Eurocode EN 1998-2 - Seismic design of bridges.pdf

8/17/2019 Eurocode EN 1998-2 - Seismic design of bridges.pdf

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EUROCODE EN1998-2 SEISMIC DESIGN OF BRIDGES

B. Kolias


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Basic Requirements

Non-Collapse

Retain structural strength + residual resistance

for emergency traffic. Limit damage to areas of energy dissipation.

Damage Minimization

Under probable seismic effects.


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Analysis Methods

Equivalent Linear Analysis:

Elastic force analysis (response spectrum)forces from unlimited elastic response dividedby q = behaviour factor.

design spectrum = elastic spectrum / q


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Analysis Methods

My

Yield of first bar

Secant stiffness

Stiffness of Ductile Elements: secant stiffness at the theoretical yield


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Analysis Methods

Non-linear Dynamic Time-History Analysis:

In combination with response spectrumanalysis without relaxation of demands.

For irregular bridges.

For bridges with seismic isolation.

Non-linear Static Analysis (Push-Over): For irregular bridges.


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Seismic behaviour of bridges

Ductility Classes

Limited Ductile Behaviour:

q < 1.50

Ductile Behaviour:

1.50 < q ≤ 3.50


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Compliance Criteria

for Elastic Analysis

Limited Ductile Behaviour:

Section verification with seismic design effects AEd Verification of non-ductile failure modes (shear

and soil) with elastic effects qAEd and reduction

of resistance by γBd = 1.25


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Compliance Criteria


Ductile Behaviour:

Flexural resistance of plastic hinge regions with

design seismic effects AEd. All other regions and non-ductile failure modes

(shear of elements & joints and soil) with

capacity design effects AC. Local ductility ensured by special detailing

rules (mainly confinement).


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Compliance Criteria


Control of Displacements: Assessment of seismic displacement dE

dE = ημddEe.

dEe = result of elastic analysis.η = damping correction factor.μd = displacement ductility as follows:

when T ≥T 0 =1.25T C : μd = q

when T


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Compliance Criteria


Provision of adequate clearances for the

total seismic design displacement:

d Ed = d E + d G + 0.5d T d G due to permanent and quasi-permanent

actions.d T due to thermal actions.

For roadway joints: 40% dE and 50% dT


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Compliance Criteria

for Non-linear Analysis

Chord rotation: θ = θ y + θ p

Plastic

hinge

L

Lp

θ

M


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Compliance Criteria


Ductile Members:Plastic chord rotations of plastic hinges:

demand ≤ design capacity

θ p,E ≤ θ p,d , θ p,d = θ p,u / γ R,p , γ R,p = 1.40

θ p,u = probable (mean) capacity from tests or

derived from ultimate curvatures


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Compliance Criteria


Non-ductile members:

Force verification as in elastic analysis for

regions outside plastic hinges and non-ductilefailure modes, with capacity design effects

replaced by:

γ R,Bd1 AEd with γ R,Bd1 = 1.25 Design resistances:

R d = R k / γ M


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Seismic Action

Two types of elastic response spectra:

Type 1 and 2.

5 types of soil:

A, B, C, D, E.

4 period ranges:

short, constant acceleration, velocity and

displacement. Design spectrum = elastic spectrum / q.

3 importance classes:

γ I = 1.3, 1.0, 0.85.


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Seismic Action

Elastic Spectrum Type 1 (ξ = 0.05)

4

0

1

2

3

1 TD 3 (s)TC

S e / A

g

AB

E D

C

TB


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Seismic Action:

Spatial Variability

Spatial variability model shouldaccount for:

Propagation of seismic waves

Loss of correlation due toreflections/refractions

Modification of frequency content due

to diff mechanical properties of

foundation soil


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Seismic Action:

Spatial Variability

Rigorous model in Inf. Annex D: Simplified method:

⇒ Uniform support excitation +

pseudostatic effects of two sets ofdisplacement (A and B) imposed at

supports.

⇒ Sets A and B applied in the twoprincipal horizontal directions but

considered independently


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Seismic Action:

Spatial Variability

Displacement sets defined from:

dg = 0.025 agSTCTD : max particle displ.

corresponding to the ground type (EC8-1)

Lg is the distance beyond which seismicmotion is completely uncorrelated

Recommended Values of Lg(m)

500300400500600Lg(m)

EDCB AGroundType


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Seismic Action:

Spatial Variability

Displacement set A

uniform expansion/contraction

displacement of

support i relativeto support 0

2gir ri d Ld ≤= ε

g

g

r L

d 2=ε


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Seismic Action:

Spatial VariabilityDisplacement set B

with opposite directions at adjacent piers

2/ii d d Δ±=

typegrounddifferent 0.1

same 5.0

⎭⎬

⎫

⎩⎨

⎧

=r β

iavr r i Ld ,ε β ±=Δ


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Regular / Irregular Bridges

Criterion based on final required forcereduction factors r i of the ductile members i :

r i = qM Ed,i /M Rd,I =

q x Seismic moment / Section resistance A bridge is considered regular when the

“irregularity” index:

ρir = max (r i ) / min( r i ) ≤ ρ0 = 2

Piers contributing less than 20% are excepted.


