performance based design by ashraf h

8/17/2019 performance based design by Ashraf H.

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Nonlinear Analysis & Performance Based Design

http://www.civil808.com/


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CALCULATED vs MEASURED



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ENERGY DISSIPATION



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IMPLICIT NONLINEAR BEHAVIOR



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STEEL STRESS STRAIN RELATIONSHIPS



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INELASTIC WORK DONE!



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CAPACITY DESIGN

STRONG COLUMNS & WEAK BEAMS IN FRAMES

REDUCED BEAM SECTIONSLINK BEAMS IN ECCENTRICALLY BRACED FRAMES

BUCKLING RESISTANT BRACES AS FUSES

RUBBER-LEAD BASE ISOLATORS

HINGED BRIDGE COLUMNS

HINGES AT THE BASE LEVEL OF SHEAR WALLSROCKING FOUNDATIONS

OVERDESIGNED COUPLING BEAMS

OTHER SACRIFICIAL ELEMENTS



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STRUCTURAL COMPONENTS



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MOMENT ROTATION RELATIONSHIP



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Nonlinear Analysis

&

Performance

Based

Design

IDEALIZED MOMENT ROTATION



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Nonlinear Analysis

&

Performance

Based

Design

PERFORMANCE LEVELS



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Nonlinear Analysis

&

Performance

Based

Design

IDEALIZED FORCE DEFORMATION CURVE



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Nonlinear Analysis

&

Performance

Based

Design 17

ASCE 41 BEAM MODEL



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Nonlinear Analysis

&

Performance

Based

Design

• Linear Static Analysis

• Linear Dynamic

Analysis

(Response Spectrum or Time History Analysis)

• Nonlinear Static Analysis

(Pushover Analysis)

• Nonlinear Dynamic Time History Analysis(NDI or FNA)

ASCE 41 ASSESSMENT OPTIONS



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Nonlinear Analysis

&

Performance

Based

Design

ELASTIC STRENGTH DESIGN ‐ KEY STEPS

CHOSE DESIGN CODE AND EARTHQUAKE LOADS

DESIGN CHECK PARAMETERS STRESS/BEAM MOMENT

GET ALLOWABLE STRESSES/ULTIMATE– PHI FACTORS

CALCULATE STRESSES – LOAD FACTORS (ST RS TH)

CALCULATE STRESS RATIOS

INELASTIC DEFORMATION BASED DESIGN ‐‐ KEY STEPS

CHOSE PERFORMANCE LEVEL AND DESIGN LOADS – ASCE 41

DEMAND CAPACITY MEASURES – DRIFT/HINGE ROTATION/SHEAR

GET DEFORMATION

AND

FORCE

CAPACITIES

CALCULATE DEFORMATION AND FORCE DEMANDS (RS OR TH)

CALCULATE D/C RATIOS – LIMIT STATES

STRENGTH vs DEFORMATION



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Nonlinear Analysis

&

Performance

Based

Design

STRUCTURE and MEMBERS

• For a structure, F = load, D = deflection.

• For a component, F depends on the component type, D is the

corresponding deformation.

• The component F‐D relationships must be known.

• The structure F‐D relationship is obtained by structural analysis.



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Nonlinear Analysis

&

Performance

Based

Design

FRAME COMPONENTS

• For each component type we need :

Reasonably accurate nonlinear F‐D relationships.

Reasonable deformation and/or strength capacities.

• We must choose realistic demand‐capacity measures, and it must be feasible to calculate the demand values.

• The best model is the simplest model that will do the job.



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Nonlinear Analysis

&

Performance

Based

Design

Force (F)

Initiallylinear

StrainHardening

Ultimatestrength

Strength loss

Residual strength

Complete failure

First yield

Ductile limit

Hysteresis loopStiffness, strength and ductile limit mayall degrade under cyclic deformation

Deformation (D)

F-D RELATIONSHIP



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Nonlinear Analysis

&

Performance

Based

Design

LATERALLOAD

Partially DuctileBrittle Ductile

DRIFT

DUCTILITY



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Nonlinear Analysis

&

Performance

Based

Design

ASCE 41 - DUCTILE AND BRITTLE



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Nonlinear Analysis

&

Performance

Based

Design

FORCE AND DEFORMATION CONTROL



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Nonlinear Analysis

&

Performance

Based

Design

F

Relationship allowingfor cyclic deformation

Monotonic F-D relationship

Hysteresis loopsfrom experiment.

