TRABE AASHTO TIPO VI L=25.06

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    DISEODETRABEPRETENSADAAASHTOTIPOVI

    Datosdelproyeto:

    L= 25.06 m

    blosa= 2.20 m

    Longitudentreejesdeapoyo

    Anchodelosa

    tlosa= 0.20 m

    bpav.= 1.70 mtpav.= 0.12 m

    talma= 0.20 m

    Materiales:

    = 2

    Espesordelosa

    EspesordepavimentoAnchodepavimento

    Anchodelalma

    106.68

    33.0212.7

    7.6

    2

    .16

    10.16

    33.02

    c= g cm

    fc= 400 kg/cm2

    fy= 4,200 kg/cm2

    Modulosdeelasticidad

    Elosa= 221,359 kg/cm

    2

    2

    es s enc a econcre oen osa

    Esfuerzodefluenciaenestribos

    Resistenciadeconcretoentrabe

    20.32

    25.4

    7.6

    2

    10.1

    6

    106.6

    8

    25.4

    yc

    10.16

    182.8

    8

    Etrabe= 280,000 g cm

    Relacinmodular

    b= 2.2 cm

    n= 0.79 Elosa/Etrabe

    71.12

    25.4

    20.3

    2

    y

    rop e a essecc ns mp e

    segmento binf. bsup. h Hacum yinfe yi

    1 71.12 71.12 20.32 20.32 10.16 10.16

    2 71.12 20.32 25.40 45.72 10.35 30.673 20.32 20.32 106.68 152.40 53.34 99.06

    4 20.32 40.64 10.16 162.56 5.64 158.04

    5 40.64 106.68 7.62 170.18 4.38 166.94

    6 106.68 106.68 5.00 175.18 2.50 172.68

    7 106.68 106.68 7.70 182.88 3.85 179.03

    182.88

    egmento A(cm2) Ayi

    1 1,445.2 14,682.8

    A(yi yc)2

    9,775,835.38

    I(cm4)

    49,725.78

    2 1,161.3 35,614.6

    3 2,167.7 214,7364 309.7 48,942.7

    5 561.3 93,701.2

    6 533.4 92,107.5

    7 821.4 147,062

    A =

    4,058.58

    2,533.99

    1,111.253,437,112.48

    6,163,704.23

    4,426,441.88

    95,953.941,334,179.10

    3,118,011.64

    56,011.39

    2,055,850.262,565.22

    , . ,

    yc= 92.41 I= cm4

    30,523,095.12

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    Propiedadesseccincompuesta

    egmento binf. bsup. h hacum. yi yi

    Trabe 182.88 182.88 92.41 92.41

    Losa 173.93 173.93 20.00 202.88 10 192.88

    egmento A(cm2) A(yi yc)2Ayi I(cm4)

    Trabe 6,999.99

    Losa 3,478.51A= 10,478.49

    yc= 125.76 I= cm4

    670,934.11,317,780.7

    15,670,744.78 115,950.18

    54,097,058.62

    646,846.6 7,787,268.54 30,523,095.12

    H= cm

    A= cm2

    I= cm4

    yci= cm

    = 3

    Seccinsimple

    182.88

    6,999.99

    30,523,095.12

    92.41

    Ss= cm3

    Modulodeseccinsuperiorenlatrabe

    H= cm

    A= cm2

    I = cm4

    , .

    337,371.82

    202.88

    10,478.49

    54 097 058.62

    Seccincompuesta

    yci= cm

    Si= cm3

    Modulodeseccininferiorenlatrabe

    Ss= cm

    3

    ModulodeseccinsuperiorenlalosaSst= cm

    3Modulodeseccinsuperiorenlatrabe

    , , .

    125.76

    430,159.25

    701,470.89947,086.25

    ELEMENTOSMECANICOS

    Cargas

    Pp= 1.68 Ton/m Pesopropio

    Losa= 1.06 Ton/m Losadesuperestructura

    GyB= 0.52 Ton/m Guarnicionybanqueta

    Pav= 0.49 Ton/m Pavimento

    FC= 1 Factordeconcentracin

    FI= 0.24 Factordeimpactocargaviva15.24/(L+38.1) 0.3

    Nota:loscortantes(VCV)ymomentos(Mcv)seobtienendelmodelodecargaviva

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    FUERZASCORTANTES

    X/L X(m) VPP(T) VLosa(T) VGyB(T) VPav(T) VCV(T) VCV+i(T)

    0.00 0.00 21.05 13.23 6.52 6.13 24.88 30.88

    0.05 1.25 18.95 11.91 5.86 5.52 24.88 30.88

    0.10 2.51 16.84 10.59 5.21 4.91 20.67 25.66

    0.15 3.76 14.74 9.26 4.56 4.29 18.64 23.14

    0.20 5.01 12.63 7.94 3.91 3.68 16.77 20.82

    0.25 6.27 10.53 6.62 3.26 3.07 15.13 18.780.30 7.52 8.42 5.29 2.61 2.45 13.55 16.82

    0.35 8.77 6.32 3.97 1.95 1.84 11.96 14.85

    0.40 10.02 4.21 2.65 1.30 1.23 10.45 12.97

    0.45 11.28 2.11 1.32 0.65 0.61 9.35 11.61

    0.50 12.53 0.00 0.00 0.00 0.00 9.35 11.61. . . . . . . .

