Les_16_Seismic Design of Bridges

Seismic design of bridges

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BRIDGE DESIGN

SEISMIC BEHAVIOUR OF BRIDGES Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”


SEISMIC DESIGN OF BRIDGES Theoretical basis

Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”

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Applicative field

Pier + Deck

Bridge

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Continuous Isostatic

Single pier Solid body One cell

Multiple bent Hollow core Multi cell Important structural damages

T0 = 475 years

SLU

Openness to traffic Emergency traffic

Requirements

Negligible structural damages T0 ≅ 150 years

SLD

Not urgent restoration No traffic limitation



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At SLU stable dissipative mechanism (only pier) Bending dissipation with exclusion of shear failure Elastic behavior of deck / bearings / abutments / foundations and ground

Criteria Capacity Design

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



Protection

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Importance factor γI

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

γI = 1 γI

γI = 1,3

Ordinary bridge Strategic bridge with high number of casualties in case of collapse



Ground types


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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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(S1) – Deposits with at least 10 m of clays/silts of low consistence with elevated indices of plasticity (PI > 40) and contents of water and VS30 < 100 m/sec or 10 ≤ cu < 20 kPa

Special soil (Study ad hoc) (S2) – liquefiable soils, sensitive clays or other not classified



Seismic zone Zone 1… i … n

Representation of seismic action

aG = P.G.A. on ground (A) aG/g … … … …

Spectrum of elastic response (Horiz. ≠ Vert.)

Accelerograms Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”

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Spectrum of elastic response Shape of the elastic response spectrum • ag • S Horizontal seismic action



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Spectrum of elastic response of horizontal components 14.0

12.0

(Cat. Suolo A) (Ground cat. A) 10.0

Se [m/s2]

(Cat. Suolo (Ground cat.B,C,E) B,C,E)

(Ground cat.D)D) (Cat. Suolo

8.0

6.0

4.0

2.0

0.0 0

0.5

1

1.5

2

2.5

3

T [s]

η=1 Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”

ag = 0,35 g


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Horizontal seismic action Ground category

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

ξ = viscous damping ratio

ξ = 5%

η=1



Vertical seismic action

Ground category

S

TB

TC

TD

A, B, C, D, E

1,0

0,05

0,15

1,0


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Design spectrum for S.L.U. Dissipative capacity

Structural factor “q”

Horizontal components

NB: in any case Sd(T) ≥ 0,2 ag Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”


Vertical components

q=1

No resources for dissipation


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Design spectrum for S.L.D. Reduction of elastic spectrum with a factor 2.5



Design with accelerograms

Accelerograms

Artificial

Natural

In general 3 directions


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- Duration of pseudo-stationary region ≥ 10 sec - Minimum number of groups: 3 - Coherence with elastic spectrum Average spectral coordinate (ξ = 5%) > 0.9 of correspondent elastic spectrum in 0.2 T1 ≤ T ≤ 2 T1 T1 = fundamental period in elastic field



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Seismic action components and combination 2 horizontal components

Linear analysis

1 vertical components

Negligible for L ≤ 60 m and ordinary typology Separated calculation for the 3 components Combination of effects E = E 2x + E 2y + E 2z

Alternatively the more severe combination between:

A Ex + 0.3 ⋅ A Ey + 0.3 ⋅ A Ez 0.3 ⋅ A Ex + A Ey + 0.3 ⋅ A Ez 0.3 ⋅ A Ex + 0.3 ⋅ A Ey + A Ez


q=1


Non linear analysis

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simultaneous application of 3 components maximum effects as average value of the worst effects due to each triplet of accelerograms

Seismic combination with other actions

SLU

Resistance and ductility

γ I E + Gk + Pk

Compatibility displacements

γ I E + Gk + Pk + ψ 0 ΔT ΔT

with ψ0ΔT = 0.4 Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”


Behavior factor q

(Flexible connection to deck)


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Behavior factor q

Above q factors are valid for bridges with regular geometry



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Bridges with regular geometry

ri =

MEd,i MRd,i

Acting moment on pier bottom Resistant moment on pier bottom

r ~ r = i,max < 2 ri,min

Regular if If

i = pier index

~ r ≥ 2 (irregular bridges), the values of q are reduced 2 qr = q ~ r

(q ≥ 1)

