27.-teoria-e-progetto-dei-ponti-analisi-sismica-ii.pptx

8/10/2019 27.-Teoria-e-Progetto-dei-Ponti-Analisi-sismica-II.pptx

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Lezione n27

Universit degli Studi Roma TreDipartimento di Ingegneria

Corso di Teoria e Progetto di Ponti A/A 2013-2014 - Dott. Ing. Fabrizio Paolacci


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Most of the bridges are realized with simply supported deck.

For the evaluation of the seismic behaviour of as-built condition of the

retrofitted condition that maintain the static scheme (presence of

discontinuity of the deck) a simplified methodology can be adopted. It is

base on the following steps:The pier can be considered a simple oscillator with a mass given by

the tributary mass relative to the deck and the mass of the pier.

The non linearity can be considered as concentrated at the pier base

and assumed of elasto-perfectly plastic type

The capacity of the pier represented by the shear displacement curve

evaluated starting to the yielding and ultimate rotation on the plastichinge at the pier base

The response is evaluated by Push-over analysis using the N2

method

The verification is made in term of ductile and fragile mechanisms

Analysis methodsSimplified non-linear analysis: Simply supported Bridges


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Transversal direction: determination of the SDOF characteristics

Mass of the simplified system

Effective height the pier


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Transversal direction: determination of the capacity

On the basis of the simplified model the

capacity of the pier can be evaluated

starting form the linearized Moment-

Curvature relationship and evaluating the

yielding and ultimate top displacements

using the following formula

Length of the plastic hinge


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Transversal direction: Evaluation of the performance point by N2

F emax

x

F y

xmaxxy

x

F y

xmax,exy xmax,e

y

e

F

FR

max, 12 RF emax

Principle of equal displacement Principle of equal Energy


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(behaviour factor)

Evaluation of strength reduction

factors for earthquake-resistant design,

Miranda Bertero ( 1994) E. Spectra vol

10 n2
http://www.ce.berkeley.edu/~mahin/CE227/MirandaAndBertero1994.pdfhttp://www.ce.berkeley.edu/~mahin/CE227/MirandaAndBertero1994.pdfhttp://www.ce.berkeley.edu/~mahin/CE227/MirandaAndBertero1994.pdfhttp://www.ce.berkeley.edu/~mahin/CE227/MirandaAndBertero1994.pdfhttp://www.ce.berkeley.edu/~mahin/CE227/MirandaAndBertero1994.pdfhttp://www.ce.berkeley.edu/~mahin/CE227/MirandaAndBertero1994.pdfhttp://www.ce.berkeley.edu/~mahin/CE227/MirandaAndBertero1994.pdfhttp://www.ce.berkeley.edu/~mahin/CE227/MirandaAndBertero1994.pdfhttp://www.ce.berkeley.edu/~mahin/CE227/MirandaAndBertero1994.pdfhttp://www.ce.berkeley.edu/~mahin/CE227/MirandaAndBertero1994.pdfhttp://www.ce.berkeley.edu/~mahin/CE227/MirandaAndBertero1994.pdfhttp://www.ce.berkeley.edu/~mahin/CE227/MirandaAndBertero1994.pdfhttp://www.ce.berkeley.edu/~mahin/CE227/MirandaAndBertero1994.pdfhttp://www.ce.berkeley.edu/~mahin/CE227/MirandaAndBertero1994.pdf


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Lezione n27Universit degli Studi Roma TreDipartimento di Ingegneria



V

1u1y

1uV

1yV

2y 2u

2yV2u

V1 2

Pila 2

Pila 1

V

1u1y

1uV

1yV

2y 2u

2yV2u

V1 2

Pila 2

Pila 1

imm

As soon as we have found the global multilinear capacity curve of the bridge,

built considering all the piers in parallel, the above procedure can be easily

applied considering the global mass as the sum of the single masses


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Analysis methodsSimplified non-linear analysis: Continuous deck bridges

Mono-modal method

Distribution of force

Participation

factor V*

u*

Bi-linearization


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Analysis methodsSimplified non-linear analysis: Continuous deck bridges

Evaluation of the maximum

displacement

To be compared

With the capacity

V *

u*


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Simply supported bridge (ordinary bridge)

Geometry

1 2 3 45

fc= 25 MPa

fsy= 400 MPa

Concrete

Steel

Soil BVS,30> 500m/s

Class IV

Data


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Simply supported bridge

Definition of the seismic input

Nominal life (ordinary bridge): VN= 50 years

Class: IV Cu = 2

Reference life : VR= Cu VN= 100 years

Soil B

Life safety level (SLV)

PR=10% TR=949 y.

Collapse prevention (SLC)

PR=5% TR=1950 y.

NTC08 provide discrete TR. Therefore

an interpolation of data is needed

U i it d li St di R T Di ti t di I i


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Definition of the seismic input

Nominal life (ordinary bridge): VN= 50 years

Class: IV Cu = 2

Reference life : VR= Cu VN= 100 years

Soil B

Life safety level (SLV)

PR=10% TR=949 y.

Collapse prevention (SLC)

PR=5% TR=1950 y.

NTC08 provide discrete TR. Therefore

an interpolation of data is needed



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Evaluation of weight and mass (pier 5)

Mass of the deck

Height of the deck respect to ground

Total weight of the pier cap

Height of the pier cap

Linear weight of the pier

Height of the pier

Total weight of the pier

Height of foundation

Axial force on the pier

Total mass

10.0 m



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Evaluation of Moment-rotation of the pier base

Bi-linearization

Concrete: Kent-Park model

Steel

N=5437 kN



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Evaluation of the capacity of the piers (Force-displacement law)

Pier 5

Universit degli Studi Roma Tre Dipartimento di Ingegneria


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Evaluation of the seismic Demand (transversal direction)

Fundamental period

Spectral acceleration (SLV)

Spectral Displacement

Base-shear

Base Moment

17

(T > Tc) equal

displacement



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Evaluation of the seismic Capacity (Longitudinal direction)

Bilinearization of the

Multilinear law



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Evaluation of the seismic Demand (Longitudinal direction)

(non-linear response)

For example for the pier 5

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Verification format (Ductile mechanisms)

ySLD

SLCSLV

eleluSLC

/

./

43

51

Pier 5

L i 27



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Verification format (Ductile mechanisms)

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Verification format (Fragile mechanisms)

Axial force contribution

Concrete contribution

Reinforcement contribution

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Lezione n 27Universit degli Studi Roma TreDipartimento di Ingegneria




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Pier 5

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The level of safety is encountered both for SLV and SLC

In conclusion the bridge does not have an enough level of safety both

with respect to ductile mechanism and to fragile one

A retrofitting action has to be adopted.

SLV

SLC

27.-teoria-e-progetto-dei-ponti-analisi-sismica-ii.pptx

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