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EUROCODE 8Background and Applications

Dissemination of information for training Lisbon, 10-11 February 2011 1

Assessment and retrofitting of buildings

Paolo Emilio PintoUniversity of Rome, La Sapienza

Paolo FranchinUniversity of Rome, La Sapienza


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Introduction

Dissemination of information for training Lisbon 10-11 February 2011 2

Document of the last generation, performance- and displacement-

Flexible to accomodate the large variety of situations arising in

Logically structured, but missing the support from extended use:im rovements to be ex ected from future ex erience

Normative part covering only material-independent concepts andrules: verification formulas are in not-mandatory InformativeAnnexes

The presentation concentrates on the normative part, providing alsoa number of comments and tentative lines of development, based onpresently accumulated experience


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Performance requirements


Hazard Required performancere urn per o o e es gn

spectrum)

TR=2475 years Near Collapse (NC)

(2% in 50 years) (heavily damaged, very low residualstrength & stiffness, large permanent

drift but still standing)

TR=475 years(10% in 50 years)

Significant damage (SD)(significantly damaged, some residual

stren th & stiffness non-strutural

comp. damaged, uneconomic to

repair)

R

(20% in 50 years)

(only lightly damaged, damage to non-

structural components economically

TR values above same as for new buildings. National authorities may selectlower values, and require compliance with only two limit-states


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Performance requirements: comment


EC8-3 is a displacement-based document: direct

and corresponding distortions induced by the designseismic action, for ductile components

Apart from specific (and rare) cases, use of the standard ,

action is introduced in the analysis without modification.Reasons:

Existing buildings represent a very inhomogeneous population, in terms of

age, morfology, construction type and design code, such as to rule out the

parameter to be calibrated via statistical analysis

It is now unanimousl a reed that dis lacements/distortions are the uantitiesbest suited for identifying the attainment of different LSs


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Compliance criteria: remarks


The description of the requirements for all LSs is

severe states of damage involving the structural systemas a whole.

When turning to the verification phase, however, the

requirements be satisfied all individual elements shouldsatisfy the verification inequalities, which would lead tocons er a u ng as se sm ca y e c en even n eextreme case where a single element would be found as

nonconformin .

This indeterminacy is at the origin of large discrepancies


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Example of a fault tree representation for the NC-LS of a simplerame

Structural failure4 5 6

7 8

9 10 Structural failure4 5 6

7 8

9 10

4 5 6

7 8


7 8


7 8

9 10

4 5 6

7 8

9 10

Weak storey failure Shear column failure

=max . ; . = .1 2 3


=max . ; . = .1 2 31 2 3


=max . ; . = .1 2 3


=max . ; . = .1 2 31 2 3

Floor 1

max(2.1;1.3)=2.1 max()=1.1

Floor 2Floor 1

max(2.1;1.3)=2.1 max()=1.1

Floor 2

or or

Floor 1

max(2.1;1.3)=2.1 max()=1.1

Floor 2Floor 1

max(2.1;1.3)=2.1 max()=1.1

Floor 2

or or

min()=2.1 min()=1.3

1=1.1

2=0

.7

3=0.3

4=0

.1

5=0.4

6=0.5

=2

.1

=2

.3

=1

.3

=1

.4

=1

.4

=2

.4

min()=2.1 min()=1.3

1=1.1

2=0

.7

3=0.3

4=0

.1

5=0.4

6=0.5

=2

.1

=2

.3

=1

.3

=1

.4

=1

.4

=2

.4

and andmin()=2.1 min()=1.3

1=1.1

2=0

.7

3=0.3

4=0

.1

5=0.4

6=0.5

=2

.1

=2

.3

=1

.3

=1

.4

=1

.4

=2

.4

min()=2.1 min()=1.3

1=1.1

2=0

.7

3=0.3

4=0

.1

5=0.4

6=0.5

=2

.1

=2

.3

=1

.3

=1

.4

=1

.4

=2

.4

and and

V1

/V

V2

/V

V3

/V

V4

/V

V5

/V

V6

/VU

1

/Y1

2

/Y

4

/Y4

5

/Y

6

/Y6

3

/Y3

V1

/V

V2

/V

V3

/V

V4

/V

V5

/V

V6

/VU

1

/Y1

2

/Y

4

/Y4

5

/Y

6

/Y6

3

/Y3

V1

/V

V2

/V

V3

/V

V4

/V

V5

/V

V6

/VU

1

/Y1

2

/Y

4

/Y4

5

/Y

6

/Y6

3

/Y3

V1

/V

V2

/V

V3

/V

V4

/V

V5

/V

V6

/VU

1

/Y1

2

/Y

4

/Y4

5

/Y

6

/Y6

3

/Y3


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With reference to a fault tree representation as in the,

