shape remains unchanged even after yielding occurs.
• The invariant lateral force distribution can represent and bound the distribution of inertia forces during an earthquake.
Dr. E. Kalkan Slide: 10/55
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Two Important Components of Nonlinear Static Analysis
Dr. E. Kalkan Slide: 11/55
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*
*1
*
*
Uniform:
First Mode :
ELF : 1 2
SRSS : from story shears
j j
j j j
kj j j
j
s m
s m
s m h k to
s
ELF and SRSS distributions intended to consider higher mode responses
Height-wise Distribution of Lateral Forces: FEMA Recommendations
Dr. E. Kalkan Slide: 12/53
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g. FEMA Recommended Force
Distributions
Each force distribution pushes all floors in same direction
Dr. E. Kalkan Slide: 13/53
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Initial Yielding Initial Yielding
Initial Yielding Initial Yielding
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Two Important Components of Nonlinear Static Analysis
Dr. E. Kalkan Slide: 15/53
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Eq
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g. Target Displacement Estimation
(Displacement Coefficient Method)
2
0 24e
t inel A
Tu C C S u
f
Elastic SDF System
u
f
Inelastic SDF System
u
f
Inelastic MDF System
C0 = Constant to relate elastic deformation of SDF and MDF system
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Dr. E. Kalkan Slide: 16/55
Displacement Coefficient Method
FEMA-356: Cinel =C1C2C3
• C1 = Ratio of inelastic and elastic SDF systems
• C2 = Constant to account for effects of pinching, stiffness degradation, and strength deterioration
• C3 = Constant to account for P-Delta effects
ASCE-41: Cinel = C1C2
• C1 = Ratio of inelastic and elastic SDF systems
• C2 = Constant to account for cyclic degradation of stiffness and strength
• Upper limit on R to avoid dynamic instability
Dr. E. Kalkan Slide: 17/53
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Eq
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g. Capacity Spectrum Method
0 ( , )t D eq equ C S T
u
f
Inelastic MDF System
u
f
Equivalent Linear Elastic SDF System
Teq, eq
u
f
Inelastic SDF System
Dr. E. Kalkan Slide: 18/55
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Capacity Spectrum Method – Equivalent Damping Concept
1
1 110.05
1
eq o
eq
T T
For bilinear systems
Requires iterations to compute Teq and eq
because of unknown ductility (uinel / uelas)
10.05
4D
eqSo
E
E
Teq= Tsec
Sd
Sa
ESo
ED
Dr. E. Kalkan Slide: 19/55
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FEMA-440 Capacity Spectrum Method
2 3
2
2
1 1 ; 4.0
1 ; 4.0 6.5
1 1; 6.5
1
eq o
o
eqo
o
A B
C D
F TE
TF
A to K = Constants that depend on hysteretic behavior and post-yield stiffness ratio
2 31 1 1 ; 4.0
1 1 ; 4.0 6.5
-1K 1 1 ; 6.5
1+L 2
eq o
o
o
T G H T
I J T
T
Dr. E. Kalkan Slide: 20/53
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g. Limitations of Conventional (FEMA
& ATC) Nonlinear Static Analysis Procedures
> Restricted to single mode response, can be reliably apply to 2D response of low-rise structures in regular plan.
> Gives erroneous results in case of:Higher Mode EffectsPlan Irregularities (i.e., Torsion, Vertical
Irregularities)
> No established procedure for 3D pushover analysis yet.
Adaptive Nonlinear Analysis
Dr. E. Kalkan Slide: 22/53
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Adaptive Pushover – Basic Concept
Dr. E. Kalkan Slide: 23/53
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0
1
2
3
4
5
6
Sto
ry L
ev
el
Elastic
St-1
St-2
St-3
St-4,5
St-6
Mode-1 Mode-2 Mode-3
Progressive Change in Modal Shapes
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T=10.6 sec T=8.44 sec T=11.24 sec T=8.96 sec T=8.96 sec T=8.86 sec
0
1
2
3
4
5
6
-2 -1 0 1 2
Inertia Forces (%W)
Sto
ry L
evel
Story-1
-2 -1 0 1 2
Inertia Forces (%W)
Story-2
-2 -1 0 1 2
Inertia Forces (%W)
Story-3
-2 -1 0 1 2
Inertia Forces (%W)
Story-4
-2 -1 0 1 2
Inertia Forces (%W)
Story-5
-2 -1 0 1 2
Inertia Forces (%W)
Story-6
Instantaneous inertia profiles when story maxima take place
Dr. E. Kalkan Slide: 25/53
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g. Adaptive Modal Combination (AMC)
(Kalkan & Kunnath, 2006)
>Basic Elements of the Procedure• Establishing Target Displacement: An energy-based procedure is used
in conjunction with inelastic displacement spectra at a set of pre-determined ductility levels to progressively establish the target displacement as the modal pushover analysis proceeds.
