design of flat plate

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Design of flat plate

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  • . .

  • (a) (b) (c) band beam

    (d) (e)

    1.

  • 1. (SLS)2. (ULS)3.

  • 2.

    2.1 PTI (Post-tensioning Institute)

    1 L/h h/L 48 45 ( L/6)

    50

    4 55

    L = 9 L/45 = 900/45 =20 cm

  • 2. 2

    1 1.5 2 3 4

    siliceous 89 108 127 159 178 carbonate 83 105 117 146 168 lightweight 67 83 95 117 133 3

    1 1.5 2 3 4

    siliceous 19 32 38 54 - carbonate 19 27 35 48 -

    lightweight 19 25 32 41 - siliceous 19 19 19 25 32 carbonate 19 19 19 25 32

    lightweight 19 19 19 19 25

  • 3. (Load balancing theory)

    Pb

    Pb

    y

    L

    =PPv

    2LPy8w =

  • LL05.0L =

    y

    2LPy8w =

    9w9w(a)

    (b)

  • 0.08

    0.068

    0.03

    Interior span

    y = 0.08+0.068+0.03 = 0.178 m

  • 0.1L=0.8 m

    0.068

    0.080

    0.030.03

    0.049

    y = 0.08 + 0.5x(0.068+0.3) = 0.08 + 0.049 = 0.129 m

  • LL05.0L =

    y

    2LPy8w =

    9w9w(a)

    (b)

  • tendonsDeformed bars Tendon layout

    8 tendons

  • l1

    l2

  • 4.

    1 (design strip)

  • 2 2.1

    lc

    l1

    c1h h2l

    IE4Kc

    cc =

    2/clIE4K

    11

    cs =

  • 2.2 ( ecK )

    tcec K1

    K1

    K1 +=

    cK tK

    3222

    cst )l/c1(l

    CE9K =

    ( )3

    /63.01 13

    1 chchC = h c1 torsional member

    c2c1

    h

    Torsional member(including beam if present)

    l2

  • 3 1. prestress loss secondary moment 2. ( ) 3.

    equivalent column

    slab dead load

    equivalent column

    1. 2.

    psLDSLS MMMM ++=

    psLDULS MM7.1M4.1M ++=

  • 5.

    ACI cf6.1 0 cf53.0 0 cf45.0 5.2

    Bonded Prestressing system Unbonded prestressing system

    5.1

    0 0.004A 0 0.00075hl

    0 0* 0 )f5.0/(N yc

  • 1.

    1.5h 4 30 cm l/6

    2. l/3

    20 cm 6060 cm = 8.0 m = hl00075.0 = 8002000075.0 = 12 cm2

    11 DB 12 ( sA = 12.4 cm2)

    11 DB12 each way

    330 cm

    c2 + 3h =120 cm

  • 5.3

    free edge regions not prestressed in direction parallel to concentrated tendons

    interior panel edge panel

    corner panel

    ps

    s 5.00015.0bdA ==

    b ,d p

  • 6

    nu MM 6.1 psf

    (1)

    ( )

    +

    =pc

    pup

    1

    ppups d

    dff

    1ff

    puf = 1 = 0.85 280fc ksc

    = 65.000005.0)280f(85.0 c 280fc > ksc p = 0.4 stress-relieved 85.0f/f pupy

    = 0.28 low-relaxation 90.0f/f pupy

  • p = = pps bd/A d =

    pd = = cy f/f = cy f/f = = bd/As = = bd/As

    1. ( sef ) puf5.0 2. 0= pd15.0d >

  • (2) (2.1) 35

    p

    cseps 100

    f700ff

    ++=

    pyps ff 4000fse + (2.2) 35

    p

    cseps 300

    f700ff ++=

    pyps ff 2000fse + sef

  • 6.2 stress block stress block

    bf85.0fAfA

    ac

    yspsps

    +=

    )2/ad(fA)2/ad(fAM ysppspsn +=

  • 6.3 2

    (1) ACI crn M2.1M

    (2) ACI (2.1)

    1p 36.0 cpspp f/f = (2.2)

