Coupled_Axial-Shear-Flexure_Interaction_Hysteretic_Model_for_Seismic_Response_Assessment_of_Bridges.ppt...

7/21/2019 Coupled_Axial-Shear-Flexure_Interaction_Hysteretic_Model_for_Seismic_Response_Assessment_of_Bridges.ppt

1/28

1Quake Summit 2010

10/08/2010

Coupled Axial-Shear-Flexure Interaction Hyteretic!odel "or Seimic #epone

Aement o" $rid%e

Shi-&u 'u( )h*+* Student

,ian han%( Aitant )ro"eor

+epartment o" Ci.il n.ironmental n%ineerin%ni.erity o" Cali"ornia( o An%ele


2/28

2Quake Summit 2010

3utline

Introduction Motivation & Objectives

Shear-Flexure Interaction Under Constant Axial Load

Proposed Axial-Shear-Flexure Interaction ASFI! Sche"e Pri"ar# Curves and $#steretic Models Considerin% Co"bined Actions

eneration o' Pri"ar# Curve Fa"il#

Stress Level Index & ()o-sta%e Loadin% Approach

Model *eri'ication Static C#clic (ests

Co"parison )ith Fiber Section Model under Seis"ic Loadin%s

Li"itations and +no)n Issues

Factors A''ectin% ASFI & ,''ects on rid%e .esponses Arrival (i"e o' *ertical round Motion

*ertical-to-$ori/ontal PA .atio

Su""ar#


3/28

3Quake Summit 2010

Introduction

!oti.ation

rid%e colu"ns are subjected to co"bined actions o'

axial0 shear and 'lexure 'orces due to structural and

%eo"etrical constraints s1e)ed0 curved etc2! and the

"ulti-directional earth3ua1e input "otions2

Axial load variation can directl# i"pact the ulti"ate

capacit#0 sti''ness and h#steretic behavior o' shear and

'lexure responses2 Accurate seis"ic de"and assess"ent o' brid%es needs

to realisticall# account 'or co"bined actions2

345ecti.e

An e''icient anal#tical sche"econsiderin% axial-shear-

'lexural interaction Shear and 'lexural h#steretic "odelsre'lectin% the

e''ects o' axial load variationand accu"ulated "aterial

da"a%ee2%2 stren%th deterioration0 sti''ness de%radin%0

and pinchin% behavior!


4/28

4Quake Summit 2010

Axial-Shear-Flexural Interaction

4 Si%ni"icance o" 6on-linear Shear-Flexural Interaction

73ce4e and Saatcio%lu 1989:

Shear displace"ent can be si%ni'icant -- even i' a .C "e"ber is not

%overned b# shear 'ailure as is the case in "ost o' .C colu"ns!2

Inelastic shear behavior -- .C "e"bers )ith hi%her shear stren%th

than 'lexural stren%th do not %uarantee an elastic behavior in shear

de'or"ation2

4 Couplin% o" Axial-Shear-Flexural #epone

7l!andooh and ;ho4arah 200


5/28

5Quake Summit 2010

Axial-Shear-Flexure Interaction at !aterial e.el

MCFT

fsx

fs#

fcx

fc#

fx

f#

vx#

vcx#

x

6

y

fc6

fc7

c

7

6

6

7

7 77 70"ax 8 8

0

0

6 799

7

crc

c c

c c

sx s x y x

sy s y y y

ff

f f

f E f

f E f

= +

= = =

,3uilibriu" Strain Co"patibilit# Constitutive La)

*ecchio and Collins 6:;


6/28

6Quake Summit 2010

+eri.ation o" Flexural and Shear )rimary Cur.e

5iscreti/e .C "e"ber into s"all pieces2 For each piece o' .C ele"ent0

esti"ate M-= and >-? relationship b# Modi'ied Co"pression Field (heor#

MCF(0 *ecchio and Collins 6:;

M

M=V*h

dy

VN

yi

V

MCFT

M

=

M

+

+

F-UEL

S-UEL

SSI spring

FNDN

DECK

S-UEL

F-UEL

Rigid C!"#n

Input the *-@sand M- curve to

Shear-U,L & Flexural-U,L2

$s

V

S-UEL

$#

M

%

M

F-UEL

Inte%rate curvature and shear

strain to %et displace"ent2

BD E =id##i G ?id# H

Flexural de"ormation Shear de"ormation

h G @s


7/287Quake Summit 2010

Shear-Flexure Interaction 7SFI: under Contant Axial oad

0 5 10 15

0

10

20

30

40

50

60

70

Total Displacement (mm)

Shear(kN)

total displ.

shear displ.

flexural displ.

