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  • -

    __ 12 2015

    ,

    - 60542948 00036-2015

    2015

  • - 60542948 00036-2015

    II

    27 2002 . 184-

    ,

    1.42004 .

    . .

    1

    2

    3

    __ 12 2015 .

    4

    ,

  • - 60542948 00036-2015

    III

    ............................................................................................................................. IV

    1 ........................................................................................................ 1

    2 ....................................................................................................... 2

    3 , ........................................................................... 3

    4 . ..................................................................... 8

    5 ............................................................................................. 13

    5.1 ..................................... 15

    5.1.1 ......................................................................................... 16

    5.1.2 ............................................... 16

    5.1.3 ............................................. 17

    5.1.4 ........................................................ 21

    5.1.5

    ..................................................................................................................... 23

    5.2 ......................................................................................................... 26

    5.2.1 ............................................................................................ 27

    5.2.2 ............................ 28

    5.2.3 ..................................................... 30

    5.3 ...................... 35

    5.4 ...................................................... 36

    6 ( ) ....................................... 39

    ()

    ...43

    () ............................................................ 51

  • - 60542948 00036-2015

    IV

    27

    2002 . 184- [1], 30 2009 . 384-

    [2].

    ,

    .

    ,

    :

    - ETAG 001 Guideline for European technical approval of metal anchors for use in

    concrete. Annex C: design methods for anchorages - , 2008 [3];

    - ACI 318-11 Building Code Requirements for Structural Concrete. Anchoring to

    concrete. Appendix D. Anchoring to concrete - American Concrete Institute, 2011

    [4].

    , ,

    36554501-039-2014 HILTI [5].

  • - 60542948 00036-2015

    1

    1

    1.1 ( )

    .

    .8 4 30 2009

    . 384- [2].

    1.2

    ,

    .

    1.3 , ,

    , .

    1.4

    :

    - , 3 4

    -001-97 [6];

    - II III

    -5.6 [7];

    - , II III

    -031-01[8].

    1.5

    ,

    25-60.

    1.6 ,

    , .

  • - 60542948 00036-2015

    2

    1.7

    .

    ,

    -

    .

    2

    :

    1.42004 .

    .

    54257-2010 .

    31937-2011 .

    20.13330.2011 .

    2.01.07-85*

    63.13330.2012 .

    . 52-01-2003

    ,

    1 ,

    . ,

    ,

    .

    () ,

    ().

  • - 60542948 00036-2015

    3

    , , ,

    , ,

    . , , ,

    , .

    .

    3 ,

    3.1

    ,

    - [9] ,

    ,

    :

    3.1.1 :

    , .

    3.1.2 (attachment): ,

    .

    3.1.3 (anchor): ,

    ,

    , .

    3.1.4 (mechanical anchor): ,

    (, , , ..).

    3.1.5 (expansion anchor): ,

    .

  • - 60542948 00036-2015

    4

    3.1.6 (torque-controlled

    anchor): , ,

    .

    3.1.7 (deformation-controlled

    anchor): ,

    , .

    3.1.8 (undercut anchor): ,

    .

    3.1.9 - (screw-anchor): ,

    .

    3.1.10 (adhesive anchor): ,

    ,

    .

    3.1.11 (adhesive): ,

    ,

    , .

    ( ) , , ,

    , .

    3.1.12 (overall embedment depth): ,

    ,

    .

    .

    3.1.13 (effective embedment depth):

    , ,

    .

    .

  • - 60542948 00036-2015

    5

    3.1.14 () :

    ,

    .

    3.1.15 : ,

    ,

    .

    3.1.16 : ,

    .

    3.2 (.

    . 3.1-3.2):

    a -

    ;

    a1 -

    1;

    a2 -

    2;

    b, l - ;

    c - ;

    c1 - 1 ( ,

    , 1

    );

    c2 - 2 ( 2

    1);

    cmin - ;

    d - ;

  • - 60542948 00036-2015

    6

    d1 - ;

    d2 - ;

    df - ;

    dnom -

    ( );

    do - ;

    h - ;

    h1 - ;

    hef - ;

    hmin - ;

    hnom - ;

    ho - ;

    lf - ;

    s - () ;

    s1 - () 1;

    s2 - () 2;

    smin - () ;

    tfix - .

  • - 60542948 00036-2015

    7

    3.1

  • - 60542948 00036-2015

    8

    ; , ;

    ; ,, ; ,

    .

    3.2 -

    4 .

    4.1

    54257.

    , ,

    5.

    ,

    ,

    ,

    6.

    4.2

    , ,

    () , () .

    4.3

    .

    ,

    (. ).

    4.4

    (. . 4.1).

    . 4.1.

  • - 60542948 00036-2015

    9

    lc , ; 1

    ; 2 ; 3 - ,

    (c < lc); 4 - , (c lc).

    4.1

    4.5

    ( ), . 4.2.

    4.5.1

    ,

    .

    ( ,

    ..).

    4.2

  • - 60542948 00036-2015

    10

    4.6

    . , , . 4.2 (

    ) 4.7.

    4.7 , ,

    , 4.1. ,

    ,

    35.

    4 . 1

    ()

    d1)

    dnom 2)

    6 8 10 12 14 16 18 20 22 24 27 30 >30

    df ()

    7 9 12 14 16 18 20 22 24 26 30 33 1,1d

    1,1dnom

    () 1 1 2 2 2 2 2 2 2 2 3 3

    0,1d

    0,1dnom 1)

    / 2)

    /

    4.8

    4.2.