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Regular / Irregular Bridges

For regular bridges equivalent elastic analysis isallowed with the q -values specified, without checkingof local ductility demands

Irregular bridges are: either designed with reduced behaviour factor:

q r = q ρir / ρo ≥ 1.0

or verified by non-linear static (pushover) ordynamic analysis


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Capacity Design Effects

Correspond to the section forces underpermanent loads and a seismic action creating

the assumed pattern of plastic hinges, where

the flexural overstrength:M o = γ oM Rd

has developed with: γ o = 1.35

Simplifications satisfying the equilibrium

conditions are allowed.


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Detailing Rules

Confinement reinforcement

Increasing with:

Normalised axial force: ηk = N Ed / (Ac f ck ). Axial reinforcement ratio ρ (for ρ > 0.01).

Not required for hollow sections with:

ηk ≤ 0.20 and restrained reinforcement.

Rectangular hoops and crossties or Circularhoops or spirals


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Detailing Rules

Restraining of axial reinforcementagainst buckling

max support spacing:sL ≤ δ Ø L

5 ≤

= 2,5 (f t

/ f y

) + 2,25 ≤ 6

minimum amount of transverse ties:

At /sT = Asf ys /1,6f yt (mm2 /m)


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Detailing Rules

Hollow piers

In the region of the plastic hinges

b / t or D / t ≤ 8

Pile foundations

Rules for the location and requiredconfinement of probable plastic hinges


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Detailing Rules

Bearings and seismic links.

Holding down devices.

Shock transmission units (STU). Min. overlap lengths at movable supports.

Abutments and retaining walls.

Culverts with large overburden.


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Bridges with

Seismic Isolation

The isolating system arranged over the

isolation interface reduces the seismic

response by: either lengthening of the fundamental period.

or increasing of the damping.

or (preferably) by combination of both effects.


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Bridges with

Seismic Isolation

Design properties of the isolating system Nominal design properties (NDP) assessed by

prototype tests, confirming the range accepted

by the Designer. Design is required for:

Upper Bound design properties (UBDP).

Lower Bound design properties (LBDP).

Bounds of Design Properties result either from

tests or from modification factors.


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Bridges with

Seismic Isolation

Analysis methods

Fundamental or multi mode spectrum analysis

(subject to specific conditions).

Non-linear time-history analysis.


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Bridges with

Seismic Isolation

Compliance criteria Isolating system

Displacements increased by factor:γ IS = 1.50

Restoring capability is required for the

system.

Sufficient lateral rigidity under service

conditions is required.


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Bridges with

Seismic Isolation

Substructure

Design for limited ductile behaviour: q ≤ 1.50


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Seismic Deformation

Capacity of Piers

Ultimate Displacement

F Rd

d u d y

Monotonic Loading

5th cycle

Rd0.2F


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Deformation Capacity

of Piers

Chord rotation θ u = θ y + θ p

Plastic chord rotation θ p derived Directly from appropriate tests

From the curvature, by integration


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of Piers

Ultimate curvature:

Reinforcement: ε su = 0.075 (EN1992-1-1)

Unconfined concrete: ε cu = -0.035 (EN1992-1-1)

Confined concrete:

d cuεsuε

uΦ−

=

ccm,

f suε ym f s1.4 ρ0.004ccu,ε −−=


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of Piers

Mean material properties

Reinforcement

f ym /f yk = 1.15, f sm / f sk = 1.20, εsu = εuk

Concrete

f cm = f ck + 8 (MPa), E cm = 22(f cm /10)0.3

Stress-strain diagram of concrete

Unconfined concrete: ε c1 = -0.0007f cm0.31


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of Piers

Confined concrete - Mander model

f cm,c

f cm

εc1 εc1,cεcu1

εcu,c

c

Ecm Esec

Confined concrete

Unconfined

concrete


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of Piers

Chord rotation: θu = θy + θ p,u

)2L p L

(1 p )L yΦu( Φu p,θ −−=

Lp

L θ

Plastic hingeLp

ΦyΦu M

FRd


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of Piers

d

syε

1.2= yΦ

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000

0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 0.045 0.050

Curvature (1/m)

M o m e n t X ( k N m

)

First yield of confined concrete

Confined concrete reaches peak stressConfined concrete fails

First yield of longitudinal steel

Longitudinal steel fails

X

Y

MRd

Mu

Φy


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of Piers

Calibration with test results

Database:

64 tests on R/C pier elements.• 31 circular, 25 rectangular, 8 box sections

Curvature analysis for each test specimen.

Non-linear regression for the coefficients of:

Lp = 0.10L + 0.015f ykds


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0

2

4

6

8

10

12

0 2 4 6 8 10 12

P r e d i c t e d

θ p

θp,exp /θp,prd

No of exp. : 64

Average : 1.09

St. Dev. : 0.18

Experimental θp (%)

θp,exp=1.09 θp,prd

5% fract. (S.F.=1.25)

S.F.=1.40


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Non-linear Static Analysis

Based on the equal displacements rule Analysis directions

x: Longitudinal

y: Transverse


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Horizontal load increased until the

displacement at the reference point reaches the

design seismic displacement of elastic

response spectrum analysis (q = 1), forEx + 0.3Ey and Ey + 0.3Ex

Reference point is the centre of mass of thedeformed deck


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Load distribution

Load increment at point i at step j

ΔF i,j = Δα j G i ζ i

distribution constant along the deck: ζ i = 1

distribution proportional to first mode shape


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Thank you !!!

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Eurocode EN 1998-2 - Seismic design of bridges.pdf

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