Vodjenje Armature Duz Nosaca

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    16-Jul-2016

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  • 1Konstrukcija linije zateuih sila

    -

    z

    s=

    s-

    s= = u

    au

    vv

    u

    v

    aua Nh

    M1NzMA)0N(

    uau

    vaau NhMAZ -

    z=s=

    -+=+= 1uu1auuau a2dNMyNMM

    va1aaauv1a AAZ s=s=s=s

  • 2.min

    uvaau h9.0

    MAZ

    s=

    .min.min h9.0z

    9.0.consthh

    z==

    uauu MM0N ==

    u.min

    auvaau Nh9.0

    MAZ -

    s=

    Konstrukcija linije zateuih sila

    isto savijanje:

  • 3L = 12.0 m

    Reakcije oslonaca

    Bg = (30122/2)/9 = 240 kNAg = 3012 240 = 120 kN

    Ap1 = Bp1 = 409/2 = 180 kN

    Bp2 = [(603(9+3/2)]/9Bp2 = 210 kNAp2 = 603 210 = -30 kN

  • 4Dijagrami momenata savijanjaoslonac:Mg = 3032/2 = 135 kNmpolje:xmax = 120/30 = 4.0 mMg = 1204 3042/2Mg = 240 kNm

    polje:Mp1 = 4092/2 = 405 kNm

    oslonac:Mp2 = 6032/2 = 270 kNm

  • 5Anvelopa momenata savijanja

    ( )

    ( )212

    1

    21

    2

    1

    PP8.1G0.1P8.1G0.1P8.1G0.1

    G1.0

    PP8.1G6.1P8.1G6.1P8.1G6.1

    G6.1

    ++

    +

    +

    ++

    ++

  • 6Anvelopa momenata savijanja

    9.0 m

    Mu

    = 11

    09.4

    kN

    m Mu

    = 70

    2.0

    kNm

    4.3 m1.6G+1.8P1

    1.6G+1.8P2

    3.0 m

  • 7Anvelopa momenata savijanja

    1.0 m8.0 m

    1.0 m8.0 m

    1.0G+1.8P1

    Mu

    = 11

    09.4

    kN

    m Mu

    = 70

    2.0

    kNm

    4.3 m 1.6G+1.8P1

    1.0G+1.8P21.6G+1.8P2

    1.6G+1.8P1 1.0G+1.8P1

    1.0G+1.8P2 1.6G+1.8P2

  • 8Anvelopa momenata savijanja

    1.0G+1.8P21.6G+1.8P2

    1.0G+1.8P1

    1.6G+1.8P1

    nu

    lta t

    acka

    dijagra

    ma M

    g

    MG i MP istog znaka

    MG i MP istog znaka MG i MP razlicitog znaka

    MG i MP razlicitog znaka

  • 9Anvelopa momenata savijanja

    1.0 m8.0 m

    1.0 m8.0 m

    4.3 m

    Mu

    = 11

    09.4

    kN

    m Mu

    = 70

    2.0

    kNm

    1.6G+1.8P1 1.0G+1.8P1

    1.0G+1.8P2 1.6G+1.8P2

  • 10

    Dimenzionisanje - presek u polju

    aI = 2.5 + 1.0 + 2.5/2 = 4.75 cmaII = 4.75 + 3.0 + 2.5 = 10.25 cm

    a1 = (54.75 + 410.25)/9a1 = 7.19 cm

    h = 75 - 7.19 = 67.81 cmh 68 cm = hra.

    40

    21.7

    5

    4.75

    4.75

    5.5

    4.75

    4.75

    5R25

    4R25

    U10/30

    30.5

    16.2

    5

    1560

    75

    2R25

    2R12

    22 2R12

  • 11

    Dimenzionisanje - oslonac

    aI = 2.5 + 1.0 + 2.5/2 = 4.75 cmaII = 4.75 + 3.0 + 2.5 = 10.25 cm

    a1 = (44.75 + 210.25)/6a1 = 6.58 cm

    h = 75 - 6.58 = 68.42 cmh 68 cm = hra.

