adaptive nonlinear analysis as applied to …erolkalkan.com/ppts/p20.pdfdr. e. kalkan csus, math...

Adaptive Nonlinear Analysis as Applied to Performance based Earthquake Engineering

Erol Kalkan, PhD CSUS, Feb. 28, 2008

Dr. E. Kalkan CSUS, Math Colloquium Slide: 2/53

Ad

apti

ve N

onlin

ear

An

alys

is a

s A

pp

lied

to

Per

form

ance

bas

ed E

q.

Eng

.

This study is based on a paper published in Journal of Structural Engineering,

and winner of 2008 ASCE Raymond Reese Research

Award


Ad

apti

ve N

onlin

ear

An

alys

is a

s A

pp

lied

to

Per

form

ance

bas

ed E

q.

Eng

.

Outline

•  Seismic Analysis Methods of Structures •  Performance Based Earthquake Engineering

(Why and When) •  Nonlinear Static Analysis

– Fundamental Theory – Conventional Methods (FEMA and ATC) – Limitations

•  Adaptive Nonlinear Static Analysis – Methodology Developed – Comparative Results

•  Summary & Conclusions


Ad

apti

ve N

onlin

ear

An

alys

is a

s A

pp

lied

to

Per

form

ance

bas

ed E

q.

Eng

.

•  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


Ad

apti

ve N

onlin

ear

An

alys

is a

s A

pp

lied

to

Per

form

ance

bas

ed E

q.

Eng

.

-2.0

-1.0

0.0

1.0

2.0

Acc

eler

atio

n (g

)

1994 Northridge, California EarthquakePacoima Dam - Upper Left Abutment

-2.0

-1.0

0.0

1.0

2.0

Acc

eler

atio

n (g

)

-2.0

-1.0

0.0

1.0

2.0

0 5 10 15 20Time (s)

Acc

eler

atio

n (g

)

210o Component

120o Component

Up Component


Ad

apti

ve N

onlin

ear

An

alys

is a

s A

pp

lied

to

Per

form

ance

bas

ed E

q.

Eng

.

0( )G gmu cu k k u mu+ + − = −&& & &&

c

k

m

φ l

u u+ug

mg mg

gmu− &&

gu

Equation of Motion


Ad

apti

ve N

onlin

ear

An

alys

is a

s A

pp

lied

to

Per

form

ance

bas

ed E

q.

Eng

.

SPECTRUM – A plot of the maximum response, as a function of oscillator frequency, of an array of single-degree-of-freedom (SDF) damped oscillators subjected to the same base excitation.

0 1 2 3 4 50

0.5

1

1.5

2

2.5

Period (s), Tn

Spec

tral A

cc. (

g)

0 1 2 3 4 50

0.5

1

1.5

2

2.5

Period (s), Tn

Spec

tral A

cc. (

g)

Median SpectrumDesign Spectrum

Terminology


Ad

apti

ve N

onlin

ear

An

alys

is a

s A

pp

lied

to

Per

form

ance

bas

ed E

q.

Eng

.

Terminology

ELASTIC vs. INELASTIC (NONLINEAR) SDF Oscillator

u

f

Elastic SDF System

u

f

Inelastic SDF System


Ad

apti

ve N

onlin

ear

An

alys

is a

s A

pp

lied

to

Per

form

ance

bas

ed E

q.

Eng

.

Major challenge in structural engineering is to develop simple, yet accurate, methods for estimating force demands on structures to predict their performance

level with confidence.


Ad

apti

ve N

onlin

ear

An

alys

is a

s A

pp

lied

to

Per

form

ance

bas

ed E

q.

Eng

.

Unlike elastic analysis methods (used commonly), nonlinear analysis helps us to identify sequence and magnitudes of yielding (damage) of structural components, internal forces, deformations,

and failure mechanism

Why Performance-based Earthquake Engineering Need Nonlinear Analysis?


Ad

apti

ve N

onlin

ear

An

alys

is a

s A

pp

lied

to

Per

form

ance

bas

ed E

q.