    0.55 13.78 2.11 1.32 0.65 0.61 9.35 11.61

    0.60 15.04 4.21 2.65 1.30 1.23 10.45 12.97

    0.65 16.29 6.32 3.97 1.95 1.84 11.96 14.85

    0.70 17.54 8.42 5.29 2.61 2.45 13.55 16.82

    0.75 18.80 10.53 6.62 3.26 3.07 15.13 18.78

    0.80 20.05 12.63 7.94 3.91 3.68 16.77 20.820.85 21.30 14.74 9.26 4.56 4.29 18.64 23.14

    0.90 22.55 16.84 10.59 5.21 4.91 20.67 25.66

    0.95 23.81 18.95 11.91 5.86 5.52 24.88 30.88

    1.00 25.06 21.05 13.23 6.52 6.13 24.88 30.88

    MOMENTOSFLEXIONANTES

    m PP Losa GyB Pav CV CV+i

    0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

    0.05 1.25 25.06 15.75 7.76 7.30 31.72 39.37

    0.10 2.51 47.48 29.84 14.70 13.84 60.10 74.600.15 3.76 67.26 42.28 20.82 19.60 83.71 103.91

    0.20 5.01 84.40 53.05 26.12 24.60 103.52 128.50

    0.25 6.27 98.91 62.17 30.62 28.83 122.38 151.91

    0.30 7.52 110.78 69.63 34.29 32.28 140.92 174.92

    0.35 8.77 120.01 75.44 37.15 34.97 154.88 192.25

    0.40 10.02 126.61 79.58 39.19 36.90 166.30 206.43

    0.45 11.28 130.56 82.07 40.41 38.05 174.28 216.33

    0.50 12.53 131.88 82.90 40.82 38.43 176.54 219.14

    0.55 13.78 130.56 82.07 40.41 38.05 174.28 216.33

    0.60 15.04 126.61 79.58 39.19 36.90 166.30 206.43

    0.65 16.29 120.01 75.44 37.15 34.97 154.88 192.250.70 17.54 110.78 69.63 34.29 32.28 140.92 174.92

    0.75 18.80 98.91 62.17 30.62 28.83 122.38 151.91

    0.80 20.05 84.40 53.05 26.12 24.60 103.52 128.50

    0.85 21.30 67.26 42.28 20.82 19.60 83.71 103.91

    0.90 22.55 47.48 29.84 14.70 13.84 60.10 74.60. . . . . . . .

    0.95 23.81 25.06 15.75 7.76 7.30 31.72 39.37

    1.00 25.06 0.00 0.00 0.00 0.00 0.00 0.00

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    RESUMENELEMENTOSMECANICOSULTIMOS

    X/L X(m) Vu(T) Mu(Tm)

    0.00 0.00 128.06 0.00

    0.05 1.25 121.96 158.11

    0.10 2.51 104.51 299.57

    . . . .

    0.20 5.01 81.80 523.600.25 6.27 71.28 616.48

    0.30 7.52 60.92 700.84

    0.35 8.77 50.53 765.22

    0.40 10.02 40.36 815.10

    0.45 11.28 31.30 848.08

    0.50 12.53 25.20 857.99

    0.55 13.78 31.30 848.08

    0.60 15.04 40.36 815.10

    0.65 16.29 50.53 765.22

    0.70 17.54 60.92 700.84

    0.75 18.80 71.28 616.480.80 20.05 81.80 523.60

    0.85 21.30 92.94 420.53

    0.90 22.55 104.51 299.57

    0.95 23.81 121.96 158.11

    1.00 25.06 128.06 0.00

    Vumax= 128.06 T

    Mumax= 857.99 Tm

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    ESFUERZOSENTRABE(kg/cm2)

    FIBRASUPERIORDETRABE

    X/L X(m) fPPsup. f Losa

    sup. f GyB sup. f Pav sup. f CV+i sup. f Total sup.

    0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

    0.05 1.25 7.43 4.67 0.82 0.77 4.16 17.84

    0.10 2.51 14.07 8.85 1.55 1.46 7.88 33.81

    0.15 3.76 19.94 12.53 2.20 2.07 10.97 47.71

    0.20 5.01 25.02 15.73 2.76 2.60 13.57 59.670.25 6.27 29.32 18.43 3.23 3.04 16.04 70.06

    0.30 7.52 32.84 20.64 3.62 3.41 18.47 78.97

    0.35 8.77 35.57 22.36 3.92 3.69 20.30 85.85

    0.40 10.02 37.53 23.59 4.14 3.90 21.80 90.94

    . . . . . . . .

    0.50 12.53 39.09 24.57 4.31 4.06 23.14 95.17

    0.55 13.78 38.70 24.33 4.27 4.02 22.84 94.15

    0.60 15.04 37.53 23.59 4.14 3.90 21.80 90.94

    0.65 16.29 35.57 22.36 3.92 3.69 20.30 85.85

    0.70 17.54 32.84 20.64 3.62 3.41 18.47 78.97

    0.75 18.80 29.32 18.43 3.23 3.04 16.04 70.06

    0.80 20.05 25.02 15.73 2.76 2.60 13.57 59.67

    0.85 21.30 19.94 12.53 2.20 2.07 10.97 47.71

    0.90 22.55 14.07 8.85 1.55 1.46 7.88 33.81

    0.95 23.81 7.43 4.67 0.82 0.77 4.16 17.84

    1.00 25.06 0.00 0.00 0.00 0.00 0.00 0.00

    X/L X(m) fPPinf. f Losa

    inf. f GyB inf. f Pav inf. f CV+i inf. f Total inf.

    0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

    0.05 1.25 7.59 4.77 1.80 1.70 9.15 25.010.10 2.51 14.37 9.03 3.42 3.22 17.34 47.38

    0.15 3.76 20.36 12.80 4.84 4.56 24.16 66.71

    . . . . . . . .

    0.25 6.27 29.94 18.82 7.12 6.70 35.31 97.90

    0.30 7.52 33.54 21.08 7.97 7.51 40.66 110.76

    0.35 8.77 36.33 22.84 8.64 8.13 44.69 120.63

    0.40 10.02 38.33 24.09 9.11 8.58 47.99 128.10

    0.45 11.28 39.53 24.85 9.39 8.85 50.29 132.90

    0.50 12.53 39.93 25.10 9.49 8.93 50.94 134.39

    0.55 13.78 39.53 24.85 9.39 8.85 50.29 132.90

    0.60 15.04 38.33 24.09 9.11 8.58 47.99 128.100.65 16.29 36.33 22.84 8.64 8.13 44.69 120.63

    0.70 17.54 33.54 21.08 7.97 7.51 40.66 110.76

    0.75 18.80 29.94 18.82 7.12 6.70 35.31 97.90

    0.80 20.05 25.55 16.06 6.07 5.72 29.87 83.28

    . . . . . . . .

