les_16_seismic design of bridges

8/18/2019 Les_16_Seismic Design of Bridges

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1/126Seismic design of bridges

Politecnico di Torino

Department of structural and geotechnical engineering

“Bridge design”

BRIDGE DESIGN

SEISMICSEISMIC

BEHAVIOUR OFBEHAVIOUR OF

BRIDGESBRIDGES




“Bridge design”

SEISMIC DESIGN OF BRIDGES

Theoretical basis


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“Bridge design”

Applicative Applicative

fieldfieldBridge Pier + Deck

Continuous

Isostatic

Single pier Multiplebent

Solid body Hollow core

One cell Multi cell

Requirements

T0 = 475 years

T0 ≅ 150 years

Important structural damages

Openness to traffic

Emergency traffic

SLU

Negligible structural damages

Not urgent restoration

No traffic limitation

SLD




“Bridge design”

CriteriaCriteria

At SLU stable dissipative mechanism (only pier)

Bending dissipation with exclusion of shear failure

Elastic behavior of deck / bearings / abutments /

foundations and ground

Capacity Design

Cinematism to avoid hammering and fall from bearings(uncertainty of evaluation)


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“Bridge design”

ProtectionProtection Importance factor γI

Applied to design seismic action (SLUand SLD) with variation of T0

γI = 1 Ordinary bridge

γI = 1,3 Strategic bridge with high number ofcasualties in case of collapse

γI




“Bridge design”

Ground typesGround types


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“Bridge design”




“Bridge design”

Average velocity of propagation of

shear waves within 30 m of depth

hi = Thickness of layer i

Vi = Velocity of layer i


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“Bridge design”

Special soilSpecial soil

(Study ad hoc)(Study ad hoc)

(S1) – Deposits with at least 10 m of clays/siltsof low consistence with elevated indices of

plasticity (PI > 40) and contents of waterand VS30 < 100 m/sec or 10 ≤ cu < 20 kPa

(S2) – liquefiable soils, sensitive clays or other

not classified




“Bridge design”

Seismic zoneSeismic zone aG = P.G.A. on ground (A)

Zone aG /g

1… …

i …

… …

n …

Representation ofRepresentation of

seismic actionseismic action

Spectrum of elastic response

(Horiz. ≠ Vert.)

Accelerograms


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“Bridge design”

Spectrum of elastic responseSpectrum of elastic response

Shape of the elastic response spectrum • ag • S

Horizontal seismic action




“Bridge design”

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

0 0.5 1 1.5 2 2.5 3

S e

[ m / s 2 ]

T [s]

(Cat. Suolo A)

(Cat. Suolo B,C,E)

(Cat. Suolo D)

η = 1 ag = 0,35 g

Spectrum of elastic response of horizontal components

(Ground cat. A)

(Ground cat. B,C,E)

(Ground cat. D)


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“Bridge design”

ξ = viscous damping ratio

ξ = 5% η = 1

Horizontal seismic action

Groundcategory

S TB TC TD

A 1,0 0,15 0,40 2,0

B,C,E 1,25 0,15 0,50 2,0

D 1,35 0,20 0,80 2,0




“Bridge design”

Vertical seismic action

Groundcategory

S TB TC TD

A, B, C,D, E 1,0 0,05 0,15 1,0


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“Bridge design”

Design spectrum for S.L.U.

Dissipative capacity Structural factor “q”

Horizontal components

NB: in any case Sd(T) ≥ 0,2 ag




“Bridge design”

Vertical components

q = 1 No resources for dissipation


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“Bridge design”

Design spectrum for S.L.D.

Reduction of elastic spectrum with a factor 2.5




“Bridge design”

Accelerograms Accelerograms

Artificial Natural

In general 3 directions

Design with accelerograms


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“Bridge design”

- Duration of pseudo-stationary region ≥ 10 sec

- Minimum number of groups: 3

- Coherence with elastic spectrum

Average spectral coordinate (ξ = 5%) > 0.9 ofcorrespondent elastic spectrum in

0.2 T1 ≤ T ≤ 2 T1

T1 = fundamental period in elastic field




“Bridge design”