Eng

.

Nonlinear Static Analysis

Fundamental Theory &

Current Practice


Ad

apti

ve N

onlin

ear

An

alys

is a

s A

pp

lied

to

Per

form

ance

bas

ed E

q.

Eng

. Multi-degree-of-freedom (MDF) system seismic behavior can be approximated

with certain accuracy by

equivalent SDF systems.

Equivalent SDF (ESDF) systems’ properties are computed by conducting

pushover analyses…


Ad

apti

ve N

onlin

ear

An

alys

is a

s A

pp

lied

to

Per

form

ance

bas

ed E

q.

Eng

.

Conventional Nonlinear Static (Pushover) Analysis l  Choose height-wise distribution of lateral forces l  Monotonically increase lateral forces till the “control node” reaches a “target displacement” i.e., increasing load factor while fixing load pattern.

l  Develop pushover (capacity) curve: Plot of base shear vs. roof displacement

ur

Vb


Ad

apti

ve N

onlin

ear

An

alys

is a

s A

pp

lied

to

Per

form

ance

bas

ed E

q.

Eng

. Summary of Nonlinear Static Analysis

V

D

D

V

InelasticSDF System

Target Displacementof MDF System ut

ut

uj

dj

Capacity estimation at target displacement

Pushover Analysis

Participation Factor, Gn

Dn

Fsn/Ln

ESD System Backbone Curve


Ad

apti

ve N

onlin

ear

An

alys

is a

s A

pp

lied

to

Per

form

ance

bas

ed E

q.

Eng

.

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.

•  Modal responses are assumed to be uncoupled similar to elastic case.


Ad

apti

ve N

onlin

ear

An

alys

is a

s A

pp

lied

to

Per

form

ance

bas

ed E

q.

Eng

.

Two Important Components of Nonlinear Static Analysis

•  Construct loading vector shape •  Determine target roof displacement


Ad

apti

ve N

onlin

ear

An

alys

is a

s A

pp

lied

to

Per

form

ance

bas

ed E

q.

Eng

.

( )φ

=

=

= =

=

*

*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


Ad

apti

ve N

onlin

ear

An

alys

is a

s A

pp

lied

to

Per

form

ance

bas

ed E

q.

Eng

.

FEMA Recommended Force Distributions

Each force distribution pushes all floors in same direction


Ad

apti

ve N

onlin

ear

An

alys

is a

s A

pp

lied

to

Per

form

ance

bas

ed E

q.

Eng

.

Two Important Components of Nonlinear Static Analysis

•  Construct loading vector shape •  Determine target roof displacement


Ad

apti

ve N

onlin

ear

An

alys

is a

s A

pp

lied

to

Per

form

ance

bas

ed E

q.

Eng

. Target Displacement Estimation (Displacement Coefficient Method)

π⎞⎛

= ⎟⎜⎝ ⎠

2

0 24e

t inel ATu C C S u

f

Elastic SDF System

u

f


u

f

Inelastic MDF System

C0 = Constant to relate elastic deformation of SDF and MDF system

Ad

apti

ve N

onlin

ear

An

alys

is a

s A

pp

lied

to

Per

form

ance

bas

ed E

q.

Eng

.


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


Ad

apti

ve N

onlin

ear

An

alys

is a

s A

pp

lied

to

Per

form

ance

bas

ed E

q.

Eng

. Capacity Spectrum Method

ξ= 0 ( , )t D eq equ C S T

u

f

Inelastic MDF System

u

f

Equivalent Linear Elastic SDF System

Teq, zeq

u

f



Ad

apti

ve N

onlin

ear

An

alys

is a

s A

pp

lied

to

Per

form

ance

bas

ed E

q.

Eng

.

Capacity Spectrum Method – Equivalent Damping Concept

( )( )( )

µαµ α

µ αζ κ

π µ αµ α

=+ −

− −= +

+ −

1

1 110.051

eq o

eq

T T

For bilinear systems

Requires iterations to compute Teq and zeqbecause of unknown ductility (uinel / uelas)

10.054

Deq

So

EE

ξπ

= + Teq= Tsec

Sd

Sa

ESo

ED


Ad

apti

ve N

onlin

ear

An

alys

is a

s A

pp

lied

to

Per

form

ance

bas

ed E

q.