    0.90 22.55 14.37 9.03 3.42 3.22 17.34 47.38

    0.95 23.81 7.59 4.77 1.80 1.70 9.15 25.01

    1.00 25.06 0.00 0.00 0.00 0.00 0.00 0.00

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    ESFUERZOENLECHOSUPERIORDELALOSA

    X/L X(m) fGyBinf. f Pav

    inf. f CV+i inf. f Total inf.

    0.00 0.00 0.00 0.00 0.00 0.00

    0.05 1.25 1.11 1.04 5.61 7.76

    0.10 2.51 2.09 1.97 10.64 14.70

    0.15 3.76 2.97 2.79 14.81 20.58

    0.20 5.01 3.72 3.51 18.32 25.55

    0.25 6.27 4.36 4.11 21.66 30.130.30 7.52 4.89 4.60 24.94 34.43

    0.35 8.77 5.30 4.99 27.41 37.69

    0.40 10.02 5.59 5.26 29.43 40.27

    0.45 11.28 5.76 5.42 30.84 42.03

    0.50 12.53 5.82 5.48 31.24 42.54. . . . . .

    0.55 13.78 5.76 5.42 30.84 42.03

    0.60 15.04 5.59 5.26 29.43 40.27

    0.65 16.29 5.30 4.99 27.41 37.69

    0.70 17.54 4.89 4.60 24.94 34.43

    0.75 18.80 4.36 4.11 21.66 30.13

    0.80 20.05 3.72 3.51 18.32 25.550.85 21.30 2.97 2.79 14.81 20.58

    0.90 22.55 2.09 1.97 10.64 14.70

    0.95 23.81 1.11 1.04 5.61 7.76

    1.00 25.06 0.00 0.00 0.00 0.00

    PRESFUERZO

    Toron= 1.27 Diametrodetoron

    an= 0.99 cm2

    Areanominaldeltoron

    = 2

    ,

    Ep= 1,960,000 kg/cm2

    Tension= 0.75 %

    Fuerzadetensado

    Fi= 14,250.00kg/cm2

    Ti= 14,107.50 kg

    #Tor= 32.65 #detoronesaproximados

    Seproponen33torones

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    distribuciondelacerodepresfuerzo

    Zonacentraldeclaro

    lecho #toron yi(cm) #toryi

    1 11 5 55

    2 13 10 130

    3 9 15 135

    5 0 25 06 0 0 0

    #torones 33 320

    yg= 9.70

    Enductadodetorones

    LT= 63.50 cm Longituddetransferencia

    Long.Realenductada

    9.6

    Tipodetoron Long.Prop LT(m)

    A

    #detoronesenduc

    5 6.88

    5 toronesa 6.88 m 4 toronesa 5.63 m

    7.9

    6.2

    4.5

    2.8

    14 0.62

    B 4

    4

    5.63

    4.38C

    D

    E

    3.12

    1.87

    5

    4

    F

    lecho #toron yi #toryi lecho #toron yi #toryi

    1 11 5 55 1 11 5 55

    2 13 10 130 2 13 10 130

    3 4 15 60 3 0 15 04 0 20 0 4 0 20 0

    5 0 25 0 5 0 25 0

    6 0 0 0 6 0 0 0

    #torones 28 245 #torones 24 185

    yg= 8.84 yg= 7.79

    4 torones a 4.38 m 5 torones a 3.12 m. .

    lecho #toron yi #toryi lecho #toron yi #toryi1 11 5 55 1 11 5 55

    2 9 10 90 2 4 10 40

    3 0 15 0 3 0 15 0

    4 0 20 0 4 0 20 0

    5 0 25 0 5 0 25 0

    6 0 0 0 6 0 0 0

    #torones 20 145 #torones 15 95

    yg= 7.32 yg= 6.40

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    | toronesa 1.87 m 4 toronesa 0.62 m

    lecho #toron yi #toryi lecho #toron yi #toryi

    1 11 5 55 1 7 5 35

    2 0 10 0 2 0 10 0

    3 0 15 0 3 0 15 0

    5 0 25 0 5 0 25 06 0 0 0 6 0 0 0

    #torones 11 55 #torones 7 35

    yg= 5.05 yg= 5.05

    X/L X(m) #Tornes e(cm) Pi(kg) Pi/A Pie/Ss Pie/Si fspfzo fipfzo

    0.00 0.00 0 87.36 0.00 0.00 0.00 0.00 0.00 0.00

    0.05 1.25 7 87.36 98,753 14.11 25.57 26.12 11.46 40.220.10 2.51 11 86.01 155,183 22.17 39.56 40.41 17.39 62.58

    0.15 3.76 15 85.08 211,613 30.23 53.37 54.51 23.14 84.74

    0.20 5.01 20 84.62 282,150 40.31 70.77 72.28 30.46 112.59

    0.25 6.27 24 83.57 338,580 48.37 83.87 85.66 35.50 134.03

    0.30 7.52 28 82.71 395,010 56.43 96.84 98.91 40.41 155.34

    0.35 8.77 33 82.71 465,548 66.51 114.13 116.57 47.63 183.08

    0.40 10.02 33 82.71 465,548 66.51 114.13 116.57 47.63 183.08

    0.45 11.28 33 82.71 465,548 66.51 114.13 116.57 47.63 183.08

    0.50 12.53 33 82.71 465,548 66.51 114.13 116.57 47.63 183.08

    0.55 13.78 33 82.71 465,548 66.51 114.13 116.57 47.63 183.08

    0.60 15.04 33 82.71 465,548 66.51 114.13 116.57 47.63 183.080.65 16.29 33 82.71 465,548 66.51 114.13 116.57 47.63 183.08