    40

    21.7

    5

    4.75

    4.75

    5.5

    4.75

    4.75

    4R25

    2R25

    U10/15

    30.5

    16.2

    5

    1560

    75

    2R25

    22

    2R12

    2R12

  • 12

    Analitiki izrazi za momente savijanja

    2)xL(gM:lx

    2xgxAM:lx

    2

    g

    2

    gg

    --=

    -=

    0M:lx2

    xpxAM:lx

    1p

    21

    1p1p

    =

    -=

    2)xL(pM:lx

    xAM:lx2

    22p

    2p2p

    --=

    =

  • 13Vrednosti momenata savijanja - Excelx Mg Mp1 Mp2

    1.6G+1.8P1

    1.6G+1.8P2

    1.0G+1.8P1

    1.0G+1.8P2 MAX MIN

    0 0 0 0 0 0 0 0 0 00.5 56.25 85 -15 243 63 209.3 29.3 243 0

    1 105 160 -30 456 114 393 51 456 01.5 146.3 225 -45 639 153 551.3 65.3 639 0

    2 180 280 -60 792 180 684 72 792 02.5 206.3 325 -75 915 195 791.3 71.3 915 0

    3 225 360 -90 1008 198 873 63 1008 03.5 236.3 385 -105 1071 189 929.3 47.3 1071 0

    4 240 400 -120 1104 168 960 24 1104 04.5 236.3 405 -135 1107 135 965.3 -6 .8 1107 -6 .8

    5 225 400 -150 1080 90 945 -45 1080 -455.5 206.3 385 -165 1023 33 899.3 -90 .8 1023 -90 .8

    6 180 360 -180 936 -36 828 -144 936 -1446.5 146.3 325 -195 819 -117 731.3 -204.8 819 -204.8

    7 105 280 -210 672 -210 609 -273 672 -2737.5 56.25 225 -225 495 -315 461.3 -348.8 495 -348.8

    8 0 160 -240 288 -432 288 -432 288 -4328.5 -63 .8 85 -255 51 -561 89.3 -522.8 89.3 -561

    9 -135 0 -270 -216 -702 -135 -621 0 -7029.5 -93 .8 0 -188 -150 -487.5 -93 .8 -431.3 0 -487.5

    10 -60 0 -120 -96 -312 -60 -276 0 -31210.5 -33 .8 0 -67 .5 -54 -175.5 -33 .8 -155.3 0 -175.5

    11 -15 0 -30 -24 -78 -15 -69 0 -7811.5 -3 .75 0 -7 .5 -6 -19 .5 -3 .8 -17 .3 0 -19 .5

    12 0 0 0 0 0 0 0 0 0

  • 14

    -800

    -400

    0

    400

    800

    12000 1 2 3 4 5 6 7 8 9 10 11 12

    Mu

    [kN

    m]

    1.6G+1.8P11.6G+1.8P2G+1.8P1G+1.8P2

    Anvelopa momenata savijanja - Excel

  • 15

    Mu

    = 11

    09.4

    kN

    m Mu

    = 70

    2.0

    kNm

    Z au

    18

    12.8 Zau 1109.4/(0.90.68) = 1812.8 kN

    Z au

    11

    47.1

    Zau 702/(0.90.68) = 1147.1

    .min

    uu

    .min

    auvaau h9.0

    MNh9.0

    MAZ

    =-

    s=

    M/z linija

  • 16

  • 17

  • 18

  • 19

  • 20

    Tg

    Tp1

    Tp2

    1,6Tg+1,8(Tp1+Tp2)

  • 21

  • 22

    M/z linija

    kN3.1964091.4aZ v)1(

    a)1(

    au ==s=

    Z au

    18

    12.8

    Z au

    11

    47.1

    Z(1) au

    =196

    .3

  • 23

    Linija zateuih silaZ a

    u

    1812

    .8

    Z au

    11

    47.1

    9Z(

    1) au=1

    767.

    1

  • 24

    M/z linija

    z = 0.964Aa,potr. = 42.33 cm2 (usv. 44.18 cm2)

    z = 0.894Aa,potr. = 28.85 cm2 (usv. 29.45 cm2)

    Z au

    18

    12.8

    Z au

    11

    47.1

    9Z(

    1) au=1

    767.

    1 6Z(

    1) au=1

    178.

