VIGA30

DISEÑO DE VIGA POSTENSADA

1. DATOS

Longitud de cálculo de la viga = 30 m

1.1 MATERIALES

Hormigón: fci V = 35 MPa

fc V = 35 MPa

fc L = 21 MPa

EciV = 28249.5 MPa

EcV = 28249.5 MPa

EcL = 21882.0 MPa

Acero : fy = 420 MPa

Acero Pº : Tipo : FREYSSNET - Torones de 1/2" (7 alambres )

Tesado de 2 lados

Ea = 199948 MPa

F's = 18.654 T

An = 0.987 cm2

f's = 18.89969605 T /cm2

φ vaina = 6.4 cm

µ = 0.25 1/rad

k = 0.0000492 rad/cm

h = 0.6 cm

Homogeneizando: n1 = Ea/EcV = 7.08

n2 = EcL/EcV = 0.77

1.2 GEOMETRIA DE LA SUPERESTRUCTURA

# Vigas = 2

TABLERO: Lt = 30.7 m

AL = 4 m

Aa = 0.7 m

AT = 5.4 m

Ab = 0.15 m

eL = 0.2 m

eR = 0 m

Hb = 0.25 m

eA = 0.15 m

Voladizo = 1.3 m

DIAFRAGMA: ed = 0.2 T/m

#d = 4

BARANDA: Pb = 0.14 T/m

VIGA: L ejes = 30 m

L borde = 0.3 m

L Total = 30.6 m

Sv = 2.8 m

Lv1 = 1.25 m

Lv2 = 0.35

HT = 1.65 m

Bt = 0.6 m

Tt = 0.12 m

Hct = 0.12 m

Hcb = 0.15 m

Tb = 0.15 m

Bb = 0.6 m

Tw = 0.18 m

Hw = 1.11 m

1.3 PESO SUPERESTRUCTURA

Pv = 75.31 T Peso de todas las vigas

Pde = 3.17 T Peso diafragmas exteriores

Pdi = 3.67 T Peso diafragmas interiores

Pt = 68.89 T Peso tablero

Pac = 15.47 T Peso aceras

Pb = 8.60 T Peso barandas

Prod = 0.00 T Peso capa de rodadura

1.4 DETERMINACION DEL NUMERO DE CABLES

TORONES: Tipo : FREYSSNET - Torones de 1/2" (7 alambres )

f's = 18.90 T /cm2

0.7*f's = 13.23 T /cm2

adm f's = 0.7 * f's

adm f's = 13.23 T /cm2

fy* = 0.9 * F's

fy* = 16.79 T

CABLES: Nº torones = 12

F's = 223.85 T

F80= 179.08 T

F = 0.7 * F80

F = 125.35 T

Lborde

HCb

HCt

Tt

Hw

Tb

Lv2Lv1

LejesLtotaljes

HCb

HCtTt

Tt

Hw

Tb

Bt

Bb

Tw HT

ESTADO 1 : A = 0.4574 m2

I = 0.1508 m4

yb = 0.82 mwb = 0.1850 m3

M1 = 262.96 T mfb1 = 1421.4 T/m2

ESTADO 2 : I = 0.3760 m4

yb = 1.21 m

wb = 0.3099 m3

M2 = 45.13 T m

fb2 = 145.62 T/m2

ESTADO 3 : M3 = 169.17 T m

fb3 = 545.9 T/m2

TOTAL : fb = 2112.91 T/m2

e = 0.65 m

PoT = 370.70 T

A nec = PoT / adm f´s

A nec = 28.02 cm2

Nº torones = A nec / An

Nº torones = 28.4

Nº cables 12 = 2.4

1.5 CABLES

Cable o # torones Area torón Area cable Area vaina I vaina ηηPo Tesado

Vaina Nº (m2) (m2) (m2) (m4) Adop. (T) Fase Nº

1 10 0.0000987 0.000987 0.003216991 8.24E-07 94.000 1

2 10 0.0000987 0.000987 0.003216991 8.24E-07 94.000 1

3 12 0.0000987 0.0011844 0.003216991 8.24E-07 113.500 1

4 0 0 0 0 0.00E+00 0.000 0

5 0 0 0 0 0.00E+00 0.000 0

ΣΣ 32 0.0002961 0.0031584 0.009651 2.47E-06 301.50

Cable h d L/2 - s s

(m) (m) (m) (m)1 0.40 0.07 0.15 15.152 0.80 0.07 0.15 15.153 1.20 0.13 0.15 15.154 0.00 0.00 0.00 0.005 0.00 0.00 0.00 0.00