    4 . 2

    ,

    *,

    ,

    I -43 +40 24 40

    II -43 +58 35 58

  • - 60542948 00036-2015

    11

    III -43 +70 43 70

    IV -43 +80 50 80

    V -43 +120 72 120

    * - .

    4.9 .

    (

    63.13330)

    31937 (-

    ) .

    4.10

    ().

    ( ) ()

    ,

    54257

    20.13330.

    4.11

    .

    4.12

    .

    4.13

    (. . 4.3).

  • - 60542948 00036-2015

    12

    ; ; ;

    ; .

    4.3

    4.14 , :

    M

    ls

    eal

    3 , (4.1)

    el

    a3 , , : a3= d/2

    ; a3 = 0 ,

    . 4.4; d (dnom

    / )

    M ,

    (. . 4.5).

    M = 1,0. ,

    . 4.7 M = 2,0.

    ,

    .

    4.4 -

  • - 60542948 00036-2015

    13

    4.5 -

    4.15

    :

    )

    ;

    ) ,

    -

    30 d/2 (d

    dnom / );

    )

    , . 4.1.

    5

    ,

    , , :

    ( ),

    , ,

    (

    ), ,

    (. . 5.1 5.2).

  • - 60542948 00036-2015

    14

    .5.3.

    - ; - ; -

    ; - ;

    ( ); -

    5.1

  • - 60542948 00036-2015

    15

    - ; -

    ; -

    .

    5.2

    5.1

    , 5.1, 5.2.

    5 . 1 -

    ..

    1

    (. 5.1.1) Nsd NRk,s/Ms N

    hsd NRk,s/Ms

    2

    (.5.1.2) Nsd NRk,p/Mp N

    hsd NRk,p/Mp

    3

    (.5.1.3)

    Nsd NRk,c/Mc Ng

    sd NRk,c/Mc

    4

    (.5.1.4)

    Nsd NRk,sp/Msp Ng

    sd NRk,sp/Msp

    5

    (. 5.1.1) Nsd NRk,s/Ms N

    hsd NRk,s/Ms

    5.2

    ..

    6 Nsd NRk,c/Mc Ng

    sd NRk,c/Mc

  • - 60542948 00036-2015

    16

    (.5.1.3)

    7

    (.5.1.5)

    Nsd NRk,p/Mp Ng

    sd NRk,p/Mp

    8

    (.5.1.4)

    Nsd NRk,sp/Msp N

    gsd

    NRk,sp/Msp

    , . 5.1-5.2:

    Nsd , ;

    Nhsd - ,

    ;

    Ngsd - ,

    ;

    NRk

    (. . 5.1.1-5.1.5);

    M , (.

    . 5.1.1-5.1.5).

    5.1.1

    5.1.1.1

    NRk,s .

    .

    5.1.1.2 M,s

    .

    5.1.2

  • - 60542948 00036-2015

    17

    5.1.2.1

    .

    5.1.2.2

    NRk,p ,

    ( ,

    ).

    5.1.2.3

    Mp .

    5.1.3

    5.1.3.1

    NRk,

    :

    NecNreNs

    Nc

    Nc

    cRkcRkA

    ANN ,,,0

    ,

    ,0

    ,, , (5.2)

    N0Rk, -

    :

    5.1

    ,1

    0

    , efnbcRk hRkN , (5.3)

    N0Rk, ;

    Rb,n , ;

    hef , TC

    .

    k1 ,

    :

    8,4 - ;

    11,8 - ;

    0

    ,

    ,

    Nc

    Nc

    A

    A - ,

    ;

  • - 60542948 00036-2015

    18

    Ac,N ,

    ( s

  • - 60542948 00036-2015

    19

    5.1.3.2 () scr,N,

    ,

    :

    efNcr hs 3, (5.8)

    cr,N,

    ,

    :

    efNcr hc 5,1, (5.9)

    Ac,N = (c1 + 0,5 scr,N) scr,N

    c1 ccr,N ;

    Ac,N = (c1 + s1 + 0,5 scr,N) scr,N

    c1 ccr,N ;

    s1 scr,N ;

  • - 60542948 00036-2015

    20

    Ac,N = (c1 + s1 + 0,5 scr,N)(c2 + s2 + 0,5 scr,N)

    c1 ccr,N ; c2 ccr,N ;

    s1 scr,N ; s2 scr,N ;

    ;

    ; .

    5.3 -

    5.1.3.3

    (. . 5.4) . 5.1.3.1

    , hef,red

    :

    5,1

    max

    ,

    max,

    ch

    c

    ch ef

    Ncr

    redef (5.12)

    cmax (

    )

    (5.2) (5.7)

  • - 60542948 00036-2015

    21

    redefNcr hs ,, 3 ; redefNcr hc ,, 5,1

    cmax = max (c1,1;1,2;2,1;2,2) (c1,1;1,2;2,1;2,2) cr,N

    5.4

    5.1.3.4

    M .

    5.1.4.

    5.1.4.1.

    :

    sph

    sp

    cRkspRk NN ,,, , (5.13)

    NspRk,c , (5.2)

    scr,N , cr,N scr,sp , cr,sp;

    scr,sp (),

    ;

    ccr,sp ,

  • - 60542948 00036-2015

    22

    ;

    scr,sp , cr,sp .5.1.4.2

    h,sp ,

    , :

    5,1

    3/2

    min

    ,

    h

    hsph , (5.14)

    h - ;

    hmin - ,

    .

