Prestressed composite box girder bridges with corrugated · PDF file1 Prestressed composite...

1

Prestressed composite box girder bridges with corrugated webs

A critical comparison with flat steel websA critical comparison with flat steel webs

Ing. Gabriele Bertagnoli

Politecnico di Torino

2

Some examples of the use of corrugated webs in bridges

(and other civil structures)

3

• Pont de la Corniche, France

4

• Himi Yuma Bridge, Japan

5

• Ginzan-Miyuki Bridge, Japan

6

• Hontani Bridge, Japan

7

• Long span building structures (by “Zeman & Co”)

8

Some examples of the use of flat steel webs in composite steel-concrete bridges

9

Verrieres bridge Verrieres bridge –– FranceFrance

10

Roccaprebalza Viaduct : Parma Roccaprebalza Viaduct : Parma –– La Spezia Highway La Spezia Highway -- ItalyItaly

11

Gassino bridge Gassino bridge –– Torino Torino -- ItalyItaly

12

Gassino bridge Gassino bridge –– Torino Torino -- ItalyItaly

13

Some theory stuff

14

As the web is corrugated, it has very little ability to sustain longitudinal stresses. Conventionally the contribution of the web to the ultimate

Bending behaviour of corrugated webs

stresses. Conventionally the contribution of the web to the ultimate bending capacity of a beam with corrugated web is assumed

negligible, and the ultimate bending capacity is calculated using the plastic modulus of the flanges.

Elgaaly (1997) carried out experimental and analytical studies to verify

if the web can contribute to the bending capacity of the whole girder.

Dimentions

in cm

15

In order to verify if the web can contribute to the bending capacity of

the whole girder, the failure moment is compared with the bending

Bending behaviour of corrugated webs

the whole girder, the failure moment is compared with the bending

moment corresponding to the yielding of the flanges. It was found

that the web contribution could be neglected.

Mf ≃≃≃≃MMMMy,fy,fy,fy,f My,w ≃≃≃≃ 0000

The bending capacity of the whole girder is affected by manyThe bending capacity of the whole girder is affected by many

parameters. The following factors were analyzed:

a. ratio between the flange and web thickness;

b. ratio between the flange and web yield stresses;

c. corrugation configurations.

The stresses in the web due to bending are equal to zero except for

small regions very close to the flanges where the web is restrained.

16

Shear behaviour of corrugated webs

FAILURE MODESMODES

Local buckling

Zonal buckling

Global buckling

17


FAILURE MODESMODES

Local buckling

Zonal buckling

Global buckling

18


FAILURE MODESMODES

Local buckling

Zonal buckling

Global buckling

60° 6

60° 45° 30°

θ

19


FAILURE MODESMODES

Local buckling

Zonal buckling

Global buckling

n=LTOT

/a

1/d

20


21

Strength of corrugated webs

subjected to shear:


- Local buckling (similar

expression of the local buckling

formula for normal plate girder

developed by Timoshenko and

Gere)

Ecr,L l

E ak ( )wπ

τν

= ⋅ −

22

212 1

- The shear yield stress τy is

defined by the Huber-Von ( )wν− 12 1

- Global buckling (calculated

from the orthotropic-plate

buckling theory)

defined by the Huber-Von

Mises-Hencky yield criterion

y xEcr,G g

D Dk

w hτ

⋅= ⋅

⋅

314 4

2

yy y

f . fτ = ≈ 0 583

INTERACTIVE BUCKLING STRENGTH

22

LIVE LOADS : LIVE LOADS :

ELASTIC ANALYSISELASTIC ANALYSIS

• The structure is not homogeneous from the rheological point of view:

viscoelasticity theorems CAN NOT be used

DEAD LOAD + CREEP + SHRINKAGE + PRESTRESSING + DEAD LOAD + CREEP + SHRINKAGE + PRESTRESSING + CONSTRUCTION PHASES:CONSTRUCTION PHASES:

VISCOELASTIC ANALYSISVISCOELASTIC ANALYSIS

viscoelasticity theorems CAN NOT be used

• step by step analysis with detailed time history:

[ ] [ ] )(),(),(2

1)()()()(),()(

1

110

kcs

k

i

ikikicickcs

t

tkc tttJttJtttdtJt

k

εσσετστε ∑∫=

−− +

+⋅⋅−≈+=

23

Creep and relaxation functions used in phased analysis

∫+⋅=t

tdtRttRt

0

)(),(),()( 00 τετεσ

∫+⋅=t

tdtJttJt

0

)(),(),()( 00 τστσε

),(1 ttϕ

),()(),( 02800 ttEtEttR ρ⋅+=

0),( 0 ≥ttϕ28

0

0

0

),(

)(

1),(

E

tt

tEttJ

ϕ+=

0),( 0 ≤ttρ

24

Comparison of flat webs solution and corrugated webs solution on the same

“testing” bridge

25

Construction procedure common to both flat and corrugated webs solutions

26

Gassino bridge reduced to 3 hammers schemeGassino bridge reduced to 3 hammers scheme

92m 92m 50m50m

Soletta superiore

Concrete top slab with bonded prestressing

Trave in acciaio

Soletta inferiorePredalle prefabbricata

Steel webs

Concrete bottom slab

Precast slab used as

scaffolding

27

PositionDeck depth

[m]

Depth/Span

length L/h

Continuity

support4 23

support4 23

Midspan and

abutments2 46

28

Hammers construction phases

Single hammer construction phases

29

Phase 1 - Positioning of steel box pier segment(formwork for concrete diaphragm casting)

30

Phase 2 - Webs assembling by bolts and adjustment/stiffening bytemporary ties

Phase 3 – Slabs Phase 3 – Slabs concreting

31

Phase 4 – Internal prestressing

28 tendons: 6 for each segment apart from segment 1 which has 2

N°of strandsStrand cross

sectionNominal

areaDuct

diameter

15 139 mm2 2085 mm2 90 mm

33

Phase 4 – Internal prestressing

Layout of the connection connection

reinforcement

between precast anchorage blocks and

upper slab.

34

Phase 5

Repetition of previous operations working in

parallel on several piersparallel on several piers

Phase 6 – Alignment of bolted joint on webs between two segments

35

Phase 7 – External prestressing: 10 tendons with 27 strands in main spans and 22 strands in lateral ones

36

Phase 7 – External prestressing

37

Pay attention to the geometrical interferences between external tendons and stiffeners

38

Transversal truss stiffeners detail.detail.