    1p

    p 36.0dd)( +

    cy f/f = cy f/f =

  • 7 Wide beam shear failure

    d/2

    Punching shear failure

    h/2

    Shear and moment transfer

    Corner shear failure

  • 7.1

    dbf53.0V wcc = wb

    d 0.8h h/2

  • 7.2 d/2 4 ACI

    p0pccpc Vdb)f3.0f(V ++=

    p = 0.93 )5.1b/d(27.0 0s + s = 40

    = 30 = 20

    0b = pcf =

    8.8 ksc 35 ksc cf = 350 ksc

    pV =

  • pV

    += )dc()L(Ph2V 12

    2p

    pV

    (a) Tendon pro file through column region

    point of inflection of tendon profile

    h2

    d/2Vp

    1 l

    c1 +d

    21

    21 )l2(

    Ph8)l2(

    Ph8r,forceradial 22 ==

    P P

    (b) Free- body diagram of tendonc1

  • 4h pcf 8.8 ksc

    ( ) dbf/4227.0V 0ccc += dbf)2b/d(27.0 0c0s + dbf06.1 0c

    c

  • 7.3

    c1Vu

    Mu1

    fMu1

    C2+3h

    c2

    Vu (1-gf) Mu1

    span

    = uM (unbalanced moment) uf M h3c 2 + ufuv M)1(M =

    2

    22u2v

    1

    11u1vuu J

    eMJ

    eMAVv

    ++=

    dbVv

    0

    cu

    uf M h3c2 +

  • d/2D

    Vu

    vMu1

    1

    2

    B

    C

    Acritical section

    AVu

    A = area of critical

    = bod

    u1

    11u1vu VJ

    eMAV =+

    +e1

    1

    11u1v

    JeM

  • )2(2)}(){(2 2121 dccdddcdcA ++=+++=

    2)dc(e 11

    +=

    2)dc)(dc(d

    6d)dc(

    6d)dc(J

    212

    31

    31

    1++++++=

    dcdc

    321

    11

    2

    1v

    +++

    =

    e

    1

    c

    1

    +

    d

    c

    1

    c2+d

    c2

    Mu1

  • )d2cc2(dA 21 ++=

    2)dc(

    e 22+=

    21

    11

    212

    31

    31

    1 ]e2)2/dc([d)2/dc(2]e[d)dc(

    6]d)2/dc(d)2/dc[(J ++++++++=

    dc2/dc

    321

    11

    2

    11v

    +++

    =

    )d2cc2(

    )2dc(

    e21

    21

    1 +++

    =

    211

    32

    32

    2 ]e[d)2/dc(212d)dc(d)dc(J +++++=

    2/dcdc

    321

    11

    1

    22v

    +++

    =e

    c

    1

    +

    d

    /

    2

    1

    e2

    c2+d

    c2 Mu1Mu2

  • )dcc(dA 21 ++=

    )]dcc(2[)2/dc(e

    21

    21

    1 +++=

    2/dc2/dc

    321

    11

    2

    1v

    +++

    =

    211

    212

    31

    31

    1 ]e2)2/dc(

    [d)2/dc(]e[d)2/dc(12

    ]d)2/dc(d)2/dc[(J ++++++++=

    c

    1

    e

    1

    c

    1

    +

    d

    /

    2

    c2

    c2+d/2

    Mu1

  • (column capital drop panel) shear head

    scn VVV +=

    = dbfsdfA

    dbf cyv

    c 00 6.106.1 + vA

    columnShear cracks

    ldS < 0.75h

  • Plan

    Elevation

  • 8. ACI 1. 2. (sustained load)

    x

    yx

    y

    ly

    l x

    yx +=

  • ll ll

    w

    EIwl 4

    3841=

    EIwl 4

    38465.2=

    EIwl

    38460.2 4=

    EIwl

    38480.3 4=

  • 9.

    1 2 3 4 5 6

    1

    B

    C

    D5 @ 8 = 40.0

    3

    @

    8

    =

    2

    4

    .