    5.1.4.2 scr, sp , cr, sp

    ;

    5.1.4.3

    :

    ) c cr,sp

    c 1,2cr,sp ,

    h 2hef ;

    )

    0,3,

    :

    - 60%

    N30;

    -

    30.

    N:

    ) - 1,5N;

    ) 1,0N;

    ) 2,0N;

  • - 60542948 00036-2015

    23

    ) 0,5N.

    5.1.4.4

    Msp .

    5.1.5

    .

    5.1.5.1

    .

    5.1.5.2

    NRk,p (5.15):

    NpgNecNreNsc

    Np

    Np

    pRkpRkA

    ANN ,,,,0

    ,

    ,0

    ,, , (5.15)

    N0Rk,p -

    :

    RkefnompRk hdN 0

    ,, (5.16)

    Rk - 25,

    , ,

    (Rk,rc), (Rk,urc);

    hef, ;

    dnom ;

    hef , dnom , ;

    0

    ,

    ,

    Np

    Np

    A

    A

    - ,

    ;

  • - 60542948 00036-2015

    24

    Ap,N ,

    ( s

  • - 60542948 00036-2015

    25

    cr,Np,

    , :

    2/,, NpcrNcr sc (5.19)

    5.1.5.4 , g,Np

    :

    0,110,5,0

    ,

    0

    ,,

    Npg

    Npcr

    NpgNpgs

    s , (5.20)

    0g,Np ,

    ,

    :

    0,1)1(

    5,1

    ,

    0

    ,

    nbef

    cRknomNpg

    Rhk

    dnn

    , (5.21)

    0g,Np ;

    Rk - 25,

    ,

    (Rk,rc), (Rk,urc),

    /2;

    c - , ,

    ,

    .

    . 25 c = 1,0.

    hef, , ;

    dnom , ;

    k ,

    :

    3,7 - ;

  • - 60542948 00036-2015

    26

    2,7 - ;

    Rb,n - ,

    63.13330 , ;

    n (

    );

    s ;

    .

    5.1.5.5

    Mp

    .

    5.2

    , 5.3.

    5 . 3 -

    ..

    1

    (.5.2.1.1) Vsd VRk,s/Ms

    Vh

    sd

    0,8VRk,s/Ms

    2 c

    (.5.2.1.2) Vsd VRkm,s/Ms V

    hsd VRkm,s/Ms

    3

    (.5.2.2)

    Vsd VRk,cp/Mc V

    gSd

    VRk,cp/Mc

    4

    (.5.2.3)

    Vsd VRk,c/Mc Vg

    sd VRk,c/Mc

    , . 5.3:

    Vsd , ;

  • - 60542948 00036-2015

    27

    Vh

    sd - ,

    Vg

    sd - , ;

    VRk

    (. .5.2.1-.5.2.3);

    M , (. .5.2.1-

    5.2.3).

    5.2.1

    (. .4.13-4.15).

    5.2.1.1

    VRk,s

    .

    .

    5.2.1.2

    VRkm,s :

    s

    sRk

    sRkml

    MV

    ,

    , , (5.21)

    MRk,s

    :

    MsRks

    h

    sd

    sRksRkN

    NMM

    /10 ,, , (5.22)

    M0Rk,s - ,

    ;

  • - 60542948 00036-2015

    28

    Nh

    sd - ,

    ;

    NRk,s / Ms

    .5.1.1;

    ls . 4.14.

    .

    5.2.1.3.

    M,s , .

    5.2.2.

    5.2.2.1

    VRk,cp :

    cRkcpRk NkV ,, , (5.21)

    NRk,c -

    ,

    .5.1.3.1.;

    k - , ,

    .

    5.2.2.2

    , ,

    .

    , , ,

    ,

    (5.22).

    Vh

    Sd Vh

    Rk,cp/Mc , (5.22)

    Vhsd - ;

  • - 60542948 00036-2015

    29

    Vh

    Rk,cp -

    ,

    . 5.2.2.3.

    ( .2).

    5.2.2.3

    VhRk,cp

    (5.21)

    (5.2), Ac,N

    Acp, N

    (. . 5.5).

    5.2.2.4.

    M,c ,

    .

    Acp,N = (0,5scr,N + 0,5s1 )(0,5scr,N + 0,5s2)

    s1 scr,N ; s2 scr,N ;

    Acp,N = (c1 + 0,5s1 )scr,N

    c1 ccr,N ;

    s1 scr,N ;

  • - 60542948 00036-2015

    30

    Acp,N = (c1 + 0,5s1 )(c2 + 0,5s2 )

    c1 ccr,N ; c2 ccr,N ;

    s1 scr,N ; s2 scr,N ;

    ; ;

    .