D

BACKBONE CURVE



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Nonlinear Analysis

&

Performance

Based

Design

HYSTERESIS LOOP MODELS



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Nonlinear Analysis

&

Performance

Based

Design

STRENGTH DEGRADATION



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Nonlinear Analysis

&

Performance

Based

Design

ASCE 41 DEFORMATION CAPACITIES

• This can be used for components of all types.

• It can

be

used

if

experimental

results

are

available.

• ASCE 41 gives capacities for many different components.

• For beams and columns, ASCE 41 gives capacities only for the chord rotation model.



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Nonlinear Analysis

&

Performance

Based

Design

θi θ j

Currentθ

Elasticθ

Plastic (hinge) θ

Totalrotation

Zero length hinges

Elastic beam

Plasticrotation

Elasticrotation

Similar atthis end

Mi M j

M or Mi j

M

θ θi jor

θ

BEAM END ROTATION MODEL



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Nonlinear Analysis

&

Performance

Based

Design

PLASTIC HINGE MODEL

• It is

assumed

that

all

inelastic

deformation

is

concentrated

in

zero

‐

length plastic hinges.

• The deformation measure for D/C is hinge rotation.



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Nonlinear Analysis

&

Performance

Based

Design

PLASTIC ZONE MODEL

• The inelastic behavior occurs in finite length plastic zones.

• Actual plastic

zones

usually

change

length,

but

models

that

have

variable lengths are too complex.

• The deformation measure for D/C can be :

‐ Average curvature in plastic zone.

‐ Rotation over plastic zone ( = average curvature x plastic zone length).



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Nonlinear Analysis

&

Performance

Based

Design

ASCE 41 CHORD ROTATION CAPACITIES

IO LS CP

Steel Beam θp/θy = 1 θp/θy = 6 θp/θy = 8

RC Beam

Low shear

High shear

θp = 0.01

θp = 0.005

θp = 0.02

θp = 0.01

θp = 0.025

θp = 0.02



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Nonlinear Analysis

&

Performance

Based

Design

COLUMN AXIAL‐BENDING MODEL

Mi

P

PP

P

or

V

V

M j

MM



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Nonlinear Analysis

&

Performance

Based

Design

STEEL COLUMN AXIAL‐BENDING



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Nonlinear Analysis

&

Performance

Based

Design

CONCRETE COLUMN AXIAL‐BENDING



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Nonlinear Analysis

&

Performance

Based

Design

NodeZero-lengthshear "hinge"Elastic beam

SHEAR HINGE MODEL

PANEL ZONE ELEMENT



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Nonlinear Analysis

&

Performance

Based

Design

PANEL ZONE ELEMENT

• Deformation, D = spring rotation = shear strain in panel zone.

• Force, F = moment

in

spring

= moment

transferred

from

beam

to

column elements.

• Also, F = (panel zone horizontal shear force) x (beam depth).



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Nonlinear Analysis

&

Performance

Based

Design

BUCKLING-RESTRAINED BRACE

The BRB element includes “isotropic” hardening.

The D‐C measure is axial deformation.



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WALL FIBER MODEL


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Nonlinear Analysis

&

Performance

Based

Design

Steel

fibers

σ

σ

ε

ε

Concretefibers

WALL FIBER MODEL

ALTERNATIVE MEASURE STRAIN



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Nonlinear Analysis

&

Performance

Based

Design

ALTERNATIVE MEASURE - STRAIN

NONLINEAR SOLUTION SCHEMES



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Nonlinear Analysis

&

Performance

Based

Design

∆ ƒ

ƒ

∆ u u

1 2

iteration

NEWTON – RAPHSON

ITERATION

∆ ƒ

ƒ

∆ u u

1 2

iteration

CONSTANT STIFFNESS

ITERATION

3 4 56

NONLINEAR SOLUTION SCHEMES

CIRCULAR FREQUENCY



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Nonlinear Analysis

&

Performance

Based

Design

Y

+Y

-Y

0 Radius, R

θ

CIRCULAR FREQUENCY

THE D V & A RELATIONSHIP



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Nonlinear Analysis

&

Performance

Based

Design

u.

t

ut1.

..

