diseño puente viga

PUENTE LOSA

SECCION TRANSVERSAL

INGRESO DE DATOSLONGITUD TOTAL DEL PUENTE = 9.48 mLUZ DEL PUENTE = 9 mAncho de la via = 7.2 7.20Ancho de bermas = 0.6 0.60ANCHO DE LA VIA + BERMAS = 8.4 m 8.40ANCHO TOTAL DEL PUENTE = 9 mNUMERO DE VIAS = 2 ViasANGULO DE ESVIAM = 90 SOBRECARGA PEATONAL = 0.51 T/m2f'c (Losa) = 280 Kg/cm2Fy (Acero corrugado) = 4200 Kg/cm2VEHICULO = HL-93

BARRERA (SI / NO) NO 0 m 0.00BASE BARRERA = 0.3 0.30VEREDA LIBRE NO 0 m 0.00ANCHO VEREDA = 1.2 m 1.20ALTURA VEREDA = 0.2 mALTURA DE BARANDA = 0.9ANCHO ADICIONAL POR BARANDA= 0 m 0.00VIGA PERIMETRAL 0.3 m 0.30ANCHO VIGA = 0.3 m 0.30ALTURA VIGA SOBRE LOSA = 0.3 m

CARPETA ASFALTICA = 0.05 mBOMBEO = 2 %

CONTROLES ACERO FRANJA INTERIORFRANJA INTERIOR E = 3.07 m Elegir diametro para acero principal

PERALTE = 0.480 m As princPeralte Asumido = 0.48 m Elegir diametro para acero distribucionAcero maximo 0.20 15.51 OK Elegir diametro para acero temperaturaFisuracion 2111.75 < 2520 OK As temp

FRANJA DE BORDE E borde = 1.37 m MOM DISEO =Acero maximo 0.19 15.51 OK Igual diametros que la franja interiorFisuracion 2451.28 < 2520 OK As princ

As distrFATIGA 1392.52 > 487.3504 OK As temp

MOM DISEO =

BARRERA

ANCHO SUPERIOR = 0.15 m 0.15ANCHO INFERIOR = 0.3 m 0.30ANCHO INTERMEDIO = 0.025 m 0.03ANCHO DERECHO = 0.125 m A3 0.13ALTURA TOTAL = 0.85 mALTURA INFERIOR = 0.13 mALTURA MEDIA = 0.25 m A5ALTURA SUPERIOR = 0.47 mf'c = 280 A4Fy = 4200 A2

A1

AREAA1 0 0.13 = 0.000A2 0 0.25 0.5 = 0.000A3 0 0.47 = 0.000A4 0 0.25 = 0.000A5 0 0.47 0.5 = 0.000

0.0001.2 (S + 3000)

30

PESO = 0 2.4 = 0.00 T/m0.00 Kg/m

BARRERA = 0 T

SOLUCIONA) PREDIMENSIONAMIENTO

t min = S = Longitud del puente en mm

t min = 1.2 ( 9000 + 3000 )30

t = 0.48 =

B) DISEO DE LA FRANJA INTERIOR

B.1) MOMENTOS DE FLEXION POR CARGASCARGA MUERTA (DC)Wpp = 0.48 m X 1.00 m X 2.4 t/m3 =

Mdc = Wpp L2 = 1.15 X 81 =8 8

CARGA POR SUPERFICIE DE RODADURA (DW)

W asf2" = 0.05 X 2250 = 112.5 Kg/m

Mdw = Wpp L2 = 0.113 X 81 =8 8

CARGA VIVA (LL)a) camion de diseo (HL-93)

caso 114.8

A

Ra= 7.4 T luz = 94.5 m

Mmax = 14.8 x 9 = 0 T-m4

caso 2

14.8 T

3.425 2.15

1.075A

Ra= 11.264444444 T luz = 94.5 m

Mmax = 3.425 x 11.264444 = 38.58072 T-m1.275 x 18.335556 = 23.37783 T-m

38.58072caso 3posicion de la resultante

33.2 X = 14.8 x 4.3 + 3.6X = 94.6 = 2.849398 m.

33.2

R= 33.2 T

14.8 T 14.8

X= 2.85 1.450.925 4.3

0.73A

Ra= 19.275555556 T luz = 94.5 m

Mmax = 5.23 x 19.275556 - 4.30 x19.28 x 0.92513.92 x -0.53

caso 1 0caso 2 38.5807222222caso 3 0

Momento Maximo def = 38.580722 T-mpor camion de diseo

b) Tandem de diseocaso 1 R=

11.2 T

4.2 0.6

0.3A

Ra= 10.45 T luz = 94.5 m

Mmax = 4.2 x 10.453333 = 43.904 T-mMmax = 3.6 x 11.946667 = 43.008 T-mMmax = 43.904 T-mcaso 2

