F O R C E D E T E R M IN A T IO N A N D D Y N A M IC P R O P E R T...

M E T U F O O T B R I D G E : C A B L E M E T U F O O T B R I D G E : C A B L E

F O R C E D E T E R M I N A T I O N

I S T A N B U L B R I D G E C O N F E R E N C E , 2 0 1 4

M ond ay, A ug us t 2 5 , 2 0 1 41

P R O P E R T I E S

A N D D Y N A M I C

P R O P E R T I E S

N J O M O W . 1 a n d A . T U R E R 2

1 P h D . C a n d i d a t e , D e p t . o f C i v i l E n g i n e e r i n g , M i d d l e E a s t T e c h n i c a l

U n i v e r s i t y , 0 6 8 0 0 A n k a r a , T U R K E Y

2 A s s o c i a t e P r o f e s s o r , D e p t . o f C i v i l E n g i n e e r i n g , M i d d l e E a s t

T e c h n i c a l U n i v e r s i t y , 0 6 8 0 0 A n k a r a , T U R K E YM ond ay, A ug us t 2 5 , 2 0 1 41M E TU F ootb rid g e

C O N T E N T S2

�� C as e D efinitionC as e D efinition

�� C ab l e Tens il e F orc esC ab l e Tens il e F orc es

M ond ay, A ug us t 2 5 , 2 0 1 4M E TU F ootb rid g e

�� D ec k’ s D ynam ic P rop ertiesD ec k’ s D ynam ic P rop erties

�� C onc l us ion/ D is c us s ionsC onc l us ion/ D is c us s ions

C A S E C A S E

D E F I N I T I O ND E F I N I T I O N�� D efinitionD efinition

�� L oc ationL oc ation

M ond ay, A ug us t 2 5 , 2 0 1 4M E TU F ootb rid g e 3

�� L oc ationL oc ation

�� D im ens ionsD im ens ions

�� H is toryH is tory

C A S E D E F I N I TI O NC A S E D E F I N I TI O N4

S t a y e d -

c a b l e B r i d g e

w i t h

m e t a l l i c


L o c a t i o n :

D um l up inar

B oul ev ard ;

W i d t h : ab out

5 . 0 0 m ;

L e n g t h :

d e c k


S t a y e d -

c a b l e B r i d g e

w i t h

m e t a l l i c


d e c k

C A B L E T E N S I L E C A B L E T E N S I L E

F O R C E SF O R C E S�� TheoryTheory

�� M eas urem entsM eas urem ents

M ond ay, A ug us t 2 5 , 2 0 1 4M E TU F ootb rid g e 7

�� M eas urem entsM eas urem ents

�� D ata P roc es s ingD ata P roc es s ing

�� Res ul ts and I nterp retationRes ul ts and I nterp retation

C A B L E T E N S I L E F O R C E S

8

M ethod 0 1 : T a ut guita r strin g method

• m (= 1 4 . 1 0 kg / m ) is the l inear m as s d ens ity

in kg / m ;

• L is the c ab l e l eng th b etween anc horag es in m ;

• f is the frequenc y in H z c orres p ond ing to

� =4��2��

2

�2


• fn is the frequenc y in H z c orres p ond ing to

m od e ord er nD oes not ac c ount for:• c ab l e b end ing s tiffnes s ;• m aterial ’ s m od ul us of el as tic ity;• c ros s -s ec tional area;• m om ent of inertia;• b ound ary c ond itions


9

M ethod 0 2 : Zui H , S hinke T, and N am ita Y [3 ]

1 -I n the c as e of us ing the natural frequenc y of firs t-ord er m od e (s uffic ientl y s m al l s ag 3 ≤ Γ)

2 - I n the c as e of us ing the natural frequenc y of s ec ond -ord er m od e (s uffic ientl y


2 - I n the c as e of us ing the natural frequenc y of s ec ond -ord er m od e (s uffic ientl y s m al l s ag 3 ≥Γ)

3 -I n the c as e of us ing the natural frequenc y of hig h-ord er m od es (v ery l ong c ab l e 2 ≤ Γ)

• E : the m od ul us of el as tic ity ;

• A : the c ros s -s ec tional area, (= 1 . 73 5 E -3

m 2 );

• I : m om ent of inertia, (= 2 . 3 95 3 1 E -3


1 0

M ethod 0 3: Wenzel H . and P ic hl er D . [4 ]


M E A S U R E M E N T S1 1

M a teria l:

Two triaxial ac c el erom eters (M ic ros train)

O ne d atal og g er

O ne P C to run with ap p rop riate s oftware and s av e d ata

P roced ure:


P roced ure:

E xc itation of eac h c ab l e and d ata rec ord two or three tim es

E xc itation of d ec k and d ata rec ord three tim es

P erson n el:

F our g roup s of M E TU inv es tig ators , eac h in years 2 0 0 5 , 2 0 1 1 ,

2 0 1 2 and 2 0 1 3 , res p ec tiv el y.