    5.5

    5.2.3

    5.2.3.1

    :

    VreVecVVhVs

    Vc

    Vc

    cRkcRkA

    AVV ,,,,,0

    ,

    ,0

    ,, , (5.23)

    V0Rk,c ,

    ,

    :

    5,11,10 , cRldkV nbfnomcRk

    , (5.24)

    V0Rk,c

    k , :

    - 2,8 - ;

    - 2,0 - ;

    dnom , ;

    lf ,

    , ;

  • - 60542948 00036-2015

    31

    1 - , ;

    Rb,n - , 63.13330

    , ;

    , :

    5,0

    1

    1,0

    c

    l f , (5.25)

    , :

    2,0

    1

    1,0

    c

    dnom , (5.26)

    0

    ,

    ,

    Vc

    Vc

    A

    A - ,

    ;

    Ac,V

    ( s 31),

    ( c2 1,5c1)

    ( h 1,5c1) - . . 5.6;

    A0

    ,V (

    ,

    ) (5.27):

    2

    111

    0

    , 5,45,13 A Vc , (5.27)

    s,V ,

    :

    0,15,1

    3,07,01

    2,

    c

    cVs , (5.28)

    1

    ;

    2 - , 1

    ( );

    h,V , :

  • - 60542948 00036-2015

    32

    0,15,1 1

    ,

    h

    cVh , (5.29)

    h - ;

    ,V ,

    :

    22, sin4,0cos1

    VV

    V

    , (5.30)

    V

    , 0 900.

    ,

    ( V>900) ,

    ( .2.6).

    ec,V ,

    :

    0,1

    5,11

    1

    1

    ,

    evVec ,

    (5.31)

    eV ,

    , (. .2.);

    ec,V = 1,0.

    Ac,V = 1,5c1 (1,5c1 + c2)

    h > 1,5c1 ;

    c2 1,5c1 ;

  • - 60542948 00036-2015

    33

    Ac,V = h(3c1 + s2)

    h 1,5c1 ;

    s2 3c1 ;

    Ac,V = h(1,5c1 + s2+c2 )

    h 1,5c1 ;

    s2 3c1 ;

    c2 1,5c1 ;

    ;

    ; .

    5.6-

    s,V , :

    1,0 ;

    1,2

    12;

    1,4

    s100.

  • - 60542948 00036-2015

    34

    5.2.3.2 , ,

    ,

    (. . 5.7).

    5.7-

    5.2.3.3 (h 1,5c1)

    ( , 2,1 1,5 c1 2,2

    1,5 c1 . . 3.1.) . 5.2.3.1 ,

    A,V A0,V

    red

    1.

    red (5.32), h/1,5

    s2/3 .

    5,1/max,2ccred , (5.32)

    2,max - 2,1, 2,2 . 3.1();

    s2- ;

    h - .

    5.2.3.4 ,

    ( .4.4),

    .

  • - 60542948 00036-2015

    35

    5.2.3.5

    M,c , .

    5.3

    5.3.1

    (5.33) (5.35):

    N 1,0 , (5.33)

    V 1,0 , (5.34)

    N + V 1,2 , (5.35)

    N - ,

    5.1. :

    MspcpRk

    Sd

    MccRk

    Sd

    MppRk

    Sd

    MssRk

    SdN

    N

    N

    N

    N

    N

    N

    N

    N

    /;

    /;

    /;

    /max

    ,,,,

    (5.36)

    Nsd ,

    , .5.1;

    NRk

    ,

    .5.1;

    M ,

    .5.1;

    N - ,

    5.2. :

    MccRk

    Sd

    McpRk

    Sd

    MssRk

    SdV

    V

    V

    V

    V

    V

    V

    /;

    /;

    /max

    ,,,

    (5.37)

  • - 60542948 00036-2015

    36

    Vsd ,

    , .5.2;

    VRk

    ,

    .5.2;

    M ,

    .5.2.

    0,8 (. . 5.3).

    5.4

    5.4.1 ,

    , .

    .

    .

    5.4.2 ( )

    , .

    5.4.3

    ,

    ,

    .

    5.4.4 ,

    ()

    .

  • - 60542948 00036-2015

    37

    5.4.5

    .

    5.4.6 , ,

    .

    ,

    .

    .

    5.4.7 , ,

    14.13330.

    5.4.8 ,

    , .

    5.4.9

    , , :

    , (5.38)

    ,

    ( ; );

    ,

    , .

    ,

    .

    5.4.10 ,

    :

    ) ,

    :

    - ,

    ( ) (. . 5.6. 5.6.);

  • - 60542948 00036-2015

    38

    - , ,

    (. . 5.6.).

    ) ; )

    ; ) .

    5.8 - ,

    ) .

    :

    , (5.39)

    , : ,

    , ,

    , ;

    , , .

    )

    , 2,5 ,

    ( 5.40).

    .

    , (5.40)

    5.4.11

    :

  • - 60542948 00036-2015

    39

    (5.41)

    .

    6 ( )

    6.1

    ,

    . ,

    , ,

    .

    6.2

    , .

    6.3 :

    ult, (6.1)

    .

    ult ,

    , , ,

    , - ,

    .

    6.4 ,

    ( )

    (

    ).

    6.5

    (6.1),

    .

  • - 60542948 00036-2015

    40

    6.6

    :

    0,

    0,

    N

    skN

    C

    NSk

    , (6.2)

    :

    ,

    ,

    N

    skN

    C

    NSk

    , (6.3)

    Nsk ;

    N,0 ();

    N, ();

    N,0, N, 6.8.