Slope = ut1..

t1

u

t1 t

Slope = ut1.

u

ut1..

t1 t

THE D, V & A RELATIONSHIP

UNDAMPED FREE VIBRATION



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Nonlinear Analysis

&

Performance

Based

Design

UNDAMPED FREE VIBRATION

)cos(0 t uut ω =

0ukum &&

m

k where =ω

RESPONSE MAXIMA



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Nonlinear Analysis

&

Performance

Based

Design

RESPONSE MAXIMA

ut )cos(0 t u ω =

)cos(02

t u ω ω −=ut &&

)sin(0 t u ω ω −=ut &

max2uω −=maxu&&

BASIC DYNAMICS WITH DAMPING



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Nonlinear Analysis

&

Performance

Based

Design

BASIC DYNAMICS WITH DAMPING

guuuu &&&&& −22

guMKuuCuM

KuuC

t

uM

&&&&&

&&&

−

= 0

gu&&

M

K

C

RESPONSE FROM GROUND MOTION



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Nonlinear Analysis

&

Performance

Based

Design

ug..

2ug2..

ug1

..

1

t1 t2

Time t

&& A Bt u

g

= + = −&& &u u u+ +22ξω ω

RESPONSE FROM GROUND MOTION

DAMPED RESPONSE



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Nonlinear Analysis

&

Performance

Based

Design

{ [ & ] cos

[ (&

)] sin }

e uB

t

A u u

B

t

B

t

t d

dt t d

&ut = −

+ − − + +

−ξω

ωω

ω ω ξω ω ω ω

1 2

2

1 1 2 2

1

e A B

t

u u A B

t

A B Bt

t

t d

dt t d

ut = − +

+ + − +−

+ − +

−ξω

ω

ξ

ω

ω

ωξω

ξ

ω

ξ

ωω

ωξ

ω ω

{ [u ] cos

[ &( )

] sin }

[ ]

1 2 3

1 1

2

2

2 3 2

2

1 2 1

2

DAMPED RESPONSE

SDOF DAMPED RESPONSE



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Nonlinear Analysis

&

Performance

Based

Design

SDOF DAMPED RESPONSE

RESPONSE SPECTRUM GENERATION



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Nonlinear Analysis

&

Performance

Based

Design

RESPONSE SPECTRUM GENERATION

-0.40

-0.20

0.00

0.20

0.40

0.00 1.00 2.00 3.00 4.00 5.00 6.00

TIME, SECONDS

G R O

U N D

A C C , g

Earthquake Record

Displacement

Response Spectrum5% damping

-4.00

-2.00

0.002.00

4.00

0.00 1.00 2.00 3.00 4.00 5.00 6.00

D I S P L ,

i n .

-8.00

-4.00

0.00

4.00

8.00

0.00 1.00 2.00 3.00 4.00 5.00 6.00

D I S P

L , i n .

0

2

4

6

8

10

12

14

16

0 2 4 6 8 10

PERIOD, Seconds

D I S P L A C E M E N T ,

i n c h e s

T= 0.6 sec

T= 2.0 sec

SPECTRAL PARAMETERS



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Nonlinear Analysis

&

Performance

Based

Design

0

4

8

12

16

0 2 4 6 8 10

PERIOD, sec

D I S P L

A C E M E N T , i n .

0

10

20

30

40

0 2 4 6 8 10

PERIOD, sec

V

E L O C I T Y , i n / s e c

0.00

0.20

0.40

0.60

0.80

1.00

0 2 4 6 8 10

PERIOD, sec

A C C E L E R A T I O N , g

dV SPS ω

va PSPS ω

SPECTRAL PARAMETERS



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ASCE 7 RESPONSE SPECTRUM


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Nonlinear Analysis

&

Performance

Based

Design

PUSHOVER



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Nonlinear Analysis

&

Performance

Based

Design

THE LINEAR PUSHOVER



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Nonlinear Analysis

&

Performance

Based

Design

EQUIVALENT LINEARIZATION



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Nonlinear Analysis

&

Performance

Based

Design

How far to push? The Target Point!

DISPLACEMENT MODIFICATION



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Nonlinear Analysis

&

Performance

Based

Design

DISPLACEMENT MODIFICATION



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Nonlinear Analysis

&

Performance

Based

Design

Calculating the Target Displacement

C0

Relates spectral to roof displacement

C1 Modifier for inelastic displacement

C2 Modifier for hysteresis loop shape

δ = C 0C

1C

2S

aT

e

2/ (4π

2)

LOAD CONTROL AND DISPLACEMENT CONTROL



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Nonlinear Analysis

&

Performance

Based

Design

P-DELTA ANALYSIS



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Nonlinear Analysis

&

Performance

Based

Design

P-DELTA DEGRADES STRENGTH



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Nonlinear Analysis

&

Performance

Based

Design

P-DELTA EFFECTS ON F-D CURVES



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Nonlinear Analysis

&

Performance

Based

Design

STRUCTURESTRENGTH

The "over-ductility" is reduced,and is more uncertain.