Longitudinal spacing = 3m

The shape of plenty of them is modified to avoid external

tendons geometrical interferences.

(See arrows in the picture (See arrows in the picture

beside and in the previous slide)

39

Construction time scheduling common to both flat and corrugated webs solutions

40

Day Time [d] Phase Segment Side Set Segment side Load

Monday 1 1 0 Web+TS+BS

Wednesday 3 1 0 Web+TS+BS

Elements activation Loads activationTime steps

Hammers 1 and 3

Wednesday 3 1 0 Web+TS+BS

Thursday 46 2 1 Right Web 1 Right Web

Friday 47 3 1 Left Web 1 Left Web

Saturday 48 3 1 Right BS

Monday 50 3 1 Left BS

Tuesday 51 4 1 Right BS

Wednesday 52 5 1 Left BS

Thursday 53 5 1 Right TS

Friday 54 5 1 Left TS

Saturday 55 6 1 Right TSSaturday 55 6 1 Right TS

Monday 57 7 1 Left TS 1 Prestress

Tuesday 58 8 2 Right Web 2 Right Web

Wednesday 59 9 2 Left Web 2 Left Web

Thursday 60 9 2 Right BS

Friday 61 9 2 Left BS

Saturday 62 10 2 Right BS

Monday 64 11 2 Left BS

Tuesday 65 11 2 Right TS

41

Evolution of internal actions during construction and service life of

FLAT WEB SOLUTIONFLAT WEB SOLUTION

42

3,00E+07

Bending moment diagrams during hammer construction phases

-2,00E+07

-1,00E+07

0,00E+00

1,00E+07

2,00E+07

40 45 50 55 60 65 70 75 80 85

Mo

men

ti

[N

m]

Fine concio 1

End of segment 1

Be

nd

ing m

om

en

t [N

m]

-3,00E+07

Coordinata [m]Longitudinal axis [m]

43

3,00E+07


-2,00E+07

-1,00E+07

0,00E+00

1,00E+07

2,00E+07

40 45 50 55 60 65 70 75 80 85

Mo

men

ti

[N

m]

Fine concio 1

Tiro cavi 1-2

End of segment 1

Prestressing of tendons 1

and 2Be

nd

ing m

om

en

t [N

m]

-3,00E+07


44

3,00E+07


-2,00E+07

-1,00E+07

0,00E+00

1,00E+07

2,00E+07

40 45 50 55 60 65 70 75 80 85

Mo

men

ti

[N

m]

Fine concio 1

Tiro cavi 1-2

Fine concio 2End of

segment 1


and 2

End of segment 2

Be

nd

ing m

om

en

t [N

m]

-3,00E+07


45

3,00E+07


-2,00E+07

-1,00E+07

0,00E+00

1,00E+07

2,00E+07

40 45 50 55 60 65 70 75 80 85

Mo

men

ti

[N

m]

Fine concio 1

Tiro cavi 1-2

Fine concio 2End of

segment 1


and 2

End of segment 2

Be

nd

ing m

om

en

t [N

m]

-3,00E+07

Coordinata [m]

Tiro cavi 3-5Prestressing of tendons 3,

4, 5Longitudinal axis [m]

46

5,00E+07

6,00E+07


-2,00E+07

-1,00E+07

0,00E+00

1,00E+07

2,00E+07

3,00E+07

4,00E+07

5,00E+07

20 30 40 50 60 70 80 90 100 110Mo

men

ti

[N

m]

Fine concio 3End of

segment 3

Be

nd

ing m

om

en

t [N

m]

-3,00E+07

-2,00E+07


47

5,00E+07

6,00E+07


-2,00E+07

-1,00E+07

0,00E+00

1,00E+07

2,00E+07

3,00E+07

4,00E+07

5,00E+07

20 30 40 50 60 70 80 90 100 110Mo

men

ti

[N

m]

Fine concio 3

Tiro cavi 6-8

End of segment 3

Prestressing of tendons 6,

Be

nd

ing m

om

en

t [N

m]

-3,00E+07

-2,00E+07

Coordinata [m]

Tiro cavi 6-8of tendons 6, 7, 8

Longitudinal axis [m]

48

5,00E+07

6,00E+07


-2,00E+07

-1,00E+07

0,00E+00

1,00E+07

2,00E+07

3,00E+07

4,00E+07

5,00E+07

20 30 40 50 60 70 80 90 100 110Mo

men

ti

[N

m]

Fine concio 3 Fine concio 4

Tiro cavi 6-8

End of segment 3


End of segment 4

Be

nd

ing m

om

en

t [N

m]

-3,00E+07

-2,00E+07

Coordinata [m]

Tiro cavi 6-8of tendons 6,

7, 8


49

5,00E+07

6,00E+07


-2,00E+07

-1,00E+07

0,00E+00

1,00E+07

2,00E+07

3,00E+07

4,00E+07

5,00E+07

20 30 40 50 60 70 80 90 100 110Mo

men

ti

[N

m]

Fine concio 3

Tiro cavi 9-11

Fine concio 4

Tiro cavi 6-8

End of segment 3

Prestressing

End of segment 4


-3,00E+07

-2,00E+07

Coordinata [m]

Tiro cavi 6-8Prestressing of tendons 6,

7, 8

of tendons 9, 10, 11


50

8,00E+07

9,00E+07


0,00E+00

1,00E+07

2,00E+07

3,00E+07

4,00E+07

5,00E+07

6,00E+07

7,00E+07

8,00E+07

Mo

men

ti

[N

m]

Fine concio 5

End of segment 5

Be

nd

ing m

om

en

t [N

m]

-1,00E+07

0,00E+00

10 30 50 70 90 110


51

8,00E+07

9,00E+07


0,00E+00

1,00E+07

2,00E+07

3,00E+07

4,00E+07

5,00E+07

6,00E+07

7,00E+07

8,00E+07

Mo

men

ti

[N

m]

Fine concio 5

Tiro cavi 12-14

End of segment 5

Prestressing of tendons 12, 13, 14

Be

nd

ing m

om

en

t [N

m]

-1,00E+07

0,00E+00

10 30 50 70 90 110


52

6,00E+07

7,00E+07


0,00E+00

1,00E+07

2,00E+07

3,00E+07

4,00E+07

5,00E+07

6,00E+07

Mo

men

ti

[N

m] Sigillatura cavi

interniGrouting of all internal tendons

Be

nd

ing m

om

en

t [N

m]