    6.7

    :

    0,

    0,

    V

    skV

    C

    VSk

    , (6.4)

    :

    ,

    ,

    V

    skV

    C

    VSk

    , (6.5)

    Vsk ;

    V,0 ()

    V, ()

    V,0, V, . 6.9

    6.8

    ,

    ,

    :

  • - 60542948 00036-2015

    41

    2

    )(0,

    2

    )(0, SkSk VN , (6.6)

    6.9 N,0, N,

    :

    )(0,

    )(0,

    N

    N

    NC

    , (6.7)

    N ;

    N,0 ,

    ;

    N, ,

    ;

    6.10

    :

    )(0,

    )(0,

    N

    efnom

    Nc

    hdC

    , (6.8)

    N,0

    ;

    N,

    ;

    dnom ;

    hef ;

    ,

    , , ;

    6.11

    :

    )(0,

    )(0,

    V

    V

    VC

    , (6.9)

    V

    V,0 ,

  • - 60542948 00036-2015

    42

    V, ,

    ,

    .

    ,

    , .

    , , .

  • - 60542948 00036-2015

    43

    ()

    .1

    .1.1

    Nhsd, Ng

    sd,

    , eN,1, eN,2 .

    (. .

    .1).

    isgsd NN , 1,shsd NN

    , ; - ,

    ; ,

    .

    .1 -

  • - 60542948 00036-2015

    44

    .1.2 ,

    .

    , .

    .1.3

    :

    ) . .1.5;

    )

    ;

    )

    ( Nb = 0,5bxEbb);

    .

    )

    63.13330

    )

    (.1) (.2):

    Ns,i = Es As s,i , (.1)

    Ns,i = Es s,i, (.2)

    Es , 2105;

    As (As=d2/4);

    s,i ;

    EAs :

    EAs = CN hef, (.3)

    CN (/)

    .6.8 ;

    hef -

    .

    .

    .1.4

    ,

    .

    . .2.

  • - 60542948 00036-2015

    45

    .2 -

    .1.5 ,

    16.13330.

    .1.6

    (. . .3).

    .3

    .2

    .2.1

    Vhsd, Vg

    sd,

  • - 60542948 00036-2015

    46

    ,

    , Vgsd.

    .2.2 ,

    Vgsd, . .2.3.

    .2.3

    :

    ) ,

    ,

    4.1,

    (. . .4);

    )

    ,

    (. . .5);

    )

    ,

    , (. . .5).

    .2.4

    .

    (. . .5).

    .2.5

    ,

    (. . .6).

    .2.6

    , ,

    Vgsd, (.

    . .7).

  • - 60542948 00036-2015

    47

    Vhsd =Vsd,1 = Vsd,2 = V/2;

    Vg

    sd = Vsd,1 + Vsd,2 = V;

    ev=0

    Vh

    sd = Vsd,1 = Vsd,2 = Vsd,3 = V/3;

    Vgsd = Vsd,1 + Vsd,2 + Vsd,3 = V;

    ev=0

    V1=Vcos; V2=Vsin;

    Vsd,1,1 = Vsd,2,1 = Vsd,3,1 = Vsd,4,1= V1/4;

    Vsd,1,2 = Vsd,2,2 = Vsd,3,2 = Vsd,4,2= V2/4;

    Vhsd =Vsd,1 = Vsd,2 = Vsd,3 = Vsd,4= V/4;

    Vg

    sd,1= Vsd,1,1 + Vsd,2,1 + Vsd,3,1 + Vsd,4,1;

    Vg

    sd,2= Vsd,1,2 + Vsd,2,2 + Vsd,3,2 + Vsd,4,2;

    Vg

    sd = [(Vg

    sd,1)2 +(V

    gsd,2)

    2 ]

    0.5 = V

    v=arctan(Vgsd,2/V

    gsd,1) = ;

    ev=0

    .4 -

  • - 60542948 00036-2015

    48

    Vsd,1 = Vsd,2 = V/2;

    Vg

    sd = Vsd,1 + Vsd,2 = V;

    ev=0

    Vsd,1 =Vsd,2 =Vsd,3 =Vsd,4 =V/4;

    Vgsd = Vsd,1 + Vsd,2 = V/2;

    ev=0;

    v= 90

    Vsd,1 = Vsd,2 = V/2;

    Vg

    sd = Vsd,1 + Vsd,2 = V;

    ev=0

    V1=Vcos; V2=Vsin;

    Vsd,1,1 = Vsd,2,1 = V1/2;

    Vsd,1,2 = Vsd,2,2 =

    = Vsd,3,2 = Vsd,4,2= V2/4;

    Vgsd,1= Vsd,1,1 + Vsd,2,1 = V1;

    Vg

    sd,2= Vsd,1,2 + Vsd,2,2 = V2/2;

    Vg

    sd = [(Vg

    sd,1)2 +(V

    gsd,2)

    2 ]

    0.5

    v=arctan(Vg

    sd,2/Vg

    sd,1);

    ev=0

    .5 -

  • - 60542948 00036-2015

    49

    Vsd,1 = V/2+T/s1;

    Vsd,2 = V/2 - T/s1;

    Vg

    sd = Vsd,1 + Vsd,2 = V;

    ev=T / Vgsd

    V1=Vcos; V2=Vsin;

    Vsd,1,1 = V1/2+T/s1;

    Vsd,2,1= V1/2 - T/s1;

    Vsd,1,2 = Vsd,2,2 = V2/2;

    Vgsd,1= Vsd,1,1 + Vsd,2,1 = V1;

    Vgsd,2= Vsd,1,2 + Vsd,2,2 = V2;

    Vg

    sd = [(Vgsd,1)

    2 +(V

    gsd,2)

    2 ]

    0.5=V

    v=arctan(Vg

    sd,2/Vgsd,1)=;

    ev= T / Vgsd

    Vh

    sd = Vsd,1 = Vsd,2 = Vsd,3 = Vsd,4 =

    2

    2

    2

    12 ss

    T

    Vg

    sd = 0;

    .6 -

  • - 60542948 00036-2015

    50

    V1=Vcos; V2=Vsin;

    90

    Vsd,1,1 = Vsd,2,1 = V1/2

  • - 60542948 00036-2015

    51

    ()

    ( 36554501-039-2014 HILTI)

    1.