value of a scalar quantity defined as:

i=1,NS j=1,Ni ij

where:

Rij = ratio between demand and capacity at thej-th component of the i-thsubsystem

S = o a num er o su -sys ems

Ni = number of components in subsystem i

Y=1 implies attainment of the LS under consisderation


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Information for structural assessment: knowledge levels 1/2


Amount and quality of theKL Geometry Details Materials

1 From original Simulated design in Default values in

assessment is discretized in

EC8-3 into three levels,

construction

drawings with

sample visual

survey

relevant practice

and

from limited in-situ

inspection

standards of the time

of construction

and

from limited in-situ

(KL), ordered by increasing

completeness.

or

from full

survey

es ng

2 From incompleteoriginal detailed

construction drawings

From original design

specifications with

limited in-situ testing

The information refers to threeaspects: Geometry, Details and

Materials.

with limited in-situ

inspection

or

or

from extended in-situ

testin

The term Geometry includes

structural geometry and member sizes,

Details refer to the amount and layout

from extended in-situ

inspection

3 From original detailedconstruction drawings

From original test

reports with limited in-

of reinforcement (for RC structures),

Materials to the mechanical properties

of the constituent materials.

with limited in-situ

inspection

or

situ testing

or

from comprehensive

in-situ in-spection

in-situ testing


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Information for structural assessment: knowledge levels 2/2


The quantitative definition of the terms: visual, limited, extended,, ,

and Material is given in the Code (as a recommended minimum, if not

otherwise specified in National Annexes).

In particular, for what concerns the levels of inspection and testing,the recommended requirements are reported in the table below.

Inspection (of details) Testing (of materials)

For each type of primary element (beam, column, wall)

Level of inspection and Percentage of elements Material samples per floor

Limited 20 1

Extended 50 2

Comprehensive 80 3


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Information for structural assessment: remarks


The reliability format adopted by EC8-3 has theadvantage of simplicity, but is subject to a number of

practical and also theoretical limitations that might

The followin main as ects are illustrated next:

Extension of material tests

Nature of the uncertainties to be dealt with

Use of a single factor (CF)


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On the availability of documentation, both original and throughsurve s

In the majority of cases, seismic assessments are being carried out not

because of planned renovation or extension works, or because of a visibly.Authorities who want to be aware of the state of risk of their building stockconsisting, for example, of schools, hospitals, administration offices, statebanks, etc.

Availability of original drawings is quite rare, at least in some countries, forpre-WWII RC buildings, and continues until well into the late Sixties of the lastcentury.

Complete or partial lack of the original drawings, i.e. of the structuralgeometry and of the details, could in theory be remedied by a more or less

extensive survey and in-situ inspections.

All mentioned public buildings, however, are in continuous use, which makesit completely impractical to collect the needed information by exposingsufficient portions of the concrete structure, examining reinforcement layoutan a ng s ee an concre e samp es.


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On the nature of uncertainties

In all those cases where assessment is conducted with the structure

still in use the ma or sources of uncertaint inevitabl refer to

geometry and details, more than to materials.

,

different in nature. They are in principle removable, if surveys andinvestigations were possible to the point of allowing the setting up of a

, .

equally quite rare in many countries to be able to start the assessment

process on the basis of a complete and credible designocumen a on.


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On the limits of the CF approach

In the first place, it is clear that the Confidence Factor covers only one

art of the over-all uncertaint i.e. that related to the material

properties, whose role is in the majority of cases secondary.

factors, since a certain element is there or it is not, with a particulararrangement of the reinforcement or with another, and so on, and one

.