-1,00E+07

0,00E+00

10 30 50 70 90 110


53

6,00E+07

7,00E+07

Bending moment diagrams: external prestressing

introduction on lateral spans

0,00E+00

1,00E+07

2,00E+07

3,00E+07

4,00E+07

5,00E+07

6,00E+07

Mo

men

ti

[N

m]

Precompressione

campate laterali (50%)

Sigillatura cavi

interniGrouting of all internal tendons50% of lateral

spans prestressing

Be

nd

ing m

om

en

t [N

m]

-1,00E+07

0,00E+00

10 30 50 70 90 110


54

6,00E+07

8,00E+07

Bending moment diagrams: end of construction of central

hammer

-6,00E+07

-4,00E+07

-2,00E+07

0,00E+00

2,00E+07

4,00E+07

6,00E+07

0 50 100 150 200 250 300

Mo

men

ti

[N

m]

Fine stampella 2End of construction of hammer 2

Be

nd

ing m

om

en

t [N

m]

-8,00E+07

-6,00E+07


55

6,00E+07

8,00E+07

Bending moment diagrams: introduction of central spans

external prestressing

-6,00E+07

-4,00E+07

-2,00E+07

0,00E+00

2,00E+07

4,00E+07

6,00E+07

0 50 100 150 200 250 300

Mo

men

ti

[N

m]

Fine stampella 2

Precompressione

campate centrali (50%)

End of construction of hammer 2

50% of central span prestressingB

en

din

g m

om

en

t [N

m]

-8,00E+07

-6,00E+07


56

6,00E+07

8,00E+07

Bending moment diagrams: permanent loads introduction

-6,00E+07

-4,00E+07

-2,00E+07

0,00E+00

2,00E+07

4,00E+07

6,00E+07

0 50 100 150 200 250 300

Mo

me

nti

[

Nm

]

Perm. portatiPermanent loads

Be

nd

ing m

om

en

t [N

m]

-8,00E+07

-6,00E+07


57

6,00E+07

8,00E+07

Bending moment diagrams: introduction of 2nd 50% of

external prestressing

-6,00E+07

-4,00E+07

-2,00E+07

0,00E+00

2,00E+07

4,00E+07

6,00E+07

0 50 100 150 200 250 300

Mo

me

nti

[

Nm

]

Perm. portati

Ritesatura cavi

Permanent loads

Second 50% of external B

en

din

g m

om

en

t [N

m]

-8,00E+07

-6,00E+07

Coordinata [m]

of external prestressing


58

6,00E+07

8,00E+07

Bending moment diagrams: end of service life (50 years)

-6,00E+07

-4,00E+07

-2,00E+07

0,00E+00

2,00E+07

4,00E+07

6,00E+07

0 50 100 150 200 250 300

Mo

me

nti

[

Nm

]

Perm. portati

Ritesatura cavi50 anni

Permanent loads

Second 50% of external 50 years

Be

nd

ing m

om

en

t [N

m]

-8,00E+07

-6,00E+07

Coordinata [m]

50 anni of external prestressing

50 years


59

Evolution of stresses during construction and service life of

FLAT WEBS SOLUTIONFLAT WEBS SOLUTION

60

Axial stress in concrete top slab – continuity support section

0,00

0 50 100 150 200 250 300 350 400

-6,00

-4,00

-2,00

0,00

Te

ns

ion

i N

orm

ali [

MP

a]

Applicazione carichi

permanenti portati

Tiro dei cavi interniInternal tendons prestressing

Permanent loads introduction

Axia

l str

ess [M

Pa

]

-12,00

-10,00

-8,00

Tempi [gg]

Te

ns

ion

i N

orm

ali [

MP

a]

Tiro dei cavi esterni



campate centrali (50%)Ritesatura cavi esterni

First 50% of external prestressing on

lateral spansFirst 50% of external

prestressing on central spans

Second 50% of external prestressing everywhere

Time [days]

Axia

l str

ess [M

Pa

]

61

-7,00

100 1000 10000 100000


-9,00

-8,00

-7,00

Te

ns

ion

i N

orm

ali [

MP

a]

50 anni50 years: end of

service life

Axia

l str

ess [M

Pa

]

-11,00

-10,00

Tempi [gg]

Te

ns

ion

i N

orm

ali [

MP

a]

377 gg.377 days: end of construction

Time [days]

Axia

l str

ess [M

Pa

]

62

0,00

0 50 100 150 200 250 300 350 400

Axial stress in concrete bottom slab – continuity support section

-5,00

-4,00

-3,00

-2,00

-1,00

0,00

Te

ns

ion

i N

orm

ali [

MP

a]

Tiro dei cavi interni



Internal tendons prestressing

First 50% of external prestressing on central

spans

Axia

l str

ess [M

Pa

]

-9,00

-8,00

-7,00

-6,00

-5,00

Tempi [gg]

Te

ns

ion

i N

orm

ali [

MP

a]




permanenti portati

Ritesatura cavi esterniFirst 50% of external prestressing on lateral spans



Time [days]

Axia

l str

ess [M

Pa

]

63

-6,00

100 1000 10000 100000


-7,00

-6,50

-6,00

Te

ns

ion

i N

orm

ali [

MP

a] 50 anni50 years:

end of service life

Axia

l str

ess [M

Pa

]

-8,00

-7,50

Tempi [gg]

Te

ns

ion

i N

orm

ali [

MP

a]

377 gg.377 days: end of construction

Time [days]

Axia

l str

ess [M

Pa

]

64

60,00

0 50 100 150 200 250 300 350 400

Axial stress in steel top flange – continuity support section

-20,00

0,00

20,00

40,00

60,00

Te

ns

ion

i N

orm

ali [

MP

a]





Axia

l str

ess [M

Pa

]

-100,00

-80,00

-60,00

-40,00

Tempi [gg]

Te

ns

ion

i N

orm

ali [

MP

a]



permanenti portati


campate centrali (50%) Ritesatura cavi esterni


lateral spans

introduction

First 50% of external prestressing on central spans Second 50% of external

prestressing everywhere

Time [days]

Axia

l str

ess [M

Pa

]

65

-80,00

100 1000 10000 100000


-120,00

-100,00

-80,00

Te

ns

ion

i N

orm

ali [

MP

a]

377 gg.377 days: end of

construction

Axia

l str

ess [M

Pa

]