Arch bridges / Trestle / Cable stayed / Very skew (α ≥ 15÷20°) / Curved (αTOT, Rmin) q=1 q > 1 only if justified with non linear dynamic analysis Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”


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Modeling for linear analysis Deck (usually not cracked)

Rigidity modeling

Piers (cracked) If on the bottom S.L.U is reached

Secant stiffness

E c Ieff = ν

MRd φy

ν = 1.2 – coefficient for un-cracked regions



Only if relevant

Soil-structure Interaction

effects ≥ 30% on maximum displacement

modal analysis with response spectrum Analysis

simplified analysis non linear dynamic analysis non linear static analysis (Push-over)


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Modal analysis with response spectrum - Important modal shapes for every direction of verification - If total mass ≡ ∑ masses related to modal shape ≥ 90% total mass

∑

j

i

∑∑

Ej Ei j ri

E

=

2

i

=

For independent shapes

Ei

E

- combination of modal response

.

j ri

. .

ρ=

Ti Tj

0︵ 02 1 + ︶ ρ ρ3 2 = 2 2 ︵ 1 − ρ︶ ρ 1 + ρ︶ + 0 01︵

For correlated shapes

i = j = 1,.. , n

≥0 8

rij = coefficient of correlation with Tj < Ti



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Simplified analysis - Static forces equivalent to the inertia ones - Forces evaluation from design spectrum with T0 (fundamental period in the direction considered) and distribution according to the fundamental shape.

Applicable if the dynamic deflection is essentially governed by 1ST shape (1 degree of freedom oscillator)



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Applicable if the dynamic deflection is essentially governed by 1ST shape (1 degree of freedom oscillator) a) Longitudinal direction of straight bridges with continuous beam deck and effective mass of the piers < 1/5 deck’s mass (rigid deck model) b) Transverse direction of bridges that respect a) and are longitudinally symmetric (emax < 0.05 lbridge) with “e “ distance between centroids of masses and stiffnesses of the piers in transverse direction (flexible deck model) c) Girder bridges simply supported in longitudinal and transversal direction with effective mass of each pier < 1/5 mass carried deck (individual pier model)



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Case a) and c)

M=

Sd =

deck mass and mass of the upper half of all the piers in a) deck mass on pier i and upper half mass of pier i in c) Response spectrum value for T1

K=stiffness of the system

Case b)

Apply Rayleigh’s method

The fundamental period is derived by the principle of energy conservation (kinetic “Ek” and potential “Ep”) Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”


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ω

2

︵ & ︶

t 2 s o c

20 v m 1 2 = t 2 v m 1 2 = Ek

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

ω

1 1 Ep = p v( t ) = p v 0 sin ωt 2 2

p v 0 m v 02 ω2 = 2 2

Epmax = Ekmax

with n masses

ω = 2

i=1 n

∑ mi v 02i

p v0 m v 02

n

n

∑ pi v 0 i

ω2 =

=g

i=1

∑ mi v 0 i i=1 n

∑ mi v 02i i=1

The fundamental period is

n

T = 2π

∑ mi v 02i i=1 n

g ∑ mi v 0 i i=1

The seismic force in each node of the model is

Fi = ω2

Sd (T ) v i mi (ω2 = g/v0 for 1 mass) g



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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 linear analysis Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”


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Non linear static analysis (Pushover) Assign horizontal forces and increase them until a pre-defined displacement in a referring node (pier cap) is reached

Evaluation of the plastic hinges formation sequence up to collapse

Analysis of redistributions due to the formation of plastic hinges

Evaluation of rotation in plastic hinges under the predefined displacement

Control that for the displacement evaluated with complete modal analysis and elastic spectrum (q = 1) the ductility requests in plastic hinges are compatible with those available and that the actions in other elements are smaller than the resistance, with the capacity design criteria. Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”


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Capacity design criterion In the plastic hinges

Mu = γ 0 MRd,i

. .

