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7/27/2019 METODA ANMETODA ANALIZEI GLOBALE DUPA EC3ALIZEI GLOBALE DUPA EC3_IG.ppt
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METODA ANALIZEI GLOBALE A STRUCTURILOR DUPA ENV 1993-1-1
C .
T E L E M A N .
I N G I N E R I E
G
E O T E H N I C A - M A S T E R .
C U R S 1
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7/27/2019 METODA ANMETODA ANALIZEI GLOBALE DUPA EC3ALIZEI GLOBALE DUPA EC3_IG.ppt
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ANALIZA STRUCTURALA A
CONSTRUCTIILOR CU SCHELET DIN OTEL
Comportarea structurilor metalice este consecinţă directă a caracteristicilor şi proprietăţilor fizico
mecanice ale oţelului: Sectiunile elementelor sunt uniforme datorita omogenitatii otelului asadar este usor de anticipat
rezistenta elementului in sine,
Masa raportata la sectiune a elementelor de otel este considerabil redusa fata de cea a elementelor
din beton armat cu aceeasi destinatie in structura,
Elementele din otel prezinta o zveltete crescuta raportata la elementele din beton armat datorita
sectiunilor reduse ce rezulta din calculul de dimensionare,
Rezistenta pe sectiune a elementelor de otel este mult mai mare decat a elentelor de beton armat
supuse la aceleasi solicitari, Innadirile respectiv imbinarile dinte elementele din otel prezinta tolerante foarte reduse.
Structurile din otel sunt usoare, zvelte si in consecinta relativ sensibile la toate formele de
instabilitate
In acelasi timp datorita caracteristicilor de material otelul are o comportare duala: elastic pana la
limita de proportionalitate a deformatiilor (0.2%) dar si ductil (plastic) cu rezerve importante de
rezistenta pe sectiune (cel putin 20% la otelul structural). Datorita acestor rezerve sectiunile de otel
pot dezvolta deformatii importante care sunt luate in consideratie in calculul in domeniul plastic.
Formarea articulatiilor plastice este usor de anticipat si dirijat in intreaga structura tocmai datorita
omogenitatii sectiunilor din otel.
Structurile din otel pot fi proiectate atat in elastic cat si in plastic datorita rezervelor de
rezistenta peste limita de curgere f y pana la limita de rupere f u (f u/f y1,2)
C . T e l e m a n .
S t e l S t r u c t u r e s I I I .
L e c t u r e 1
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7/27/2019 METODA ANMETODA ANALIZEI GLOBALE DUPA EC3ALIZEI GLOBALE DUPA EC3_IG.ppt
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• Evaluarea comportarii structurale (forte interne, momente si deformatii) sub actiuni
statice si apoi dinamice este utila in identificarea optiunilor de optimizare cat si de
asigurare a sigurantei in exploatare pe toata durata de viata a constructiei.
• Sub termenul generic de “analiza globala” aceasta evaluare se dezvolta pe baza mai
multor metode specifice care se bazeaza pe diferiti factori de influenta: abilitatea de
deformatie a structurii, caracteristicile geometrice precum si proprietatile
materialului, toate acestea aducand o contributie individuala la asigurarea
capacitatii de rezistenta a structurii la solicitari exterioare prin deformari lanivelul
tuturor elementelor componente ale acestei structuri.
C . T e l e m a n .
S t e l S t r u c t u r e s I I I .
L e c t u r e 1
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ANALIZA STRUCTURALA A
CONSTRUCTIILOR CU SCHELET DIN OTEL
TIPUL DE ANALIZA
7/27/2019 METODA ANMETODA ANALIZEI GLOBALE DUPA EC3ALIZEI GLOBALE DUPA EC3_IG.ppt
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Structurile curente din otel sunt modelate pe baza sistemului de cadre orientate
bidirectional si alcatuite din elemente lineare care preiau solicitarile exterioaredezvoltand tensiuni interne si deformatii.
Deformatiile sunt la inceput infinitezimale dar la cresterea fortelor interne si
momentelor aceste deformatii cresc ajungand la limita impusa de rezistenta,
stabilitate sau de alte criterii anexa.
Amplitudinea acestor deformatii este cea care sta la baza clasificarii structurilor incadre in categorii cu caracteristici importante:
Cadre cu noduri deplasabile sau ne-deplasabile (fixe),
Cadre cu noduri rigide, semi-rigide sau articulate (flexibile);
Cadre contravantuite sau ne-contravantuite.
C . T e l e m a n .
S t e l S t r u c t u r e s I I I .