-180,00

-160,00

-140,00

Tempi [gg]

Te

ns

ion

i N

orm

ali [

MP

a]


service life

Time [days]

Axia

l str

ess [M

Pa

]

66

0,00

0 50 100 150 200 250 300 350 400

Axial stress in steel bottom flange – continuity support section

-80,00

-60,00

-40,00

-20,00

0,00

Te

ns

ion

i N

orm

ali [

MP

a]

Tiro dei cavi interniInternal tendons

prestressing

First 50% of external

Axia

l str

ess [M

Pa

]

-140,00

-120,00

-100,00

-80,00

Tempi [gg]

Te

ns

ion

i N

orm

ali [

MP

a]


campate centrali (50%) Ritesatura cavi esterni


permanenti portati




lateral spansPermanent loads

introduction

First 50% of external prestressing on central spans


Time [days]

Axia

l str

ess [M

Pa

]

67

-100,00

100 1000 10000 100000


-140,00

-120,00

-100,00

Te

ns

ion

i N

orm

ali [

MP

a]

377 gg.377 days:

end of construction

Axia

l str

ess [M

Pa

]

-180,00

-160,00

Tempi [gg]

Te

ns

ion

i N

orm

ali [

MP

a]

50 anni

50 years: end of

service life

Time [days]

Axia

l str

ess [M

Pa

]

68

1,00

0 50 100 150 200 250 300 350 400

Axial stress in concrete top slab – midspan key segment

-3,00

-2,00

-1,00

0,00

1,00

Te

ns

ion

i N

orm

ali [

MP

a] Tiro dei cavi esterni



Axia

l str

ess [M

Pa

]

-6,00

-5,00

-4,00

-3,00

Tempi [gg]

Te

ns

ion

i N

orm

ali [

MP

a]

Ritesatura cavi esterni


permanenti portati



Time [days]

Axia

l str

ess [M

Pa

]

69

-4,00

100 1000 10000 100000

Axial stress in concrete top slab – midspan key segment

-5,00

-4,50

-4,00

Te

ns

ion

i N

orm

ali [

MP

a]


service life

Axia

l str

ess [M

Pa

]

-6,00

-5,50

Tempi [gg]

Te

ns

ion

i N

orm

ali [

MP

a]

377 gg.

377 days: end of

construction

Time [days]

Axia

l str

ess [M

Pa

]

70

2,00

0 50 100 150 200 250 300 350 400

Axial stress in concrete bottom slab – midspan key segment

-4,00

-3,00

-2,00

-1,00

0,00

1,00

2,00

Te

ns

ion

i N

orm

ali [

MP

a] Tiro dei cavi esterni



permanenti portati

Permanent loads introductionFirst 50% of external

prestressing on central spans

Axia

l str

ess [M

Pa

]

-9,00

-8,00

-7,00

-6,00

-5,00

-4,00

Tempi [gg]

Te

ns

ion

i N

orm

ali [

MP

a]

Ritesatura cavi esterniSecond 50% of external prestressing everywhere

Time [days]

Axia

l str

ess [M

Pa

]

71

-6,00

100 1000 10000 100000

Axial stress in concrete bottom slab – midspan key segment

-7,00

-6,50

-6,00

Te

ns

ion

i N

orm

ali [

MP

a]


service life

Axia

l str

ess [M

Pa

]

-8,00

-7,50

Tempi [gg]

Te

ns

ion

i N

orm

ali [

MP

a]

377 gg.

377 days: end of

construction

Time [days]

Axia

l str

ess [M

Pa

]

72

Modeling of

CORRUGATED WEBS

73

Overall characteristicsOverall characteristics

• High longitudinal deformability (accordion effect)

• better U.L.S. shear buckling behaviour;

• Out of the plane inertia (transverse bending/ folded plate) .

74

An analytical method to calculate this ratio is developed

through the use of a model that satisfies equilibrium and

compatibility conditions.

75




Hypothesis: the web is under

pure bending moment and thepure bending moment and the

axial deformation in each

plate element of the

corrugated web is negligible.

VIRTUAL WORKS PRINCIPLE

dxc

xsenc

c

x

EJ

sencFdx

EJ

sencsencFdS

EJ

MMB

A

C

BS

iD

−⋅⋅

−⋅⋅

+⋅⋅⋅⋅

=⋅

= ∫ ∫∫ 113 αααα

δccEJEJEJ

A BS

+⋅⋅

=3

22

3

ca

EJ

sencFD

αδ

76




Hypothesis: the web is under

pure bending moment and thepure bending moment and the

axial deformation in each

plate element of the

corrugated web is negligible.

VIRTUAL WORKS PRINCIPLE

dxc

xsenc

c

x

EJ

sencFdx

EJ

sencsencFdS

EJ

MMB

A

C

BS

iD

−⋅⋅

−⋅⋅

+⋅⋅⋅⋅

=⋅

= ∫ ∫∫ 113 αααα

δ

+⋅⋅

⋅⋅=∆

348

3

22

3

ca

HtE

sencF

w

D

α

ccEJEJEJA BS

EtH

LF

w

hFLAT ⋅⋅

⋅=∆

+⋅⋅⋅

=∆∆

=3

482

22

3 ca

tL

sencr

whflat

Deq

α

77

Longitudinal profileLongitudinal profile

Web corrugationWeb corrugationReduction of Reduction of

modulus of modulus of

elasticity to take elasticity to take

into account into account

longitudinal longitudinal

stiffnessstiffness

350

SS

EE =

78

Comparison of results between corrugated and flat webs

79

0,00

0 50 100 150 200 250 300 350 400


-6,00

-4,00

-2,00

0,00

Te

ns

ion

i N

orm

ali [

MP

a]

Anime lisce

Anime corrugate


permanenti portati

Tiro dei cavi interniInternal tendons prestressing


Flat webs

Corrugated webs

Axia

l str

ess [M

Pa

]

-12,00

-10,00

-8,00

Tempi [gg]

Te

ns

ion

i N

orm

ali [

MP

a]


campate laterali (50%)Tiro dei cavi esterni

campate centrali (50%)Ritesatura cavi esterni


lateral spans First 50% of external prestressing on central

spansSecond 50% of

external prestressing everywhere

Time [days]

Axia

l str

ess [M

Pa

]

80

-7,00

100 1000 10000 100000


-9,00

-8,00

-7,00

Te

ns

ion

i N

orm

ali [

MP

a]