0 5 10 15

0.02

0.025

0.03

0.035

0.04

0.045

0.05

0.055

0.06

Total Displ. (mm)

Shear-to-TotalDispl.Ratio

0 0.5 1 1.5 2

0

0.2

0.4

0.6

0.8

1

1.2

1.4 M/V =0.076(m)1M/V =0.229(m)

2M/V =0.381(m)

3M/V =0.534(m)

4M/V =0.686(m)

5M/V =0.838(m)

6M/V =0.991(m)

7M/V =1.143(m)

8M/V =1.296(m)

9

M/V ratio

ColumnHeight(m)

0 2 4 6 8 10 120

50

100

150

200

250

300

Shear Strain (mm/m)

Shear

(kN)

V-1

V-2

V-3

V-4

V-5

V-6

V-7

V-8

V-9

0 5 10 15 20 25 300

30

60

90

Curvature (rad/km)

Moment(kN-m)

M-1

M-2

M-3

M-4

M-5

M-6

M-7

M-8

M-9

dy

V

N

yi

M

M=V*h

Sections )ith di''erent M* ratio

level o' shear-'lexural interaction!

de"onstrate di''erent "echanicalproperties and behaviors

Section )ith hi%her M* ratioJ Lar%er "o"ent capacit#

S"aller shear capacit#

Maxi"u" "o"ent capacit# isbounded b# pure bendin% case



Impro.ed Hyteretic #ule "or Shear Flexural Sprin%

nloadin% reloadin% ti""ne depend on>

Pri"ar# curve +elastic0 Crac10 & Kield!

Crac1ed Kielded

Shear 'orce level

Max ductilit# experienced

Loadin% c#cles at "ax ductilit# level

Axial load ratio

-80 -60 -40 -20 0 20 40 60 80-25

-20

-15

-10

-5

0

5

10

15

20

25

Shear Displacement

Shear

Force

Hysteretic Loop

,

FA

C

5

I

+

L

M

N

O

P

.

S

(

U

*

Shear 5isplace"ent

ShearForce

*cr

*#

"axi"u" pea1 @"0*"!

hardenin% re'erence point

@"0*

"!

previous pea1 @p0*

p!

pinchin% re'erence point @p0*p!

$

Structural characteristics

5a"a%e in the colu"n

Loadin% histor#

*ar#in% durin% earth3ua1e QQ

O/cebe and Saatcio%lu06:;:!

&" 'nd (h'ng ), . EESD



3utline











Su""ar#



""ect o" Axial oad ?ariation on =otal )rimary Cur.e

4 Ulti"ate capacit#and sti''nessincrease )ith co"pressive axial load level24 Kieldin% displace"entis al"ost 'ixed0 re%ardless o' applied axial load2

4 Crac1in% pointis %ettin% s"aller as axial 'orce decreasin%0 i"pl#in% the

colu"n bein% relativel# eas# to be crac1ed2

0 10 20 30 400

20

40

60

80

100

Column Tip Drift (mm)

Shear(kN)

PEER-93

P/P0=-5%(T)

P/P0=-2%(T)

P/P0= 0 (-)

P/P0= 5%(C)

P/P0=10%(C)P/P0=20%(C)

0 5 10 15 20 250

100

200

300

400

500

600

700


Shear(kN)

PEER-121

P/P0=-5%(T)

P/P0=-2%(T)

P/P0= 0 (-)

P/P0= 5%(C)

P/P0=10%(C)P/P0=20%(C)

0 50 100 150

50

100

150

200

250


Shear(kN)

PEER-122

P/P0=-5%(T)

P/P0=-2%(T)

P/P0= 0 (-)

P/P0= 5%(C)

P/P0=10%(C)P/P0=20%(C)

+unnath et al2

$5R2

Calderone-;7;

$5;29

Calderone-T7;

$5T29



6ormaliation o" )rimary Cur.e

-10 0 10 20 30 40

0

0.5

1

1.5

2

P/P0(%), Compression is "+".