    0

  • 60 65 cm : = 240 . .. () = 120 . .. ( ) 2 = 3.6 m =cf 345 ksc yf = 4000 ksc 15 mm Grade 1860 (low-relaxation) bonded 2 . 75% = 20% l/360 l

  • 1.

    cm8.1745

    80045lh ===

    22 cm 2 4 2

    2. 2

    1 1.5 2 3 4

    siliceous 89 108 127 159 178 carbonate 83 105 117 146 168 lightweight 67 83 95 117 133

  • 2. 6060 (1) B2 = 528240022.0 = . .. ( ) 315,12407.11205284.1w u =++= . .. 160,84315,188Vu == . uV 20% 992,100160,842.1Vu == . d = 0.8h = 6.17228.0 = cm 4.310)6.1760(4b0 =+= cm 13fpc = ksc pV

    674,1156.174.310)133.034593.0(Vc =+= .

    674,115V814,11885.0992,100V

    cu === . okay

  • (2) B1 uV 50% 120,63315,1485.1Vu == . 2.215)2/6.1760(26.1760b0 =+++= cm 197,806.172.215)133.034593.0(Vc =+= . 197,80V259,74

    85.0120,63V

    cu =

  • 3. 80-100%

    = 90% 2.4755289.0w b == . ..

    8.612.1211eEW == cm

    8.428.6eNS == cm N-S E-W

    81211ee NSEW === cm

    20 mm

    (a) At columns

    12 mm

    N-S tendons

    E-W tendons

    20 mm

    110 mm

    20 mm (b) Near midspan

    4 4.1

  • 4.2 0.1L ( 0.05-0.125L)

    80L = cm 1.0=

    For exterior span1.0=5.0=

    m08.0e1 =m068.0e2 =

    m)068.008.0(5.01.0h2 +=

    m03.0=

    For interior span1.0=5.0=

    m08.0e1 =m068.0e2 =

    m)068.008.0(5.01.0h2 +=

    m03.0=

    Sym.

    0.5L=4.0 m 0.5L=4.0 m

    0.1L=0.8 m

    0.0680.080

    E-W

    064.0)80/605.0(03.0068.0e 2 ==

    h2 )ee(h 212 +=

    222 )

    2/(

    Lhhee c=

  • 0.5L=4.0 m 0.5L=4.0 m

    0.1L=0.8 m

    0.048

    0.080

    For exterior span

    1.0=5.0=

    m08.0e1 =m048.0e2 =

    m)048.008.0(5.01.0h2 +=

    m026.0=

    For interior span

    1.0=5.0=

    m08.0e1 =m048.0e2 =

    m)048.008.0(5.01.0h2 +=

    m026.0=

    N-S

    044.0)80/605.0(026.0048.0e 2 ==

    Sym.

    h2

  • E-W 178.003.0068.008.0y =++ m

    357,21178.08

    82.475P2

    i == kg/m

    129.0)03.0068.0(5.008.0y =++ 470,29

    129.0882.475P

    2

    e == kg/m

    N-S 154.0026.0048.008.0y =++ m

    686,24154.08

    82.475P2

    i == kg/m

    117.0)026.0048.0(5.008.0y =++ 492,32

    117.0882.475P

    2

    e == kg/m

    y8wLP

    LPy8w

    2

    2 ==

  • 5. 5.1

    15 = 1.4 cm2 040,26600,184.1Fpu == . Jacking force 040,2675.0Fpj = = 19,530 . 624,15195308.0Fpe == .

    5.2 E-W 70-75%

    2 N-S

    2

  • 5

    (kg)

    (kg) P/A (ksc)