• Dynamic Target Point: This concept is analogous to the performance point in CSM, however, it represents a more realistic representation of demand since inelastic spectra are used to target this demand point.
• Adaptive Modal Combination: The method recognizes the need to alter the applied lateral load patterns as the system characteristics change yet retain the simplicity of combining the response measures at the end of the analysis.
Dr. E. Kalkan Slide: 26/53
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Energy Based Incremental Modal Displacement
> The basic limitation of current non-adaptive procedures is that elastic modal properties are used to compute the inelastic system parameters
> This approach may necessitate several iterations for convergence of target displacement computed from inelastic dynamic analysis.
> The roof displacement is approximated from the maximum deformation of an ESDF system. Such an approach is only meaningful for the first mode, while for higher modes, the roof displacement does not proportionally change with the other story deformations
Dr. E. Kalkan Slide: 27/53
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Energy-based ESDF system representation of nth-mode MDF system capacity curve
Roof Displacement, u r,n
Bas
e S
hea
r, V
b,n
F 1(i)
F 2(i)
F 3(i)
d 3(i)
d 2(i)
d 1(i)
Forces
(sn(i))
( ) ( ) ( ) ( ), , , ,
1,3 1,3
( ) / ( )i i i id n n n j n j n j
j j
S D F d F
d 3(i)
Capacitycurve
(i-1)
(i)
(i)(i-1)
ur,n(i)ur,n
(i-1)
Spectral Displacement, S d,n
Sp
ectr
al A
ccel
erat
ion
, S
a,n
D n(i)
wn
(i)
n
(i)
,,
b na n
n
VS
W
D n(i)
Tn
(elastic)
wn
(i)) 2
Capacity spectrum
MDF Level
SDF Level
Dr. E. Kalkan Slide: 28/53
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g. Performance point evaluation using system
ductility through a set of inelastic spectra
Spectral Displacement, S d,n
Sp
ectr
al A
ccel
erat
ion
, S a
,n
wn
(i)
n
(i)
wn
(ip)) 2Global Yield
( ),yieldd nS
( ),ipd nS
With computed system ductility, ( )ipn
Tn
(elastic)
Tn
(ip)
( ),( )
( ),
ipd nip
n yieldd n
S
S
Spectral Displacement, S d,n
Sp
ectr
al A
ccel
erat
ion
, S a
,n
( )ipn
Dynamic Target Point
Inelastic phase, period elongation
Tn
(elastic)T
n(ip)
Inelastic Demand Spectra plotted at different ductility levels
M odal CapacityCurve
Capacity Side
DemandSide
Dr. E. Kalkan Slide: 29/53
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the AMC procedure
0.0
0.1
0.2
0 5 10 15 20 25 30 35 40
Spectral Displacement, S d (cm)
Sp
ec
tra
l Ac
ce
lera
tio
n, S
a (g
)
T1(1)
w 12
Mode-1
Global Yield
( ),1yielddS
( ),1ipdS
T1(ip)
( )1 1.6ip
0.0
0.1
0.2
0.3
0.4
0.5
0 10 20 30 40 50
Spectral Displacement, S d (cm)
Sp
ec
tra
l Ac
ce
lera
tio
n, S
a (g
)
= 1.0
2.0
1.5
0.0
0.1
0.2
0.3
0.4
0.5
0 10 20 30 40 50
Spectral Displacement, S d (cm)
Sp
ec
tra
l Ac
ce
lera
tio
n, S
a (g
)
Dynamic TargetPoint
1.5
0.0
0.2
0.4
0.6
0.8
1.0
0 5 10 15 20 25 30 35
Spectral Displacement, S d (cm)
Sp
ec
tra
l Ac
ce
lera
tio
n, S
a (g
)
T2(1)
w 22
Mode-2
Global Yield
( ),2yielddS
( ),2ipdS
T2(ip)
( )2 1.5ip
0.0
0.5
1.0
1.5
2.0
0 10 20 30 40 50
Spectral Displacement, S d (cm)
Sp
ec
tra
l Ac
ce
lera
tio
n, S
a (g
) = 1.0
2.0
1.5
0.0
0.5
1.0
1.5
2.0
0 10 20 30 40 50
Spectral Displacement, S d (cm)
Sp
ec
tra
l Ac
ce
lera
tio
n, S
a (g
)
Dynamic TargetPoint
1.5
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Validation Studies
> Several regular and irregular building frames of varying height were developed used for validation studies.