Anime lisce

Anime corrugate

50 anni

Flat webs

Corrugated webs

50 years: end of

service life

Axia

l str

ess [M

Pa

]

-12,00

-11,00

-10,00

Tempi [gg]

Te

ns

ion

i N

orm

ali [

MP

a]


construction

Time [days]

Axia

l str

ess [M

Pa

]

81

0,00

0 50 100 150 200 250 300 350 400


-4,00

-2,00

0,00

Te

ns

ion

i N

orm

ali [

MP

a]

Anime lisce

Anime corrugate






Flat webs

Corrugated websInternal tendons prestressing

First 50% of external

First 50% of external prestressing on central

spans

Second 50% of external

Axia

l str

ess [M

Pa

]

-10,00

-8,00

-6,00

Tempi [gg]

Te

ns

ion

i N

orm

ali [

MP

a]




permanenti portati

Ritesatura cavi esterniFirst 50% of external prestressing on lateral spans



Time [days]

Axia

l str

ess [M

Pa

]

82

-6,00

100 1000 10000 100000


-7,50

-7,00

-6,50

-6,00

Te

ns

ion

i N

orm

ali [

MP

a]

Anime lisce

Anime corrugate

50 anni

Flat webs

Corrugated webs

50 years: end of

service life

Axia

l str

ess [M

Pa

]

-9,00

-8,50

-8,00

Tempi [gg]

Te

ns

ion

i N

orm

ali [

MP

a]


construction

Time [days]

Axia

l str

ess [M

Pa

]

83

80,00

0 50 100 150 200 250 300 350 400


-20,00

0,00

20,00

40,00

60,00

80,00

Te

ns

ion

i N

orm

ali [

MP

a]

Anime lisce

Anime corrugate


permanenti portati

Tiro dei cavi interniFlat webs

Corrugated websInternal tendons

prestressing


Axia

l str

ess [M

Pa

]

-100,00

-80,00

-60,00

-40,00

-20,00

Tempi [gg]

Te

ns

ion

i N

orm

ali [

MP

a]





permanenti portati



lateral spans

introduction


Second 50% of external prestressing

everywhereTime [days]

Axia

l str

ess [M

Pa

]

84

-60,00

100 1000 10000 100000


-120,00

-100,00

-80,00

-60,00

Te

ns

ion

i N

orm

ali [

MP

a]

377 gg.377 days:

end of construction

Axia

l str

ess [M

Pa

]

-180,00

-160,00

-140,00

Tempi [gg]

Te

ns

ion

i N

orm

ali [

MP

a]

Anime lisce

Anime corrugate

50 anniFlat webs

Corrugated webs

50 years: end of

service life

Time [days]

Axia

l str

ess [M

Pa

]

85

0,00

0 50 100 150 200 250 300 350 400


-100,00

-80,00

-60,00

-40,00

-20,00

0,00

Te

ns

ion

i N

orm

ali [

MP

a]

Anime lisce

Anime corrugate


permanenti portati


Flat webs

Corrugated webs



Axia

l str

ess [M

Pa

]

-180,00

-160,00

-140,00

-120,00

-100,00

Tempi [gg]

Te

ns

ion

i N

orm

ali [

MP

a]







lateral spans



Time [days]

Axia

l str

ess [M

Pa

]

86

-100,00

100 1000 10000 100000


-180,00

-160,00

-140,00

-120,00

-100,00

Te

ns

ion

i N

orm

ali [

MP

a]

Anime lisce

Anime corrugate377 gg.

Flat webs

Corrugated webs377 days:

end of construction

Axia

l str

ess [M

Pa

]

-240,00

-220,00

-200,00

-180,00

Tempi [gg]

Te

ns

ion

i N

orm

ali [

MP

a]

50 anni50 years:

end of service life

Time [days]

Axia

l str

ess [M

Pa

]

87

Cumbering design

88

Cumbering designCumbering design

Displacements without cumbering

-5,00E-03

-4,00E-03

-3,00E-03

-2,00E-03

-1,00E-03

0,00E+00

1,00E-03

40,00 45,00 50,00 55,00 60,00 65,00 70,00 75,00 80,00 85,00

Ab

ba

ssa

me

nto

[

m]

Fine concio 1End of

segment one

Ve

rt. d

isp

lacem

en

t [m

]

-9,00E-03

-8,00E-03

-7,00E-03

-6,00E-03

Coordinata [m]

Ab

ba

ssa

me

nto

[

m]


Ve

rt. d

isp

lacem

en

t [m

]

89



-5,00E-03

-4,00E-03

-3,00E-03

-2,00E-03

-1,00E-03

0,00E+00

1,00E-03

40,00 45,00 50,00 55,00 60,00 65,00 70,00 75,00 80,00 85,00

Ab

ba

ssa

me

nto

[

m]

Fine concio 1Tiro cavi 1-2 End of segment one


and 2

Ve

rt. d

isp

lacem

en

t [m

]

-9,00E-03

-8,00E-03

-7,00E-03

-6,00E-03

Coordinata [m]

Ab

ba

ssa

me

nto

[

m]


Ve

rt. d

isp

lacem

en

t [m

]

90



-5,00E-03

-4,00E-03

-3,00E-03

-2,00E-03

-1,00E-03

0,00E+00

1,00E-03

40,00 45,00 50,00 55,00 60,00 65,00 70,00 75,00 80,00 85,00

Ab

bas

sa

men

to

[m

]

Fine concio 1Tiro cavi 1-2 End of segment 1


and 2

Ve

rt. d

isp

lacem

en

t [m

]

-9,00E-03

-8,00E-03

-7,00E-03

-6,00E-03

Coordinata [m]

Ab

bas

sa

men

to

[m

]

Fine concio 2

End of segment 2


Ve

rt. d

isp

lacem

en

t [m

]

91



-5,00E-03

-4,00E-03

-3,00E-03

-2,00E-03

-1,00E-03

0,00E+00

1,00E-03

40,00 45,00 50,00 55,00 60,00 65,00 70,00 75,00 80,00 85,00

Ab

ba

ssa

me

nto

[

m]

Fine concio 1Tiro cavi 1-2 Tiro cavi 3-5End of

segment 1


and 2Prestressing

tendons 3 , 4, 5

Ve

rt. d

isp

lacem

en

t [m

]

-9,00E-03

-8,00E-03

-7,00E-03

-6,00E-03

Coordinata [m]