    E-W 856,1708357,21

    == 12 8 4 187,488 10.7

    E-W 760,235

    8470,29=

    = 16 12 (8+4) 4 (4+0) 249,984 14.2

    N-S 488,1978686,24

    == 13 7 6 203,112 11.5

    N-S 936,2598492,32

    == 17 9 (7+2) 8 (6+2) 265,608 15.1

    pcf = 11.1 ksc = 14.7 ksc

  • 1. 6.1

    631213121 1008.16060bhI === cm4 h = 22 cm, l = 3.6 m

    c6

    ccc E671,13222360

    1008.1E4h2lIE4K =

    == ( ) 766,163

    36022)60/2263.01(

    3yxy/x63.01C

    33=== cm4

    c33222

    ct E656,4)800/601(800

    766,163E92)l/c1(l

    CE9K =

    ==

    tcec K

    1K1

    K1 += ccec E656,4

    1E671,132

    1K

    1 +=

    cec E979,3K =

  • 6.2 867,70922800bhI 31213121 === cm4

    cc

    11

    cs E688,3)2/60800(

    867,709E42/cl

    IE4K ===

    6.3 Distribution factor (DF) Carry over factor distribution factor

    += )KK(KDF

    ecs

    s

    carry over factor 0.5

  • 7. . = 240 < 75% . = 486 . (0.75(528+120)) B (E-W) 2 (N-S)

    1 2 3 4 5 6

    A

    B

    C

    D5 @ 8 = 40.0

    3

    @

    8

    =

    2

    4

    .

    0

  • 1. E-W

    0.48 0.32 0.32

    Given Ks = 3688 EcGiven Kec = 3979 Ec

    1

    48.039793688

    3688KecKs

    KsDF12 =+=+=32.0

    39793688x23688

    KecKs2KsDF 21 =+=+=

    1 2

    Fixed

  • WD = 528+120 = 648 kg/m2 WL = 240 kg/m

    2

    WD = 648x 8 = 5,148 kg/m WL = 240x 8 = 1920 kg/m WDU = 1.4x5,148 = 7,258 kg/m WLU = 1.7x5,148 = 3,264 kg/m

    FEM D = WD x L2/12 k.m FEM D = WD x L

    2/12 k.m

    = 5184 x 82/12 =27,648 kg.m = 1,920 x 82/12 =10,240 kg.mWSLS = 5,184+1,920 = 7,104 kg/m WULS = 7,258+3,264 =10,522 kg/m

    FEM - : + :

  • FEM due to restraining post-tension

    129.0049.008.0f =+=086.0129.0f 3

    232 ==

    499,21086.0984,249FEML ==

    0.5L=4.0 m 0.5L=4.0 m

    0.1L=0.8 m

    0.068

    0.080

    Exterior span (E-W)

    0.03

    0.03

    0.11

    0.049

    0.086

    0.086

    0.012

    New

    000,3012.0984,249FEMR ==

    CGC

  • 0.5L=4.0 m 0.5L=4.0 m

    0.1L=0.8 m

    0.048

    0.080

    Exterior span (N-S)

    0.026

    0.026

    0.11

    0.037

    117.0037.008.0f =+=078.0117.0f 3

    232 ==

    0.078

    0.078

    0.004

    717,20078.0608,265FEML ==

    New

    062,1004.0608,265FEMR ==

    CGC

  • 0.08

    0.068

    0.03

    178.003.0068.008.0f =++=119.0178.0f 3

    232 ==

    937,3021.0488,187FEML == 937,3021.0488,187FEMR ==

    Interior span (E-W)

    0.119

    new

    0.021

  • 0.08

    0.048

    0.03

    158.003.0048.008.0f =++=105.0158.0f 3

    232 ==

    484,5027.0112,203FEML == 484,5027.0112,203FEMR ==

    Interior span (N-S)