    0.70 17.54 28 82.71 395,010 56.43 96.84 98.91 40.41 155.34

    0.75 18.80 24 83.57 338,580 48.37 83.87 85.66 35.50 134.03

    0.80 20.05 20 84.62 282,150 40.31 70.77 72.28 30.46 112.59

    0.85 21.30 15 85.08 211,613 30.23 53.37 54.51 23.14 84.74

    0.90 22.55 11 86.01 155,183 22.17 39.56 40.41 17.39 62.58

    0.95 23.81 7 87.36 98,753 14.11 25.57 26.12 11.46 40.22

    1.00 25.06 0 87.36 0.00 0.00 0.00 0.00 0.00 0.00

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    REVISIONDEESFUERZOSENLATRANSFERENCIA

    fci= 360 kg/cm2

    al90%delaresistenciadelconcreto

    Fibrasuperior 0.6fci 0.8fci

    X/L X(m) fPPsup. fspfzo f total fcomperm f tensperm

    0.00 0.00 0.00 0.00 0.00 216.00 15.18

    0.05 1.25 7.43 11.46 4.04 216.00 15.180.10 2.51 14.07 17.39 3.32 216.00 15.18

    0.15 3.76 19.94 23.14 3.20 216.00 15.18

    0.20 5.01 25.02 30.46 5.44 216.00 15.18

    0.25 6.27 29.32 35.50 6.18 216.00 15.18

    . . . . . . .

    0.35 8.77 35.57 47.63 12.05 216.00 15.18

    0.40 10.02 37.53 47.63 10.10 216.00 15.18

    0.45 11.28 38.70 47.63 8.93 216.00 15.18

    0.50 12.53 39.09 47.63 8.54 216.00 15.18

    0.55 13.78 38.70 47.63 8.93 216.00 15.18

    0.60 15.04 37.53 47.63 10.10 216.00 15.18

    0.65 16.29 35.57 47.63 12.05 216.00 15.18

    0.70 17.54 32.84 40.41 7.57 216.00 15.18

    0.75 18.80 29.32 35.50 6.18 216.00 15.18

    0.80 20.05 25.02 30.46 5.44 216.00 15.18

    0.85 21.30 19.94 23.14 3.20 216.00 15.18

    0.90 22.55 14.07 17.39 3.32 216.00 15.18

    . . . . . . .

    1.00 25.06 0.00 0.00 0.00 216.00 15.18

    TRANSFERENCIAFIBRASUPERIOR

    100.00

    150.00

    200.00

    250.00

    TRANSFERENCIAFIBRASUPERIOR

    50.00

    0.00

    50.00

    100.00

    3.00 2.00 7.00 12.00 17.00 22.00 27.003.00 2.00 7.00 12.00 17.00 22.00 27.00

    fcomperm f tensperm f total

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    Fibrainferior

    X/L X(m) fPPinf. fipfzo f total fcomperm f tensperm

    0.00 0.00 0.00 0.00 0.00 216.00 15.18

    0.05 1.25 7.59 40.22 32.64 216.00 15.18

    0.10 2.51 14.37 62.58 48.20 216.00 15.18

    0.15 3.76 20.36 84.74 64.38 216.00 15.18

    0.20 5.01 25.55 112.59 87.04 216.00 15.18

    0.25 6.27 29.94 134.03 104.08 216.00 15.180.30 7.52 33.54 155.34 121.80 216.00 15.18

    0.35 8.77 36.33 183.08 146.75 216.00 15.18

    0.40 10.02 38.33 183.08 144.75 216.00 15.18

    0.45 11.28 39.53 183.08 143.55 216.00 15.18

    0.50 12.53 39.93 183.08 143.15 216.00 15.18. . . . . . .

    0.55 13.78 39.53 183.08 143.55 216.00 15.18

    0.60 15.04 38.33 183.08 144.75 216.00 15.18

    0.65 16.29 36.33 183.08 146.75 216.00 15.18

    0.70 17.54 33.54 155.34 121.80 216.00 15.18

    0.75 18.80 29.94 134.03 104.08 216.00 15.18

    0.80 20.05 25.55 112.59 87.04 216.00 15.180.85 21.30 20.36 84.74 64.38 216.00 15.18

    0.90 22.55 14.37 62.58 48.20 216.00 15.18

    0.95 23.81 7.59 40.22 32.64 216.00 15.18

    1.00 25.06 0.00 0.00 0.00 216.00 15.18

    150.00

    200.00

    250.00

    TRANSFERENCIAFIBRAINFERIOR

    0.00

    50.00

    100.00

    150.00

    50.00

    0.00

    0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00

    fcomperm f tensperm f total

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    ETAPADESERVICIO

    Perdidasdepresfuerzo

    Pordeslizamientodelanclaje

    L= 25.06 m2

    Ep= 1,960,000kg/cm

    I= 1mm Deslizamiento(110mm)proporcionadoporelfabricanteDA= 78.21 kg/cm

    2

    Relajacininstantaneadelacero

    t= 10 horas Tiempoestimadodecuradodelconcreto2

    p = , . g cm

    fpy= 16,150.0 kg/cm2

    REi= 118.40 kg/cm2

    Contraccindelconcreto

    RH= 80 % humedadmediaambiental2= . g cm

    Acortamientoelstico

    Eci= 305,594.3 kg/cm2

    = 2,400 kg/m3

    d= 173.18 cm

    f= 134.62 kg/cm2

    2= . g cm

    fcir= 136.02 kg/cm2

    E= 872.4 kg/cm2

    E=(Ep/Eci)fcir

    %= 0.94

    Flujoplastico

    = .