Seismic action components and combination

2 horizontal components 1 vertical components q = 1

Negligible for L ≤ 60 mand ordinary typology

Linear analysis Separated calculation for the 3 components

Combination of effects

2

z

2

y

2

x EEEE ++=

Alternatively the more

severe combinationbetween:EzEyEx

EzEyEx

EzEyEx

A A3.0 A3.0 A3.0 A A3.0

A3.0 A3.0 A

+⋅+⋅⋅++⋅

⋅+⋅+


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“Bridge design”

Non linearanalysis

simultaneous application of 3 components

maximum effects as average value of theworst effects due to each triplet of

accelerograms

Seismic combination with other actions

SLU

Resistance and ductility kkI PGE ++γ

Compatibility displacementsTPGE

T0kkI

Δψ+++γ Δ

with ψ0ΔT = 0.4




“Bridge design”

Behavior factor q

(Flexible

connection to deck)


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“Bridge design”

Behavior factor q

Above q factors are valid for bridges with regular geometry




“Bridge design”

Bridges with regular geometry

i,Rd

i,Ed

iM

Mr =

Acting moment on pier bottom

Resistant moment on pier bottomi = pier index

Regular if 2

r

r r ~

min,i

max,i 1 only if justified with non linear dynamic analysis


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“Bridge design”

Modeling for linear analysis

Rigiditymodeling

Deck (usually not cracked)

Piers (cracked)

If on the bottomS.L.U is reached

Secantstiffness

y

Rdeff c

MIE

φν=

ν = 1.2 – coefficient for un-cracked regions




“Bridge design”

Soil-structureInteraction

Only ifrelevant

effects ≥ 30% onmaximum displacement

Analysis

modal analysis with response spectrum

simplified analysis

non linear dynamic analysis

non linear static analysis (Push-over)


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“Bridge design”

Modal analysis with response spectrum

- Important modal shapes for every direction of verification

- If total mass ≡ ∑ masses related to modal shape

≥ 90% total mass

- combination of modal response

For independentshapes

i

i

E E= ∑ 2

ij i j

i j

E r E E= ∑∑

ij

. ︵︶r ︵︶. ︵︶

ρ ρ

ρ ρ ρ

+

= − + +

3 2

2 2

0 02 1

1 0 01 1

j iT T . ρ = ≥ 0 8

i = j = 1,.. , n

rij

= coefficient of correlation

with T j < Ti

For correlated

shapes




“Bridge design”

Simplified analysis

- Static forces equivalent to the inertia ones

- Forces evaluation from design spectrum with T0 (fundamental periodin the direction considered) and distribution according to the

fundamental shape.

Applicable if the dynamic deflection is essentially governedby 1ST shape

(1 degree of freedom oscillator)


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“Bridge design”

a) Longitudinal direction of straight bridges with continuous beamdeck and effective mass of the piers < 1/5 deck’s mass (rigiddeck model)

b) Transverse direction of bridges that respect a) and arelongitudinally symmetric (emax < 0.05 lbridge) with “e “ distancebetween centroids of masses and stiffnesses of the piers intransverse direction (flexible deck model)

c) Girder bridges simply supported in longitudinal and transversal

direction with effective mass of each pier < 1/5 mass carrieddeck (individual pier model)

Applicable if the dynamic deflection is essentially governedby 1ST shape

(1 degree of freedom oscillator)




“Bridge design”

Case a) and c)

deck mass and mass of the upper half of allthe piers in a)

M = deck mass on pier i and upper half mass of

pier i in c)

S d = Response spectrum value for T1

Case b) Apply Rayleigh’s method

The fundamental period is derived by the principle of energyconservation (kinetic “Ek ” and potential “Ep”)

K =stiffness of the system


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“Bridge design”

The static deformation of the element subjected to concentrated forcescorrespondent to masses is evaluated and Ek = Ep is imposed.