    0.105

    new

    0.027

  • Due to P/T

    0.48 0.32 0.3221,499 3,000 3,937 3,937- 10,320- 5,160-

    284- 569- 569- 284- 136 68 11- 22- 22- 11-

    5 3 1- 1-

    11,026 2,680- 3,346 4,232-

    E-W

    1. EW

  • Due to DL

    0.48 0.32 0.3227,648- 27,648 27,648- 27,648 13,271 6,636

    1,062- 2,123- 2,123- 1,062- 510 255

    41- 82- 82- 41- 20 10

    3- 3-

    14,950- 32,340 29,856- 26,546

    E-W

  • Due to L

    0.48 0.32 0.3210,240- 10,240 10,240- 10,240

    4,915 2,458 393- 786- - - 189 94

    15- 30- 30- 15- 7 4

    1- 1-

    5,537- 11,978 10,271- 10,225

    Sum SLS 9,461- 41,638 36,782- 32,538 Sum ULS 19,318- 62,958 55,914- 50,314

    E-W

  • 2. N-S

    0.48 0.39 0.19

    Given Ks = 3688 EcGiven Kec = 3979 Ec

    To take into account symmetry48.039793688

    3688KecKs

    KsDF12 =+=+=

    19.0397936883688x5.0

    3688x5.0DF CB =++=

    39.0397936883688x5.0

    3688DF CD =++=

  • WD = 528+120 = 648 kg/m2 WL = 240 kg/m

    2

    WD = 648x 8 = 5,148 kg/m WL = 240x 8 = 1920 kg/m WDU = 1.4x5,148 = 7,258 kg/m WLU = 1.7x5,148 = 3,264 kg/m FEM D = WD x L

    2/12 k.m FEM D = WD x L2/12 k.m

    = 5184 x 82/12 =27,648 kg.m = 1,920 x 82/12 =10,240 kg.mWSLS = 5,184+1,920 = 7,104 kg/m WSLS = 7,258+3,264 =10,522 kg/m

  • Due to P/T

    0.48 0.39 0.1920,717 1,062- 5,484 9,944- 4,972-

    107 215 105 52 51- 26- 5 10 5 2 2- 1-

    0.5 0.2

    10,831 5,836- 5,594 55

    N-S

  • Due to DL

    0.48 0.39 0.1927,648- 27,648 27,648- 27,648 13,271 6,636

    1,294- 2,588- 1,261- 630- 621 311

    61- 121- 59- 30- 29 15

    6- 3-

    15,081- 31,894 28,971- 26,988

    N-S

  • Due to L

    0.48 0.39 0.1910,240- 10,240 10,240- 10,240

    4,915 2,458 479- 958- 467- 233- 230 115

    22- 45- 22- 11- 11 5

    2- 1-

    5,586- 11,813 10,730- 9,996

    Sum SLS 9,836- 37,871 34,107- 37,038 Sum ULS 19,778- 58,897 53,206- 54,831

    N-S

  • 8.

    psLDSLS MMMM ++= psLDULS MM7.1M4.1M ++=

    6 E-W 1-2 () 2-3 () P/T 11,025 -2,681 3,345 -4,233 DL -14,952 32,340 -29,857 26,543 LL -5,537 11,979 -11,057 9,832 SLS -9,464 41,638 -37,569 32,142 ULS -19,321 62,959 -57,252 49,642

  • 1. SLS E-W

    2. ULS E-W

    7,104 kg/m1 2

    V1=24,394 kg

    M2=41,638 kg.mM2= 9,464 kg.m

    V2= 32,438 kg

    SLS E-W EXTERIOR

    7,104 kg/m1 2

    V1=24,394 kg

    M2=41,638 kg.mM2= 9,464 kg.m

    V2= 32,438 kg

    SLS E-W EXTERIOR

    10,522 kg/m1 3

    V1=36,633 kg

    M2=62,959 kg.mM2=-19,321 kg.m

    V2=47,543 kg

    ULS E-W EXTERIOR

    10,522 kg/m1 3

    V1=36,633 kg

    M2=62,959 kg.mM2=-19,321 kg.m

    V2=47,543 kg

    ULS E-W EXTERIOR

  • 3. SLS E-W

    4. ULS E-W

    7,104 kg/m2 3

    V1=29,098 kg

    M2=-32,142 kg.mM2=-37,596 kg.m

    V2=27,734 kg

    SLS E-W INTERIOR

    7,104 kg/m2 3

    V1=29,098 kg

    M2=-32,142 kg.mM2=-37,596 kg.m

    V2=27,734 kg

    SLS E-W INTERIOR

    10,522 kg/m1 3

    V1=43,039 kg

    M2=49,642 kg.mM2=52,252 kg.m

    V2= 41,137 kg

    ULS E-W INTERIOR

    10,522 kg/m1 3

    V1=43,039 kg

    M2=49,642 kg.mM2=52,252 kg.m

    V2= 41,137 kg

    ULS E-W INTERIOR

  • 7 N-S D-C () C-B () P/T 10,832 -5,836 5,594 SYM DL -15,085 31,895 -28,971 SYM LL -5,587 11,813 -10,730 SYM SLS -9,840 37,872 -34,107 SYM ULS -19,785 58,899 -53,206 SYM