    finf= 90.52 kg/cm2

    fsup= 11.77 kg/cm2

    f= 102.29 kg/cm2

    X= 108.06 kg/cm2

    fcds= 96.28 kg/cm2

    CRc= 958.2 kg/cm CRc=(12*fcr 7*fcd)

    Relajaciondelacerodepresfuerzo

    CRs= 198.82

    fs= 2579.00

    El orcenta e es:

    PT= 0.82 % 18.10 %

    Esfuerzototalconperdidasdepresfuerzo=

    Tef= 11554.29 kg esfuerzototalefectivo

    Totaldeperdidas=

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    REVISIONDEESFUERZOSENSERVICIO

    Esfuerzosenlafibrasuperior

    0.6fc 0.8fc 1.6fc

    ftperm

    (kg/cm2)

    fstotal

    (kg/cm2)X/L X(m)

    fscarga

    total2

    fsefpfzo

    (kg/cm2)

    fcperm

    (kg/cm2)

    ftperm

    (kg/cm2)

    0.00 0.00 0.00 0.00 0.00 240.00 16.00 32.000.05 1.25 17.84 9.39 8.45 240.00 16.00 32.00

    0.10 2.51 33.81 14.25 19.56 240.00 16.00 32.00

    0.15 3.76 47.71 18.95 28.76 240.00 16.00 32.00

    0.20 5.01 59.67 24.95 34.72 240.00 16.00 32.00

    0.25 6.27 70.06 29.07 40.99 240.00 16.00 32.00

    (kg cm )

    . . . . . . . .

    0.30 7.52 78.97 33.10 45.88 240.00 16.00 32.00

    0.35 8.77 85.85 39.01 46.84 240.00 16.00 32.00

    0.40 10.02 90.94 39.01 51.94 240.00 16.00 32.00

    0.45 11.28 94.15 39.01 55.14 240.00 16.00 32.00

    0.50 12.53 95.17 39.01 56.16 240.00 16.00 32.00

    0.55 13.78 94.15 39.01 55.14 240.00 16.00 32.000.60 15.04 90.94 39.01 51.94 240.00 16.00 32.00

    0.65 16.29 85.85 39.01 46.84 240.00 16.00 32.00

    0.70 17.54 78.97 33.10 45.88 240.00 16.00 32.00

    0.75 18.80 70.06 29.07 40.99 240.00 16.00 32.00

    0.80 20.05 59.67 24.95 34.72 240.00 16.00 32.00

    0.85 21.30 47.71 18.95 28.76 240.00 16.00 32.00

    0.90 22.55 33.81 14.25 19.56 240.00 16.00 32.00. . . . . . . .

    0.95 23.81 17.84 9.39 8.45 240.00 16.00 32.00

    1.00 25.06 0.00 0.00 0.00 240.00 16.00 32.00

    SERVICIOFIBRA SUPERIOR

    150.00

    200.00

    250.00

    300.00

    SERVICIOFIBRASUPERIOR

    50.00

    0.00

    50.00

    100.00

    150.00

    0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00

    fstotal fcperm ftperm ftpermfstotal fcperm ftperm ftperm

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    Esfuerzosenlafibrainferior

    0.6fc 0.8fc 1.6fc

    0.00 0.00 0.00 0.00 0.00 240.00 16.00 32.00

    ftperm

    (kg/cm2)X/L X(m)

    ficarga

    total

    (kg/cm2)

    fiefpfzo

    (kg/cm2)

    fitotal

    (kg/cm2)

    fcperm

    (kg/cm2)

    ftperm

    (kg/cm2)

    . . . . . . . .

    0.10 2.51 47.38 51.25 3.87 240.00 16.00 32.000.15 3.76 66.71 69.40 2.69 240.00 16.00 32.00

    0.20 5.01 83.28 92.21 8.93 240.00 16.00 32.00

    0.25 6.27 97.90 109.77 11.87 240.00 16.00 32.00

    0.30 7.52 110.76 127.23 16.47 240.00 16.00 32.00

    0.35 8.77 120.63 149.95 29.32 240.00 16.00 32.00

    0.40 10.02 128.10 149.95 21.85 240.00 16.00 32.00

    0.45 11.28 132.90 149.95 17.04 240.00 16.00 32.00

    0.50 12.53 134.39 149.95 15.56 240.00 16.00 32.00

    0.55 13.78 132.90 149.95 17.04 240.00 16.00 32.00

    0.60 15.04 128.10 149.95 21.85 240.00 16.00 32.00

    0.65 16.29 120.63 149.95 29.32 240.00 16.00 32.000.70 17.54 110.76 127.23 16.47 240.00 16.00 32.00

    0.75 18.80 97.90 109.77 11.87 240.00 16.00 32.00

    0.80 20.05 83.28 92.21 8.93 240.00 16.00 32.00

    0.85 21.30 66.71 69.40 2.69 240.00 16.00 32.00

    0.90 22.55 47.38 51.25 3.87 240.00 16.00 32.00

    0.95 23.81 25.01 32.94 7.94 240.00 16.00 32.00

    1.00 25.06 0.00 0.00 0.00 240.00 16.00 32.00

    250.00

    300.00SERVICIOFIBRAINFERIOR

    50.00

    100.00

    150.00

    200.00

    250.00

    50.00

    0.00

    50.00

    0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00

    fitotal fcperm ftperm ftperm

    RevisindelaseccinAASHTO9.15.2.2incisosb)yc)despuesdelasperdidas

    b)Esfuerzosdebidoalpresfuerzoefetivo+lascargaspermanentes

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    Esfuerzosenlafibrasuperior 0.4fc 1.6fc