S

L/2

h

d

1.6 PUNTOS CRITICOS

PUNTO : Apoyo C B A B' C' ApoyoX 0.30 5.30 10.30 15.30 20.30 25.30 30.30

2. PROPIEDADES GEOMETRICAS VIGA 30 [m]

2.1. DIMENSIONES VIGA - SECCION CENTRAL

AL = 2.580 m

HT = 1.650 m

Bt = 0.600 m

Tt = 0.120 m

Hct = 0.120 m

Hcb = 0.150 m

Tb = 0.150 m

Bb = 0.600 m

Tw = 0.180 m

yc = 0.093 m

CALCULO DE LAS PROPIEDADES GEOMETRICAS

SECCION VIGA LLENA

Seccion Area "A" y A*y A*y2 Io

alma 0.2970 0.8250 0.2450 0.2021 6.74E-02

ala sup 0.0504 1.5900 0.0801 0.1274 6.05E-05

chanfle sup 0.0252 1.4900 0.0375 0.0559 2.02E-05

chanfle inf 0.0315 0.2000 0.0063 0.0013 3.94E-05

ala inf 0.0630 0.0750 0.0047 0.0004 1.18E-04

Total 0.4671 4.1800 0.3737 0.3871 0.0676

A [m2] = 0.4671yi [m] = 0.8001 wi [m

3] =0.1946ys [m] = 0.8499 ws [m

3] =0.1832

I [m4] = 0.1557

SECCION VIGA HUECA


vainas 0.0097 0.0929 0.0009 0.0001 2.47E-06

Total 0.4574 4.0871 0.3728 0.3870 0.0676

A [m2] = 0.4574yi [m] = 0.8150 wi [m

3] =0.1850ys [m] = 0.8350 ws [m

3] =0.1806

I [m4] = 0.1508

c.g.

HL

HCb

HC t

Tt

Hw

Tb

Bt

Bb

Yg

TwHT

LOSA

AL

yc

SECCION VIGA HOMOGENIZADA


Viga llena 0.4671 0.8001 0.3737 0.2990 0.1557

Cables 0.0192 0.0929 0.0018 0.0002 0.0000

Total 0.4863 0.8930 0.3755 0.2992 0.1557

A [m2] = 0.4863yi [m] = 0.7722 wi [m

3] =0.2136ys [m] = 0.8778 ws [m

3] =0.1879

I [m4] = 0.1649

SECCION VIGA T COMPUESTA

Seccion Area y A*y A*y2 Io

Viga Homog. 0.4863 0.7722 0.3755 0.2900 0.1649

Losa 0.3997 1.7500 0.6995 1.2241 0.0013

Total 0.8860 2.5222 1.0750 1.5140 0.1663

A [m2] = 0.8860yi [m] = 1.2133 wi [m

3] =0.3099ys [m] = 0.6367 ws [m

3] =0.5906

I [m4] = 0.3760

RESUMEN "PROPIEDADES GEOMETRICAS"

Viga Hueca Viga HomogViga T comp.