11.2

A

Ra= 5.6 T luz = 94.5 m

Mmax = 11.2 x 9 = 0 T-m4

caso 1 43.904caso 2 0

Momento Maximo def = 43.904 T-m

por tandem de diseo

c) Carga de Carril

0.96 T/mA

Ra= 4.32 T luz = 9

Mmax = 0.96 x 9 ^2 =8

CAMION DE DISEO 38.580722 T-mTANDEM DE DISEO 43.904 T-mCARGA DE CARRIL 9.72 T-m

Mmax(ll+im) = 43.904 x 1.33 + 9.72

distruibuido en un ancho de faja critico E

Caso de 2 carriles cargados

E = 2100 + 0.12 L1 W1

DW 1.14 1.5 1 0LL + IM 26.66 1.75 1 0.75

RESISTENCIA 1 U= 1.25 DC + 1.50 DW + 1.75 (LL+IM)SERVICIO 1 U= 1.00 DC + 1.00 DW + 1.00 (LL+IM)FATIGA U= 0.75 (LL+IM)

D) ESTADO LIMITE DE RESISTENCIA 1

CALCULO DE ACERO PRINCIPAL

PARA EL DISEO POR ESTADO DE RESISTENCIA 1, con n=1

Mu = n ( 1.25 Mdc + 1.50 Mdw + 1.75 Mll+im)

Mu = 1.25 x 11.664 + 1.5 xMu = 62.94 T-m

VALOR DE nn1 = Factor de ductilidad = 1 componentes y conexiones son ductilesn2 = Factor de redundancia = 1 es no redundanten3 = Factor de opertividad = 1 es de importancia operativan = 1.00 Mu = 62.94 T-m

As PRINCIPAL PARARELO AL TRAFICO

Numero del diametro a usar = 8Recub. = 3 cm

= 1"Area = 5.1Diametro= 2.54

z = 3.00 + 2.54 = 4.27 cm2

d = 48 cm - 4.27 cm =

Fy = 4200 Kg/cm2f'c = 280 Kg/cm2d = 43.73 cmb = 1.00 mMu = 62.94 T-m

1 = 0.850

As = Mu = 41.562 cm20.9 Fy (d-a/2)

7.334a = As Fy = 7.334 cm

1 f'c b

As principal total

As = 41.562 cm2

Usando varilla de 1" , la separacion sera =

USAR 1 1" @ 0.12 m

As MAXIMOUna seccion no sobre reforzada cumple con = c/d

Menor valor = 15.512016042 T-m la cantidad de acero calculadaMu = 62.94 T-m > 15.51202 T-m OK

As de distribucion =Numero del diametro a usar = 5

= 5/8"Area = 2Diametro= 1.59

% = 1750 = 1750 = 18.44662 %

e) ESTADO LIMITE DE SERVICIO

PARA EL DISEO CON ESTADO LIMITE DE SERVICIO 1 CON n = 1

Ms = n ( 1.00 Mdc + 1.00 Mdw + 1.00 Mll+im)

Mu = 1 x 11.664 + 1 xMu = 35.02 T-m

CONTROL DE LA FISURACION MEDIANTE DISTRIBUCION DE ARMADURA

Esfuerzo maximo del acero

f sa = Z

siendoMs = 35.02 t-m/m x 0.120 m = 4.202228Es = 200000 Mpa= 2039400 Kg/cm2Ec = 15344 280 = 256754 Kg/cm2

