s9 Ec8-Lisbon p Pinto
Transcript of s9 Ec8-Lisbon p Pinto
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EUROCODE 8Background and Applications
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Assessment and retrofitting of buildings
Paolo Emilio PintoUniversity of Rome, La Sapienza
Paolo FranchinUniversity of Rome, La Sapienza
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Introduction
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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
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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
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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
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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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Compliance criteria: remarks
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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
9 10 Structural failure4 5 6
7 8
9 10 Structural failure4 5 6
7 8
9 10
4 5 6
7 8
9 10
Weak storey failure Shear column failure
=max . ; . = .1 2 3
Weak storey failure Shear column failure
=max . ; . = .1 2 31 2 3
Weak storey failure Shear column failure
=max . ; . = .1 2 3
Weak storey failure Shear column failure
=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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Compliance criteria: remarks
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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
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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
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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
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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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Information for structural assessment: remarks
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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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Information for structural assessment: remarks
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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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Information for structural assessment: remarks
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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
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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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Methods of analysis: linear
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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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Methods of analysis: linear
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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
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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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Methods of analysis: non-linear static 2/3
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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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Methods of analysis: non-linear static 3/3
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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
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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
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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
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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
properties divided by
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
properties divided by
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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Members verifications under bidirectional loading
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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)
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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
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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
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Variability of the results for the 25=32 combinations of the choices,
the choices indicated along the branches)
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Discussion
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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
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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
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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
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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