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ANALIZA STRUCTURALA A
CONSTRUCTIILOR CU SCHELET DIN OTEL
7/27/2019 METODA ANMETODA ANALIZEI GLOBALE DUPA EC3ALIZEI GLOBALE DUPA EC3_IG.ppt
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ANALIZA IN DOMENIUL ELASTIC
• Analiza in domeniul elastic este cea mai utilizata in vdrul proiectarii structurilor din oteldtorita faptului ca ea se poate aplica oricarui tip de structura datorita faptului ca in cadrulacesteia nu se impun restrictii sau alte conditii pentru asigurarea comportrii dutile a
imbinarilor.• Structurile analizate in elastic sunt structuri ce conserva energia datorita incapacitatii
disiparii acesteia (structuri nedisipative).
• Verificarile au ca scop mentinerea tensiunilor combinate rezultate din eforturisectionale si momente de incovoiere sub nivelul capacitatii de plasticizare pesectiune.
• Baza conceptului:
Analiza la nivelul unui element structural:
Efecte de ordin II globale (P- ), si locael (P- )
Deformatii in urma
imperfectiunilor locale la nivel
de element
Deformatii globale hHhM;xHxM
VhHLM
h
xVVxHxM
C . T e l e m a n .
S t e l S t r u c t u r e s I I I
.
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Imperfectiunil
e locale sunt
neglijate
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CRITERII DE CLASIFICARE STRUCTURALA
PE BAZA SENSIBILITATII LA EFECTELE DE ORDIN II
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EFECTELE DE ORDIN II
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I N G I N E R I E
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E O T E H N I C A - M A S T E R
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EFECTUL DEPLASARILOR
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C .
T E L E M A N .
I N G I N E R I E
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E O T E H N I C A - M A S T E R
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METODE DE SIMULARE A EFECTELOR DE ORDIN II
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EFECTELE CURBURII INITIALE e0DATORITA INCOVOIERII DIN FLAMBAJ
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T E L E M A N .
I N G I N E R I E
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E O T E H N I C A - M A S T E R
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Daca NNcr /4 structura este considerata cu noduri fixe iar efectul curburii initiale
asupra comportarii globale se neglijeaza ;
Rezulta ca:
Daca se tine cont de curbura
valoarea critica se modifica:
Curbura initiala depinde de mai multi factori:
- fveltete,
- axa flambaj,
- forma sectiunii,
- clasa sectiunii,
- curba de flambaj,
- metoda de analiza globala.
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ANALIZA DE ORDIN II PRIN METODA PAS CU PAS (ITERATIVA)
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Unghiurile i se stabilesc la fiecare pas iterativ al analizei
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EVALUAREA SARCINII CRITICE SI FACTORUL DE AMPLIFICAREcr
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Actiunile laterale se voramplifica cu acest coeficient
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DETERMINAREA RAPORTULUI V/VcrSAUcr
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. T E L E M A N .
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CONSIDERAREA EFECTUL UI IMPERFECTIUNILOR
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. T E L E M A N .
I N G I N E R I E
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E O T E H N I C A - M A S T E R
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INCLINAREA GENERALA A STRUCTURII
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. T E L E M A N .
I N G I N E R I E
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E O T E H N I C A - M A S T E R
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VALORILE CURBURII INITIALE ECHIVALENTE e0,d
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. T E L E M A N .
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SECTIUNEA TRANSVERSALA METODA DE ANALIZA GLOBALA
VERIFICARI DE
REZISTENTA
TIPURILE DE SECTIUNI SI AXELE ELASTICA SAU RIGID-PLASTICA
SAU ELASTICA CU ARTICULATIIPLASTICE PERFECTE
ELASTO-PLASTICA (MEODA
ZONELOR DE PLASTICIZARE)
ELASTICA Oricare
LINEAR PLASTICA Oricare
NE-LINEAR
PLASTICA
Sectiuni in I- Axa y-y
Sectiuni in I- Axa z-z
Sectiuni tubulare rectangulare
Sectiuni tubulare circulare
Curba de flambaj eff k
M1 =1,05 M1 = 1,1 M1 =1,15 M1 = 1,2
a 0,21 l/600 0,12 0,23 0,33 0,42
b 0,34 l/380 0,08 0,15 0,22 0,28
c 0,49 l/270 0,06 0,11 0,16 0,20
d 0,76 l/180 0,04 0,08 0,11 0,14
Elemente neuniforme: Wel/A sau pl/A se utilizeaza la centrul lungimii de flambaj
AW k el y /2,0
AW k pl y /2,0
AW k pl y /2,033,1 AW k pl y /2,0
/0,2 eff y ek /eff y ek
AW k pl y /2,033,1 AW k pl y /2,0
/5,1 eff y ek /eff y ek
0,121 k k k y
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C
. T E L E M A N .