  • 5. SLS N-S

    6. ULS N-S

    7,104 kg/mD C

    VD=24,912 kg

    M2= 37,872 kg.mMD= 9,840 kg.m

    V2= 31,920 kg

    SLS N-S EXTERIOR

    7,104 kg/mD C

    VD=24,912 kg

    M2= 37,872 kg.mMD= 9,840 kg.m

    V2= 31,920 kg

    SLS N-S EXTERIOR

    10,522 kg/m1 3

    V1=37,199 kg

    M2=58,899 kg.mM2=19,785 kg.m

    V2=46,977 kg

    ULS N-S EXTERIOR

    10,522 kg/m1 3

    V1=37,199 kg

    M2=58,899 kg.mM2=19,785 kg.m

    V2=46,977 kg

    ULS N-S EXTERIOR

  • 7. SLS N-S

    8. ULS N-S

    7,104 kg/mC B

    V1=28,416 kg

    M2=-34,107 kg.mMc=-34,107 kg.m

    V2=28,416 kg

    SLS N-S INTERIOR

    7,104 kg/mC B

    V1=28,416 kg

    M2=-34,107 kg.mMc=-34,107 kg.m

    V2=28,416 kg

    SLS N-S INTERIOR

    10,522 kg/m1 3

    V1=42,088 kg

    M2=53,206 kg.mM2=53,206 kg.m

    V2= 42,088 kg

    ULS N-S INTERIOR

    10,522 kg/m1 3

    V1=42,088 kg

    M2=53,206 kg.mM2=53,206 kg.m

    V2= 42,088 kg

    ULS N-S INTERIOR

  • 8 E-W 1-2 () 2-3 () SLS -2,465 31,281 -32,226 -29,186 21,997 -26,459 ULS -8,805 44,449 -49,170 -44,814 30,770 -37,774 9 N-S D-C () C-B() SLS -2,686 33,840 -28,616 -25,902 22,725 -25,902 ULS -9,099 45,971 -45,279 -41,053 30,970 -41,053

  • 9.

    2

    2cen )L/c5.0(hee = E-W 064.0)80/605.0(03.0068.0e 2 == m N-S 044.0)80/605.0(026.0048.0e 2 == m 533,6411/22800c/bhc/IS 31213121 ==== cm3

    9.293506.1f6.1 c == ksc 9.935053.0f53.0 c == ksc 5.15735045.0f45.0 c == ksc

  • 9.1 10 E-W 1-2 () 2-3 () SLS (kg-m) -2,465 31,281 -32,226 -29,186 21,997 -26,459

    eP (kg) 249,984 249,984 249,984 - 187,488 187,488 A/Pe (ksc) -14.2 -14.2 -14.2 - -10.7 -10.7

    e (cm) 0 8.0 6.4 - 8.0 6.4 0 31.0 -24.8 - 23.2 -18.6

    S/ePe (ksc) 0 -31.0 24.8 - -23.2 18.6 3.8 -48.5 49.9 - -34.1 41.0 M/S (ksc) -3.8 48.5 -49.9 - 34.1 -41.0 -10.4 -31.7 10.9 - -21.6 11.7 (ksc) -18.0 3.3 -39.3 - 0.2 -33.1

    status - Sym.

    0.5L=4.0 m 0.5L=4.0 m

    0.1L=0.8 m

    0.0680.080

    E-W- +

  • 9.2 11 N-S D-C () C-B() SLS -2,686 33,840 -28,616 -25,902 22,725 -25,902

    eP (kg) 265,608 265,608 265,608 - 203,112 203,112 A/Pe (ksc) -15.1 -15.1 -15.1 - -11.5 -11.5

    e (cm) 0 8.0 4.4 - 8.0 4.4 0 32.9 -18.1 - 25.2 -12.6

    S/ePe (ksc) 0 -32.9 18.1 - -25.2 12.6 4.2 -52.4 44.3 - -35.2 40.1 M/S (ksc) -4.2 52.4 -44.3 - 35.2 -40.1 -10.9 -34.6 11.1 - -21.5 16.0 (ksc) -19.3 4.4 -41.3 - -1.5 -39.0

    status - - +

    0.5L=4.0 m 0.5L=4.0 m

    0.1L=0.8 m

    0.048

    0.080

    N-SSym.

    h2

  • 10.