A [m2] 0.4574 0.4863 0.8860

yi [m] 0.8150 0.7722 1.2133

ys [m] 0.8350 0.8778 0.6367

I [m4] 0.1508 0.1649 0.3760

wi [m3] 0.1850 0.2136 0.3099

ws [m3] 0.1806 0.1879 0.5906

ws viga [m3] 0.8611

3. SOLICITACIONES (Sobre 1 viga)

PUNTO : Apoyo C B A B' C' ApoyoX 0.30 5.3 10.3 15.3 20.3 25.3 30.3

3.1 VIGA

d1= 1.125 md2= 27.75 mq1= 2.376 T/mq2= 1.121 T/mR = 18.23 T

SECCION : Apoyo C B A B' C' ApoyoX (m) 0.30 5.30 10.30 15.30 20.30 25.30 30.30

M (Tm) 0.00 70.86 112.90 126.91 112.90 70.86 0.00Q (T) 18.23 11.21 5.61 0.00 -5.61 -11.21 -18.23

3.2 LOSA

q= 1.15 T/mR = 17.22 T


M (Tm) 0.00 71.76 114.82 129.17 114.82 71.76 0.00Q (T) 17.22 11.48 5.74 0.00 -5.74 -11.48 -17.22

3.3 DIAFRAGMAS

q= 0.06 T/mR = 0.92 T


M (Tm) 0.00 3.82 6.12 6.88 6.12 3.82 0.00Q (T) 0.92 0.61 0.31 0.00 -0.31 -0.61 -0.92

d1

q2 q1 q1

d1 d2

L

q

L

3.4 ACERAS

q= 0.26 T/mR = 3.87 T


M (Tm) 0.00 16.12 25.79 29.01 25.79 16.12 0.00Q (T) 3.87 2.58 1.29 0.00 -1.29 -2.58 -3.87

3.5 CAPA DE RODADURA Y BARANDAS

q= 0.14 T/mR = 2.15 T


M (Tm) 0.00 8.95 14.33 16.12 14.33 8.95 0.00Q (T) 2.15 1.43 0.72 0.00 -0.72 -1.43 -2.15

3.6 CARGA VIVA

CAMION TIPO: HS20-44

Fm = 0% Factor de Mayoración del camión tipo escogido

VIGA EXTERNA (Camión)SECCION : Apoyo C B A B' C' Apoyo

X (m) 0.30 5.30 10.30 15.30 20.30 25.30 30.30M (Tm) 0.00 97.92 154.31 169.17 154.31 97.92 0.00

Q (T) 24.25 19.78 15.32 10.85 -15.32 -19.78 -24.25

VIGA EXTERNA (Carga equivalente)SECCION : Apoyo C B A B' C' Apoyo

X (m) 0.30 5.30 10.30 15.30 20.30 25.30 30.30M (Tm) 0.00 76.86 122.98 138.35 122.98 76.86 0.00

Q (T) 21.40 16.44 12.03 8.17 -12.03 -16.44 -21.40

VIGA INTERNA (Camión)SECCION : Apoyo C B A B' C' Apoyo

X (m) 0.30 5.30 10.30 15.30 20.30 25.30 30.30M (Tm) 0.00 95.95 151.20 165.76 151.20 95.95 0.00

Q (T) 20.19 16.41 12.63 8.85 -12.63 -16.41 -20.19

VIGA INTERNA (Carga equivalente)SECCION : Apoyo C B A B' C' Apoyo

X (m) 0.30 5.30 10.30 15.30 20.30 25.30 30.30M (Tm) 0.00 75.31 120.50 135.57 120.50 75.31 0.00

Q (T) 20.97 16.11 11.78 8.00 -11.78 -16.11 -20.97

ENVOLVENTE:


M (Tm) 0.00 97.92 154.31 169.17 154.31 97.92 0.00Q (T) 24.25 19.78 15.32 10.85 -15.32 -19.78 -24.25

RESUMEN DE SOLICITACIONES

Momentos: Unidades en ( T m )

SECCION : Apoyo C B A B' C' ApoyoX (m) 0.30 5.30 10.30 15.30 20.30 25.30 30.30Viga 0.00 70.86 112.90 126.91 112.90 70.86 0.00Losa 0.00 71.76 114.82 129.17 114.82 71.76 0.00

Diafragmas 0.00 3.82 6.12 6.88 6.12 3.82 0.00Aceras 0.00 16.12 25.79 29.01 25.79 16.12 0.00