Vy(P/P0=n%)/Vy(P/P0=5%C) Y =-2.15*(X-0.60)

2

+1.65

-10 0 10 20 30 40

0

0.5

1

1.5

2

2.5


Vu(P/P0=n%)/Vy(P/P0=5%C) Y =-3.20*(X-0.60)

2

+2.32

c! #ield load d! ulti"ate capacit#

79

9 9

U!92 I SU!

y

y

V P P n P

V P P P

== +

=

79

9 9

U!T279F 92

U!

u

y

V P P n P

V P P P

== +

=

-10 0 10 20 30 400

0.1

0.2

0.3

0.4

0.5


cr(P/P0=n%)/y(P/P0=5%C) Y = 0.68*(X+0.25)

2+0.01

-10 0 10 20 30 400

0.2

0.4

0.6

0.8

1


Vcr(P/P0=n%)/Vy(P/P0=5%C) Y = 1.47*(X+0.25)

2+0.02



;eneration o" )rimary Cur.e Family

i! 9crac1J strai%ht line

ii! crac1

#ieldJ interpolation

iii! #ieldulti"ateJ interpolation

U U

!

F U

U U

!

U U

U F U U

!

U U U U

!

2

F !

F !

I I

ii cr

I

y cr

I I

ii cr

I I

y cr

n n n

ii y cr cr

n n n n

ii y cr cr

DL def level

V VSL stress level

V V

DL

V SL V V V

=

=

= +

= +

iv! ulti"ate'ailureJ constant residual stren%th ratio

! !

!

!

!

n I

iii iii

I I

iii y

I I

u y

n n n n

iii u y y

ductility unchanged

V VSL stress level

V V

V SL V V V

=

=

= +

U U

! !

U

!

U

U U

!

F

n I

iv iv

I

iv

I

u

n n

iv u

ductility unchanged

VRSR residual strength ratio

V

V RSR V

=

=

=

n pri"ar# curve predicted!

I initial pri"ar# curve %iven!

n critical points0 predicted 'ro" e3uations

loadin%

de'lection

I critical points0 on initial pri"ar# curve

a a

a

b bb

i ii iii iv

!

!

!

!

2

2

I

i n n

i crI

cr

I

i n n

i crI

cr

DL def level DL

VSL stress level V SL V

V

= =

= =

ObjectiveJ eneratin% the pri"ar# curves related to various axial load levels

'ro" a %iven pri"ar# curve subject to an initial axial load



Stre e.el Index =@o-ta%e oadin% Approach

,3uivalent

stress level ,3uivalent

stress level

-

@#

SU

yV

@6

dc

@"ax

SU

effV

SU

mV

9

@#

9U

yV

@6

d

c

@"ax

9U

effV

9U

mV

69

dc

@#

69U

yV

@6 @"ax

69U

effV

69U

mV

+eep @0 chan%e NJ 69- +eep N0 chan%e @J @6@7

69

-

69U

effV

SU

effV

@6@7

69

c d

-

69U

effV

SU

effV

@6

c d

@"ax

Aumption>

,''ective stress level o' a loaded colu"n at

'ixed ductilit# is independent o' axial load2"ax

,''ective Lateral Load0Stress Level Index

Lateral Capacit# at 0

eff

m

V c

V d =



3utline











Su""ar#



Cyclic =et> xperimental )ro%ram =)0



?eri"ication o" )rimary Cur.e )rediction

-80 -60 -40 -20 0 20 40 60 80-200

-150

-100

-50

0

50

100

150

200

Displacement (mm)

ShearForce(kN)

Hysteretic Loop

Analytical

Experimental

-80 -60 -40 -20 0 20 40 60 80-200

-150

-100

-50

0

50

100

150

200

Displacement (mm)

ShearForce(kN)

Hysteretic Loop

Analytical

Experimental

(P-9T7

Sa1ai and +a)ashi"a

$5T2TV

(P-9T6

Sa1ai and +a)ashi"a

$5T2TV

(P-9T6

(P-9T7

iven the pri"ar# curve o' (P-9T60 predicts the response o' (P-

9T72

iven the pri"ar# curve o' (P-

9T70 predicts the response o' (P-

9T62



-80 -60 -40 -20 0 20 40 60 80-200

-150

-100

-50

0

50

100

150

200

Displacement (mm)