γ 0 = 0.7 + 0.2 q ≥ 1 factor of over resistance

⎧1 35 Concrete members ⎩1 25 Steel members

γ0 = ⎨ Non dissipative mechanism (shear)

Structural elements that require to remain in linear field (supports, foundations, abutments)

Department of structural and geotechnical engineering “Bridge design”

i , d R

Politecnico di Torino

M γ0 = c M

Designed for actions corresponding to


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Safety verification (R.C.) - γm same value used in non seismic verification - In the plastic hinges MEd ≤ MRd - Out of plastic hinges

Mc ≤ MRd

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



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Pier design Plastic hinges

Acting moments derived by calculation

Other sections

moments obtained placing γ0 MRd,i in the plastic hinges

Shear with capacity design.

(hinge on top) Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”


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Confinement reinforcement ηk ≤ 0.08

Not necessary if

Box sections or double T if it is possible to reach a curvature μc = 13 (7) with εcmax ≤ 0.0035 . .

r.c. gross area 0 18 → ductile behaviour

If necessary

0 12 → limited ductile

rectangular section

behaviour Area of confined concrete s ≤ 6 φl s ≤ 1/5 Minimum confined dim.

circular section

s ≤ 6 φl s ≤ φnucleus



≤ 1/3 minimum nucleus dimension ≤ 200 mm

Stirrups Spacing

Extension of confinement

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dimension of section orthogonal to the axis of the hinges 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 fys = fyd longitudinal reinforcing fyt = fyd transversal reinforcing



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Bearings Fixed bearings

max q = 1

Capacity design (γ0 MRd,i)

Independent verification in the two directions Free supports

Stroke with full functionality for design seismic action

Connections (when there’s insufficient room for the stroke) weight of connected part Design action: 1.5 α Q (minor weight) Overlap of displacement l = lm + deg + dEs

ag/g relative total displacement

temperature effects

= dE + 0.4 dT

±μd dEd effective relative displacement of ground (L = distance between fixed and free bearings)

dimension support (> 400 mm) Politecnico di Torino

Department of structural and geotechnical engineering “Bridge design”


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Foundations

Actions

Remain in elastic field or with negligible residual deformation in presence of the design seismic action. Capacity design (γ0 MRdx, γ0 MRdy) (max q = 1)

Foundations on piles

Plastic hinges in the connection with footings and concrete rafts

Criteria

Confining reinforcement



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Abutments Criteria

Functionality with design seismic action

Free bearings (longitudinal) - 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 in any case q = 1



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Seismic isolation Reduction of seismic horizontal response

Strategy

General requirement

Increase of T0 to reduce the value of the acceleration spectrum Dissipation of relevant part of mechanic energy transmitted by the earthquake Deck, piers and abutments remain in elastic field also for the ultimate combination

Don’t apply the capacity design neither the details for ductility Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”


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Characteristic of isolation devices

Isolators

Re-centering of vertical loads Dissipation capacity Lateral restraint for non seismic actions High vertical rigidity and low horizontal rigidity

Auxiliary devices

Re-centering of vertical load Dissipation capacity Lateral restraint for non seismic actions Devices with non linear behavior not dependent on deformation speed Devices with damping behavior dependent on deformation speed Devices with linear or almost linear behavior



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Elastomeric isolators Ke = equivalent rigidity force correspondent to “d”

F Ke = d Characteristic parameters

K e = Gdin

max displacement in a cycle

A te

single layer cross section ∑ layers thickness

ξe = equivalent damping

ξe =

Wd 2 πF d

ξe =


Energy dissipated in a complete cycle

Wd 2 π K e d2


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Sliding isolators Sliding bearings with low friction made of steel and teflon (0 ≤ f ≤ 3%) auxiliary devices with non linear behaviour response F/δ monotonic with decreasing rigidity, independent from velocity elastic stiffness K 1 = parameters

F1 d1

post-elastic stiffness K2 =

F2 − F1 d2 − d1



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Auxiliary devices with damping behavior Resisting force proportional to velocity (Vα) (fluid viscous dampers) - Behaviour characterized by Fmax and dd for a fixed amplitude and frequency - Relation F/d for a cycle of sinusoidal displacement Fmax (ellipse)



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Auxiliary devices with linear or almost-linear behavior - Defined by parameters

f f

ξeff = equivalent damping

d

f f

= 2π

M Ke

Te

Keff = equivalent rigidity - Iperelastic behaviour

Design criteria - Accessibility / Inspectionability / Easy substitution / Recentering - Protection by fire / aggressive agents - Joints and sliding surfaces to allow displacement of the insulators Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”