P- e ects may reduce the dri t at which the"worst" component reaches its ductile limit.Δ

P- effects will reduce the drift atwhich the structure loses strength.Δ

DRIFT

THE FAST NONLINEAR ANALYSIS METHOD (FNA)



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Nonlinear Analysis

&

Performance

Based

Design

NON LINEAR FRAME AND SHEAR WALL HINGES

BASE ISOLATORS (RUBBER & FRICTION)

STRUCTURAL DAMPERS

STRUCTURAL UPLIFT

STRUCTURAL POUNDINGBUCKLING RESTRAINED BRACES

RITZ VECTORS



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Nonlinear Analysis

&

Performance

Based

Design

FNA KEY POINT



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Nonlinear Analysis

&

Performance

Based

Design

The Ritz modes generated by the

nonlinear

deformation

loads

are

used

to modify the basic structural modes

whenever the nonlinear elements go

nonlinear.



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MESH REFINEMENT


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Nonlinear Analysis

&

Performance

Based

Design71

APPROXIMATING BENDING BEHAVIOR



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Nonlinear Analysis

&

Performance

Based

Design72

This is for a coupling beam. A slender pier is similar.

ACCURACY OF MESH REFINEMENT



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Nonlinear Analysis

&

Performance

Based

Design73

PIER / SPANDREL MODELS



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Nonlinear Analysis

&

Performance

Based

Design74

STRAIN & ROTATION MEASURES



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Nonlinear Analysis

&

Performance

Based

Design75

STRAIN CONCENTRATION STUDY



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Nonlinear Analysis

&

Performance

Based

Design

76

Compare calculated strains and rotations for the 3 cases.

STRAIN CONCENTRATION STUDY



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Nonlinear Analysis

&

Performance

Based

Design

77

The strain over the story height is insensitive to the number of elements.

Also, the rotation over the story height is insensitive to the number of elements.

Therefore these are good choices for D/C measures.

No. of

elems

Roof

drift

Strain in bottom

element

Strain over story

height

Rotation over

story height

1 2.32% 2.39% 2.39% 1.99%

2 2.32% 3.66% 2.36% 1.97%

3 2.32% 4.17% 2.35% 1.96%

DISCONTINUOUS SHEAR WALLS



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Nonlinear

Analysis

&

Performance

Based

Design

PIER AND SPANDREL FIBER MODELS



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Nonlinear

Analysis

&

Performance

Based

Design79

Vertical and horizontal fiber models

RAYLEIGH DAMPING



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Nonlinear

Analysis

&

Performance

Based

Design 80

• The αM dampers

connect

the

masses

to

the

ground.

They

exert

external damping forces. Units of α are 1/T.

• The βK dampers act in parallel with the elements. They exert internal damping forces. Units of β are T.

• The

damping

matrix

is

C =

αM +

βK.

RAYLEIGH DAMPING



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Nonlinear

Analysis

&

Performance

Based

Design 81

• For linear

analysis,

the

coefficients

α and

β can

be

chosen

to

give

essentially

constant damping over a range of mode periods, as shown.

• A possible method is as follows :

Choose TB = 0.9 times the first mode period.

Choose TA = 0.2 times the first mode period.

Calculate α and

β to

give

5%

damping

at

these

two

values.

• The damping ratio is essentially constant in the first few modes.

• The damping ratio is higher for the higher modes.

RAYLEIGH DAMPING



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Nonlinear

Analysis

&

Performance

Based

Design

KuuC &tuM && = 0

Kuu& + = 0

M +

K

u&& +

C

Mu&

MuK = 0

2uu& =

2 0 ω2 M

= C

ω2=

+

ω

2

ω2=CM 2

=

C

MMK =

2

C

MK 2 MK

M+

K=

tuM &&

u&&

;

2 MK

RAYLEIGH DAMPING



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Nonlinear

Analysis

&

Performance

Based

Design

Higher Modes

(high

ω) = β

Lower Modes (low ω) = α

To get

ζ from

α &

β for

any

ω M

K=

To get α & β from two values of ζ1

& ζ2

; Τ 2πω

=

ζ1

= α 2ω

1

+

β ω1

2

ζ2 = α 2ω2

+

β ω22

Solve for α & β

DAMPING COEFFICIENT FROM HYSTERESIS



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Nonlinear

Analysis

&

Performance

Based

Design



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A BIG THANK YOU!!!


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Nonlinear

Analysis

&

Performance

Based

Design

performance based design by ashraf h

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