2 2 2 2

k 0

1 1E = mv ︵t ︶= mv cos t

2 2ω ω &

tsinvp2

1

)t(vp2

1

E 0p ω==

Epmax = Ekmax2

vm

2

vp 2200 ω= 20

02

vm

vp=ω

with n masses

∑

∑

∑

∑

=

=

=

= ==ωn

1i

2

i0i

n

1ii0i

n

1i

2

i0i

n

1ii0i

2

vm

vmg

vm

vp

The fundamental period is ∑

∑

=

=π=n

1ii0i

n

1i

2

i0i

vmg

vm2T

The seismic force in eachnode of the model is

iid2

i mvg

)T(SF ω= ( 2 = g/v0 for 1 mass)




“Bridge design”

Displacements calculation (linear analysis)

+ displacements due to spatial variability of motion

displacements evaluated with dynamic or static analysis

with for

for

FOR non linear dynamic analysis

- Verify coherence of the chosen q value

- ∑ actions on piers bottoms and abutments > 80% ∑ …… from linearanalysis


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“Bridge design”

Non linear static analysis (Pushover)

Assign horizontal forces and increase them until a pre-defineddisplacement in a referring node (pier cap) is reached

Evaluation of theplastic hinges

formation sequenceup to collapse

Analysis ofredistributions due to

the formation ofplastic hinges

Evaluation of rotationin plastic hingesunder the pre-

defined displacement

Control that for the displacement evaluated with complete modal

analysis and elastic spectrum (q = 1) the ductility requests in plastichinges are compatible with those available and that the actions in other

elements are smaller than the resistance, with the capacity designcriteria.




“Bridge design”

Capacity design criterion

In the plastic hingesi,Rd0u MM γ=

1q2.07.00 ≥+=γ factor of over resistance

Non dissipative mechanism(shear)

Structural elements that require toremain in linear field (supports,

foundations, abutments)

Designed for actions corresponding to c 0 Rd,iM = γ M

.

.γ

⎧

= ⎨⎩01 35

1 25

Concrete members

Steel members


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“Bridge design”

Safety verification (R.C.)

- γm same value used in non seismic verification

- In the plastic hinges

- Out of plastic hinges

If Mc > MRd in the plastic hinge then Mc = MRd in the plastic hinge

RdEd MM ≤

Rdc MM ≤




“Bridge design”

Plastic hinges Acting moments derived by calculation

Pier design

Other sections moments obtained placing γ0 MRd,i inthe plastic hinges

Shear with capacity design.

(hinge on top)


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“Bridge design”

Confinement reinforcement

Not necessary if ηk ≤ 0.08

Box sections or double T if it is possible to reacha curvature μc = 13 (7) with cmax ≤ 0.0035

I f n e c e s s a r y

rectangularsection

r.c. gross area

Area of confined concrete

s ≤ 6 φls ≤ 1/5 Minimum confined dim.

circularsection s ≤ 6 φl

s ≤ φnucleus

.

.

0 18

0 12

→ ductile behaviour

→ limited ductilebehaviour




“Bridge design”

StirrupsSpacing

≤ 1/3 minimum nucleus dimension≤ 200 mm

Extension ofconfinement

dimension of section orthogonal to the axis of thehinges

sections of Mmax and 0.8 Mmax

(for a further length place half of the reinforcement)

In the hinge zone all the longitudinal bars (no overlap allowed)have to be held by a transverse bar of minimum area

f ys = f yd longitudinal reinforcing

f yt = f yd transversal reinforcing


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“Bridge design”

Fixed bearings

Bearings

Free supports

Capacity design (γ0 MRd,i) max q = 1

Independent verification in the two directions

Stroke with full functionality for designseismic action

Connections (when there’s insufficient room for the stroke)

Design action: 1.5 α Qweight of connected part(minor weight)

ag /gOverlap of displacement

l = lm + deg + dEs

dimension support(> 400 mm)

effective relative displacement of ground

(L = distance between fixed and free bearings)

= dE + 0.4 dT

±μd dEd

temperatureeffects

relative total

displacement




“Bridge design”

CriteriaRemain in elastic field or with negligible residualdeformation in presence of the design seismicaction.