    0.00 0.00 0.00 0.00 0.00 0.00 0.00 160.0 32.00

    0.05 1.25 9.39 4.67 0.82 0.77 3.13 160.0 32.00

    0.10 2.51 14.25 8.85 1.55 1.46 2.39 160.0 32.00

    ftperm

    (kg/cm2)X/L X(m)

    fsefpfzo

    (kg/cm2)

    fslosa

    (kg/cm2)

    fsgyb

    (kg/cm2)

    fspav

    (kg/cm2)

    fstotal

    (kg/cm2)

    fcperm

    (kg/cm2)

    0.15 3.76 18.95 12.53 2.20 2.07 2.15 160.0 32.00

    0.20 5.01 24.95 15.73 2.76 2.60 3.87 160.0 32.000.25 6.27 29.07 18.43 3.23 3.04 4.37 160.0 32.00

    0.30 7.52 33.10 20.64 3.62 3.41 5.43 160.0 32.00

    0.35 8.77 39.01 22.36 3.92 3.69 9.03 160.0 32.00

    0.40 10.02 39.01 23.59 4.14 3.90 7.39 160.0 32.00

    0.45 11.28 39.01 24.33 4.27 4.02 6.40 160.0 32.00. . . . . . . . .

    0.50 12.53 39.01 24.57 4.31 4.06 6.07 160.0 32.00

    0.55 13.78 39.01 24.33 4.27 4.02 6.40 160.0 32.00

    0.60 15.04 39.01 23.59 4.14 3.90 7.39 160.0 32.00

    0.65 16.29 39.01 22.36 3.92 3.69 9.03 160.0 32.00

    0.70 17.54 33.10 20.64 3.62 3.41 5.43 160.0 32.00

    0.75 18.80 29.07 18.43 3.23 3.04 4.37 160.0 32.000.80 20.05 24.95 15.73 2.76 2.60 3.87 160.0 32.00

    0.85 21.30 18.95 12.53 2.20 2.07 2.15 160.0 32.00

    0.90 22.55 14.25 8.85 1.55 1.46 2.39 160.0 32.00

    0.95 23.81 9.39 4.67 0.82 0.77 3.13 160.0 32.00

    1.00 25.06 0.00 0.00 0.00 0.00 0.00 160.0 32.00

    Esfuerzos en la fibra inferior 0.4 fc 1.6fc . .

    0.00 0.00 0.00 0.00 0.00 0.00 0.00 160.0 32.00

    0.05 1.25 32.94 4.77 1.80 1.70 24.68 160.0 32.00

    0.10 2.51 51.25 9.03 3.42 3.22 35.58 160.0 32.00

    0.15 3.76 69.40 12.80 4.84 4.56 47.21 160.0 32.00

    ftperm

    (kg/cm2)

    fipav

    (kg/cm2)

    fitotal

    (kg/cm2)

    fcperm

    (kg/cm2)X/L X(m)

    fiefpfzo

    (kg/cm2)

    filosa

    (kg/cm2)

    figyb

    (kg/cm2)

    0.20 5.01 92.21 16.06 6.07 5.72 64.36 160.0 32.00

    0.25 6.27 109.77 18.82 7.12 6.70 77.13 160.0 32.00

    0.30 7.52 127.23 21.08 7.97 7.51 90.67 160.0 32.00

    0.35 8.77 149.95 22.84 8.64 8.13 110.34 160.0 32.00

    0.40 10.02 149.95 24.09 9.11 8.58 108.17 160.0 32.00

    0.45 11.28 149.95 24.85 9.39 8.85 106.86 160.0 32.00

    . . . . . . . . .

    0.55 13.78 149.95 24.85 9.39 8.85 106.86 160.0 32.000.60 15.04 149.95 24.09 9.11 8.58 108.17 160.0 32.00

    0.65 16.29 149.95 22.84 8.64 8.13 110.34 160.0 32.00

    0.70 17.54 127.23 21.08 7.97 7.51 90.67 160.0 32.00

    0.75 18.80 109.77 18.82 7.12 6.70 77.13 160.0 32.00

    0.80 20.05 92.21 16.06 6.07 5.72 64.36 160.0 32.00

    0.85 21.30 69.40 12.80 4.84 4.56 47.21 160.0 32.00

    0.90 22.55 51.25 9.03 3.42 3.22 35.58 160.0 32.00

    0.95 23.81 32.94 4.77 1.80 1.70 24.68 160.0 32.00

    1.00 25.06 0.00 0.00 0.00 0.00 0.00 160.0 32.00

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    150.0

    200.0

    CONDICINDESERVICIO

    0.0

    50.0

    100.0

    150.0

    c)Esfuerzosdebidoalacargaviva+1/2(presfuerzoefetivo+lascargasmuertas)

    50.0

    0.0

    0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00

    fcperm fitotal fstotal ftperm

    Es uerzosen a i rasuperior

    0.4fc 1.6fc

    0.00 0.00 0.00 0.00 0.00 160 32.00

    0.05 1.25 4.16 1.56 2.59 160 32.00

    1/2pfzo

    ef+CM

    (kg/cm2)

    fstotal

    (kg/cm2)

    fcperm

    (kg/cm2)

    ftperm

    (kg/cm2)X/L X(m)

    fsCV+i

    (kg/cm2)

    . . . . . .

    0.10 2.51 7.88 1.19 6.68 160 32.00

    0.15 3.76 10.97 1.08 9.90 160 32.00

    0.20 5.01 13.57 1.93 11.63 160 32.00

    0.25 6.27 16.04 2.18 13.85 160 32.00

    0.30 7.52 18.47 2.71 15.76 160 32.00

    0.35 8.77 20.30 4.52 15.78 160 32.00

    0.40 10.02 21.80 3.69 18.10 160 32.00

    0.45 11.28 22.84 3.20 19.64 160 32.00

    0.50 12.53 23.14 3.03 20.10 160 32.00

    0.55 13.78 22.84 3.20 19.64 160 32.00

    0.60 15.04 21.80 3.69 18.10 160 32.00

    0.65 16.29 20.30 4.52 15.78 160 32.00

    . . . . . .