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Modelling Worst combination of mechanical properties in time System of isolation with linear or viscoelastic linear behaviour

Deck and piers with elastic-linear response

Vertical deformability has to be modeled if Kv / Keff < 800 vertical rigidity

Sum of dissipated energy of all isolators in a full deformation cycle at design displacement

Department of structural and geotechnical engineering

d c

Politecnico di Torino “Bridge design”

equivalent horizontal rigidity ∑j Keff,j

d

=

j , d

d c

f f e

∑

j

d

K

2π

2

E

j , d

∑

j

=

f f e

ξ

E

- With linear model use secant stiffness referred to the total displacement for the L.S. considered


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Linear modeling of system of isolation When? - Distance of the bridge from the nearest known seismically active fault exceeds ten kilometers - Linear equivalent damping ≤ 30% - Ground conditions corresponding to type A/B/C/E

If the previous requests are not fulfilled

Non linear model able to describe the behavior of the structure



SEISMIC DESIGN OF BRIDGES Taller piers work better: Pinerolo bridge


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Pier



H

Ground level

360

100

200÷250

150

400

400

640

700

- longitudinal direction H/LX=10/1=10.0>3.5 - transverse direction: H/LX=10.0/4.0=2.5

qx=3.5 qy=2.5


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The height of the pier has been enhanced to 10 m by placing the extrados of the foundation more than 2 m below the ground level. In such a way we get :


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Pier base section

y x Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”


Pier reinforcement: base and top sections


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Pier reinforcement: base and top sections Pos

L

Shape

N°

W

Pos

Shape

L

N°

W



Reinforcement under bearings

section

Top view


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Reinforcement of seismic end of strokes

section

Front view



Reinforcement table


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Seismic end of stroke (on piers and abutments) Bridge deck

M12 fasteners

Grouting

M12 fasteners Grouting Neoprene layer 60x40x6.9 cm

Neoprene layer 60x40x6.9 cm Steel plate S275 JR

Sealing

Steel plate S275 JR

Policloroprene (hardness Sh A60±5)

Policloroprene (hardness Sh A60±5)

Sealing

Abutment or pier Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”


Reinforcement cage of the pier


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Detail of reinforcement cage at the foot of the pier



SEISMIC DESIGN OF BRIDGES Hysteretic damping bearings application: Highway in Algeria


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General dimensions Carriageway in direction of Oran

Segments for each half hammer



Construction by launching girder


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Tallest pier ∼ 24 m

Shortest pier ∼ 6.5 m AXE GENER ALE DE L'AUTOR OUTE

COUPE A-A AXE GEN ER ALE DE L 'A UT OR OU TE

AXE D E TRACAGE

Ech: 1/50

COUPE A-A AXE DE T R AC AGE

Ech: 1/50

CHAUSSEE VERS ORAN

CHAUSSEE VERS ORAN

COUPE B-B Ech: 1/50

COUPE B-B ORAN

C

C

C

C

C

E

E

E

E

AXE DE L A PI LE

AXE DE L A PI LE

E

C

AXE DE LA PILE

AXE D E LA PILE

C

ORAN

ALGER

Ech: 1/50

ALGER

C

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E

E

E



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Hysteretic damping bearings scheme

Longitudinal damper

A

B

Transverse damper

Long. sledge


Trans. sledge

inclination


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Longitudinal damper Front view

Top view


Seismic design of bridges Front view VUE FRONTALE

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Transverse damper Assonometric view VUE AXONOMETRIQUE

A

PLAN Top view

Longitudinal axis of the bridge A-A (1 : 3)

A



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Finite element model – non linear analysis




X axis = East – West direction Y axis = North – South direction


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1st Accelerograms X direction (horizontal) 0.4000

0.3000

0.2000

0.1000

ag/g 0.0000 0.00

5.00

10.00

15.00

20.00

25.00

-0.1000

-0.2000

-0.3000

-0.4000

Time [s] Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”


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1st Accelerograms Y direction (horizontal) 0.4000

0.3000

0.2000

0.1000

ag/g 0.0000 0.00

5.00

10.00

15.00

-0.1000

-0.2000

-0.3000

-0.4000


20.00

25.00


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1st Accelerograms Z direction (vertical) 0.4000