Foundations

Actions Capacity design (γ0 MRdx, γ0 MRdy)

Foundationson piles

(max q = 1)

Plastic hinges in the connection withfootings and concrete rafts

Confining reinforcement


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“Bridge design”

Criteria Functionality with design seismic action

Abutments

Free bearings (longitudinal)

in any case q = 1

- Displacement uncoupled with respect to bridge

- Own seismic forces and friction forces of bearings x 1.3

Fixed bearings (transverse and longitudinal)

- Coupled displacement

transversal dir. seismic action evaluated with ag

longitudinal dir. interaction with ground




“Bridge design”

Reduction of seismic horizontal response

Seismic isolation

Strategy

Increase of T0 to reduce the value of the acceleration

spectrumDissipation of relevant part of mechanic energytransmitted by the earthquake

General

requirementDeck, piers and abutments remain in elastic field

also for the ultimate combination

Don’t apply the capacity design neither the details for ductility


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“Bridge design”

Characteristic of isolation devices

Isolators

Re-centering of vertical loadsDissipation capacityLateral restraint for non seismic actions

High vertical rigidity andlow horizontal rigidity

Auxiliarydevices

Re-centering of vertical loadDissipation capacityLateral restraint for non seismic actions

Devices with non linear behavior not dependent ondeformation speedDevices with damping behavior dependent ondeformation speedDevices with linear or almost linear behavior




“Bridge design”

Elastomeric isolators

Characteristicparameters

K e = equivalent rigidity

d

FKe =

force correspondent to “d”

max displacement in a cycle

e

dinet

AGK =

single layer cross section

∑ layers thickness

ξe = equivalent damping

dF2Wde π=ξ 2e

de

dK2W

π=ξ

Energy dissipatedin a completecycle


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“Bridge design”

Sliding bearings with low friction made ofsteel and teflon (0 ≤ f ≤ 3%)

Sliding isolators

response F/δ monotonic with decreasingrigidity, independent from velocity

auxiliary devices with non linear behaviour

parameters

elastic stiffness1

11

d

FK =

post-elastic stiffness

12

122

dd

FFK

−−

=




“Bridge design”

Resisting force proportional to velocity (Vα)

(fluid viscous dampers)

Auxiliary devices with damping behavior

- Behaviour characterized by Fmax and dd for a fixed amplitude and

frequency

- Relation F/d for a cycle of sinusoidal displacement

(ellipse)

Fmax


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“Bridge design”

Auxiliary devices with linear or almost-linear behavior

- Defined by parameters

- Iperelastic behaviour

K eff = equivalent rigidity

ξeff = equivalent damping

Design criteria

- Accessibility / Inspectionability / Easy substitution / Re-centering

- Protection by fire / aggressive agents- Joints and sliding surfaces to allow displacement of theinsulators

d

eff eff

M

T Kπ = 2




“Bridge design”

Modelling

Worst combination of mechanical properties in time

Deck and piers withelastic-linear response

System of isolation with linear orviscoelastic linear behaviour

- With linear model use secantstiffness referred to the totaldisplacement for the L.S.considered

Vertical deformability has to bemodeled if K v / K eff < 800

verticalrigidity

equivalent horizontalrigidity ∑ j K eff,j

cd

d,j

j

eff eff

E

K dξ π =

∑22

d,j

j

E =

∑

Sum of dissipated energy of allisolators in a full deformation cycleat design displacement

cdd


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“Bridge design”

Linear modeling of system of isolation

When?

- Distance of the bridge from the nearest known seismicallyactive fault exceeds ten kilometers

- Linear equivalent damping ≤ 30%

- Ground conditions corresponding to type A/B/C/E

If the previous requestsare not fulfilled

Non linear model able to describethe behavior of the structure




“Bridge design”


Taller piers work better:

Pinerolo bridge


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“Bridge design”

Pier




“Bridge design”

700

4 0 0

1 5 0

H

6 4 0

200÷250

1 0 0

400

- longitudinal directionH/LX=10/1=10.0>3.5 qx=3.5

- transverse direction:

H/LX=10.0/4.0=2.5 qy=2.5

Ground level

3 6 0

The height ofthe pier hasbeen enhancedto 10 m byplacing theextrados of the

foundation morethan 2 m belowthe groundlevel. In such away we get :


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“Bridge design”

Pier base section

x

y




“Bridge design”

Pier reinforcement: base and top sections


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“Bridge design”

Pier reinforcement: base and top sections

Pos Shape L N° W Pos Shape L N° W




“Bridge design”

Reinforcement under bearings

section Top view


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“Bridge design”

Reinforcement of seismic end of strokes

section Front view




“Bridge design”

Reinforcement table


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“Bridge design”

Seismic end of stroke (on piers and abutments)