Ab

ba

ssa

me

nto

[

m]

Fine concio 2


End of segment 2

Ve

rt. d

isp

lacem

en

t [m

]

92



-2,00E-02

-1,50E-02

-1,00E-02

-5,00E-03

0,00E+00

5,00E-03

20,00 30,00 40,00 50,00 60,00 70,00 80,00 90,00 100,00 110,00

Ab

ba

ss

am

en

to

[m

]

Fine concio 3End of segment 3

Ve

rt. d

isp

lacem

en

t [m

]

-4,00E-02

-3,50E-02

-3,00E-02

-2,50E-02

Coordinata [m]

Ab

ba

ss

am

en

to

[m

]


Ve

rt. d

isp

lacem

en

t [m

]

93



-2,00E-02

-1,50E-02

-1,00E-02

-5,00E-03

0,00E+00

5,00E-03

20,00 30,00 40,00 50,00 60,00 70,00 80,00 90,00 100,00 110,00

Ab

ba

ss

am

en

to

[m

]

Fine concio 3

Tiro cavi 6-8

End of segment 3

Prestressing of tendons 6, 7 ,8

Ve

rt. d

isp

lacem

en

t [m

]

-4,00E-02

-3,50E-02

-3,00E-02

-2,50E-02

Coordinata [m]

Ab

ba

ss

am

en

to

[m

]


Ve

rt. d

isp

lacem

en

t [m

]

94



-2,00E-02

-1,50E-02

-1,00E-02

-5,00E-03

0,00E+00

5,00E-03

20,00 30,00 40,00 50,00 60,00 70,00 80,00 90,00 100,00 110,00

Ab

ba

ss

am

en

to

[m

]

Fine concio 3

Tiro cavi 6-8

End of segment 3


Ve

rt. d

isp

lacem

en

t [m

]

-4,00E-02

-3,50E-02

-3,00E-02

-2,50E-02

Coordinata [m]

Ab

ba

ss

am

en

to

[m

]

Fine concio 4


End of segment 4

Ve

rt. d

isp

lacem

en

t [m

]

95



-2,00E-02

-1,50E-02

-1,00E-02

-5,00E-03

0,00E+00

5,00E-03

20,00 30,00 40,00 50,00 60,00 70,00 80,00 90,00 100,00 110,00

Ab

ba

ss

am

en

to

[m

]

Fine concio 3

Tiro cavi 6-8

Tiro cavi 9-11 End of segment 3


Prestressing tendons 9 , 10 ,11

Ve

rt. d

isp

lacem

en

t [m

]

-4,00E-02

-3,50E-02

-3,00E-02

-2,50E-02

Coordinata [m]

Ab

ba

ss

am

en

to

[m

]

Fine concio 4


End of segment 4

Ve

rt. d

isp

lacem

en

t [m

]

96



-4,00E-02

-3,00E-02

-2,00E-02

-1,00E-02

0,00E+00

1,00E-02

10,00 30,00 50,00 70,00 90,00 110,00

Ab

ba

ss

am

en

to

[m

]V

ert

. d

isp

lacem

en

t [m

]

-8,00E-02

-7,00E-02

-6,00E-02

-5,00E-02

Coordinata [m]

Ab

ba

ss

am

en

to

[m

]

Fine concio 5


End of segment 5

Ve

rt. d

isp

lacem

en

t [m

]

97



-4,00E-02

-3,00E-02

-2,00E-02

-1,00E-02

0,00E+00

1,00E-02

10,00 30,00 50,00 70,00 90,00 110,00

Ab

ba

ss

am

en

to

[m

]

Tiro cavi 12-14


Ve

rt. d

isp

lacem

en

t [m

]

-8,00E-02

-7,00E-02

-6,00E-02

-5,00E-02

Coordinata [m]

Ab

ba

ss

am

en

to

[m

]

Fine concio 5


End of segment 5

Ve

rt. d

isp

lacem

en

t [m

]

98



-4,00E-02

-3,00E-02

-2,00E-02

-1,00E-02

0,00E+00

1,00E-02

2,00E-02

10,00 30,00 50,00 70,00 90,00 110,00

Ab

ba

ss

am

en

to

[m

]

Sigillatura cavi interniGrouting of internal

Ve

rt. d

isp

lacem

en

t [m

]

-8,00E-02

-7,00E-02

-6,00E-02

-5,00E-02

Coordinata [m]

Ab

ba

ss

am

en

to

[m

]

Sigillatura cavi interni


Grouting of internal tendons

Ve

rt. d

isp

lacem

en

t [m

]

99



-4,00E-02

-3,00E-02

-2,00E-02

-1,00E-02

0,00E+00

1,00E-02

2,00E-02

10,00 30,00 50,00 70,00 90,00 110,00

Ab

ba

ss

am

en

to

[m

]


Ve

rt. d

isp

lacem

en

t [m

]

-8,00E-02

-7,00E-02

-6,00E-02

-5,00E-02

Coordinata [m]

Ab

ba

ss

am

en

to

[m

]

Precompressione


Sigillatura cavi interni


Grouting of internal tendons

First 50% of lateral spans external prestressing

Ve

rt. d

isp

lacem

en

t [m

]

100



-4,00E-02

-2,00E-02

0,00E+00

2,00E-02

8,00 58,00 108,00 158,00 208,00 258,00

Ab

ba

ss

am

en

to

[m

]V

ert

. d

isp

lacem

en

t [m

]

-1,00E-01

-8,00E-02

-6,00E-02

Coordinata [m]

Ab

ba

ss

am

en

to

[m

]

Sutura campate


Closure of key segments

Ve

rt. d

isp

lacem

en

t [m

]

101



-4,00E-02

-2,00E-02

0,00E+00

2,00E-02

8,00 58,00 108,00 158,00 208,00 258,00

Ab

ba

ss

am

en

to

[m

]V

ert

. d

isp

lacem

en

t [m

]

-1,00E-01

-8,00E-02

-6,00E-02

Coordinata [m]

Ab

ba

ss

am

en

to

[m

]

Sutura campatePrec. Est. Campate

centrali (50%)



First 50% of central spans external prestressing

Ve

rt. d

isp

lacem

en

t [m

]

102



-4,00E-02

-2,00E-02

0,00E+00

2,00E-02

8,00 58,00 108,00 158,00 208,00 258,00

Ab

ba

ss

am

en

to

[m

]V

ert

. d

isp

lacem

en

t [m

]