> Different suite of records were compiled from near-fault forward directivity, near-fault fling and far-fault recordings.
> Each building model was also subjected to a series of ground motions to generate benchmark results.
> Engineering demand parameters considered are roof drift ratio, inter-story drift ratio in global level and member plastic rotations and story ductility in local level for cross comparisons.
Dr. E. Kalkan Slide: 31/53
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> The structural system is essentially symmetrical.
> Moment continuity of each of the perimeter frames is interrupted at the ends where a simple shear connection is used to connect to the weak column axis.
4
7
6
5
3
2
1
BA
6@6.
1 m
DC E GF
[email protected] m 6@ 6.1m
5@4m
5.3m
3rdFloor
2ndFloor
1st Floor
4th Floor
5th Floor
Roof
W14
x176
W14
x90
W14
x132
W24x68
W24x84
W24x68
W24x68
W27x102
W30x116
A C E F GDB
Moment resisting connection
Moment resisting connectionSimple hinge connection
Structural Details of 6-story Building
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Eart
hq
uake
Structural Details of 13-story Building
> The exterior frames of the building are the moment resisting frames and interior frames are for load bearing.
> The foundation consists of piles, pile caps and grade beams.
> The corner columns of outer frames are composed of box sections.
[email protected] = 48.8 m
5
E
F
G
C
D
B
4
5@9.
76 =
48.
8 m
86 7 9
Moment resisting connection
(a) Plan view of perimeter frames
(b) Elevation
W33x118
W27x84
W33x141
W33x130
W33x130
W33x152
W33x152
W33x152
W33x141
W33x118
W36x230
W33x152
W33x152
W33x194
W14
x314
W14
x426
W14
x500
W14
x398
W14
x246
W14
x287
W14
x167
6th Floor
5th Floor
1st Floor
2nd Floor
3rd Floor
Plaza Level
4th Floor
12th Floor
Roof
9th Floor
10th Floor
11th Floor
7th Floor
8th Floor12
@4.
013
= 4
8.2
m
4.88
4.42
[email protected] = 48.8 m
Moment resisting connectionSimple hinge connection
Dr. E. Kalkan Slide: 33/53
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g. Analytical Modeling in OpenSEES
(Open source Finite Element Software)
One half of the total building mass was applied to the frame distributed proportionally to the floor nodes.
The simulation of special features such as local connection fracture did not accounted for; consequently, the modeling of the members and connections was based on the assumption of stable hysteresis derived from a bilinear stress-strain model.
The columns were assumed to be fixed at the base level (No SSI).
Centerline dimensions were used in the element modeling. A force-based nonlinear beam-column element that utilizes a
layered ‘fiber’ section is utilized to model all components
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Dr. E. Kalkan Slide: 34/55
Recorded Earthquake Data from 6-Story Building
Earthquake1994 Northridge 6.7 22 0.35 0.49
1992 Bigbear 6.5 137 0.04 0.111992 Landers 7.3 172 0.05 0.22
1991 Sierra Madre 5.8 30 0.11 0.161987 Whittier 6.1 26 0.22 0.30
Magnitude (Mw)
Epicentral Distance (km)
PGA Base Level (g)
PGA Roof Level (g)
The building performed well in all these earthquakes with no visible signs of damage. Recorded data indicates an essentially elastic response in each case.
-12
0
12
0 10 20 30 40 50 60Time (sec)
Dis
p. (
cm
)
RecordedSimulated
6-Story Bld.Roof
Dr. E. Kalkan Slide: 35/53
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g. Recorded Earthquake Data from
13-Story Building
Approximately 12% of the connections on the west perimeter of
the North-South frame fractured
during the Northridge
earthquake.
Earthquake1994 Northridge 6.7 32 0.18 0.37
1991 Sierra Madre 5.8 33 0.17 0.18
Magnitude (Mw)
Epicentral Distance (km)
PGA Base Level (g)
PGA Roof Level (g)
-40
0
40
0 10 20 30
Dis
p. (
cm)
6th Floor
-40
0
40
0 5 10 15 20 25 30Time (sec)
Dis
p. (
cm
) 13-Story Bld.Roof
Dr. E. Kalkan Slide: 36/53
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Eq
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g.