S en sor L oca tion s


D A T A P R O C E S S I N G1 3

A bsolute va lues a fter F F T plotted in frequen cy d oma in for ca ble 1



Mo d e 1 Mo d e 2 Mo d e 3 Mo d e 4 Mo d e 5

C a bl e 1 0.5631 1.126 1.766 2.278 2.918

C a bl e 2 0.5631 1.152 1.715 2.304 2.969

C a bl e 3 0.8191 1.638 2.483 3.328 4.198

C a bl e 4 0.6655 1.357 2.048 2.739 3.481

F irst five frequen cies for ea ch ca ble (2 0 1 3)


C a bl e 4 0.6655 1.357 2.048 2.739 3.481

C a bl e 5 0.8447 1.689 2.534 3.507 4.377

C a bl e 6 0.9727 1.945 2.944 4.070 5.068

C a bl e 7 1.305 2.611 3.993 5.299 6.681

C a bl e 8 1.3820 2.765 4.198 5.606 7.039

C a bl e 9 0.8959 1.817 2.867 3.942 5.094

C a bl e 1 0 0.8191 1.638 2.611 3.66 4.761

C a bl e

1 1 1.305 2.713 4.172 5.734 7.756

C a bl e

1 2 1.3310 2.790 4.300 5.964 7.910


1 5

G ra phica l represen ta tion of a xia l loa d d istribution -Y ea r 2 0 0 5

60

80

100

120

Ax

ial

loa

d i

n k

N

Method 1

Method 2

Method 3


1 2 3 4 5 6 7 8 9 10 11 120

20

40

60

Cables ID

Ax

ial

loa

d i

n k

N

0 P a n el


1 6


60

80

100

120

Ax

ial

loa

d i

n k

N

Method 1

Method 2

Method 3


1 2 3 4 5 6 7 8 9 10 11 120

20

40

60

Cables ID

Ax

ial

loa

d i

n k

N

0 P a n el


1 7

G ra phica l represen ta tion of a xia l loa d d istribution - Y ea r 2 0 1 2

100

150

200

Ax

ial

loa

d i

n k

N

Method 1

Method 2

Method 3


1 2 3 4 5 6 7 8 9 10 11 120

50

Cables ID

Ax

ial

loa

d i

n k

N

1 P a n el


1 8


100

150

200

Ax

ial

loa

d i

n k

N

Method 1

Method 2

Method 3


1 2 3 4 5 6 7 8 9 10 11 120

50

Cables ID

Ax

ial

loa

d i

n k

N

2 P a n els


1 9

E volution of ca bles’ forces a lon g ca mpa ign s

120

140

160

180

200

Axi

al C

able

Fo

rce

(kN

)


0

20

40

60

80

100

120

1 2 3 4 5 6 7 8 9 10 11 12

Axi

al C

able

Fo

rce

(kN

)

Cable ID

2005

2011

2012

2013

D E C K’S D Y N A M I C D E C K’S D Y N A M I C

P R O P E R T I E SP R O P E R T I E S�� M eas urem entM eas urem ent

�� A nal ytic al m od elA nal ytic al m od el

�� M od e id entific ationM od e id entific ation

M ond ay, A ug us t 2 5 , 2 0 1 4M E TU F ootb rid g e 2 0

�� M od e id entific ationM od e id entific ation

�� S truc tural I d entific ationS truc tural I d entific ation

�� M as sM as s

�� S tiffnes sS tiffnes s


S en sor L oca tion s



A b s ol ute v al ue of Y-D irec tion

A b s ol ute v al ue of Z-D irec tion


I m ag inary p art of Z-D irec tion

I m ag inary p art of Y-D irec tion

W est N od e

F I N I T E E L E M E N T M O D E L

2 3

F in ite E lemen t M od els



2 4

F in ite E lemen t M od els



2 5

S t r u c t u r a l

p o r t i o n s

M o d eF r e q u e n c y

( H z )