n = Es = 7.9430045Ec

0

0.5

0

0.5

0

0.75

0

0.75

0

2

3

12 cm

yEN

43.73 48.00c

4.27

1 1" @ 0.12 m

Area de acero transformada

Ast = n x As =7.943004516 x 5.1 = 40.50932 cm2

Momentos respecto al eje neutro para determinar y

12 y (y/2) = 40.509323032 ( 43.73 - y)6 y^2 + 40.509323032 y - 1771.473 =

y = -40.50932303 + 1641.005 + 42515.3412

y = 14.135400059

y = -20.8869539

Entonces y = 14.135400059

Inercia respecto al eje neutro de la seccion tranformada

I = Ast (ds - y)^2 + by^3/3

I = 46777.25032845 cm4

Luego

fs = Ms c n = 4.2022279 x 100000 xI 46777.25

= 2111.7485 Kg/cm2 < 2520

0

0.5

0

0.5

0

0.75

0

0.75

0

2

3

C) DISEO DE LA FRANJA DE BORDE

C.1) Ancho de franja para bordes longitudinales de losaSegn el Art. 4.6.2.1.4b, el ancho efectivo Eborde en bordes longitudinales setoma como la sumatoria de la distancia entre el borde del tablero y la carainterna de la barrera, mas 0.30m, mas la mitad del ancho de faja E yaespecificado. Eborde no deber ser mayor que E, ni 1.80m.

ANCHO DE BARRERA / VEREDA / VIGA /BARRERA + VEREDA = 0.30ANCHO LIBRE ENTRE LLANTA Y MAS CERCANO = 0.30ANCHO ESTNDAR DE VIA = 3.00ANCHO DE CAMION O TANDEM = 1.80

Con E = 3.07 m E hallado para la franja interior

E borde = 0.30 + 0.3 + 0.766495

E borde = 1.37 m

M ll+im = 32.66296 = 23.84 t-m 1.37

c) RESUMEN DE MOMENTOS FLECTORES Y CRITERIOS LRFD APLICABLES

CARGA M (+) T-mResist 1 Serv 1 Fatiga

DC 14.368927007 1.25 1 0DW 0.89 1.5 1 0LL + IM 23.84 1.75 1 0.75

RESISTENCIA 1 U= 1.25 DC + 1.50 DW + 1.75 (LL+IM)SERVICIO 1 U= 1.00 DC + 1.00 DW + 1.00 (LL+IM)FATIGA U= 0.75 (LL+IM)




Mu = n ( 1.25 Mdc + 1.50 Mdw + 1.75 Mll+im)

Mu = 1.25 x 14.368927 + 1.5 xMu = 61.02 T-m

As PRINCIPAL PARARELO AL TRAFICO

z = 3.00 + 2.54 = 4.27 cm2

d = 48 cm - 4.27 cm =

Fy = 4200 Kg/cm2f'c = 280 Kg/cm2d = 43.73 cmb = 1.00 mMu = 61.02 T-m1 = 0.850

As = Mu = 40.17 cm20.9 Fy (d-a/2)

7.089

a = As Fy = 7.089 cm1 f'c b

As principal total

As = 40.17 cm2

Usando varilla de 1" , la separacion sera =

USAR 1 1" @ 0.125 m

As MAXIMOUna seccion no sobre reforzada cumple con = c/d 15.51202 T-m OK

As de distribucion =

% = 1750 = 1750 = 18.44662 %

2b = espaciamiento del acero = 0.125 m = 12.5

1

A = = 2 x 4.27 x1

Z = 30000 N/mmZ = 30000 x 1.0197 = 30591 kg/cm

luego

f sa = 30591 Kg/cm =( 4.27 cm x 106.75

f sa

1 1" @ 0.125 m 0


Ast = n x As =7.943004516 x 5.1 = 40.50932 cm2


12.5 y (y/2) = 40.509323032 ( 43.73 - y)6.25 y^2 + 40.509323032 y - 1771.473 =

y = -40.50932303 + 1641.005 + 44286.8212.5

y = 13.903876201

y = -20.38536789


I = Ast (ds - y)^2 + by^3/3

I = 47236.4423 cm4

Luego

fs = Ms c n = 4.8875171 x 100000 xI 47236.44

= 2451.2789 Kg/cm2 < 2520

F ) VERIFICACION POR FATIGA

PARA EL DISEO POR FATIGA, CON n = nd nr n1 =

Mfat = n (0.75 Mll+im)