    (...1.1).

    : , ,

    N=10. HILTI HKD

    M12x50 M12 4.6. 200

    30 10400 200200.

    .

    .1.1 - 1.

    .1.1 .

    .

    HKD (.4.3): h=200;

    1=600; h>hmin=100; 1>cmin=175.

    , ,

    Nsd=N=10 (.4.11)

    .1.2 (.5.1.1)

    NRk,s=33,7.

    Ms = 2,0.

    Nsd NRk,s/Ms (.1 .5.1) - .

    10 < 33,7/2,0

    10 < 16,85

    .1.3 (.5.1.2)

  • - 60542948 00036-2015

    52

    HKD 1250 .

    .1.4 (.5.1.3)

    (5.2):

    A

    ANN NecNreNs

    Nc

    Nc

    cRkcRk 6,1911122500

    225006,19

    2

    2

    ,,,0

    ,

    ,0

    ,,

    hRkN efnbcRk 6,191956650228,115,15.1

    ,1

    0

    ,

    hef = 50

    Rb,n = 22 ( .6.7. 63.13330 30):

    hs efNcr 1505033, ; hc efNcr 75505,15,1,

    2

    ,,

    0

    , 22500150150 ssA NcrNcrNc

    Ac,N = A0

    c,N

    s,N = 1,0 cccr,N

    re,N = 1,0 ( 150)

    e,N = 1,0

    M=1,5.

    Nsd NRk,c/Mc (.3

    .5.1) - .

    10 < 19,6/1,5

    10 < 13,0

    .1.5 (.5.1.4)

    c spcr 175, .

    .5.1.4.4

    c cr,sp (600 > 175) h

    2hef (200 > 250) .

    ,

    .5.1 .

    2. (...2.1).

    : , V=8.

    HILTI HSA M12 (hnom=79)

  • - 60542948 00036-2015

    53

    300 25.

    .

    15 4 .13 .

    .2.1 - 2.

    .2 .

    .

    HSA . .1 (.4.3):

    h=300; 1=90; 2=70; s1=100, s2=80; h>hmin=140; >cmin=65;

    s >smin=70.

    (.4.15).

    (. . .2.2).

    : (.

    5.2.3.2).

    Vhsd = Vsd,1 = Vsd,2 =Vsd,3 = Vsd,4 =

    = V/4 = 2

    Vgsd = Vsd,i = 8

    Vsd,1 = Vsd,2 = V/2 = 4

    Vgsd = Vsd,1 + Vsd,2 = 8

    Vsd,1 = Vsd,2 =Vsd,3 =

    = Vsd,4 = V/4 = 2

    Vg

    sd = Vsd,2 + Vsd,4 = 4

  • - 60542948 00036-2015

    54

    ) ; )

    ; )

    .

    .2.2 - 2.

    .2.2 (.5.2.1.1)

    VRk,s=29,5.

    Ms = 1,25.

    Vhsd 0,8VRk,s/Ms (.1 .5.3) -

    .

    2 < 0,829,5/1,25

    2 < 18,88

    .2.3

    (.5.2.2)

    , . 5.2.2.2

    .

    .2.3.1 NRk,c

    (.5.1.3.1)

    (5.2):

    A

    ANN NecNreNs

    Nc

    Nc

    cRkcRk 5,371825,091,038025

    714246,26

    2

    2

    ,,,0

    ,

    ,0

    ,,

    hRkN efnbcRk 6,2626590655,188,115,15.1

    ,1

    0

    ,

    hef = 65

    Rb,n = 18,5 ( .6.7. 63.13330 25)

    hs efNcr 1956533, ; hc efNcr 98655,15,1,

    2

    ,,

    0

    , 38025195195 ssA NcrNcrNc

    Ac,N = (70+80+98)(90+100+98) = 714242 - . . .2.3()

  • - 60542948 00036-2015

    55

    91,098

    703,07,0,

    Ns

    825,0200

    655,0, Nre ( )

    e,N = 1,0

    .2.3.2

    (5.21):

    NkV cRkcpRk 755.370,2,, ,

    NRk,c . .2.3.1 ; k=2,0

    M=1,5

    Vgsd VRk,cp/Mc

    (.3 .5.3) - .

    8 < 75/1,5

    8 < 50

    ) Ac,N ; )

    Ac,V.

    ; ) Ac,V.

    .

    .2.3 - 3.