0.3000

0.2000

0.1000

ag/g 0.0000 0.00

5.00

10.00

15.00

20.00

25.00

-0.1000

-0.2000

-0.3000

-0.4000



1st Accelerograms spectrum X direction (horizontal)


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1st Accelerograms spectrum Y direction (horizontal)



1st Accelerograms spectrum Z direction (vertical)


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1st Accelerograms

Displacement [m]

Longitudinal (abutment C1) damper displacements



1st Accelerograms

Force [kN]

Longitudinal (abutment C1) damper reaction


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1st Accelerograms

Force [kN]

Longitudinal (abutment C1) damper reaction vs. displacement

Displacement [m] Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”


1st Accelerograms

Displacement [m]

Transverse Pier P1 damper displacements


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1st Accelerograms

Force [kN]

Transverse Pier P1 damper reaction



1st Accelerograms

Force [kN]

Transverse Pier P1 damper reaction vs. displacement


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Piers dimensions and orientation of the internal actions

M3 M2



Pier P1 design internal actions – Seismic combination

Vertical coordinate along the pier [m]

Maximum F1 (axial force)

Internal action F1=N[kN] M2,M3 [kNm] Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”

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Maximum M2 (transverse bending moment)





Maximum M3 (longitudinal bending moment)


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Minimum F1 (axial force)





Minimum M2 (transverse bending moment)


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Minimum M3 (longitudinal bending moment)



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


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Pier P1 reinforcement table

Pos

Shape

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L

N°

W

Politecnico di Torino

Total weight Department of structural and geotechnical engineering

37019 kg

“Bridge design”


SEISMIC DESIGN OF BRIDGES Lead-rubber bearings application: Highway in Sicily


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General dimensions

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



Two solutions:

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Hysteretic Damping Bearings (HDB)

Type 1

Type 2

Type 2

Type 1

Type 1

Type 2

Type 2

Type 1

Transverse HDB Longitudinal HDB Two direction free bearing

Lead rubber bearings (LRB)

Lead rubber bearing LRB Two direction free bearing



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Hysteretic damping Bearings Front view

fy [kN] fu [kN] δy [mm] δu [mm] K1 [kN/m] K2 [kN/m]

Type1 1750 2012.5 10 150 175000 1875

Type2 1950 2242.5 10 150 195000 2089.286

Type3 7250 8337.5 10 150 725000 7767.857

Top view



Lead rubber bearings


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y

x Politecnico di Torino Department of structural and geotechnical engineering “Bridge design”


1st Accelerograms X direction (horizontal)

ag/g


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1st Accelerograms Y direction (horizontal)

ag/g



1st Accelerograms Z direction (vertical)

ag/g


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1st Accelerograms spectrum X direction (horizontal)



1st Accelerograms spectrum Y direction (horizontal)


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1st Accelerograms spectrum Z direction (vertical)



1st Accelerograms – Lead Rubber Bearings

Displacement [m]

Pier P2 longitudinal damper displacements


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Force [kN]

Pier P2 longitudinal damper reaction




Force [kN]

Pier P2 longitudinal damper reaction vs. displacement


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Displacement [m]

Pier P2 transverse damper displacements




Force [kN]

Pier P2 transverse damper reaction


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Force [kN]

Pier P2 transverse damper reaction vs. displacement



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1st Accelerograms – Hysteretic Damper Bearings

Displacement [m]

Pier P2 transverse damper displacements



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Force [kN]

Pier P2 transverse damper reaction



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Force [kN]

Pier P2 transverse damper reaction vs. displacement



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F1max M2max M3max

F1 = axial force M2 = transverse bending moment M3 = longitudinal bending moment



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F1min M2min M3min




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F1max M2max M3min




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F1max M2min M3max




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F1max M2min M3min




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F1min M2max M3max




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F1min M2max M3min




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F1min M2min M3max




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Pier P1 (53m tall) reinforcement Upper half (front view and vertical section)



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


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Pier P1 (53m tall) reinforcement Lower half (front view and vertical section)



Pier P1 (53m tall) reinforcement Base (front view and vertical section)


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



Pier P1 (53m tall) reinforcement table Pos

Shape


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Les_16_Seismic Design of Bridges

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