ShearForce(kN)

Hysteretic Loop

Analytical

Experimental

-80 -60 -40 -20 0 20 40 60 80-200

-150

-100

-50

0

50

100

150

200

Displacement (mm)

ShearForce(kN)

Hysteretic Loop

Analytical

Experimental

?eri"ication o" !appin% 4et@een +i""erent Axial oad e.el

(P-9TT

Sa1ai and +a)ashi"a

$5T2TV

(P-9TR

Sa1ai and +a)ashi"a

$5T2TV

(P-9T6

(P-9T7

T/-00

T/-01

Axial load decreasin%

Axial load decreasin%

Axial load

increasin%

Axial load

increasin%


18/28

18Quake Summit 2010

+ynamic ?alidation @ith Fi4er Section !odel

0 2 4 6 8 10-200

0

200

Time (s)

Shear(kN)

0 2 4 6 8 10

-20

0

20

Time (s)

TipDispl.(mm)

-20 -10 0 10 20 30-200

-150

-100

-50

0

50

100

150

200

Tip Displ. (mm)

Shear(kN)

OpenSees w/ V-EQ

OpenSees w/o V-EQ

ABAQUS w/ V-EQ

ABAQUS w/o V-EQ

4 Proposed ASFI "odel in

%eneral produces lar%er

displace"ent de"and than

the 'iber section "odel2

4 *ibration 're3uencies o' the

t)o "odels a%ree )ith each

other indicatin% reasonable

prediction on the tan%ent

sti''ness o' the proposed

ASFI "odel2

4 Considerin% onl# the SFI

can #ield %ood prediction on

the displace"ent de"and2

AAUS ASFI Model

OpenSees Fiber Model


19/28

19Quake Summit 2010

*

@s

M

imitation and Eno@n Iue

4 ,sti"ation on post-pea1 sti''ness o' pri"ar# curve 'a"il#

"a# not be ade3uate2

4 Ma# conver%e at an incorrect solution 'or s#ste"s )ith

#ieldin% plat'or"2

4 Ma# conver%e at an inconsistent de'or"ed con'i%uration

'or so'tenin% s#ste"s2

4 Use o' 'ull sti''ness "atrix can so"eho) i"prove the

above-"entioned conver%ence issues0 ho)ever0 it is an

as#""etric "atrix )hich o''sets "ost o' the advanta%es2


20/28

20Quake Summit 2010

3utline











Su""ar#


21/28

21Quake Summit 2010

Factor A""ectin% ASFI> Arri.al =ime o" ?ertical ;round !otion

-0.4s-0.3s-0.2s-0.1s 0.0 0.1s 0.2s 0.3s 0.4s0

1

2

3x 10

6

MaxBaseShear

(N)

tpeak

V- tpeak

H

w/o V-EQ

no shift on V-EQ

-0.4s-0.3s-0.2s-0.1s 0.0 0.1s 0.2s 0.3s 0.4s0

1

2

3x 10

6

MaxBase

Shear(N)

tpeakV- tpeakH

w/o V-EQ

no shift on V-EQ

-0.4s-0.3s-0.2s-0.1s 0.0 0.1s 0.2s 0.3s 0.4s0

2

4

6

8

10x 10

6

MaxBaseMoment(N-m)

tpeak

V- tpeak

H

w/o V-EQ

no shift on V-EQ

-0.4s-0.3s-0.2s-0.1s 0.0 0.1s 0.2s 0.3s 0.4s0

2

4

6

8

10x 10

6

MaxBaseMoment(N-m)

tpeak

V- tpeak

H

w/o V-EQ

no shift on V-EQ

-0.4s-0.3s-0.2s-0.1s 0.0 0.1s 0.2s 0.3s 0.4s0

0.02

0.04

0.06

0.08

MaxColumnDrift(m)

tpeakV- tpeakH

w/o V-EQ

no shift on V-EQ

-0.4s-0.3s-0.2s-0.1s 0.0 0.1s 0.2s 0.3s 0.4s0

0.02

0.04

0.06

0.08

MaxColumnDrift(m)

tpeak

V- tpeak

H

w/o V-EQ

no shift on V-EQ

a! $J WN77X *J WN77 b! $J WN77X *J NOR

0 2 4 6 8 10-0.5

0

0.5 0.4521(g)

-0.4432(g)

Time (s)

Acceleration(g)

H

V

0 2 4 6 8 10-0.5

0

0.5

1

0.4521(g)0.5352(g)

Time (s)

Acceleration(g)

H

V

a! $ori/ontalJ WN77 (p92R;;s!X

*erticalJ WN77 (p926T;s!

b! $ori/ontalJ WN77 (p92R;;s!X

*erticalJ NOR (p92T77s!