    .2.4 (.5.2.3)

  • - 60542948 00036-2015

    56

    .2.4.1

    . .2.2(). Vgsd = 8, v=0,

    c1=90, c2=70,

    (5.23):

    A

    AVV VreVecVVhVs

    Vc

    Vc

    cRkcRk 1,150,10,10,10,1855,036450

    3847578,16

    2

    2

    ,,,,,0

    ,

    ,0

    ,,

    cRldkV nbfnomcRk 78,1616781905,1865128,2 5,1067,0085,05,11,10 ,

    dnom=12; lf = 65

    Rb,n = 18,5 ( .6.7. 63.13330 25);

    085,090

    651,01,0

    5,05,0

    1

    c

    l f ; 067,0

    90

    121,01,0

    2,02,0

    1

    c

    d nom

    222

    111

    0

    , 36450)90(5,45,45,13 A Vc

    Ac,V= 1,590(1,590 +80+70) = 384752 - . . .2.3()

    855,0905,1

    703,07,0

    5,13,07,0

    1

    2

    ,

    c

    cVs

    h,V = 1,0 ( h>1,51) ; ,V=1,0 ( V=0); ec,V=1,0

    s,V = 1,0

    Msp=1,5

    Vgsd VRk,c/Msp (.4 .5.1) - .

    8 < 15,1/1,5

    8 < 10

    .2.4.2

    . .2.2(). Vgsd = 4, v=90,

    c1=70, c2=90,

    .3.4.1.

    :

    A

    AVV VreVecVVhVs

    Vc

    Vc

    cRkcRk 3,400,10,15,20,1957,022050

    3097512

    2

    2

    ,,,,,0

    ,

    ,0

    ,,

    cRldkV nbfnomcRk 0,1211992705,1865128,2 5,107,0096,05,11,10 ,

    096,070

    651,01,0

    5,05,0

    1

    c

    l f ; 07,0

    70

    121,01,0

    2,02,0

    1

    c

    dnom

  • - 60542948 00036-2015

    57

    222

    111

    0

    , 22050)70(5,45,45,13 A Vc

    Ac,V= 1,570(1,570 +100+90) = 309752 - . . .3.3()

    957,0705,1

    903,07,0

    5,13,07,0

    1

    2

    ,

    c

    cVs

    h,V = 1,0 ( h>1,51); ec,V=1,0; s,V = 1,0

    5,2

    )14,0(

    1

    sin4,0cos

    1222,

    VV

    V

    ( V=90)

    Vgsd VRk,c/Msp (.4 .5.1) - .

    4 < 40,3/1,5

    4 < 26,8

    ,

    .5.2 .

    3.

    (.. .3.1).

    :

    HILTI HIT-RE 500-SD HAS-5.8 12

    (hef=110). 200, 30

    12400 200200. 20 4 .14

    c 10. ,

    : V=4, M=2.

    43 40.

  • - 60542948 00036-2015

    58

    .3.1 - 3.

    .3.1 .

    .

    HILTI HIT RE 500 + HAS 12

    (.4.3): h=200; 1=80; s2=150; h>hmin=140;

    >cmin=60; s >smin=60.

    I

    . 4.2.

    . ..1.4.

    , . .3.2.

    .3.2 - 3.

    Nb = 0,5bxEbb.

    63.13330 Eb = 32000,

    Rb=17.

    (6.8) N0 =

    0,05/ :

    c

    hdCC

    N

    efnom

    NN /82896/05,0

    1101214,3

    0,

    0,

  • - 60542948 00036-2015

    59

    (.2): 1,2,1 sas EAN , EA0

    =CN hef = 9118 -

    . .1.3.

    EAa .

    :

    N=0: 02,1, sb NN 0,5bxEbb - EA s,1 = 0; (3.)

    M=0: MxaN s )3/( 12,1, ; (3.)

    bsx

    xa

    11, ,

    (3.)

    (3.) (3.):

    bE

    EFEFbaEEFx

    b

    aaba

    5,33

    22032

    182361823622025032218236

    2

    2

    2

    2

    1

    2

    Ns1,2 (3.) :

    xa

    MNs 4,8

    238,0

    2

    )3/( 12,1

    :

    b

    s

    bb R

    xb

    NE

    2

    2,128,2

    5,332205,0

    8400

    5,0

    (

    ) :

    Nh

    sd=Ns1,2 / 2 =8,4 / 2 = 4,2; Ng

    sd=Ns1,2 =8,4

    ..2.3.

    : Vgsd = V = 4, Vh

    sd = V/4 = 1. . .2.6

    Vgsd = 0

    ( ).

    .4.13 (4.1):

    ea

    lM

    ls 26

    0,1

    2/20102/123

  • - 60542948 00036-2015

    60

    .3.2 (. 5.1)

    .3.2.1 (.5.1.1)

    NRk,s=38

    Ms = 1,5

    NRk,s/Ms = 38/1,5=25,3

    .3.2.2 (.5.1.3)

    (5.2):

    A

    ANN NecNreNs

    Nc

    Nc

    cRkcRk 5,4111845,0108900

    11760045,45

    2

    2

    ,,,0

    ,

    ,0

    ,,

    hRkN efnbcRk 45,4545454110224,85,15.1

    ,1

    0

    ,

    hef = 110

    Rb,n = 22 ( .6.7. 63.13330 30):

    hs efNcr 33011033, ; hc efNcr 1651105,15,1,

    2

    ,,

    0

    , 108900330330 ssA NcrNcrNc

    2,1,2,, 1176005,05,05,0 scsssA NcrNcrNcrNc

    845,0165

    803,07,0,

    Ns

    re,N = 1,0 ( 150)

    e,N = 1,0

    M=1,8

    HIT-RE 500 SD.

    NRk,c/Mc

    = 41,5/1,8 = 23.