CARGA DE FATIGA

Se calcula con un camion de diseo, con una separacion constante de 9.00 m entre los ejes de 14.8 t

caso 114.8

A

Ra= 7.4 T luz = 94.5 m

Mmax = 14.8 x 9 = 0 T-m4

caso 2aposicion de la resultante

18.4 X = 3.6 x 4.3X = 15.48 = 0.841304 m.

18.4

R= 18.4

14.8 T

X= 0.844.079

0.42A

Ra= 8.34 T luz = 9

4.5 m

Mmax = 4.08 x 8.340.62 x 10.060

caso 2b

14.8 T

2.25 4.5

2.25A

Ra= 7.4 T luz = 94.5 m

Mmax = 2.25 x 7.4 = 0 T-m-2.25 x 22.2 = 0 T-m

0

caso 3posicion de la resultante

33.2 X = 14.8 x 9 + 3.6X = 181.08 = 5.454217 m.

33.2

R= 33.2 T

14.8 T 14.8

X= 5.45 3.55-2.727 9

1.77A

Ra= 23.14 T luz = 94.5 m

Mmax = 6.27 x 23.14 - 9.00 x23.14 x -2.72710.06 x -1.57

caso 1 0caso 2a 34.0217608696caso 2b 0caso 3 0

Momento Maximo def = 34.021761 T-mpor fatiga

CONSIDERANDO EL ANCHO EFECTIVO PARA UN SOLO CARRIL CARGADO Y IM=(TABLA 3,6,2,1,-,1)

Mfat = 1.00 x 0.75 x 1.15 x

Mfat = 29.34376875 = 8.08 T-m/m 3.63

SECCION FISURADA

SE UTILIZA LA SECCION FISURADA SI LA SUMA DE ESFUERZOS DEBIDO A CARGAS PERMANENTES NO MAYORADAS MAS 1.5 VECES LA CARGA DE FATIGA, DAN POR RESULTADOUNA TENSION DE TRACCION MAYOR QUE 0.25 f'c

ESFUERZO DE TRACCION POR FATIGA MINIMO

f trac = 0.25 f'c = 1.3100347 MPa

f trac = 13.3584243083 Kg/cm2

ESFUERZO DEBIDO A CARGAS PERMANENTES NO MAYORADAS MAS 1.5 VECES LA CARGADE FATIGA

M' fat = 1 x 11.664 + 1 x

M' fat = 24.93 T-m

f fat = Mfat = 24.93 x 100000 =S 38400

Como f fat = 64.91 Kg/cm2 > 13.35842 Kg/cm2

3,- VERIFICACION DE ESFUERZOSEsfuerzo en el refuerzo debido a la carga viva (b = 100 cm)

As = 1 1" @ 0.12 m

5.1 cm2 / 0.12 m =

jd = d - y/3 = 43.73 - 14.1354 SECCION AGRIETADA3

jd = 39.01819998 cm

f ll = Mfat = 8.08 X 100000As (jd) 42.5 X 39.0182

= 487.35035 Kg/cm2

RANGO MAXIMO DE ESFUERZO

El esfuerzo mnimo es el esfuerzo por carga viva mnimo combinado con el esfuerzo por carga permanente.

El momento por carga muerta para una franja interior es:

Mdl = Mdc + Mdw = 11.664 + 1.139063 = 12.80306

El esfuerzo por carga permanente es:

fDL = Mdl / (As (jd)) = 12.8030625 X 100000 = 772.071842.5 X 39.0182

Por ser la losa simplemente apoyada, el esfuerzo por carga viva mnimo es ceroMmin = 0Luego, el esfuerzo mnimo es:

f min = 0 + 772.07183 = 772.0718 kg/cm2

El esfuerzo mximo es el esfuerzo por carga viva mximo combinado con el esfuerzo por cargas permanentes

f max = 487.3503505922 + 772.07183 = 1259.422 kg/cm2

El rango de esfuerzos es ;

f = f max - f min = 487.35035059 kg/cm2

El rango limite es :

f f = 487.35

ACOTAMIENTOSbarrera/vereda/viga per berma

0.30 0.600.00 0.5 0.30 0.50.30 0.5 0.90 0.5

SINO

ACERO FRANJA INTERIOR recub = 3.00 cmElegir diametro para acero principal 8

1 1" @ 0.12 mElegir diametro para acero distribucion 5

1 5/8" @ 0.26 mElegir diametro para acero temperatura 4

1 1/2" @ 0.29 mMOM DISEO = 62.94 T-mACERO FRANJA EXTERIOR 1.37 mIgual diametros que la franja interior