No si%ni'icant correlation is 'ound2


22/28

22Quake Summit 2010

Factor A""ectin% ASFI> ?ertical-to-Horiontal );A #atio

0.0 0.2 0.4 0.6 0.8 1.00

1

2

3x 10

6

MaxBaseS

hear(N)

PGAV/ PGA

H

w/o V-EQ

0.0 0.2 0.4 0.6 0.8 1.00

1

2

3x 10

6

MaxBaseS

hear(N)

PGAV/ PGA

H

w/o V-EQ

0.0 0.2 0.4 0.6 0.8 1.00

2

4

6

8

10x 10

6

MaxBaseMome

nt(N-m)

PGAV/ PGA

H

w/o V-EQ

0.0 0.2 0.4 0.6 0.8 1.00

2

4

6

8

10x 10

6

MaxBaseMome

nt(N-m)

PGAV/ PGA

H

w/o V-EQ

0.0 0.2 0.4 0.6 0.8 1.00

0.02

0.04

0.06

0.08

MaxColumnDrift(m)

PGAV/ PGA

H

w/o V-EQ

0.0 0.2 0.4 0.6 0.8 1.00

0.02

0.04

0.06

0.08

MaxColumnDrift(m)

PGAV/ PGA

H

w/o V-EQ

a! $J WN77X *J WN77 b! $J WN77X *J NOR

0.0 0.2 0.4 0.6 0.8 1.0-1

0

1

2x 10

7

PGAV/ PGA

H

AxialForce(N),comp.is"+"

Column of Bridge#4 (H/D=2.5, P/P0=15%)

subject to WN22 (T&V)

Max

min

0.0 0.2 0.4 0.6 0.8 1.0-1

0

1

2x 10

7

PGAV/ PGA

H

AxialForce(N),comp

.is"+"

Column of Bridge#4 (H/D=2.5, P/P0=15%)

subject to WN22(T) & NO4(V)

Max

min

a! $ori/ontalJ WN77 (p92R;;s!X

*erticalJ WN77 (p926T;s!

b! $ori/ontalJ WN77 (p92R;;s!X

*erticalJ NOR (p92T77s!

t*pea1Y t$

pea1 -926s

4 Lar%er PA*PA$ratio tends to have

lar%er in'luence on 'orce de"and2

4 No si%ni'icant correlation exists )ithdri't de"and2


23/28

23Quake Summit 2010

$rid%e #epone Coniderin% ASFI

1 2 3 4 5 6 7 8 9 100

0.02

0.04

0.06

MaxCo

lumnDriftRatio

Bridge #4, H/D=5.0

V+H

H only

1 2 3 4 5 6 7 8 9 100.5

1

1.5

2

2.5x 10

6

MaxSectionForce(N)

1 2 3 4 5 6 7 8 9 100

5

10

15x 10

6

MaxSectionMoment(N-m)

1 2 3 4 5 6 7 8 9 100

1

2

3

4

MaxDeckAcc.(g)

Earthquake Index Number

1 2 3 4 5 6 7 8 9 100

0.01

0.02

0.03

0.04

MaxCo

lumnDriftRatio

Bridge #4, H/D=2.5

V+H

H only

1 2 3 4 5 6 7 8 9 101.5

2

2.5

3

3.5x 10

6

MaxSectionForce(N)

1 2 3 4 5 6 7 8 9 104

6

8

10x 10

6

MaxSectionMoment(N-m)

1 2 3 4 5 6 7 8 9 100

1

2

3

4

MaxDeckAcc.(g)

Earthquake Index Number

-0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06-3

-2

-1

0

1

2

3x 10

6Force-Displacement //Longi.

