TRANSVERSAL FRAME.ppt

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    DESIGN OF THE TRANSVERSAL FRAME

    1. Static scheme-preliminary conditions

    2. Actions and combinations

    3. Connection between the truss and the column

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    I k I k A y A yx s s i i ( )2 2

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    dc

    d

    ddc

    c

    c KK

    K

    MMKK

    K

    MM

    ;

    111 hMI Ni

    M

    iii IIII 0

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    1. STATIC SCHEMES

    Articulated (hinged) connection between the truss and the column

    Rigid (fully restraint) connection between the truss and the column

    Left- Static scheme and rigidities (Ir, I -second moment area of the truss and of the column with constant cross section);

    Right- Transversal frames carrying crane girders ( Is, Ii - second moment areas of the top and bottom part of the columns)

    Models of the frame geometry for different layouts ofthe connection between the column and the truss

    Effect of the redundancy of a rigid connection: a)- the column on the truss;b) the truss on the column; c) bending moment effects upon the chords of the truss

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    Determination of the redundancy effects upon the truss members

    N N N

    N N N

    ik ik ik

    I

    ik ik ik

    I

    0

    0

    ( )

    ( )

    max

    min

    N q T

    N q T

    ik ik ik B

    ik ik ik B

    ( )

    ( )

    max

    min

    minmax/Bik'B'k'iBik0ikik )T(/MMNN

    a. Articulated connection

    b. Rigid connection

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    1 ,1

    1 ikik ik

    ik

    lN n

    E A 2 ,2

    1 ikik ik

    ik

    lN n

    E A

    ,2ikn

    ikN

    Knowing the values in the restrained joints 1 and 2 and the rotations of the supports for the simple supported truss under

    external loading the equilibrium equations may be written.

    2

    1 ,1

    1 ikik

    ik

    ln

    E A

    2

    2 ,2

    1 ikik

    ik

    ln

    E A ,1 ,1

    1 ikik ik

    ik

    ln n

    E A

    Rotations in the supports induced by unitary bending moments:

    Rotations on the supports induced by external actions :

    ,1ikn internal efforts in the members ik when at the extremities 1 and 2 unitary bending moments are acting

    internal forces in the members ik undder external actions

    The stiffness of the members k1 and k2 also the coefficients for the transmission necessary in the static computation, k12 and k21

    21 2

    1 2

    k

    1

    2 2

    1 2

    k

    12

    2

    k

    21

    1

    k

    c. Particular situation uneven restraining conditions

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    Stiffness of the elements of the transversal frame

    The static computation follows the stages:

    a)-preliminary design of the cross section of the girder considered simply supported for determining the moment of inertia Ir;

    b)-preliminary design of the top and bottom part of the stanchion on the basis of a simplified scheme for determining the moments

    of inertia Is

    and Ii

    ;

    c)-static computation of the frame for certain loads in order to determine the maximum sectional efforts.

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    LOADING SCHEMES ON THE TRANSVERSAL FRAME WITHOUT CRANE GIRDERS

    a)-the dead and live loads are always present;

    b)-only one alternative of each temporary loads presented on the schemes may taken once (for ex. snow on the left side or on the

    right side of the roof or on the whole roof, and so on);

    c)-the snow and the maximum temperature effects are not possible together;

    d)-the action of the force RF is always taken together with the action of the pair of forces R-r (or R-r); the action of the forces R-r

    may be taken without the action of the force RF;

    e)-if the seismic load is taken into account then neither the crab effects nor the wind are considered.

    RULES FOR COMBINATIONS

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    LOADING SCHEMES AND INTERNAL FORCES AND MOMENTS FOR DESIGN OF

    THE COLUMN IN FRAMES WITH CRANE GIRDERS

    M N T N M Tcoresp corespmax max, , ; , ,

    Reactions from crane girder on the columns

    Simplified schemes for the determinations of

    sectional efforts on columns

    Combinations of the sectional efforts for the design of the columns

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    V qL

    p p

    H 2

    ii

    ss

    hG

    hG

    150

    100V q

    Lz z

    H 2

    Ti

    Ti

    LqPr

    LqPR

    min

    ma x R FF c i

    Tvv

    Tvv

    Lpq

    Lpq

    ''

    1654

    321

    ;;

    ;;)(

    eRMePMePM

    ePMeGMeVVVM

    sii

    sssvzp

    e

    b be

    be

    t be

    t bi s is

    p s

    i

    p is

    2 2 2 2; ; ;

    i

    s

    I

    In 0

    -no= 0.2 for cranes with low lifting capacity and heavy roofs;

    -no= 0.08 for cranes with heavy lifting capacity and light roofs.

    STAGE II: the static computation of the transversal frame is started considering a certain ratio I Is i/

    One span, hinged connection 11 1 1 0 X Pn

    I

    I

    s

    i

    X

    M m ds M m ds

    m ds n m ds

    P

    P

    s

    P

    i

    s i

    1

    1

    11

    1 1

    1

    2

    1

    2

    11 12

    1

    2

    12

    12

    1

    2

    1

    2

    1 1

    1

    mE I

    ds mE I

    dsE I

    m dsE I

    m ds

    E Im ds n m ds

    s i sis s i i

    s s i

    ( )

    11 1

    1 1

    1 1

    1 1

    1

    P

    P

    ss

    P

    ii s

    P

    s i

    P

    i

    s

    P

    s

    P

    i

    M m

    E Ids

    M m

    E Ids

    E IM m ds

    E IM m ds

    E IM m ds M m ds

    ( )

    M M m XP 1 1

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    11 1 1 0 X P

    is

    iP

    sP

    P

    dsmndsm

    dsmMndsmM

    X2

    1

    2

    1

    11

    11

    1

    1M M m XP 1 1

    if XR

    II Stage. Correction of the reactions

    33

    1

    33

    1i

    1

    h

    EI3

    11n

    n

    h

    EI3r

    I Stage. Determine the reactions frame considering the joint is blocked

    0RRf

    The stages for the computation of the one redundancy degree system

    irR

    i

    f

    r

    R

    f1

    1111 RR

    rXrXX

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    I Stage. Reactions, bending moments in the restraint at the base and stiffness to

    horizontal displacements of the columns with variable cross section hinged at the top

    31

    2s

    2

    1K;

    I

    In;

    h

    h

    n

    11n;

    n

    11n;

    n

    11n 4

    4

    3

    3

    2

    2

    223K1PX

    1PXhM iA

    220ih

    KM3X

    0

    iA MhXM

    4i phK4

    3X

    2

    phXhM iA

    3

    3

    1ii

    1

    h

    EI3RX

    1;hRM iA

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    Connection between the column and the roof truss

    b,c

    2

    v

    2

    h

    1

    v

    1

    2

    i

    maxih

    11

    NNNR

    n

    VN;

    n

    HT

    y

    yMN

    eVeHTM

    0

    1

    1

    M

    y2

    shear

    2

    tech

    angle

    vp2

    vt

    2

    ht2

    0

    ht

    2

    v

    22i

    ma x2h

    22

    f3

    td

    N;

    4

    d

    N

    4

    d

    N;

    4

    d

    N

    n2

    VN;

    n2

    HT

    h2

    hMN

    eVeHTM