    .3.2.3

    (.5.1.5)

    (5.15):

    A

    ANN NpgNecNreNsc

    Np

    Np

    pRkpRk 4,3006,111845,001,1108900

    1176001,31

    2

    2

    ,,,,0

    ,

    ,0

    ,,

    hdN RkefnompRk 1,31310865,71101214,30

    ,

    dnom = 12

  • - 60542948 00036-2015

    61

    Rk = Rk,rc = 7,5/2

    Rk,urc= 16/2

    ds urcRknomNpcr 4,35016123,73,7 ,, , 3hef = 330

    sc NpcrNpcr 1652/,,

    2

    ,,

    0

    , 108900330330 ssA NpcrNpcrNpc

    2,1,2,, 1176005,05,05,0 scsssA NpcrNpcrNpcrNpc

    = 1,01 30

    845,0165

    803,07,0,

    Ns

    re,N = 1,0; e,N = 1,0

    18,1221107,2

    01,15,712)12(2)1(

    5,15,1

    ,

    0

    ,

    nbef

    cRknom

    NpgRhk

    dnn

    06,1)118,1(330

    15018,11

    5,0

    0

    ,

    5,0

    ,

    0

    ,,

    s

    sNpg

    Npcr

    NpgNpg

    Mp=1,8

    HIT-RE 500 SD.

    NRk,p/Mp

    = 30,4/1,8 = 16,9.

    .3.2.4 (.5.1.4)

    HIT-RE 500-SD . 5.1.4.2.

    ccr,sp =4,6hef -1,8h = 4,6110- 1,8200 = 146 h/hef = 1,81.

    .5.1.4.4 c1 < cr,sp (80 < 146)

    .

    scr,sp = 2ccr,sp = 2146 = 292

    (5.13):

    NN sphsp

    cRkspRk 4,5827,146,,,

    A

    ANN NecNreNs

    spc

    spc

    cRk

    sp

    cRk 4611864,085264

    9989245,45

    2

    2

    ,,,0

    ,

    ,0

    ,,

    N cRk 45,450

    , - . . 3.2.2

    2

    ,,

    0

    , 85264292292 ssA spcrspcrspc

  • - 60542948 00036-2015

    62

    2,1,2,, 998925,05,05,0 scsssA spcrspcrspcrspc

    864,0146

    803,07,0,

    Ns

    re,N = 1,0; e,N = 1,0

    27,1140

    2003/23/2

    min

    ,

    h

    hsph hmin=140 (..12)

    Msp=1,8

    HIT-RE 500 SD.

    NRk,sp/Msp = 58,4/1,8 = 32,4.

    .3.3 (. 5.2)

    .3.3.1 (.5.2.1.2)

    (5.21):

    VRkm,s=MRk,s / ls =46,7 / 0,026 = 1830 = 1,83

    N

    NMM

    MsRks

    h

    sd

    sRksRk

    7,46

    3,25

    2,4156

    /10 ,,

    M0

    Rk,s = 56

    NRk,s / Ms - . 3.2.1. .

    Ms = 1,25

    VRkm,s/Ms = 1,83/1,25=1,46

    .3.3.2 (.5.2.2)

    , . 5.2.2.2

    .

    (5.21):

    NkV cRkcpRk 6,1503,750,2,,

    k=2

    A

    ANN NecNreNs

    Nc

    Nc

    cRkcRk 3,7511845,0108900

    21360045,45

    2

    2

    ,,,0

    ,

    ,0

    ,, ,

    2,11,2,, 2136005,05,05,0 sscsssA NcrNcrNcrNc ( ); . 3.2.2 .

  • - 60542948 00036-2015

    63

    M=1,5

    VRk,c/Mc = 150,6/1,5 = 100,4

    .3.4 (. 5.3)

    ,

    . . .3.1 .3.2

    . 3 . 1

    ..

    Nsd

    Nrd

    = Nsd / Nrd

    1 Nhsd =4,2 NRk,s/Ms = 25,3 0,17

    2

    Ng

    sd =8,4 NRk,c/Mc = 23 0,36

    3

    Ng

    sd =8,4 NRk,p/Mp = 16,9 0,50

    4

    Ng

    sd =8,4 NRk,sp/Msp = 32,4 0,23

    . 3 . 2

    ..

    Vsd

    Vrd

    = Vsd / Vrd

    1 Vhsd =1 VRkm,s/Ms = 1,46 0,68

    2

    Vg

    Sd = 4 VRk,cp/Mc = 100 0,04

    3

    Vg

    Sd = 0 - 0

    N=0,5; V = 0,68 ( ).

    (5.33)-(5.35)

    :

    N = 0,5 < 1,0 ,

    V = 0,68 < 1,0 ,

    N + V = 1,18 < 1,2

  • - 60542948 00036-2015

    64

    ,

    .5.3 .

  • - 60542948 00036-2015

    65

    [1]

    27 2002 .

    184-

    [2]

    30 2009 .

    384-

    [3] ETAG 001 Guideline for European technical approval of metal

    anchors for use in concrete. Annex C: design methods for anchorages -

    , 2008

    [4] ACI 318-11 Building Code Requirements for Structural Concrete.

    Anchoring to concrete. Appendix D. Anchoring to concrete - American

    Concrete Institute, 2011

    [5] 36554501-039-

    2014

    HILTI

    [6] 88/97 -001-97

    ( -01-011-97)

    .

    [7] 5.6

    [8] -031-01

    .

    [9]

    , ,

    .2009.

    ,

    -