I N G I N E R I E
G
E O T E H N I C A - M A S T E R
.
C U R S 1
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IMPERFECTIUNILOR SISTEMELOR CU ZABRELE
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. T E L E M A N .
I N G I N E R I E
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E O T E H N I C A - M A S T E R
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ANALIZA ELASTICA GLOBALA
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. T E L E M A N .
I N G I N E R I E
G
E O T E H N I C A - M A S T E R
.
C U R S 1
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CRITERII DE ANALIZA PLASTICA
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. T E L E M A N .
I N G I N E R I E
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E O T E H N I C A - M A S T E R
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EVALUAREA EFECTELOR DE ORDIN II
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. T E L E M A N .
I N G I N E R I E
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E O T E H N I C A - M A S T E R
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C U R S 1
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ELASTICA
RIGID-
PLASTICA
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CLASIFICAREA STRUCTURILOR PE BAZA IMBINARILOR STRUCTURALE
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. T E L E M A N .
I N G I N E R I E
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E O T E H N I C A - M A S T E R
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CRITERIILE DE CLASIFICARE A IMBINARILOR STRUCTURALE
DUPA
REZISTENTA
DUPA
RIGIDITATE
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C
. T E L E M A N .
I N G I N E R I E
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E O T E H N I C A - M A S T E R
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MODELAREA INFLUENTEI IMBINARILOR
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RIGIDITATEA LA ROTIRE Sj.
LIMITE IN CLASIFICAREA IMBINARILOR STRUCTURALE
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. T E L E M A N .
I N G I N E R I E
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E O T E H N I C A - M A S T E R
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CURBELE STANDARD DE MOMENT-ROTIRE
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I N G I N E R I E
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E O T E H N I C A - M A S T E R
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C
. T E L E M A N .
I N G I N E R I E
G
E O T E H N I C A - M A S T E R
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1
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Imperfections of the steel elements and structures
The structural analysis of the steel frames takes into account the effects of imperfections,
local or global.
Local imperfections of the individual compressed member are: residual stresses;
geometrical imperfections.
The lack of verticality, of straightness, of flatness, of fit and other eccentricities present in
joints of the unloaded structure are considered local imperfections. Some the
imperfections are taken care of by EN 1090 and limited at specific allowed tolerances.
In the process of analysis and design the local imperfections are considered by using
equivalent geometric imperfections unless their effects are already included in the resistance
formulae used for the design of the individual members.
The equivalent imperfections that should be taken into account are:
• a) global imperfections for frames and bracing systems (P- effect )
• b) local imperfections for individual members ( P- effect).
C . T e
l e m a n .
S t e l S t r u c t u r e s I I
I .
L e c t u r e
2
2 7
Elastic instability of a framed structure: a) sway frame ; b) non sway frame
a b
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Imperfections considered in the global analysis of frames
In the analysis of the frame the elastic buckling mode of a structure is considered for every
plane of buckling so both in and out of plane buckling including torsional buckling with
symmetric and asymmetric buckling shapes should be taken into account in the most un-
favourable direction and form.
Imperfections of the sway frames
The effect of the imperfections is inserted in the frame analysis by means of an equivalent
imperfection:
- initial sway imperfection,
- individual bow imperfections of members.
The imperfections may be determined from:
a) global initial sway imperfections:
mh0 0 – basic value of the imperfection, 0=1/200;
h – reduction factor depending on the height of the columns:
132
h
2
h
h
h – height of the structure (m) ;
m – reduction factor for the number of columns in a row:
m
115.0m
m – the number of columns in a row including only those columns
which carry a vertical load N Ed not less than 50% of the average
value of the column in the vertical plane considered.
For structures with a dominant sway buckling mode, the effects of global and local imperfections
are considered as a deviation from verticality to which a bow is added. The initial sway
imperfections should apply in all relevant horizontal directions, but will be considered in one
direction at a time.
C . T e
l e m a n .
S t e l S t r u c t u r e s I I
I .
L e c t u r e
2
2 8
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Equivalent sway imperfections
Imperfections considered in the global analysis of frames
For building frames sway imperfections
may be disregarded when:
EdEd V15.0H
For the determination of horizontal
forces applied to floor diaphragms
the configuration of imperfections
should be applied, where is a
sway imperfection obtained fromassuming one storey with height h.