    0.75 18.80 16.04 2.18 13.85 160 32.000.80 20.05 13.57 1.93 11.63 160 32.00

    0.85 21.30 10.97 1.08 9.90 160 32.00

    0.90 22.55 7.88 1.19 6.68 160 32.00

    0.95 23.81 4.16 1.56 2.59 160 32.00

    1.00 25.06 0.00 0.00 0.00 160 32.00

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    Esfuerzosenlafibrainferior

    0.4fc 1.6fc

    X/L X(m) fiCV+i

    (kg/cm2)

    1/2(pfzo

    ef+CM)

    (kg/cm2)

    fitotal

    (kg/cm2)

    fcperm

    (kg/cm2)

    ftperm

    (kg/cm2)

    . . . . . .

    0.05 1.25 9.15 12.34 3.18 160 32.000.10 2.51 17.34 17.79 0.45 160 32.00

    0.15 3.76 24.16 23.60 0.55 160 32.00

    0.20 5.01 29.87 32.18 2.31 160 32.00

    0.25 6.27 35.31 38.57 3.25 160 32.00

    0.30 7.52 40.66 45.33 4.67 160 32.00

    0.35 8.77 44.69 55.17 10.48 160 32.00

    0.40 10.02 47.99 54.08 6.09 160 32.00

    0.45 11.28 50.29 53.43 3.14 160 32.00

    0.50 12.53 50.94 53.21 2.27 160 32.00

    0.55 13.78 50.29 53.43 3.14 160 32.00

    0.60 15.04 47.99 54.08 6.09 160 32.000.65 16.29 44.69 55.17 10.48 160 32.00

    0.70 17.54 40.66 45.33 4.67 160 32.00

    0.75 18.80 35.31 38.57 3.25 160 32.00

    0.80 20.05 29.87 32.18 2.31 160 32.00

    0.85 21.30 24.16 23.60 0.55 160 32.00

    0.90 22.55 17.34 17.79 0.45 160 32.00

    0.95 23.81 9.15 12.34 3.18 160 32.00

    1.00 25.06 0.00 0.00 0.00 160 32.00

    200.00

    CONDICINDESERVICIO

    50.00

    100.00

    150.00

    200.00

    CONDICI NDESERVICIO

    50.00

    0.00

    50.00

    0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00

    fitotal fcperm ftperm fstotal

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    DISEOPORRESISTENCIAULTIMA FLEXIN

    Esfuerzoefectivodelpresfuerzo

    efpfzo= 11,671.0 kg/cm2

    (1%perdidas)*fi

    Deformacininicialdelpresfuerzo

    P= 0.00595 f ef/Ep

    a= 11.76

    c= 13.83 a/

    Lecho #torones yi(cm) sp tp fsp T(kg) T*yi

    . . , , ,

    2 13 10 0.0388 0.0448 16,500 212,355 2,123,550

    3 9 15 0.0377 0.0437 16,500 147,015 2,205,225

    4 0 20 0.0000 0.0000 0 0 0

    5 0 25 0.0000 0.0000 0 0 0

    6 0 0 0.0000 0.0000 0 0 0

    Acerode

    pfzo

    Lecho #var yi(cm) sp tp fsp T(kg) T*yi

    1 2 5 0.0399 4,200 10,641 53,204

    #var= 4 T= 549,696 kg

    db= 1.27 C= 549,687 kg 0.85*fc*a*b

    an= 1.27 yg= 9.606047 cm

    Acerode

    refuerzo

    = . cm

    MR= 927.09 Tm

    Mu= 857.99 Tm OK

    #torones reade

    d(cm) MR

    X(m)

    Mu

    0.00 0.00 0 2.53 197.88 0.00

    1.25 158.11 7 2.53 197.88 335.47 ok

    2.51 299.57 11 2.53 196.60 446.09 ok

    3.76 420.53 15 2.53 195.70 583.21 ok

    5.01 523.60 20 2.53 195.24 691.98 ok

    6.27 616.48 24 2.53 194.22 796.98 ok

    mm

    7.52 700.84 28 2.53 193.27 927.09 ok

    8.77 765.22 33 2.53 193.27 927.09 ok

    10.02 815.10 33 2.53 193.27 927.09 ok

    11.28 848.08 33 2.53 193.27 927.09 ok

    12.53 857.99 33 2.53 193.27 927.09 ok

    13.78 848.08 33 2.53 193.27 927.09 ok

    . . . . . o

    16.29 765.22 33 2.53 193.27 927.09 ok

    17.54 700.84 28 2.53 193.27 927.09 ok

    18.80 616.48 24 2.53 194.22 796.98 ok

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    20.05 523.60 20 2.53 195.24 691.98 ok

    21.30 420.53 15 2.53 195.70 583.21 ok

    22.55 299.57 11 2.53 196.60 446.09 ok

    23.81 158.11 7 2.53 197.88 335.47 ok

    25.06 0.00 0 2.53 197.88 0.00

    1200.00

    MOMENTORESISTENTEVSMOMENTOULTIMO

    0.00

    400.00

    800.00

    1200.00

    400.00

    0.00

    0.00 5.00 10.00 15.00 20.00 25.00 30.00

    Mu Mr

    REFUERZOPORCORTANTE

    FuerzaquetomaelconcretoVci=0.6fc bd+(VciMr/Mmax) > 1.7fc bd

    Vcw=(3.5fc+0.3fpc)bd+Vp

    Datos:

    b= 20.32 cm = 8 in

    I= = 1,299,687in4

    Y= 125.76 cm = 49.51 in

    fc= 400 kg/cm2

    5,689 Psi

    54,097,058.62

    0.00 0.00 128.06 36.25 91.81 197.88 22.93 10.0 210.56 209.79

    0.05 1.25 121.96 36.25 85.71 197.88 24.57 10.0 210.56 209.79

    0.10 2.51 104.51 36.02 68.50 196.60 30.54 15.0 139.47 149.16

    Vu Vc Vs d S(cm) Sreal

    (cm) Vs (Vc+Vs)X/L X(m)