1 1" @ 0.125 m1 5/8" @ 0.265 m1 1/2" @ 0.29 m

MOM DISEO = 61.02 T-m

VEREDA

ANCHO SUPERIOR = 0.00 m 0.00ALTURA TOTAL = 0.2 m

f'c = 280Fy = 4200 A1

AREAA1 0.00 0.2 = 0.000

0.000

PESO = 0 2.4 = 0.00 T/mBARANDA = 0 = 0.00 T/m

0.00 T/m

PESO VEREDA = 0.00 T/mCARGA PEATONAL

0 0.51 = 0 T/m

VEREDA = 0 T/m

= 480 mm

1.15 t/m

11.664 t-m

1.13906 t-m

TBt

m4.5 m

R= 29.6 T

14.8 T

2.15 1.275

Bt

m 18.3355555564.5 m

x 8.6

T 3.6 T

4.3 -0.5253

Bt

m 13.9244444444.5 m

14.80 = 0 T-m= 0 T-m= 0 T-m

22.4 T

11.2 T

0.6 3.6

Bt

m 11.95 T4.5 m

T

Bt

m4.5 m

0.5

0

0.5

0

0.75

0

0.75

0

2

3

Bt

m

9.72 T-m

= 68.11232 T-m

0.5

0

0.5

0

0.75

0

0.75

0

2

3

L1 = longitud de tramo modificada que se toma igual al menor valor entre la longitud real y 18.000 (mm)W1 = ancho modificado entre los bordes del puente (calzada y bermas), que se toma igual al menor valor entre el ancho real y

18.000 mm para carga en mltiples carriles 9000 mm para carga en un solo carril (mm)

1.14 + 1.75 x 26.66 =

componentes y conexiones son ductiles

43.7343.73 cm 48

4.27

41.562 41.562 41.562 41.562 41.56 42

7.33 7.334 7.334 7.334 7.33 77.33 7.334 7.334 7.334 7.334 7

s = 5.1 = 0.12 m41.562

cm

= 15.51201604 T-m

1 Mpa 10.197 kg/cm2

3.30129 Mpa = 33.6632293 kg/cm2

= 38400 cm3

T-m

la cantidad de acero calculada 41.562 cm2 resiste

50 %

= 0.26 m

=

mm x 1000 mm411.886 Mpa

8.81021 cm2

= 0.29 m

1.13906 + 1 x 22.22 =

cm

12 = 102.48 cm2

4029.38 Kg/cm2

0

0.5

0

0.5

0

0.75

0

0.75

0

2

3

T-m

0

0.5

0

0.5

0

0.75

0

0.75

0

2

3

(fs/n)

0

29.59 x 7.9430045

OK

0

0.5

0

0.5

0

0.75

0

0.75

0

2

3

1.15 t/m

T/m

14.3689 t-m

1.37 = 87.864964 Kg/m

0.88963 t-m

0.3 + 0.77 ) = 32.663 T-m3

0.89 + 1.75 x 23.84 =

43.7343.73 cm 48

4.27

40.17 40.17 40.17 40.169 40.168 40

7.09 7.089 7.089 7.088 7.085 7

7.09 7.089 7.089 7.089 7.088 7

s = 5.1 = 0.125 m40.17

cm

= 15.51201604 T-m

1 Mpa 10.197 kg/cm2

3.30129 Mpa = 33.6632293 kg/cm2

= 38400 cm2

T-m

la cantidad de acero calculada 40.17 cm2 reiste

50 %

= 0.265 m

1 1" @ 0.12 m

0.88963 + 1 x 23.84 =

cm

12.5 = 106.75 cm2

3974.92 Kg/cm2

T-m

(fs/n)

029.83 x 7.9430045

OK

1Se calcula con un camion de diseo, con una separacion constante de 9.00 m entre los ejes de 14.8 t

T

Bt

m4.5 m

T

3.6 T

3.460.62

4.3

Bt

m 10.06

4.5 m

= 34.021761 T-m= 6.2437609 T-m

34.021761

R= 29.6 T

14.8 T

4.5 -2.25

Bt

m 22.24.5 m

x 13.3

T 3.6 T

4.3 -1.57

Bt

m 10.064.5 m

14.80 = 0 T-m= 0 T-m= 0 T-m

0

CONSIDERANDO EL ANCHO EFECTIVO PARA UN SOLO CARRIL CARGADO Y IM= 0.15 0.15

34.0218 / E

SE UTILIZA LA SECCION FISURADA SI LA SUMA DE ESFUERZOS DEBIDO A CARGAS PERMANENTES NO MAYORADAS MAS 1.5 VECES LA CARGA DE FATIGA, DAN POR RESULTADO

ESFUERZO DEBIDO A CARGAS PERMANENTES NO MAYORADAS MAS 1.5 VECES LA CARGA

1.13906 + 1.5 x 8.08

64.91 Kg/cm2

SECCION AGRIETADA

42.5 cm2/m

SECCION AGRIETADA

El esfuerzo mnimo es el esfuerzo por carga viva mnimo combinado con el esfuerzo por carga permanente.