C.rod+bar. 0.00 8.95 14.33 16.12 14.33 8.95 0.00Carga viva 0.00 97.92 154.31 169.17 154.31 97.92 0.00

Cortantes: Unidades en ( T )

SECCION : Apoyo C B A B' C' ApoyoX (m) 0.30 5.30 10.30 15.30 20.30 25.30 30.30Viga 18.23 11.21 5.61 0.00 -5.61 -11.21 -18.23Losa 17.22 11.48 5.74 0.00 -5.74 -11.48 -17.22

Diafragmas 0.92 0.61 0.31 0.00 -0.31 -0.61 -0.92Aceras 3.87 2.58 1.29 0.00 -1.29 -2.58 -3.87

C.rod+bar. 2.15 1.43 0.72 0.00 -0.72 -1.43 -2.15Carga viva 24.25 19.78 15.32 10.85 -15.32 -19.78 -24.25

4. TRAYECTORIA DE LOS CABLES

Extremo X1 X2 C B A B' C' X2' X1' Extremo

X 0.15 0.30 0.30 5.3 10.3 15.3 20.3 25.3 30.30 30.30 30.45

YCABLE 1 0.400 0.393 0.393 0.214 0.106 0.070 0.106 0.214 0.393 0.393 0.400YCABLE 2 0.800 0.786 0.786 0.388 0.150 0.070 0.150 0.388 0.786 0.786 0.800YCABLE 3 1.200 1.179 1.179 0.597 0.247 0.131 0.247 0.597 1.179 1.179 1.200YCABLE 4 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000YCABLE 5 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Yg 1º fase 0.825 0.811 0.811 0.412 0.173 0.093 0.173 0.412 0.811 0.811 0.825Yg 2º fase 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Yg promedio 0.825 0.811 0.811 0.412 0.173 0.093 0.173 0.412 0.811 0.811 0.825

5. PERDIDAS

Cable o fo fmi tf X th fo' fmax c fmp Vaina Nº (Kg/cm2) (Kg/cm2) (Kg/cm2) (m) (Kg/cm2) (Kg/cm2) (Kg/cm2) (Kg/cm2) (Kg/cm2)

1 12460.27 11439.81 1020.46 13.35 1797.86 10662.41 11561.34 1916.00 9523.812 12626.16 11439.81 1186.35 12.38 1938.49 10687.67 11656.91 1916.00 9523.813 12833.86 11498.91 1334.95 11.67 2056.32 10777.54 11805.70 1916.00 9582.914 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.005 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

c = Pérdidas diferidas

DIAGRAMA DE CAIDAS DE TENSION

0.0000.2000.4000.6000.8001.0001.2001.4001.600

0 5 10 15 20 25 30

Cable 1 Cable 2 Cable 3 Cable 4 Cable 5

CABLE 1

8000.0008500.0009000.0009500.000

10000.00010500.00011000.00011500.00012000.00012500.00013000.000

0.00 5.00 10.00 15.00 20.00 25.00 30.00

6. TENSIONES Y FUERZAS EN LOS CABLES DESPUES DE LAS PERDIDAS

6.1 ESFUERZOS INICIALES (Kg/cm2)

CABLE X (m)Inicio 5.30 10.30 15.30 20.30 25.30 Final

1 12460.3 12113.4 11776.6 11439.8 11776.6 12113.4 12460.32 12626.2 12222.9 11831.3 11439.8 11831.3 12222.9 12626.23 12833.9 12380.1 11939.5 11498.9 11939.5 12380.1 12833.94 0.0 0.0 0.0 0.0 0.0 0.0 0.05 0.0 0.0 0.0 0.0 0.0 0.0 0.0

6.2 FUERZAS INICIALES (Kg)

6.2.1 TESADO 1a FASE

CABLE X (m) Fuerza deInicio 5.30 10.30 15.30 20.30 25.30 Final Cable Tesado

1 122982.9 119559.1 116235.0 112910.9 116235.0 119559.1 122982.9 122982.862 124620.2 120639.8 116775.4 112910.9 116775.4 120639.8 124620.2 124620.213 152004.2 146629.5 141411.3 136193.1 141411.3 146629.5 152004.2 152004.214 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.005 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.00

