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    METODA ANALIZEI GLOBALEA STRUCTURILOR DUPA ENV 1993-1-1

    C.

    TELEMAN.

    INGINERIE

    G

    EOTEHNICA-MASTER.

    CURS1

    1

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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: 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 fy pana la limita de rupere fu (fu/fy1,2)

    C.Teleman.

    StelStructuresIII.

    Lecture1

    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 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.Teleman.

    StelStructuresIII.

    Lecture1

    3

    ANALIZA STRUCTURALA A

    CONSTRUCTIILOR CU SCHELET DIN OTEL

    TIPUL DE ANALIZA

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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.Teleman.

    StelStructuresIII.

    Lecture1

    4

    ANALIZA STRUCTURALA A

    CONSTRUCTIILOR CU SCHELET DIN OTEL

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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.Teleman.

    StelStructuresIII

    .

    Lecture1

    5

    Imperfectiunil

    e locale sunt

    neglijate

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    CRITERII DE CLASIFICARE STRUCTURALA

    PE BAZA SENSIBILITATII LA EFECTELE DE ORDIN II

    C.

    TELEMAN.

    INGINERIE

    G

    EOTEHNICA-MASTER

    .

    CURS1

    6

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    EFECTELE DE ORDIN II

    C.

    TELEMAN.

    INGINERIE

    G

    EOTEHNICA-MASTER

    .

    CURS1

    7

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    EFECTUL DEPLASARILOR

    C.

    TELEMAN.

    INGINERIE

    G

    EOTEHNICA-MASTER

    .

    CURS1

    8

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    C.

    TELEMAN.

    INGINERIE

    G

    EOTEHNICA-MASTER

    .

    CURS1

    9

    METODE DE SIMULARE A EFECTELOR DE ORDIN II

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    EFECTELE CURBURII INITIALE e0DATORITA INCOVOIERII DIN FLAMBAJ

    C.

    TELEMAN.

    INGINERIE

    G

    EOTEHNICA-MASTER

    .

    CURS1

    10

    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)

    C.

    TELEMAN.

    INGINERIE

    G

    EOTEHNICA-MASTER

    .

    CURS1

    11

    Unghiurile i se stabilesc la fiecare pas iterativ al analizei

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    EVALUAREA SARCINII CRITICE SI FACTORUL DE AMPLIFICAREcr

    C.

    TELEMAN.

    INGINERIE

    G

    EOTEHNICA-MASTER

    .

    CURS1

    12

    Actiunile laterale se voramplifica cu acest coeficient

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    DETERMINAREA RAPORTULUI V/VcrSAUcr

    C

    .TELEMAN.

    INGINERIE

    G

    EOTEHNICA-MASTER

    .

    CURS1

    13

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    CONSIDERAREA EFECTUL UI IMPERFECTIUNILOR

    C

    .TELEMAN.

    INGINERIE

    G

    EOTEHNICA-MASTER

    .

    CURS1

    14

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    INCLINAREA GENERALA A STRUCTURII

    C

    .TELEMAN.

    INGINERIE

    G

    EOTEHNICA-MASTER

    .

    CURS1

    15

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    VALORILE CURBURII INITIALE ECHIVALENTE e0,d

    C

    .TELEMAN.

    INGINERIE

    G

    EOTEHNICA-MASTER

    .

    CURS1

    16

    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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    C

    .TELEMAN.

    INGINERIE

    G

    EOTEHNICA-MASTER

    .

    CURS1

    17

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    IMPERFECTIUNILOR SISTEMELOR CU ZABRELE

    C

    .TELEMAN.

    INGINERIE

    G

    EOTEHNICA-MASTER

    .

    CURS1

    18

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    ANALIZA ELASTICA GLOBALA

    C

    .TELEMAN.

    INGINERIE

    G

    EOTEHNICA-MASTER

    .

    CURS1

    19

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    CRITERII DE ANALIZA PLASTICA

    C

    .TELEMAN.

    INGINERIE

    G

    EOTEHNICA-MASTER

    .

    CURS1

    20

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    EVALUAREA EFECTELOR DE ORDIN II

    C

    .TELEMAN.

    INGINERIE

    G

    EOTEHNICA-MASTER

    .

    CURS1

    21

    ELASTICA

    RIGID-

    PLASTICA

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    CLASIFICAREA STRUCTURILOR PE BAZA IMBINARILOR STRUCTURALE

    C

    .TELEMAN.

    INGINERIE

    G

    EOTEHNICA-MASTER

    .

    CURS1

    22

    CRITERIILE DE CLASIFICARE A IMBINARILOR STRUCTURALE

    DUPA

    REZISTENTA

    DUPA

    RIGIDITATE

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    C

    .TELEMAN.

    INGINERIE

    G

    EOTEHNICA-MASTER

    .

    CURS1

    23

    MODELAREA INFLUENTEI IMBINARILOR

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    RIGIDITATEA LA ROTIRE Sj.

    LIMITE IN CLASIFICAREA IMBINARILOR STRUCTURALE

    C

    .TELEMAN.

    INGINERIE

    G

    EOTEHNICA-MASTER

    .

    CURS1

    24

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    CURBELE STANDARD DE MOMENT-ROTIRE

    C

    .TELEMAN.

    INGINERIE

    G

    EOTEHNICA-MASTER

    .

    CURS

    1

    25

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    C

    .TELEMAN.

    INGINERIE

    G

    EOTEHNICA-MASTER

    .

    CURS

    1

    26

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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.Teleman.

    StelStructuresII

    I.

    Lecture

    2

    27

    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

    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 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 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.

    C.Teleman.

    StelStructuresII

    I.

    Lecture

    2

    28

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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.Teleman.

    StelStructuresII

    I.

    Lecture

    2

    29

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    b) relative initial local bow imperfectionse0/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

    fA5.0

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

    .

    C.Teleman.

    StelStructuresII

    I.

    Lecture

    2

    30

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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.Teleman.

    StelStructuresII

    I.

    Lecture

    2

    31

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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

    e8Nq

    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 qmay be considered 0.

    e0

    imperfection;

    qd equivalent force per unit length.

    Equivalent stabilizing force for the bracing system

    C.Teleman.

    StelStructuresIII.

    Lecture

    2

    32

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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 NEdmay be obtained from:

    h

    MN

    Ed

    Ed

    MEd the 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. C

    .Te

    leman.

    StelStructuresIII.

    Lecture

    2

    33

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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:

    100NN2

    ;2001

    ;

    EdmEd

    0

    0m

    C.Te

    leman.

    StelStructuresIII.

    Lecture

    2

    34

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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

    4NRd0

    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.

    C.Te

    leman.

    StelStructuresIII.

    Lecture

    2

    35