Column Drift (m)

ShearForce(N)

C1@B1

C2@B1

C1@B2

C2@B2

-0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04-3

-2

-1

0

1

2

3x 10

6 Force-Displacement //Trans.

Column Drift (m)

ShearForce(N)

l

l

Force v2s2 total colu"n dri't $572!

Considerin% axial variation does not

chan%e overall brid%e responses

"uch2


24/28

24Quake Summit 2010

Summary

4 Axial load considerabl# a''ects the lateral responses o' .C

colu"ns2

4 Pri"ar# curves o' the sa"e colu"n under di''erent axial loads

can be predicted ver# )ell b# appl#in% the nor"ali/ed pri"ar#

curve and para"eteri/ed critical points2

4 Mappin% bet)een loadin% branches correspondin% to di''erent

axial load levels is "ade possible b# brea1in% the step into t)osta%esJ constant de'or"ation sta%e and constant loadin% sta%e2

4 Model veri'ication sho)s that the proposed "ethod is able to

capture the e''ects o' axial load variation on the lateral responses

o' .C colu"ns2

4 (ransient ti"e anal#sis on individual brid%e colu"n and onprotot#pe brid%e s#ste" sho)s that considerin% axial load

variation durin% earth3ua1e events does not chan%e the dri't

de"and si%ni'icantl#2


25/28

25Quake Summit 2010

ACE63+;!6=

=hank "or your attention G

(he research presented here )as 'unded b# NationalScience Foundation throu%h the Net)or1 'or ,arth3ua1e

,n%ineerin% Si"ulation .esearch Pro%ra"0 %rant CMMI-

9T9VTV0 o# Pausch1e0 pro%ra" "ana%er2

Thank You


26/28

26Quake Summit 2010

Analytical !odel "or #C Column

)latic Hin%e !odel

Usin% e3uivalent sprin%s to si"ulate shear

and 'lexural responses o' colu"ns at theele"ent level

,"pirical and approxi"ate

5i''icult to couple to%ether the axial0 shear0

and 'lexural responses

Nu"erical instabilit# in the adoptedh#steretic "odels "a# induce conver%ence

proble"

Fi4er Section Formulation

Controllin% the ele"ent responses directl# at

the "aterial level Couplin% the axial-'lexural interaction

.otation o' principal axes in concrete as

lar%e as T9Z! due to the existence o' shear

stress is not considered

,lastic or ri%id bea"

Linear or Nonlinear

sprin% ele"ents

2

y

3

'iber

y

3


27/28

27Quake Summit 2010

+e"iciencie o" Current 6umerical !odel

+e"iciencie o" Current !odel

Non-linearit# in shear de'or"ation is not accounted 'or2

Material da"a%e stren%th deterioration and pinchin%! due to c#clic loadin% is not considered2

Axial-Shear-Flexural interaction is not captured2

-60 -40 -20 0 20 40 60-150

-100

-50

0

50

100

150

Dislacement mm

Shear(kN)

(a) Nonlinear Timoshenko Beam Element

Test TP-021

nonLinear M-

-60 -40 -20 0 20 40 60-150

-100

-50

0

50

100

150

Dislacementmm

Shear(kN)

(b) OpenSees Fiber Element

Test TP-021

OpenSees Fiber


28/28

-60 -40 -20 0 20 40 60

-200

-100

0

100

200

-10.0%

25.0%


LateralLoad(kN

)

TP033: Axial Load= -10(-0.3%) ~ +310(+8.5%) kN

predicted by equations

0 5 10 15 200

50

100

150

200


LateralLoad(kN)

EXP

P/Po= 12.80%

proposed Eq's

0 10 20 30 400

50

100

150

200

-10.0%

25.0%


LateralLoad(kN

)

Primary Curve Family of TP-033

0 5 10 150

50

100

150

200


LateralLoad(kN)

P/P0= 12.80%

OpenSees

Comparion o" )rimary Cur.e Family @ith Fi4er !odel

4 Si#i!'r 5r6nds 'r6 7s6r86d 6296p5 ps5-yi6!d r6spns6:

4 Fi76r S695in Md6! 86r6s5i#'56s ini5i'! s5i;;n6ss:

4 Fi76r S695in Md6! "nd6r6s5i#'56s '2i'! !'d 6;;695s:

0

10

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