    10.1

    9.935053.0f53.0 c == ksc

    = 0.002A

    4.422100002.0A mins ==+ cm2/m DB12 @ 0.25 #, 5.4A prov,s = cm2/m

  • 10.2 0.00075 hl 1.5h 4 30 cm l/6

    2.138002200075.0A mins == cm2/ 12 DB12 @ 0.10 # 126225.1260 =+ say 120 cm 10.3

    DB12 @ 0.25 #

  • 11.

    ( )

    +

    =pc

    pup

    1

    ppups d

    dff

    1ff

  • 11.1 12 E-W 1-2 () 2-3 () ULS -8,805 44,449 -49,170 - 30,770 -37,774 16 16 16 - 12 12

    psA 22.4 22.4 22.4 - 16.8 16.8 sA 13.6 0 13.6 - 0 13.6

    pd 11.0 19.0 17.4 - 19.0 17.4 d 18.2 18.2 18.2 - 18.2 18.2

    )10( 3p 2.55 1.47 1.61 - 1.11 1.21 )10( 3 0.93 0 0.93 - 0 0.93

    0.011 0 0.011 - 0 0.011 psf (ksc) 17,610 18,091 17,968 - 18,216 18,106

    a (cm) 1.89 1.70 1.92 - 1.29 1.51 nM (kg-m) 44,145 66,196 67,992 - 50,554 54,109

    ULS -8,805 44,449 -49,170 - 30,770 -37,774 status

  • 11.2 13 N-S D-C () C-B() ULS -9,099 45,971 -45,279 - 30,970 -41,053 17 17 17 - 13 13

    psA 23.8 23.8 23.8 - 18.2 18.2 sA 13.6 0 13.6 - 0 13.6

    pd 11.0 19.0 15.4 - 19.0 15.4 D 19.4 19.4 19.4 - 19.4 19.4

    )10( 3p 2.70 1.57 1.93 - 1.20 1.48 )10( 3 0.88 0 0.88 - 0 0.88

    0.01 0 0.01 - 0 0.01 psf 17,551 18,057 17,850 - 18,184 18,006

    a (cm) 1.98 1.81 2.01 - 1.39 1.61 nM (kg-m) 46,645 69,988 64,045 - 54,522 52,150

    ULS -9,099 45,971 -45,279 - 30,970 -41,053 status

  • 12 12.1

    B2

    56.74)60.400.4()10.457.4(A =++= m2 d = 0.8h = 17.6 cm

    315,12407.1)120528(4.1W7.1W4.1W LuDuu =++=+= . .. ( )( ) 255,97176.060.056.74315,1V 2u =+= .

    1

    4.57 4.10

    4.46

    4.00

    2 3

    A

    B

    C

    3.43

    3/8WL 5/8WL 5/8WL 3/8WL

  • pV

    += )dc()L(Ph2V 12

    2p

    243,48.0

    )176.06.0(026.0624,15228.0

    )176.06.0(03.0624,1522V 22p =+++=

    (unbalanced moment)

    356,4814,44170,49M EW,u == .. 226,4053,41279,45M NS,u == ..