ΣΣ Fuerzas 386828.4 374421.7 362014.9 374421.7 386828.4

CABLE 2

8000.000

9000.000

10000.000

11000.000

12000.000

13000.000

0.00 5.00 10.00 15.00 20.00 25.00 30.00

CABLE 3

8000.000

9000.000

10000.000

11000.000

12000.000

13000.000

14000.000

0.00 5.00 10.00 15.00 20.00 25.00 30.00


CABLE X (m) Fuerza deInicio 5.30 10.30 15.30 20.30 25.30 Final Tesado

1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.02 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.03 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.04 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.05 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

ΣΣ Fuerzas 0.0 0.0 0.0 0.0 0.0

6.2.3 TESADO 1a FASE + TESADO 2a FASE

CABLE X (m)5.3 10.3 15.3 20.3 25.3

ΣΣ Fuerzas 386828.4 374421.7 362014.9 374421.7 386828.4

6.3 ESFUERZOS FINALES (Kg/cm2)


1 8746.4 9093.3 9430.1 9523.8 9430.1 9093.3 8746.42 8771.7 9174.9 9566.5 9523.8 9566.5 9174.9 8771.73 8861.5 9315.3 9755.9 9582.9 9755.9 9315.3 8861.54 0.0 0.0 0.0 0.0 0.0 0.0 0.05 0.0 0.0 0.0 0.0 0.0 0.0 0.0

6.4 FUERZAS FINALES (Kg)



1 86327.1 89750.9 93074.9 94000.0 93074.9 89750.9 86327.12 86576.4 90556.7 94421.2 94000.0 94421.2 90556.7 86576.43 104956.1 110330.8 115549.0 113500.0 115549.0 110330.8 104956.14 0.0 0.0 0.0 0.0 0.0 0.0 0.05 0.0 0.0 0.0 0.0 0.0 0.0 0.0

ΣΣ Fuerzas 290638.4 303045.1 301500.0 303045.1 290638.4



1 0.0 0.0 0.0 0.0 0.0 0.0 0.02 0.0 0.0 0.0 0.0 0.0 0.0 0.03 0.0 0.0 0.0 0.0 0.0 0.0 0.04 0.0 0.0 0.0 0.0 0.0 0.0 0.05 0.0 0.0 0.0 0.0 0.0 0.0 0.0

ΣΣ Fuerzas 0.0 0.0 0.0 0.0 0.0

6.4.3 TESADO 1a FASE + TESADO 2a FASE

CABLE X (m)5.30 10.30 15.30 20.30 25.30

ΣΣ Fuerzas 290638.4 303045.1 301500.0 303045.1 290638.4

7.1 SECCION A-A

A). ETAPA 1

σsV = 79.14 kg/cm2 σsV = -144.77 kg/cm2 σsV = 70.28 kg/cm2 σsV = 4.64 kg/cm2

σiV = 79.14 kg/cm2 σiV = 141.32 kg/cm2 σiV = -68.60 kg/cm2 σiV = 151.85 kg/cm2

B). ETAPA 2



C). ETAPA 3

σsV = 15.62 kg/cm2 σsV = 75.34 kg/cm2 σsV = 90.96 kg/cm2

σiV = 115.00 kg/cm2 σiV = -73.54 kg/cm2 σiV = 41.46 kg/cm2

σs LV = 0.00 kg/cm2 σs LV = 36.29 kg/cm2 σs L = 28.11 kg/cm2

σsV = 90.96 kg/cm2

σi LV = 0.00 kg/cm2 σi LV = 24.89 kg/cm2 σi L = 19.28 kg/cm2


σiV = 41.46 kg/cm2 σiV = 0.00 kg/cm2 σiV = -69.15 kg/cm2 σiV = -27.69 kg/cm2

Máximo esfuerzo de compresión por: Preesfuerzo efectivo+CM

f a = 90.96 kg/cm2 < 140.00 kg/cm2

Máximo esfuerzo de compresión por : CV+1/2*(Preesfuerzo efectivo+CM)