    0.15 3.76 92.94 35.85 57.09 195.70 36.48 15.0 138.83 148.48

    0.20 5.01 81.80 35.77 46.03 195.24 45.13 15.0 138.50 148.13

    0.25 6.27 71.28 35.58 35.70 194.22 57.89 20.0 103.33 118.07

    0.30 7.52 60.92 35.41 25.51 193.27 80.61 20.0 102.83 117.50

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    0.35 8.77 50.53 35.41 15.13 193.27 135.95 20.0 102.83 117.50

    0.40 10.02 40.36 35.41 4.96 193.27 414.86 25.0 82.26 100.02

    0.45 11.28 31.30 35.41 4.11 193.27 500.61 25.0 82.26 100.02

    0.50 12.53 25.20 35.41 10.21 193.27 201.44 25.0 82.26 100.02

    0.55 13.78 31.30 35.41 4.11 193.27 500.61 25.0 82.26 100.02

    0.60 15.04 40.36 35.41 4.96 193.27 414.86 25.0 82.26 100.02

    . . . . . . . . . .

    0.70 17.54 60.92 35.41 25.51 193.27 80.61 20.0 102.83 117.500.75 18.80 71.28 35.58 35.70 194.22 57.89 20.0 103.33 118.07

    0.80 20.05 81.80 35.77 46.03 195.24 45.13 15.0 138.50 148.13

    0.85 21.30 92.94 35.85 57.09 195.70 36.48 15.0 138.83 148.48

    0.90 22.55 104.51 36.02 68.50 196.60 30.54 15.0 139.47 149.16

    0.95 23.81 121.96 36.25 85.71 197.88 24.57 10.0 210.56 209.79

    1.00 25.06 128.06 36.25 91.81 197.88 22.93 10.0 210.56 209.79

    Estr#= 4

    db= 1.27 cm

    an= 1.27 cm2#ramas= 2

    300.00

    CORTANTE

    200.00

    100.000.00

    100.00

    200.00

    300.00

    300.00

    200.00

    0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00

    Vu Vc+Vs

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    REFUERZOPORCORTANTEHORIZONTAL

    s= 60.96 cm Separacinmaxima4t24in

    Superficilimpia,rugosayconrefuerzominimodeestribos

    0.00 0.00 197.88 1,071.27 24.61 128.06 3.46 1,071.27 1.84 ok

    0.05 1.25 197.88 1,071.27 24.61 121.96 3.30 1,071.27 1.84 ok

    0.10 2.51 196.60 1,064.35 24.61 104.51 2.84 1,064.35 2.76 faltaest

    d 350bvd f VuX/L X(m) fVu Vnh>

    Vu Amin

    0.15 3.76 195.70 1,059.47 24.61 92.94 2.54 1,059.47 2.76 faltaest

    0.20 5.01 195.24 1,056.99 24.61 81.80 2.24 1,056.99 2.76 faltaest

    0.25 6.27 194.22 1,051.43 24.61 71.28 1.96 1,051.43 3.68 faltaest

    0.30 7.52 193.27 1,046.33 24.61 60.92 1.69 1,046.33 3.68 faltaest

    0.35 8.77 193.27 1,046.33 24.61 50.53 1.40 1,046.33 3.68 faltaest

    0.40 10.02 193.27 1,046.33 24.61 40.36 1.12 1,046.33 4.60 faltaest0.45 11.28 193.27 1,046.33 24.61 31.30 0.87 1,046.33 4.60 a taest

    0.50 12.53 193.27 1,046.33 24.61 25.20 0.70 1,046.33 4.60 faltaest

    0.55 13.78 193.27 1,046.33 24.61 31.30 0.87 1,046.33 4.60 faltaest

    0.60 15.04 193.27 1,046.33 24.61 40.36 1.12 1,046.33 4.60 faltaest

    0.65 16.29 193.27 1,046.33 24.61 50.53 1.40 1,046.33 3.68 faltaest

    0.70 17.54 193.27 1,046.33 24.61 60.92 1.69 1,046.33 3.68 faltaest

    0.75 18.80 194.22 1,051.43 24.61 71.28 1.96 1,051.43 3.68 faltaest

    0.80 20.05 195.24 1,056.99 24.61 81.80 2.24 1,056.99 2.76 faltaest

    0.85 21.30 195.70 1,059.47 24.61 92.94 2.54 1,059.47 2.76 faltaest

    0.90 22.55 196.60 1,064.35 24.61 104.51 2.84 1,064.35 2.76 faltaest

    0.95 23.81 197.88 1,071.27 24.61 121.96 3.30 1,071.27 1.84 ok1.00 25.06 197.88 1,071.27 24.61 128.06 3.46 1,071.27 1.84 ok

    Tomandoencuantaquelasvarillasdelastrabesenlasaletastambienquedaransalidaspara

    ormaramarreslascualesseran#4@30

    Estr#= 4estriboenaletasdetrabe

    #ramas= 2

    db = 1.27 cm.

    an= 1.27cm2

    5.07 cm2

    OKAreadeacero=

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    CALCULODEDEFLEXIONESALCENTRODELCLARO

    w(t/m) (cm)

    Pp 1.68 1.06

    osa 1.06 0.63

    GyB 0.52 0.31280,000.00

    E(kg/cm2)

    265,631.32

    280,000.00

    pav 0.49 0.29

    PERM= 10.94 cm L/240+0.5

    CV= 0.77 cm DatoobtenidodelmodeloSAP2000

    CV+i= 0.956 cm

    280,000.00

    TOTAL= 3.261 cm

    Calculodecontraflecha

    CONTRAF= 1.49

    FINAL= 1.77 cm OK