Grouting

Neoprene layer60x40x6.9 cm

Sealing

Policloroprene(hardness Sh A60±5)

Steel plateS275 JR

M12fasteners

M12fasteners

Policloroprene(hardness Sh

A60±5)

Steel plateS275 JR

Neoprene layer60x40x6.9 cm

Sealing

Grouting

Bridge deck

Abutment or pier




“Bridge design”

Reinforcement cage of

the pier


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“Bridge design”

Detail of reinforcement cage at the foot of the pier




“Bridge design”


Hysteretic damping bearings application:

Highway in Algeria


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“Bridge design”

General dimensions

Segments for each half hammer

Carriageway in direction of Oran




“Bridge design”

Construction by launching girder


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“Bridge design”

Tallest pier ∼ 24 m

ORAN ALGER

A X E D E

L A P I L E

E E

COUPEA-AEch:1/50

COUPEB-BEch:1/50

C CC C

E E

A X E

D E

T R A C A G E

A X E

G E N E R A L E D E

L ' A U T O R O U T E

CHAUSSEE VERSORAN

A X E

D E

L A P I L E

Shortest pier ∼ 6.5 m

ORAN ALGER

A X E D E

L A P I L E

E E

COUPEA-AEch:1/50

COUPEB-BEch:1/50

C CC C

E E

A X E D E

T R A C A G E

A X E G E N E R A L E D E

L ' A U T O R O U T E

CHAUSSEEVERSORAN

A X E D E

L A

P I L E




“Bridge design”

Hysteretic damping bearings scheme

Longitudinal damper

Transverse damper

A B

Long. sledge Trans. sledge inclination


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“Bridge design”

Longitudinal damper

Frontview

Topview




“Bridge design”

VUE FRONTALE

PLAN

A-A (1 : 3)

VUE AXONOMETRIQUE

A

A

Transverse damper

Top view

Front view

Assonometric view

Longitudinal axisof the bridge


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“Bridge design”

Finite element model – non linear analysis




“Bridge design”


X axis = East – West direction

Y axis = North – South direction


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“Bridge design”

1st Accelerograms

-0.4000

-0.3000

-0.2000

-0.1000

0.0000

0.1000

0.2000

0.3000

0.4000

0.00 5.00 10.00 15.00 20.00 25.00

X direction (horizontal)

Time [s]

ag/g




“Bridge design”

1st Accelerograms

Y direction (horizontal)

Time [s]

ag/g

-0.4000

-0.3000

-0.2000

-0.1000

0.0000

0.1000

0.2000

0.3000

0.4000

0.00 5.00 10.00 15.00 20.00 25.00


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“Bridge design”

1st Accelerograms

Z direction (vertical)

Time [s]

ag/g

-0.4000

-0.3000

-0.2000

-0.1000

0.0000

0.1000

0.2000

0.3000

0.4000

0.00 5.00 10.00 15.00 20.00 25.00




“Bridge design”

1st Accelerograms spectrum



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“Bridge design”






“Bridge design”




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“Bridge design”

1st Accelerograms

Longitudinal (abutment C1) damper displacements

Time [s]

D i s p l a c e m e n t [ m ]




“Bridge design”

1st Accelerograms

Longitudinal (abutment C1) damper reaction

Time [s]

F o r c e [ k N ]


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“Bridge design”

1st Accelerograms

Longitudinal (abutment C1) damper reaction vs. displacement

Displacement [m]

F o r c e [ k N ]




“Bridge design”

1st Accelerograms

Transverse Pier P1 damper displacements

Time [s]

D i s p l a c e m e n t [ m

]


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“Bridge design”

1st Accelerograms

Transverse Pier P1 damper reaction

Time [s]

F o r c e [ k N ]




“Bridge design”

1st Accelerograms

Transverse Pier P1 damper reaction vs. displacement

Displacement [m]

F o r c e [ k N ]


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“Bridge design”

Piers dimensions and orientation of the internal actions

M2

M3




“Bridge design”

Pier P1 design internal actions – Seismic combination

Internal action F1=N[kN] M2,M3 [kNm]

V e r t i c a l c o o r d i n a t e a l o n g t h e p i e r [ m ]

Maximum F1 (axial force)


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“Bridge design”