f b = 70.37 kg/cm2 < 140.00 kg/cm2

+ + =

+ + =

+

=

=

+ +

7.2 SECCION B-B

A). ETAPA 1



B). ETAPA 2



C). ETAPA 3




σsV = 87.93 kg/cm2



σiV = 45.08 kg/cm2 σiV = 0.00 kg/cm2 σiV = -62.74 kg/cm2 σiV = -17.65 kg/cm2


f a = 90.96 kg/cm2 < 140.00 kg/cm2


f b = 70.37 kg/cm2 < 140.00 kg/cm2

+ + =

+ + =

+ = +

=+ +

7.2 SECCION C-C

A). ETAPA 1



B). ETAPA 2



C). ETAPA 3




σsV = 79.74 kg/cm2





f a = 79.74 kg/cm2 < 140.00 kg/cm2


f b = 54.15 kg/cm2 < 140.00 kg/cm2

+ + =

+ + =

+ =

=+ +

8. ESFUERZOS DE CORTE

Md = 14644330.44 Kg cmVd = 23303.86 Kg

V CL = 10852.1 KgV Apoyo = 24246.0 Kg

Vi = 48160.2 KgMmax = 36760415.9 Kg cm

fpc = 107.97 Kg/cm2fd = 47.25 Kg/cm2

Mcr = Wi * (1.575 * fc^0.5 + fpc - fd )Mcr = 27947013.4 Kg cmVci = 0.16 * fc^0.5 * b' * d + Vd + Vi * Mcr / Mmax = 67891.8 Kg

Vci min = 0.45 * fc^0.5 * b' * d = 22427.5 KgVci = 67891.8 Kg fpe = P∞ / Afpe = 32.80 Kg/cm2Vp = P∞ * sin αVp = 18561.5 Kg

Vcw = ( 0.919 * fc^0.5 + 0.3 * fpe ) * b' * d + VpVcw = 90580.3 Kg

Vc = 67891.8 KgVu = 78455.2 Kg

Vs calc = Vu / φ - VcVs calc = 24408.5 KgVs max = 2.12 * fc^0.5 * b*dVs max = 105658 Kg

Vs = 24408.5 Kgφ estribo = 12 mm

Av = 1.131 cm2s calc = 2*Av*fy*d / Vss calc = 58 cm

K = φ*(1.06*fc^0.5)*b*dK = 52829 Kgs = 58 cm

Separación colocada en L/4 : s= 20 cmSeparación colocada en L/2 : s= 35 cm

9. SEGURIDAD A LA ROTURA

As* = 31.58 cm2γ = 0.28

β1 = 0.28

Mu = 76778085 Kg cm

Acero Pasivo:

φφ (mm) Nº barras yb (cm) Area (cm2)16 4 4 15.900 0 0 0.000 0 0 0.000 0 0 0.000 0 0 0.000 0 0 0.000 0 0 0.00

As = 15.90

SECCION RECTANGULAR

ρ* = As* / (b*d)ρ* = 0.00090ρ = As / (b*da)ρ = 0.00044

Acero de Pº + acero pasivo :

fsu* =fs' * ( 1 - (γ / β1) * (ρ* * fs'/fc + (da /d )*(ρ * fy / fc)fsu* = 18542 Kg/cm2

Y = ( As* * fsu* + As * fy ) / (0.85 * b * fc)Y = 10.99 cm OK

φMn =φ*{As* * fsu* *d*[ 1-0.6*(ρ* * fsu* /fc+da/d*ρ * fy/fc)] + As *fy*da*[1-0.6*(d/da*ρ* *fsu* /fc + ρ * fy/fc)] }φφMn = 100204062 Kg cm > Mu OK!

10. ALARGAMIENTO DE LOS CABLES

Cable Lcable f ∆∆T

(m) (Kg/cm2) (cm)1 30.31 11439.81 17.342 30.35 11439.81 17.363 30.40 11498.91 17.484 0.00 0.00 0.005 0.00 0.00 0.00

VIGA30

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