D i r e c t i o nS h a p e

d e s c r i p t i o n

R a w

a n a l y t i c a l

P a n e l s l a t e r a l

s a m e

d i r e c t i o n1 . 4 5 0 4 3

o p p o s i t e

d i r e c t i o n1 . 4 6 0 5

1 s t b e n d i n g 4 . 6 6 4 0 3

2 n d b e n d i n g 8 . 9 8 2 4 9

R a w A n a lytica l F requen cies


D e c k

v e r t i c a l

2 n d b e n d i n g 8 . 9 8 2 4 9

3 r d b e n d i n g 2 0 . 6 0 4 0 3

4 t h b e n d i n g 2 3 . 3 2 4 7 6

5 t h b e n d i n g 2 6 . 1 7 1 2 6

l a t e r a l

1 s t b e n d i n g 5 . 5 8 0 7 9

2 n d b e n d i n g 1 2 . 9 6 0 6 7

3 r d b e n d i n g 2 2 . 8 6 1 8 6

t o r s i o n1 s t t w i s t i n g 8 . 1 0 8 7

2 n d t w i s t i n g 1 5 . 0 8 4 6 9

P y l o n

l o n g i t u d i n a l

1 s t b e n d i n g 7 . 3 0 6 9 1

2 n d b e n d i n g 1 0 . 4 1 5 1 2

3 r d b e n d i n g 2 4 . 0 9 7 2 8

t r a n s v e r s a l

1 s t b e n d i n g 1 . 7 4 0 9 9

2 n d b e n d i n g 1 0 . 1 1 8 3 8

3 r d b e n d i n g 2 5 . 6 7 7 3


F r e q u e n c y

P e a k 1 P e a k 2 P e a k 3 P e a k 4 P e a k 5

2 . 8 6 7 4 . 0 7 0 4 . 5 3 1 6 . 2 3 6 8 . 5 7 6

Y-

Dir W e s t 0 - 0 - 0

E a s t 0 - 0 + 0

Z-

Dir W e s t + 0 + - -

E a s t + 0 + + -

S a m e S a m e S a m e a n t a g o n i s

S a m e

M od e id en tifica tion


C o m m e n t s

S a m e

d i r e c t i o n

d i s p l a c e

m e n t i n

v e r t i c a l

a x i s

w i t h o u t

m o t i o n i n

Y - a x i s

S a m e

d i r e c t i o n

d i s p l a c e

m e n t i n

l a t e r a l

a x i s

w i t h o u t

m o t i o n i n

Z- a x i s

S a m e

d i r e c t i o n

d i s p l a c e

m e n t i n

v e r t i c a l

a x i s

w i t h o u t

m o t i o n i n

Y - a x i s

a n t a g o n i s

t

d i s p l a c e

m e n t i n

v e r t i c a l

a x i s w i t h

m o t i o n i n

Y - a x i s

S a m e

d i r e c t i o n

d i s p l a c e

m e n t i n

v e r t i c a l

a x i s

w i t h o u t

m o t i o n i n

Y - a x i s

C o n c l u s i o n

1 s t

v e r t i c a l

b e n d i n g

1 s t

t r a n s v e r s

a l

b e n d i n g

2 n d

v e r t i c a l

b e n d i n g

1 s t

t o r s i o n a l

3 r d

v e r t i c a l

b e n d i n g

m o d e

L e g e n d :


2 7U pd a tin g P rocess

P a ra meters R a w Va lues U pd a ted Va lues

M a ss d en sity of pa n el ma teria l:

5 4 . 1 6 kg / m 3 5 3 . 1 2 2 kg / m 3

E la stic mod ulus of pa n el ma teria l:

69 0 0 0 M P a 67 62 0 M P a


ma teria l: 69 0 0 0 M P a 67 62 0 M P a

S tiffn ess con tribution of pa n els:

1 0 0 % 1 %

T hickn ess of pa n els: 5 0 c m 3 0 c m

P a n el lin ks:75 0 0 0 0 N / m 75 0 0 0 0 N / rad

D eck supports: (s ee in the p ap er)


2 8

A n a l y t i c a l

f r e q u e n c y ( H z )