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Methods of analysis: linear


q-factor approach

The method is applicable to reinforced concrete (q=1.5) and steel

structures (q=2) without restrictions

Higher values of q are admitted if they can be analytically justified (arare situation in practice)

With such small values of q the method is generally quiteconservative (it may indicate the need for unnecessaryinterventions), hence it should find application for buildings havinga visible overcapacity relative to local seismic hazard)

No mention is made of this method for masonry structures


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Linear analysis with unreduced elastic seismic action (1/2)

Lateral force and modal response spectrum

Usable subject to a substantial uniformity, over all ductile primary,corresponding capacity, i.e.

max D /C /min D /C 2.5 su ested but not >3

Limited practical experience indicates that when the abovecondition is satisfied the results from elastic multi-modal analysis

The above condition represents a physical quantitative definition ofre ularit of a structure from a seismic oint of view more accuratethan the semi-quantitative and rather arbitrary definitions given inEC8 Part 1


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Linear analysis with unreduced elastic seismic action (2/2)

The lateral force method is less accurate and not computationallyadvantageous: it might well be dropped

applicability are satisfied but the percentage of buildings complyingwith them is anticipated being not very large

Application of linear methods to masonry structures is problematicdue:

,modelling of the structure

There are additional strict conditions to be fulfilled: vertical continuity of all walls, rigidfloors, maximum stiffness ratio between walls at each floor less than 2.5, floors at bothsides of a wall are at the same hei ht

The above remarks point towards a generalised recourse to non linearmethods


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Methods of analysis: non-linear static 1/3


The reference version of the pushover method in EC8-3 is the sameas in Part 1

This versione provides satisfactory results when:

The effects of the higher modes are negligible

The case of unsymmetrical (but still single-mode dominated)

whereby:

The loading pattern is still planar (uniform or modal) The displacements of the stiff/strong sides of the building obtained from the pushover

analysis are amplified by a factor based on the results of spatial modal analysis

In EC8 Part 3 a note is added in 4.4.5 sa in that when T 4T orT1>2s the effects of higher modes should be taken into account (nota P, hence not obligatory)


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Multi-modal pushover: a convenient proposal (Chopra,

Use several (spatial) lateral load patterns, corresponding to all significantmodes: F = M

Perform a pushover analysis and evaluate the desired response quantities R,for each modal pattern and for each of the two horizontal components of theseismic action E and E and for the two signs (R -R )

-

Combine the results from the above analyses according to the SRSS rule

= - 2 - 2 G i,EX G i,EY G


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Problem with modal combination of member forces

Unrealistically high normal forces and bending moments

Shear forces not in equilibrium with bending moments

v u : u v uboth in the demand V(N) and in the capacity VR(N)

Approximate solution: evaluate the D/C ratio mode by mode Vi(Ni)/VR(Ni)(same sign of Ni on both D and C) and then check:

i i R i

(damage variable analogy)


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Members verifications: demand quantities


Ductile members (beam-columns & walls in flexure): - ,

obtained from the analysis, either linear or non-linear

Brittle mechanisms (shear):the demand quantity is the force acting on the

Linear analysis: the ductile transmitting mechanisms can be: e ow y e ng: e orce s g ven y e ana ys s yielded: the force is obtained from equilibrium conditions, with the

capacity of the ductile elements evaluated using mean values of the

. . Non-linear analysis: forces as obtained from the analysis


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Members verifications: capacities


Ductile members (beam-columns & walls in flexure) express ons o e u ma e c or -ro a ons are g ven or e ree

performance levels, the values of the mech. properties are the mean

values divided by the CF.

Brittle mechanisms (shear) express ons or e u ma e s reng are g ven or e - , e

values to be used for the mechanical properties are the mean values,

divided by both the usual partial -factors and the CF


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Member verifications: synopsis


Linear Model (LM) Non-linear Model

Acceptability of Linear Model

(for checking of i =Di/Ci values)

From analysis. In terms of strength.

Ductile

In terms of

deformation.

Use mean values of

properties divided by

Use mean values of

properties in model.

Use mean values of

properties

Verifications (if LM accepted)

Type of

elment orFrom analysis.

Use mean values of

CF..

deformation.