V e r t i c a l c o o r d i n a t e a l o n g t h e

p i e r [ m ]

Maximum M2 (transverse bending moment)




“Bridge design”




Maximum M3 (longitudinal bending moment)


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“Bridge design”




p i e r [ m ]

Minimum F1 (axial force)




“Bridge design”




Minimum M2 (transverse bending moment)


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“Bridge design”




p i e r [ m ]

Minimum M3 (longitudinal bending moment)




“Bridge design”

Pier P1 (25m tall) reinforcement (base section)


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“Bridge design”

Pier P1 reinforcement table Pos Shape L N° W

Total weight 37019 kg




“Bridge design”


Lead-rubber bearings application:

Highway in Sicily


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“Bridge design”

General dimensions

2 decks made of three 90m spans each with 53m tall piers




“Bridge design”

Two solutions:Hysteretic Damping Bearings (HDB)

Lead rubber bearings (LRB)

Transverse HDB

Longitudinal HDB

Two direction free bearing

Lead rubber bearing LRB

Two direction free bearing

Type 1

Type 1

Type 2

Type 2

Type 2

Type 2

Type 1

Type 1


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“Bridge design”

Frontview

Topview

Hysteretic damping Bearings

Type1 Type2 Type3

f y

[kN] 1750 1950 7250

f u

[kN] 2012.5 2242.5 8337.5

δy [mm]10 10 10

δu

[mm] 150 150 150

K1

[kN/m] 175000 195000 725000

K2

[kN/m] 1875 2089.286 7767.857




“Bridge design”

Lead rubber bearings


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“Bridge design”


x

y




“Bridge design”

1st Accelerograms


Time [s]

ag/g


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“Bridge design”

1st Accelerograms


Time [s]

ag/g




“Bridge design”

1st Accelerograms


Time [s]

ag/g


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“Bridge design”






“Bridge design”




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“Bridge design”






“Bridge design”

1st Accelerograms – Lead Rubber Bearings

Pier P2 longitudinal damper displacements

Time [s]


]


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“Bridge design”

Pier P2 longitudinal damper reaction

Time [s]

F o r c e [ k N ]





“Bridge design”

Pier P2 longitudinal damper reaction vs. displacement

Displacement [m]

F o r c e [ k N ]



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“Bridge design”

Pier P2 transverse damper displacements

Time [s]

D i s p l a c e m e n t [ m ]





“Bridge design”

Pier P2 transverse damper reaction

Time [s]

F o r c e [ k N ]



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“Bridge design”

Pier P2 transverse damper reaction vs. displacement

Displacement [m]

F o r c e [ k N ]





“Bridge design”

1st Accelerograms – Hysteretic Damper Bearings

Pier P2 transverse damper displacements

Time [s]


]


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“Bridge design”

Pier P2 transverse damper reaction

Time [s]

F o r c e [ k N ]





“Bridge design”

Pier P2 transverse damper reaction vs. displacement

Displacement [m]

F o r c e [ k N ]



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“Bridge design”




p i e r [ m ]

F1max M2max M3max

F1 = axial forceM2 = transverse bending momentM3 = longitudinal bending moment




“Bridge design”




F1min M2min M3min



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“Bridge design”




p i e r [ m ]

F1max M2max M3min

F1 = axial force

M2 = transverse bending momentM3 = longitudinal bending moment




“Bridge design”




F1max M2min M3max



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“Bridge design”




p i e r [ m ]

F1max M2min M3min

F1 = axial force





“Bridge design”




F1min M2max M3max



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“Bridge design”




p i e r [ m ]

F1min M2max M3min

F1 = axial force





“Bridge design”




F1min M2min M3max



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“Bridge design”

Pier P1 (53m tall)reinforcement

Upper half

(front view and

vertical section)




“Bridge design”

Pier P1 (53m tall)reinforcement(section B-B)


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“Bridge design”

Pier P1 (53m tall)reinforcement

Lower half

(front view and

vertical section)




“Bridge design”

Pier P1 (53m tall) reinforcement

Base (front view and vertical section)


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“Bridge design”

Pier P1 (53m tall)reinforcement(section A-A)


Pier P1 (53m tall)reinforcement table

Pos Shape

les_16_seismic design of bridges

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