-1,00E-01

-8,00E-02

-6,00E-02

Coordinata [m]

Ab

ba

ss

am

en

to

[m

]


centrali (50%)


perm. portati




Introduction of permanent loads

Ve

rt. d

isp

lacem

en

t [m

]

103



-4,00E-02

-2,00E-02

0,00E+00

2,00E-02

8,00 58,00 108,00 158,00 208,00 258,00

Ab

ba

ss

am

en

to

[m

]V

ert

. d

isp

lacem

en

t [m

]

-1,00E-01

-8,00E-02

-6,00E-02

Coordinata [m]

Ab

ba

ss

am

en

to

[m

]


centrali (50%)


perm. portati

Ritesatura cavi

esterni





Second 50% of external tendons

prestressing

Ve

rt. d

isp

lacem

en

t [m

]

104



-4,00E-02

-2,00E-02

0,00E+00

2,00E-02

4,00E-02

8,00 58,00 108,00 158,00 208,00 258,00

Ab

ba

ss

am

en

to

[m

]V

ert

. d

isp

lacem

en

t [m

]

-1,00E-01

-8,00E-02

-6,00E-02

Coordinata [m]

Ab

ba

ss

am

en

to

[m

]

1 anno


1 Year after construction end

Ve

rt. d

isp

lacem

en

t [m

]

105



-4,00E-02

-2,00E-02

0,00E+00

2,00E-02

4,00E-02

8,00 58,00 108,00 158,00 208,00 258,00

Ab

ba

ss

am

en

to

[m

]V

ert

. d

isp

lacem

en

t [m

]

-1,00E-01

-8,00E-02

-6,00E-02

Coordinata [m]

Ab

ba

ss

am

en

to

[m

]

1 anno 4 anni



4 years after construction end

Ve

rt. d

isp

lacem

en

t [m

]

106



-4,00E-02

-2,00E-02

0,00E+00

2,00E-02

4,00E-02

8,00 58,00 108,00 158,00 208,00 258,00

Ab

ba

ss

am

en

to

[m

]V

ert

. d

isp

lacem

en

t [m

]

-1,00E-01

-8,00E-02

-6,00E-02

Coordinata [m]

Ab

ba

ss

am

en

to

[m

]

1 anno 4 anni 16 anni





Ve

rt. d

isp

lacem

en

t [m

]

107



-4,00E-02

-2,00E-02

0,00E+00

2,00E-02

4,00E-02

8,00 58,00 108,00 158,00 208,00 258,00

Ab

ba

ss

am

en

to

[m

]V

ert

. d

isp

lacem

en

t [m

]

-1,00E-01

-8,00E-02

-6,00E-02

Coordinata [m]

Ab

ba

ss

am

en

to

[m

]

1 anno 4 anni 16 anni 50 anni






Ve

rt. d

isp

lacem

en

t [m

]

108


Displacements WITH cumbering

-2,00E-02

-1,00E-02

0,00E+00

1,00E-02

2,00E-02

3,00E-02

20,00 30,00 40,00 50,00 60,00 70,00 80,00 90,00 100,00 110,00

Ab

ba

ss

am

en

to

[m

]

Fine concio 3

End of segment 3

Ve

rt. d

isp

lacem

en

t [m

]

-5,00E-02

-4,00E-02

-3,00E-02

-2,00E-02

Coordinata [m]

Ab

ba

ss

am

en

to

[m

]


Ve

rt. d

isp

lacem

en

t [m

]

109



-2,00E-02

-1,00E-02

0,00E+00

1,00E-02

2,00E-02

3,00E-02

20,00 30,00 40,00 50,00 60,00 70,00 80,00 90,00 100,00 110,00

Ab

ba

ss

am

en

to

[m

]

Fine concio 3

Tiro cavi 6-8

End of segment 3


Ve

rt. d

isp

lacem

en

t [m

]

-5,00E-02

-4,00E-02

-3,00E-02

-2,00E-02

Coordinata [m]

Ab

ba

ss

am

en

to

[m

]


Ve

rt. d

isp

lacem

en

t [m

]

110



-2,00E-02

-1,00E-02

0,00E+00

1,00E-02

2,00E-02

3,00E-02

20,00 30,00 40,00 50,00 60,00 70,00 80,00 90,00 100,00 110,00

Ab

ba

ss

am

en

to

[m

]

Fine concio 3

Tiro cavi 6-8

End of segment 3


Ve

rt. d

isp

lacem

en

t [m

]

-5,00E-02

-4,00E-02

-3,00E-02

-2,00E-02

Coordinata [m]

Ab

ba

ss

am

en

to

[m

]

Fine concio 4


Ve

rt. d

isp

lacem

en

t [m

]

111



-2,00E-02

-1,00E-02

0,00E+00

1,00E-02

2,00E-02

3,00E-02

20,00 30,00 40,00 50,00 60,00 70,00 80,00 90,00 100,00 110,00

Ab

ba

ss

am

en

to

[m

]

Fine concio 3

Tiro cavi 6-8

Tiro cavi 9-11

End of segment 3


Ve

rt. d

isp

lacem

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t [m

]

-5,00E-02

-4,00E-02

-3,00E-02

-2,00E-02

Coordinata [m]

Ab

ba

ss

am

en

to

[m

]

Fine concio 4


Ve

rt. d

isp

lacem

en

t [m

]

112



-3,00E-02

-2,00E-02

-1,00E-02

0,00E+00

1,00E-02

2,00E-02

10,00 30,00 50,00 70,00 90,00 110,00

Ab

ba

ss

am

en

to

[m

]

Fine concio 5End of segment 5

Ve

rt. d

isp

lacem

en

t [m

]

-6,00E-02

-5,00E-02

-4,00E-02

-3,00E-02

Coordinata [m]

Ab

ba

ss

am

en

to

[m

]


segment 5

Ve

rt. d

isp

lacem

en

t [m

]

113



-3,00E-02

-2,00E-02

-1,00E-02

0,00E+00

1,00E-02

2,00E-02

10,00 30,00 50,00 70,00 90,00 110,00

Ab

ba

ss

am

en

to

[m

]

Fine concio 5

Tiro cavi 12-14

End of segment 5


Ve

rt. d

isp

lacem

en

t [m

]

-6,00E-02

-5,00E-02

-4,00E-02

-3,00E-02

Coordinata [m]