    ( ) 463,56.17260606.172dbA 0 =++== cm2 8.38

    26.1760ee 21 =+== cm

  • ( )2

    )6.1760)(6.1760(6.176

    6.176.176066.17)6.1760(JJ

    23

    3

    21++++++==

    = 61055.5 cm4 40.0

    111

    6.17606.1760

    322v1v

    =+== ++

    2

    22u2v

    1

    11u1vuu J

    eMJ

    eMAV

    v++=

    66u 1055.58.38100226,44.0

    1055.58.38100356,44.0

    463,5255,97v

    ++= =20.2 ksc

  • dbV

    f3.0fv0

    ppccpc ++=

    310)6.1760(4b0 =+= cm 1.11fpc = ksc

    p 0.93 02.1)5.1310/6.1740(27.0)5.1b/d(27.0 0s =+=+ 93.0p =

    5.21)6.17310(

    243,41.113.035093.0vc =++= ksc

    5.218.2385.0

    2.20vu >== ksc

  • 6565 cm ( ) 815,56.17265656.172dbA 0 =++== cm2

    3.412

    6.1765ee 21 =+== cm

    ( )2

    )6.1765)(6.1765(6.176

    6.176.176566.17)6.1765(JJ

    23

    3

    21++++++==

    = 61069.6 cm4 40.0

    111

    6.17656.1765

    322v1v

    =+== ++

    89.181069.6

    3.41100226,44.01069.6

    3.41100356,44.0815,5255,97v 66u =

    ++=

    2.2285.089.18vu == 21.5

  • 14 E-W N-S )M( u 4,356 4,226 uuf M6.0M = 2,614 2,536 h3c + (cm) 126 126 2 2

    psA (cm2) 2.8 2.8 sA (cm2) 13.6 13.6

    psf (ksc) 17,968 17,850 dp (cm) 17.4 15.4 d (cm) 18.2 19.4

    a (cm) = bf85.0

    fAfA

    c

    yspsps

    + 2.79 2.78

    ))2/ad(fA)2/ad(fA(M ysppspsn += 15,473 15,118 )M( u 4,356 4,226 status

  • 12.2 B1 = 6.3146.8)3.043.3( =+ m2

    315,1W7.1W4.1W LuDuu =+= . .. ( )( ) 852,40)176.06.0(2/176.060.06.31315,1Vu =++= .

    pV E-W = 19,321 . .

    2.230)6.1765()2/6.1765(2b0 =+++= cm 052,4)6.17265652(6.17A =++= cm2

    7.236.17265652

    )2/6.1765(e2

    1 =+++= cm

  • 14.57 4.10

    4.46

    4.00

    2 3

    A

    B

    C

    3.43

  • ( ) 22331 7.2322/6.17656.172/6.176527.236.17)6.1765(

    66.17)2/6.1765(6.17)2/6.1765(J

    ++++++++=

    61052.2 = cm4 387.0

    111

    6.17652/6.1765

    321v

    =+= ++

    uM = 784,12100/6.17633,36321,19 = . .

    73.823.717.6

  • uV uM 7.14

    1052.27.23)100(784,12387.0

    052,4852,40v 6u =

    += ksc

    ( ) 3.30350)42(27.0f/4227.0v ccc =+=+= ksc 7.21350)22.230/6.1730(27.0f)2b/d(27.0 c0s =+=+ ksc 8.1935006.1f06.1 c == ksc 8.19vc = ksc 8.19v3.1785.0/7.14/v cu =

  • 15 E-W )M( u 4,356 uuf M6.0M = 2,614 h3c + (cm) 126 2

    psA (cm2) 2.8 sA (cm2) 13.6

    psf (ksc) 17,968 dp (cm) 17.4 d (cm) 18.2

    a (cm) = bf85.0

    fAfA

    c

    yspsps

    + 2.79

    ))2/ad(fA)2/ad(fA(M ysppspsn += 15,473 )M( u 4,356 status

  • 13. 13.1

    EIwl

    38480.3

    EIwl

    38480.3 44

    i +=

    78.070986735015120384

    8008001024080.3244

    =

    =

    cm (7.8 mm) < 800/360 = 2.22 cm (22 mm)

  • 13.2 90%

    10% 30% = 1252403.05281.0 =+ kg/m2 creep factor )( = 2 56.0

    709867350151203848008001012565.222

    44

    l =

    =

    cm (5.6 mm)

    1.116.58.77.07.0 liT =+=+= mm < 22 mm

  • 2 2.1

    lc

    =Il1

    cccIE

    =I

    IEcs

    c1

    222

    1cs

    )l/c1(IE

    lnc1/2

    c1/2

    h1h2lIE4K cc =

    2/clIE4K

    11

    cs =

  • lc

    =Il1

    cccIE

    =I

    1csIE

    c1

    222

    2cs

    )l/c1(IE

    lnc1/2

    c1/2

    2csIE

    h1