    1

  • 25

    Linija zateuih silaZ a

    u

    1812

    .8

    Z au

    11

    47.1

    v=0.51

    v=0.51

    v=0.51v=0.51

    POMERANJE LINIJE ZATEUCIH SILA:v = 0.75h = 0.7568 = 51 cm

    M/z linije

  • 26

    Linija pokrivanja armaturom

    5R25

    2R25

    4R25

    725

    225

    425

    225

    >425 >425

    >725 >725

  • 27

    Linija pokrivanja armaturom

    5R25

    2R25

    525

    225

    225

    >425 >425

    >725 >725

    225

    225

    225

    >5 >5

    >2>2

  • 28

    Linija pokrivanja armaturom

    3R25

    2R25

    325

    225

    225

    >425 >425

    >725 >725

    225

    225

    225

    >5 >5

    >2>2

    >3 >3

    225

  • 29

    Linija pokrivanja armaturomZ a

    u

    1812

    .8Z a

    u

    1147

    .1

    A B

    POMERENA LINIJA ZATEUCIH SILA LINIJA ZATEUCIH SILA

    LINIJA POKRIVANJA ARMATUROM

    v=51

    v=51

    v=51v=51

    POMERANJE LINIJE ZATEUCIH SILA:v = 0.75h = 0.7568 = 51 cm

    (M, N)(M, N, T)

  • 30Z a

    u

    1812

    .8Z a

    u

    1147

    .1

    A

    B

    3

    1

    1

    POMERENA LINIJA ZATEUCIH SILA LINIJA ZATEUCIH SILA

    LINIJA POKRIVANJA ARMATUROM

    v=51

    v=51

    v=51v=51

    UKUPNA DUINA IPKE (700 cm)

    STATICKI POTREBNA DUINA IPKE (460 cm)

    2

    1

    5

    225

    125

    225

    225

    225

    69

    35

    65

    125

    205

    25

    85

    165

    180280

    DUINA SIDRENJA:

    Ls1 = 79.4 80 cm (dobra adhezija)Ls2 = 119 120 cm (loa adhezija)

    POMERANJE LINIJE ZATEUCIH SILA:v = 0.75h = 0.7568 = 51 cm

    NOSIVOST JEDNE IPKE ARMATURE:

    Z(1)au = a(1)a sv = 4.9140 = 196.3 kN

    Zau Mau / (0.9h) - NuMau = Mu + Nu (d 2 - a1)Nu = 0: Mau = Mu ; Zau Mu / (0.9h)

    (M, N, T) (M, N)M/Z linija

  • 31

  • 32

  • 33

    Sidrenje armature

    75.3175.18.1

    4004

    8.14L

    p

    vs =

    =t

    s=

    donja zona (dobra adhezija)

    22...cm70cm8.692.275.31L 1s ==25...cm80cm4.795.275.31L 1s ==

    gornja zona (loa adhezija)

    22...cm105cm705.1L 2s ==

    1s1s2p

    1p2s1p2p L5.1LL3

    2=

    tt

    =t=t

    25...cm120cm805.1L 2s ==

  • 34

    Sidrenje armature1

    25v=51 v=51

    L.Z.S. LINIJA M z

    v=51 v=51 305205

    L25s1 = 80STATICKI POTREBNA

    DUINA IPKE (390 cm)

    UKUPNA DUINA IPKE (550 cm)

    L25s1 = 80

    5 5

    A B

    p

    vs 8.14

    Lt

    s=

  • 35

  • 36

  • 37

  • 38

  • 39

    1215

    6015

    5

    15 15

    BA

    1

    1

    1-1

    3

    3

    3-32-2

    2

    2

    75

  • 40

    1215

    6015

    5

    15 15

    BA

    1

    1

    1-1

    3

    3

    5

    75

    5 54x7.5=30

    40

    15

    5 530

    40

    3-3

    5

    75

    15 15

    5 530

    40

    2-2

    5

    75

    2

    2

    1 2R25 6 2R25

    6 2R25

    35

    1

    1 2R25

    6

    75

    1 2R251 2R25

  • 41

    1215

    6015

    5

    15 15

    BA

    1

    1

    1-1

    3

    3

    5

    75

    5 54x7.5=30

    40

    15

    5 530

    40

    3-3

    5

    75

    15 15

    5 530

    40

    2-2

    5

    75

    2

    2

    1 2R25 6 2R253 2R25

    6 2R25

    3 2R25 L=925 (2)

    35

    890

    35

    1

    2

    1 2R25, 3 2R25

    6

    1 2R25

    75

    1 2R25

    3

    2 1R25 L=860 (1)

    35

    825

    2 1R251 2R25

    3 2R25

    2

    3

    2 1R25

  • 42

    1215

    6015

    55

    15 15

    BA

    1

    1

    1-1

    3

    3

    5.5

    5

    75

    5 54x7.5=30

    40

    15

    5 530

    4