Global imperfections are
represented by lateral equivalent
forces acting at each floor level,
much easy to be considered in the
analysis than to incline the
structure.
The equivalent forces are
determined from the
multiplication of the
gravitational loads at every level
with the initial imperfection
angle . The equilibrium on theheight of the structure imposes a
reaction at the base of every
column.
Sway imperfections applied to the horizontal forces
acting on floor diaphragms
C . T e
l e m a n .
S t e l S t r u c t u r e s I I
I .
L e c t u r e
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2 9
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b) relative initial local bow imperfections e0 /L of the members in flexural buckling with
a length L. The values e0 / L may be chosen in the National Annex.
Imperfections considered in the global analysis of
frames
Buckling curveElastic analysis Plastic analysis
a0 1/350 1/300
a 1/300 1/250
b 1/250 1/200
c 1/200 1/150
d 1/150 1/100
Le0
Design values of initial local bow imperfection e0/L
Le0
Local bow imperfections may be neglected during the global analysis for determining
end forces and moments for members checking;
For frames sensitive to II order effects local bow imperfections of members additionally
to global sway imperfections should be introduced in the structural analysis of theframe for each compressed member if the following conditions are met:
at least one moment resistant joint at one member end;
the reduces slenderness is increased:
Ed
y
N
f A5.0
N Ed – the design value of the compression force; - in-plan reduced slenderness for the member considered as hinged at its ends.
.
C . T e
l e m a n .
S t e l S t r u c t u r e s I I
I .
L e c t u r e
2
3 0
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Local bow imperfections are taken into account in the members verifications
considering the buckling curves.
The effects of initial sway imperfection and local bow imperfections may be replacedby systems of equivalent horizontal forces, introduced for each column.
Imperfections considered in the global analysis of
frames
Replacement of initial imperfections by equivalent horizontal forces:
a)- sway imperfections; b)- initial bow imperfections
C . T e
l e m a n .
S t e l S t r u c t u r e s I I
I .
L e c t u r e
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Imperfections considered in the analysis of bracing systems
The structural bracing systems of framed structures are required to provide lateral
stability within the length of beams or of the members in compression (columns). The
effects of imperfections are included by means of an equivalent geometric imperfection
of the members to be restrained, in the form of an initial bow imperfection:
500
Le m0 L – the span of the bracing system;
m
115.0m
m – the number of members to be stabilized.
The effects of the initial bow imperfections of the members to be stabilized by the
bracing system may be replaced by the equivalent stabilizing force:
2
q0
EddL
e8 Nq
δ q - in plane deflection of the bracing system due to the load q to
which any external loads calculated from first order analysis is
added; if second order theory is used then δ q may be considered 0.
e0
– imperfection;
qd – equivalent force per unit length.
Equivalent stabilizing force for the bracing system
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Imperfections considered in the analysis of bracing systems
Where the bracing system is required to stabilize the compression flange of a beam of
constant height, the force N Ed may be obtained from:
h
M N
Ed
Ed
M Ed – the maximum moment in the beam;
h - the overall depth of the beam.
When a beam is in compression under N Ed , this force should include a part of the
compression force resulted from the imperfections of the bracing system. At points where
beams or compression members are spliced, it should also be verified that the bracingsystem is able to resist a local force equal to:
% NS EdmEd
Force which is applied to it by each beam or compression member which is spliced at that
point, and to transmit this force to the adjacent points at which that beam or compression
member is restrained.
For checking to the local force, any external loads acting on bracing systems should also beincluded, but the forces arising from the imperfection may be omitted. C
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Imperfections considered in the analysis of bracing systems
Forces at splices in compression elements
The vertical bracing system may have continuity connections which are spliced. Global
imperfection is transferred in the most un-favourable way to the splices and must be
consequently taken into account when designing the connection.The rotation is determined identically as the previous value of the global imperfections:
100 N N2
;2001
;
EdmEd
0
0m
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The effects of local bow imperfections of members are considered within the
relationships used for the determination of the buckling resistance for members.
A second order analysis may be developed considering the imperfection of one element as
a bow with the deflection in the middle.
In order to simplify the computation process, this imperfection (a variation in a parabola
shape along the element) may be introduced in the equation as a uniform distributed
loading and the reactions at both ends of the element:
Imperfections of individual
members
2
d0
eqL
e
8 Nq L
e
4 NR d0
Individual imperfections of the structural elements
For the verification of the lateral torsional buckling of a member in bending, the equivalent
initial bow imperfection of the weak axis of the profile, the eccentricity e0,d is considered by
adopting the value k∙e0 d
, where for k the value recommended is 0.5.
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