Ab

ba

ss

am

en

to

[m

]


segment 5

Ve

rt. d

isp

lacem

en

t [m

]

114



-1,00E-02

0,00E+00

1,00E-02

2,00E-02

10,00 30,00 50,00 70,00 90,00 110,00

Ab

ba

ss

am

en

to

[m

]


tendons

Ve

rt. d

isp

lacem

en

t [m

]

-4,00E-02

-3,00E-02

-2,00E-02

Coordinata [m]

Ab

ba

ss

am

en

to

[m

]


Ve

rt. d

isp

lacem

en

t [m

]

115



-1,00E-02

0,00E+00

1,00E-02

2,00E-02

10,00 30,00 50,00 70,00 90,00 110,00

Ab

ba

ss

am

en

to

[m

]


tendons

Ve

rt. d

isp

lacem

en

t [m

]

-4,00E-02

-3,00E-02

-2,00E-02

Coordinata [m]

Ab

ba

ss

am

en

to

[m

]

Precompressione



First 50% of lateral spans external prestressing

Ve

rt. d

isp

lacem

en

t [m

]

116



-2,00E-02

-1,00E-02

0,00E+00

1,00E-02

8,00 58,00 108,00 158,00 208,00 258,00

Ab

ba

ss

am

en

to

[m

]V

ert

. d

isp

lacem

en

t [m

]

-4,00E-02

-3,00E-02

Coordinata [m]

Ab

ba

ss

am

en

to

[m

]

Sutura campate



Ve

rt. d

isp

lacem

en

t [m

]

117



-2,00E-02

-1,00E-02

0,00E+00

1,00E-02

8,00 58,00 108,00 158,00 208,00 258,00

Ab

ba

ss

am

en

to

[m

]V

ert

. d

isp

lacem

en

t [m

]

-4,00E-02

-3,00E-02

Coordinata [m]

Ab

ba

ss

am

en

to

[m

]


centrali (50%)




Ve

rt. d

isp

lacem

en

t [m

]

118



-2,00E-02

-1,00E-02

0,00E+00

1,00E-02

8,00 58,00 108,00 158,00 208,00 258,00

Ab

ba

ss

am

en

to

[m

]V

ert

. d

isp

lacem

en

t [m

]

-4,00E-02

-3,00E-02

Coordinata [m]

Ab

ba

ss

am

en

to

[m

]


centrali (50%)


perm. portati

Ritesatura cavi

esterni



First 50% of central spans

external

prestressingIntroduction of

permanent loads

Second 50% of external tendons

prestressing

Ve

rt. d

isp

lacem

en

t [m

]

119



-2,00E-02

-1,00E-02

0,00E+00

1,00E-02

8,00 58,00 108,00 158,00 208,00 258,00

Ab

ba

ss

am

en

to

[m

]

-4,00E-02

-3,00E-02

Coordinata [m]

Ab

ba

ss

am

en

to

[m

]


centrali (50%)


perm. portati





120



-5,00E-03

0,00E+00

5,00E-03

1,00E-02

8,00 58,00 108,00 158,00 208,00 258,00

Ab

ba

ss

am

en

to

[m

]V

ert

. d

isp

lacem

en

t [m

]

-1,50E-02

-1,00E-02

Coordinata [m]

Ab

ba

ss

am

en

to

[m

]

1 anno


1 year after construction

Ve

rt. d

isp

lacem

en

t [m

]

121



-5,00E-03

0,00E+00

5,00E-03

1,00E-02

8,00 58,00 108,00 158,00 208,00 258,00

Ab

ba

ss

am

en

to

[m

]V

ert

. d

isp

lacem

en

t [m

]

-1,50E-02

-1,00E-02

Coordinata [m]

Ab

ba

ss

am

en

to

[m

]

1 anno 4 anni



4 years after construction

Ve

rt. d

isp

lacem

en

t [m

]

122



-5,00E-03

0,00E+00

5,00E-03

1,00E-02

8,00 58,00 108,00 158,00 208,00 258,00

Ab

ba

ss

am

en

to

[m

]V

ert

. d

isp

lacem

en

t [m

]

-1,50E-02

-1,00E-02

Coordinata [m]

Ab

ba

ss

am

en

to

[m

]

1 anno 4 anni 16 anni





Ve

rt. d

isp

lacem

en

t [m

]

123



-5,00E-03

0,00E+00

5,00E-03

1,00E-02

8,00 58,00 108,00 158,00 208,00 258,00

Ab

ba

ss

am

en

to

[m

]V

ert

. d

isp

lacem

en

t [m

]

-1,50E-02

-1,00E-02

Coordinata [m]

Ab

ba

ss

am

en

to

[m

]

1 anno 4 anni 16 anni 50 anni






Ve

rt. d

isp

lacem

en

t [m

]

124

Conclusions

125

Sustainability aspects

Durability ⇒ No tensile stresses in concrete in SLS(Frequent combination)(Frequent combination)

Economy ⇒ Time saving and elimination of launching girder

Environmental impact ⇒ Elimination of storage areas for segments

Maintenance ⇒ Very easy inspection and control of external tendons

Rehabilitation ⇒ Substitution of external tendons without significant limitation to traffic flow

126

Materials amount

Flat webs Corrugated webs

Concrete 0.80 m3/m2 0.80 m3/m2

Steel 170 kg/m2 155 kg/m2

Prestressing steel 60 kg/m2 56 kg/m2

Ordinary reinforcement 170 kg/m2 170 kg/m2

127

Use of steel

With plane webs

Main girders: 61 kg/m2 web weight

34 Kg/m2 flanges weight

15 Kg/m2 connections, studs, bolts, plates, etc…

16 Kg/m2 web stiffeners

15 Kg/m2 truss diaphragms

Partial total 141 kg/m2 + 29 Kg/m2 for pier segments and prestressing deviators

128

Use of steel

With corrugated webs

Main girders: 74 kg/m2 web weight

34 Kg/m2 flanges weight

17 Kg/m2 connections, studs, bolts, plates, etc…

0 Kg/m2 web stiffeners

0 Kg/m2 truss diaphragms

Partial total 125 kg/m2 + 29 Kg/m2 for pier segments and prestressing deviators = 154 Kg/m2

129

Thank u for kind attention !

Prestressed composite box girder bridges with corrugated · PDF file1 Prestressed composite...

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Transcript of Prestressed composite box girder bridges with corrugated · PDF file1 Prestressed composite...