E x p e r i m e n t a l


1 s t v e r t i c a l b e n d i n g

m o d e4.664 2 . 867

1 s t t r a n s v e r s a l

b e n d i n g m o d e5 . 5 81 4.0 70

2 n d v e r t i c a l

C ompa rison of frequen cy vectors



b e n d i n g m o d e8.9 82 4.5 31

1 s t t o r s i o n a l m o d e 8.1 0 9 6.2 36

3r d v e r t i c a l b e n d i n g

m o d e2 0 . 60 4 8.5 76

E r r o r N o r m 1 73. 5 0 5

A n a l y t i c a l


E x p e r i m e n t a l


1 s t v e r t i c a l b e n d i n g

m o d e3.0 5 3 2 . 867

1 s t t r a n s v e r s a l

b e n d i n g m o d e4.373 4.0 70


b e n d i n g m o d e5 . 0 2 0 4.5 31

1 s t t o r s i o n a l m o d e 6.2 71 6.2 36

3r d v e r t i c a l b e n d i n g

m o d e7.2 1 6 8.5 76


2 9

20

25

Fre

qu

en

cy i

n H

z

Updated analytical frequencies

Raw analytical frequencies

C ompa rison of F requen cy Vectors


0

5

10

15

1 2 3 4 5

Fre

qu

en

cy i

n H

z

Mode

Raw analytical frequencies

Experimental frequencies

D E C K’S D Y N A M I C P R O P E R T I E S

3 0

D eck’s M a ss Va ria tion

m d = 91 74 . 4 1 0 1 kg∆m = 3 92 4 . 771 kg


md

∆∆∆∆m

3 92 4 . 771 kg

∆m = 3 94 4 . 3 0 9 kg


3 1

2 0 0 5 2 0 1 1 2 0 1 2 2 0 1 3

N o p a n e l N o p a n e lo n e s i d e

p a n e l

t w o

s i d e

D eck’s F requen cies a n d S tiffn ess Va ria tion


N o p a n e l N o p a n e lp a n e l

s i d e

p a n e l s

V e r t i c a l b e n d i n g

m o d e

F i r s t3 . 1

r a d /se c3 . 0 5 r a d /se c 2 . 9 7 r a d /se c

2 . 8 7

r a d /se c

S e c o n d4 . 8


4 . 5 3

r a d /se c

T h i r d9 . 2

r a d /se c- 8 . 4 3 r a d /se c

8 . 5 8

r a d /se c

F o u r t h1 2 . 1

r a d /se c-

1 2 . 1 4

r a d /se c-

T o r s i o n a l b e n d i n g

m o d ef i r s t

6 . 5


6 . 2 4

r a d /se c

S t i f f n e s s B e n d i n g 9 1 6 k N/m 8 8 7 k N/m 8 5 9 k N/m8 1 6

k N/m


3 2

D eck’s S tiffn ess Va ria tion

Tors

ion

al s

tiff

ne

ss (

N/r

ad)

Ve

rtic

al s

tiff

ne

ss (

N/m

)


2005 2007 2009 2011 2013 2015

Tors

ion

al s

tiff

ne

ss (

N/r

ad)

Ve

rtic

al s

tiff

ne

ss (

N/m

)

Vertical

Torsion

C O N C L U S I O NC O N C L U S I O N

A N DA N D


D I S C U S S I O N SD I S C U S S I O N S

C O N C L U S I O N3 4

• N o c ons id eration of c oup l ers ’ p res enc e

• I n g eneral , M ethod 0 2 g iv es s m al l er

C a bles’ T en sile F orces


• I n g eneral , M ethod 0 2 g iv es s m al l er v al ues

• N o m onotonic c hang e of c ab l e forc es d ue to s ag rel ated s ens itiv ity


• D es p ite the ad d ition of ad v ertis em ent p anel s one c oul d exp ec t a s l ig ht

D eck’s D yn a mic P roperties


p anel s one c oul d exp ec t a s l ig ht s tiffnes s c ontrib ution

• D ec k’ s s tiffnes s c ontinuous l y d ec ays ov er the c ours e of years


• C al ib rated d ig ital m od el c an s erv e as a b as is of the s tud y of hum an ind uc ed v ib ration and fatig ue anal ys is

F uture I n vestiga tion s


and fatig ue anal ys is

• Rel iab il ity and l ong term b ehav ior of b rid g es s houl d ac c ount for p os s ib l e s tiffnes s and m as s c hang es as they woul d infl uenc e b oth d ynam ic c harac teris tic s and red is trib ution of forc es .

R E F E R E N C E SR E F E R E N C E S


R E F E R E N C E S3 8

1 . The M athworks , I nc . , M a t La b, M athem atic al C om p uting S oftware,

M as s ac hus etts , U S A .

2 . Turer A . , St r uc t ur a l He a l t h M o n i t o r i n g - Le c t ur e No t e s ,

M E TU : S p ring 2 0 1 3 .

3 . Zui H , S hinke T, and N am ita Y. P rac tic al F orm ul as for E s tim ation of


3 . Zui H , S hinke T, and N am ita Y. P rac tic al F orm ul as for E s tim ation of

C ab l e Tens ion b y Vib ration M ethod . A SC E Jo ur n a l o f St r uc t ur a l

E n g i n e e r i n g 1 996; 1 2 2 (6): 65 1 -65 6.

4 . Wens el H , P ic hl er D . A mbi e n t Vi br a t i o n M o n i t o r i n g . Wil ey:

E ng l and , A p ril 2 0 0 5 .

5 . Özerkan T, In s t r ume n t e d M o n i t o r i n g a n d D y n a mi c T e s t i n g

o f M E T U C a bl e St a y e d P e d e s t r i a n Br i d g e a n d

C o mp a r i s o n s a g a i n s t A n a l y t i c a l M o d e l Simul a t i o n s ,

M S c Thes is , M E TU : Turkey, 2 0 0 5 .

T HA N K Y O U F O R T HA N K Y O U F O R

Y O U R Y O U R


Y O U R Y O U R

A T T E N T I O NA T T E N T I O N

F O R C E D E T E R M IN A T IO N A N D D Y N A M IC P R O P E R T...

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