Use mean values of


CF.

(e/m)properties in model.

Verifications (if LM accepted)

In terms of strength.

If i 1: from

analysis.

In terms of strength.

Use mean values of

Brittle

Use mean values of


CF and by partial

factor.

CF and by partial

factor.

If i > 1: from

equilibrium with

strength of ductile

e/m.

properties multiplied

by CF.


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28/36


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Members verifications under bidirectional loading


Bidirectional loading is the standard situation due to the

of the seismic action

of the behaviour at ultimate)

,

the assumption of an elliptical interaction domain forbiaxial deformation at ultimate

Proposal:

the bidirectional demand/capacity ratio

BDCR = , ,

Check that (BDCRi)2 1


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Capacity models for strengthened members (Informative Annex)


The section covers traditional strengthening techniques, such asconcrete and steel acketin as well as the use of FRP latin andwrapping, for which results from recent research are incorporated.

Guidance in the use of externally bonded FRP is given fo the purposes

increasing shear strength (contribution additive to existingstren th

increasing ductility of critical regions (amount of confinementpressure to be applied, as function of the ratio between target and

preventing lap-splice failure (amount of confinement pressure to be

a lied as function of the bar diameters and of the action alreadprovided by existing closed stirrups)


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Discussion


Variability of results obtainable followingalternative allowable code rocedures

Simple demonstrative example

KL3CF=1 -250400

,or shear capacities in column elements

Choices

dynamic (NLD)

Model: standard fiber model (B), plastic hinge model

Infills: inclusion (T), exclusion (NT)

Beams: 250700 at all floors o umn re n orcemen ra o: min = , max =

Shear strength capacity model: Biskinis-Fardis (BF),Kowalsky-Priestley (PK)

Concrete fc = 20 MPa

Steel fy = 275 MPa

Infills f m = 4.4 MPa


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Discussion


Variability of the results for the 25=32 combinations of the choices,

the choices indicated along the branches)


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Discussion


All five figures show the complete CDF of the 32 values (black).

, ,

corresponding to the two alternatives for each choice

1 1

0.6

0.8

F

0.6

0.8

F

Minor Minor

0.2

0.4

Ref.NLS

NLD 0.2

0.4

Ref.

rho min

rho max

0 0.5 1 1.5 2 2.5

Y0 0.5 1 1.5 2 2.5

Y

0.8

1

0.8

1

0.8

1

0.4

0.6

F

0.4

0.6

F

Ref.

0.4

0.6

F

Ref.

Major

sensitivity

Major

sensitivity

Moderate

sensitivity

0 0.5 1 1.5 2 2.50

0.2

Y

.

B

A

0 0.5 1 1.5 2 2.50

0.2

Y

BF

PK

0 0.5 1 1.5 2 2.50

0.2

Y

NT


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Discussion


In the example the major influence on the variability ofthe results is due to fundamental uncertainties that are

epistemic in nature, i.e. they cannot be reduced by

In man cases further there are limits to the t e and

number of inspections that can be performed, hence ameasure of epistemic uncertainty is de facto in varying

egrees a ways presen

,except for material properties whose relevance is

enerall minor


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Discussion


A classical statistical tool for dealing with problems of, ,

overall knowledge available, the analyst sets up a

number of alternative models, and associates to eachchoice entering a model a weight representative of hissubjective belief on the validity of the choice itself

Each model provides an outcome of the assessment,characterised by a probability which is the product of thepro a es ass gne o e ranc es o e ree

The ensemble of the outcomes rovides thus anapproximate discrete distribution of the systems D/Cratio, from which statistics such as mean, dispersion

Di i


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Discussion


The application of the logic tree isillustrated with reference to theprevious example frame.

The uncertainties considered in

probabilities

those that have shown to havemore significance, i.e. modellingstrate shear stren th model andconsideration of infillscontribution to response.

weighting the choices are:

Modelling: 0.6 for the advancedmo e ng, . or e as c one; Shear-strength model: 0.7 for EC8-3model, 0.3 for the alternative one;

Infills: 0.3 if present, 0.7 if absent. =1Global D/C ratio:

Mean value = 0.80

Standard dev. = 0.44

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