0
1
2
3
4
5
6
0.00 0.02 0.04 0.06
Interstory Drift Ratio
Sto
ry L
evel JMA
Mode-1MMPAAMC
0
1
2
3
4
5
6
0.00 0.01 0.02 0.03
Roof Drift RatioT
arg
et
Dri
ft
0
1
2
3
4
5
6
0.00 0.02 0.04 0.06
Interstory Drift Ratio
Sto
ry L
evel LGPC
MMPAMode-1AMC
0
1
2
3
4
5
6
0.00 0.01 0.02 0.03
Roof Drift Ratio
Ta
rge
t D
rift
0
2
4
6
8
10
12
14
0.00 0.01 0.02 0.03 0.04
Interstory Drift Ratio
Sto
ry L
evel JMA
MMPA
Mode-1AMC
0
2
4
6
8
10
12
14
0.00 0.01 0.01 0.02
Roof Drift Ratio
Ta
rge
t D
rift
0
2
4
6
8
10
12
14
0.00 0.02 0.04 0.06
Interstory Drift Ratio
Sto
ry L
evel
Rinaldi
MMPA
Mode-1AMC
0
2
4
6
8
10
12
14
0.00 0.01 0.02
Roof Drift Ratio
Ta
rge
t D
rift
Dr. E. Kalkan Slide: 37/53
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Eq
. En
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0
1
2
3
4
5
6
0.00 0.02 0.04 0.06
Interstory Drift Ratio
Sto
ry L
evel Taft
MMPAMode-1AMC
0
1
2
3
4
5
6
0.00 0.01 0.02 0.03
Roof Drift Ratio
Ta
rge
t D
rift
0
1
2
3
4
5
6
0.00 0.02 0.04 0.06Interstory Drift Ratio
Sto
ry L
evel
Desert H.MMPAMode-1AMC
0
1
2
3
4
5
6
0.00 0.01 0.02 0.03
Roof Drift Ratio
Ta
rge
t D
rift
0
2
4
6
8
10
12
14
0.00 0.01 0.02 0.03 0.04
Interstory Drift Ratio
Sto
ry L
evel
Desert H.
MMPA
Mode-1AMC
0
2
4
6
8
10
12
14
0.000 0.005 0.010 0.015
Roof Drift Ratio
Ta
rge
t D
rift
0
2
4
6
8
10
12
14
0.00 0.01 0.02 0.03
Interstory Drift Ratio
Sto
ry L
evel
Moorpark
MMPA
Mode-1AMC
0
2
4
6
8
10
12
14
0.000 0.005 0.010 0.015
Roof Drift Ratio
Ta
rge
t D
rift
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Prediction of Column Plastic Rotations (Local Demands)
0
1
2
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0.00 0.02 0.04 0.06
Col. Plastic Rot. (rad)
Sto
ry L
ev
el
NTH
AMC
MMPA
Near-Fault, Forward Dir. (JMA)
0
1
2
3
4
5
6
0.00 0.02 0.04 0.06
Col. Plastic Rot. (rad)
Near-Fault, Fling (TCU074)
0
1
2
3
4
5
6
0.00 0.02 0.04 0.06
Col. Plastic Rot. (rad)
Far-Fault (Taft)
Dr. E. Kalkan Slide: 39/53
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Summary & Conclusions
> Developed AMC offers a direct multi-mode technique to estimate seismic demands and integrates concepts incorporated in:
• Capacity spectrum method recommended in 3ATC-40 (1996)
• Direct adaptive method originally proposed by Gupta and Kunnath (2000)
• Modal pushover analysis advocated by Chopra and Goel (2002)
> AMC procedure accounts for higher mode effects by combining the response of individual modal pushover analyses and incorporates the effects of varying dynamic characteristics during the inelastic response via its adaptive feature
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Summary (cont.)
> A novel feature of the procedure is that the target displacement is estimated and updated dynamically during the analysis by incorporating energy based modal capacity curves in conjunction with constant-ductility capacity spectra.
> AMC method has shown promise in predicting inelastic displacement demands for a range of regular and irregular buildings.
> Validation studies under 3D models (including torsion) are currently underway.
Dr. E. Kalkan Slide: 41/55
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Thank You