METODA ANALIZEI GLOBALE DUPA EC3.pdf

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METODA ANALIZEI GLOBALEA STRUCTURILOR DUPA ENV 1993-1-1

C.TELEMAN.MASTER

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INALTEDIN

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ANALIZA STRUCTURALA A

CONSTRUCTIILOR CU SCHELET DIN OTEL

Comportarea structurilor metalice este consecin direct a caracteristicilor i proprietilor fizico

mecanice ale oelului: 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: elasticpana 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 fypana la limita de rupere fu(fu/fy1,2)

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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 globalaaceasta 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.

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TIPUL DE ANALIZA

SENSIBILITATEA LA DEPLASARI,ROTIRI, IMPERFECTIUNI DE

BARA SI STRUCTURALE

METODA DE ANALIZA

CRITERII

NODURI DE

REZISTENTATOTALA SAU

PARTIALA

CADRE CU NODRUI

DEPLASABILE SAU

NEDEPLASABILE

CLASIFICAREA

SECTIUNILOR DE

OTEL

DIMENSIUNILEIMPERFECTIUNILOR

ELASTIC I

ELASTIC II

PLASTIC I

PLASTIC II


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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 clasificariistructurilor in cadre in categorii cu caracteristici importante:

Cadre cu noduri deplasabile sau ne-deplasabile (fixe),

Cadre cu noduri rigide, semi-rigidesau articulate(flexibile);

Cadre contravantuitesau ne-contravantuite.

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In realitate structuri sunt de multe ori

combinatii din cadre cu noduri rigide cu

cadre cu noduri articulate; cadre

necontavantuite cu cadre contravantuite

sau nucleu rigid


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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

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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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EFECTUL DEPLASARILOR

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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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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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EVALUAREA SARCINII CRITICE SI FACTORUL DE AMPLIFICARE cr

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Actiunile laterale se voramplifica cu acest coeficient


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DETERMINAREA RAPORTULUI V/VcrSAU cr

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Imperfectiunile elementelor si structurilor din otel

Analiza structurala a cadrelor din otel trebuie sa tina cont de magnitudinea efectelor

imperfectiunilor, locale sau globale (de bara sau de sistem).

Imperectiunile locale sau de bara se refera la:

tensiuni reziduale; imperfectiuni geometrice.

Ansamblul de defecte precum lipsa verticalitatii, a simetriei a planeitatilor sau orice alta

forma de excentricitate de prindere in noduri la structura initiala (neincarcata) se

considera imperfectiuni locale; o parte din aceste imperfectiuni sunt considerate de

norma EN 1090 si limitate la valori specificate ale tolerantelor

In cadrul analizei globale imperfectiuni sunt luate in calcul prin simularea lor pe baza unor

imperfectiuni geometrice echivalente, daca nu au fost deja luate in consideratie prin relatiile

de verificare la rezistenta si stabilitate de la nivelul barelor individuale.

Urmatoarele imperfectiuni echivalente sunt luate in calcul:

a) Imperfectiunile globale a cadrelor si a sistemelor de contravantuiri (P-effect)

b) Imperfectiunile locale ale barelor individuale ( P-effect).

Instabilitatea elastica a cadrelor: a) cadru contravantuit ; b) cadru necontravantuit

a b

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CONSIDERAREA EFECTUL UI IMPERFECTIUNILOR

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INCLINAREA GENERALA A STRUCTURII

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VALORILE CURBURII INITIALE ECHIVALENTE e0,d

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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

AWk ely /2,0

AWk ply /2,0 AWk ply /2,033,1 AWk ply /2,0

/0,2 effy ek /effy ek

AWk ply /2,033,1 AWk ply /2,0

/5,1 effy ek /effy ek

0,121 kkky


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IMPERFECTIUNILOR SISTEMELOR CU ZABRELE

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ANALIZA ELASTICA GLOBALA

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EVALUAREA EFECTELOR DE ORDIN II

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ELASTICA

RIGID-

PLASTICA


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CLASIFICAREA STRUCTURILOR PE BAZA IMBINARILOR STRUCTURALE

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CRITERIILE DE CLASIFICARE A IMBINARILOR STRUCTURALE

DUPA

REZISTENTA

DUPA

RIGIDITATE


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RIGIDITATEA LA ROTIRE Sj.

LIMITE IN CLASIFICAREA IMBINARILOR STRUCTURALE

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CURBELE STANDARD DE MOMENT-ROTIRE

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IMPERFECTIUNI LA NIVELUL ANALIZEI GLOBALE A CADRELOR DIN OTEL

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

Theeffect 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 0basic value of the imperfection, 0=1/200;

hreduction factor depending on the height of the columns:

132

h

2

h

h

hheight of the structure (m) ;

mreduction factor for the number of columns in a row:

m

115.0m

mthe number of columns in a row including only those columns

which carry a vertical load NEdnot 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.

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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

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b) relative initial local bow imperfectionse0/Lof 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

fA5.0

NEdthe design value of the compression force;- in-plan reduced slenderness for the member considered as hinged at its ends.

.

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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

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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 Lthe span of the bracing system;

m

115.0m

mthe 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

e8Nq

q- in plane deflection of the bracing system due to the load qto

which any external loads calculated from first order analysis is

added; if second order theory is used then qmay be considered 0.

e0

imperfection;

qdequivalent force per unit length.

Equivalent stabilizing force for the bracing system

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Where the bracing system is required to stabilize the compression flange of a beam of

constant height, the force NEdmay be obtained from:

h

MN EdEd

MEdthe maximum moment in the beam;

h- the overall depth of the beam.

When a beam is in compression under NEd , 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.

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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:

100NN2

;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

8Nq L

e

4NR 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,dis considered by

adopting the value ke0 d

, where for kthe value recommended is 0.5.

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METODA ANALIZEI GLOBALE DUPA EC3.pdf