Eng

. 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 Effects Plan Irregularities (i.e., Torsion, Vertical Irregularities) Impulsive Near-Fault Ground Motions

> No established procedure for 3D pushover analysis yet.

Adaptive Nonlinear Analysis


Ad

apti

ve N

onlin

ear

An

alys

is a

s A

pp

lied

to

Per

form

ance

bas

ed E

q.

Eng

.

Adaptive Pushover – Basic Concept


Ad

apti

ve N

onlin

ear

An

alys

is a

s A

pp

lied

to

Per

form

ance

bas

ed E

q.

Eng

.

0

1

2

3

4

5

6

Stor

y Le

vel

ElasticSt-1St-2St-3St-4,5St-6

Mode-1 Mode-2 Mode-3

Progressive Change in Modal Shapes


Ad

apti

ve N

onlin

ear

An

alys

is a

s A

pp

lied

to

Per

form

ance

bas

ed E

q.

Eng

. 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.


Ad

apti

ve N

onlin

ear

An

alys

is a

s A

pp

lied

to

Per

form

ance

bas

ed E

q.

Eng

.

Energy-based ESDF system representation of nth-mode MDF system capacity curve��

Roof Displacement, u r,n

Bas

e She

ar, V

b,n

F 1(i)

F 2(i)

F 3(i)

Δd 3(i)

Δd 2(i)

Δd 1(i)

Forces (sn

(i))

( ) ( ) ( ) ( ), , , ,

1,3 1,3( ) / ( )i i i i

d n n n j n j n jj j

S D F d F= =

⎛ ⎞⎛ ⎞ ⎛ ⎞= Δ = Δ⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎝ ⎠ ⎝ ⎠⎝ ⎠∑ ∑ ∑ ∑

Δd 3(i)

Capacitycurve

(i-1)

(i)

(i)(i-1)

ur,n(i)ur,n(i-1)S pectral Displacement, S d,n

Spe

ctral A

cceleration, S a,n

ΔD n(i)

ωn(i)

ζn(i)

,,

b na n

n

VS

Wα=

ΔD n(i)

Τn(elas tic )

(ωn(i)) 2

Capacity spectrum

MDF Level

SDF Level


Ad

apti

ve N

onlin

ear

An

alys

is a

s A

pp

lied

to

Per

form

ance

bas

ed E

q.

Eng

.

Performance point evaluation using system ductility through a set of inelastic spectra

S pectral Dis placement, S d,n

Spe

ctral A

cceleration, S a

,n

ωn(i)

ζn(i)

(ωn(ip )) 2

Global Yield

( ),yieldd nS ( )

,ipd nS

With computed system ductility, ( )ipnµ

Τn(elas tic )

Τn(ip )

( ),( )( ),

ipd nip

n yieldd n

SS

µ =

S pec tral Dis placement, S d,n

Spe

ctral A

cceleration, S a

,n

( )ipnµ

Dynamic Target Point

Inelastic phase, period elongation

Τn(elas tic )

Τn(ip )

Inelastic Demand Spectra plotted at different ductility levels

M odal CapacityCurve

Capacity Side

DemandSide


Ad

apti

ve N

onlin

ear

An

alys

is a

s A

pp

lied

to

Per

form

ance

bas

ed E

q.

Eng

.

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.


Ad

apti

ve N

onlin

ear

An

alys

is a

s A

pp

lied

to

Per

form

ance

bas

ed E

q.

Eng

.

>  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

1BA

[email protected]

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 connection Simple hinge connection

Structural Details of 6-story Building

Ad

apti

ve N

onlin

ear

An

alys

is a

s A

pp

lied

to

Per

form

ance

bas

ed E

arth

qu

ake

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

B4

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

= 48

.2 m

4.88

4.42

[email protected] = 48.8 m

Moment resisting connectionSimple hinge connection


Ad

apti

ve N

onlin

ear

An

alys

is a

s A

pp

lied

to

Per

form

ance

bas

ed E

q.

Eng

. Analytical Modeling in OpenSEES (Open source Finite Element Software)

q  One half of the total building mass was

applied to the frame distributed proportionally to the floor nodes.

q  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.

q  The columns were assumed to be fixed at the base level (No SSI).

q  Centerline dimensions were used in the element modeling. q  A force-based nonlinear beam-column element that utilizes a

layered ‘fiber’ section is utilized to model all components


Ad

apti

ve N

onlin

ear

An

alys

is a

s A

pp

lied

to

Per

form

ance

bas

ed E

q.

Eng

.

0

1

2

3

4

5

6

0.00 0.02 0.04 0.06Inters tory Drift Ratio

Story Lev

el JMAMode-‐1MMPAAMC

0

1

2

3

4

5

6

0.00 0.01 0.02 0.03Roof Drift Ratio

Target Drift

0

1

2

3

4

5

6


Story Lev

el LGPCMMPAMode-‐1AMC

0

1

2

3

4

5

6


Target Drift

0

2

4

6

8

10

12

14

0.00 0.01 0.02 0.03 0.04Inters tory Drift Ratio

Story Lev

el JMAMMPAMode-‐1AMC

0

2

4

6

8

10

12

14


Target Drift

0

2

4

6

8

10

12

14


Story Lev

el

R inaldiMMPAMode-‐1AMC

0

2

4

6

8

10

12

14

0.00 0.01 0.02Roof Drift Ratio

Target Drift

Comparison of Results: Impulsive Near-Fault Records


Ad

apti

ve N

onlin

ear

An

alys

is a

s A

pp

lied

to

Per

form

ance

bas

ed E

q.

Eng

.

0

1

2

3

4

5

6


Story Lev

el TaftMMPAMode-‐1AMC

0

1

2

3

4

5

6


Target Drift

0

1

2

3

4

5

6


Story Lev

el

Desert H.MMPAMode-‐1AMC

0

1

2

3

4

5

6


Target Drift

Comparison of Results: Scaled Far-Fault Records

0

2

4

6

8

10

12

14


Story Lev

el

Desert H.MMPAMode-‐1AMC

0

2

4

6

8

10

12

14

0.000 0.005 0.010 0.015Roof Drift Ratio

Target Drift

0

2

4

6

8

10

12

14


Story Lev

elMoorparkMMPAMode-‐1AMC

0

2

4

6

8

10

12

14

0.000 0.005 0.010 0.015Roof Drift Ratio

Target Drift


Ad

apti

ve N

onlin

ear

An

alys

is a

s A

pp

lied

to

Per

form

ance

bas

ed E

q.

Eng

.

0

1

2

3

4

5

6


Story Lev

el

NTH Mean

AMC Mean

0

1

2

3

4

5

6

0.00 0.01 0.02Roof Drift Ratio

Statistics of Results

0

2

4

6

8

10

12

14


Story Lev

el

NTH Mean

AMC Mean

0

2

4

6

8

10

12

14

0.00 0.01 0.02

Roof Drift Ratio


Ad

apti

ve N

onlin

ear

An

alys

is a

s A

pp

lied

to

Per

form

ance

bas

ed E

q.

Eng

.

Summary & Conclusions

> Developed AMC offers a direct multi-mode technique to estimate seismic demands and integrates concepts incorporated in:

• Capacity spectrum method recommended in 3 ATC-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


Ad

apti

ve N

onlin

ear

An

alys

is a

s A

pp

lied

to

Per

form

ance

bas

ed E

q.

Eng

.

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.


Ad

apti

ve N

onlin

ear

An

alys

is a

s A

pp

lied

to

Per

form

ance

bas

ed E

q.

Eng

.

Thank You

adaptive nonlinear analysis as applied to …erolkalkan.com/ppts/p20.pdfdr. e. kalkan csus, math...

Documents