T-m

kg/cm2

El esfuerzo mximo es el esfuerzo por carga viva mximo combinado con el esfuerzo por cargas permanentes

x 0.3

OK

pl0,00.3,04.5,0.0848.7,09,09,-0.480,-0.480,0

pl0.3,00.3,0.30.175,0.30.175,1.20.125,1.20.125,0.30,0.30,0

pl puente barrera8.7,0 pl pl pl8.7,0.3 0,0 0,0 0,08.825,0.3 0.3,0 0,0 0,08.825,1.2 4.5,0.084 0,0 0,08.875,1.2 8.7,0 0,0 0,08.875,0.3 9,0 0,0 0,09,0.3 9,-0.48 0,0 0,09,0 0,-0.48 0,0 0,0

0,0pl0,00,0 viga perimetral vereda0,0 pl pl pl pl0,0 0.3,0 8.7,0 0,0 0,00,0 0.3,0.3 8.7,0.3 0,0 0,00,0 0.175,0.3 8.825,0.3 0,0 0,00,0 0.175,1.2 8.825,1.2 0,0 0,0

0.125,1.2 8.875,1.2 0,0 0,0pl 0.125,0.3 8.875,0.3 0,0 0,00,0 0,0.3 9,0.3 0,0 0,00,0 0,0 9,0 0,0 0,00,0 0,0 0,00,00,00,00,0

pl

0.00

0,00,00,00,00,00,00,00,00,0

pl0,00,00,00,00,00,00,00,00,0

pl2.265,-0.416652.265,-0.616652.465,-0.61665

pl4.38,-0.43734.38,-0.6373

pl4.26,-0.43734.26,-0.63734.48,-0.6373

pl4.38,-0.43734.38,-0.63734.155,-0.6373

pl4.255,-0.43734.255,-0.6373

pl0.03,-0.049050.3,-0.049054.5,0.03495

pl2.4,-0.007052.4,0.19295

pl2.18,-0.001252.18,0.192952.5,0.19295

pl0.03,-0.416654.5,-0.41665

C4.5,-0.4373

0.0127c4.38,-0.4373

0.0127c4.26,-0.4373

0.0127c4.14,-0.4373

0.0127c4.02,-0.4373

0.0127c3.9,-0.4373

0.0127c3.78,-0.4373

0.0127c3.66,-0.4373

0.0127c3.54,-0.4373

0.0127c3.42,-0.4373

0.0127c3.3,-0.4373

0.0127c3.18,-0.4373

0.0127

c3.06,-0.4373

0.0127c2.94,-0.4373

0.0127c2.82,-0.4373

0.0127c2.7,-0.4373

0.0127c2.58,-0.4373

0.0127c2.46,-0.4373

0.0127c2.34,-0.4373

0.0127c2.22,-0.4373

0.0127c2.1,-0.4373

0.0127c1.98,-0.4373

0.0127c1.86,-0.4373

0.0127c1.74,-0.4373

0.0127c1.62,-0.4373

0.0127c1.5,-0.4373

0.0127c1.38,-0.4373

0.0127c1.255,-0.4373c

0.0127

1.13,-0.43730.0127

c1.005,-0.4373

0.0127c0.879999999999997,-0.4373

0.0127c0.754999999999997,-0.4373

0.0127c0.629999999999997,-0.4373

0.0127c0.504999999999997,-0.4373

0.0127c0.379999999999997,-0.4373

0.0127c0.254999999999997,-0.4373

0.0127c0.129999999999997,-0.4373

0.0127c0,-0.4373

0.0127c0,0

0.0127c0,0

0.0127c0,0

0.0127c0,0

0.0127c0,0

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0.0127c0,0

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0.0127

c0,0

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0.0127c0,0

0.0127c0,0

0.0127c0,0

0.0127c0,0

0.0127c0,0

0.0127

C4.5,0.04765

0.00635C4.21,0.04185

0.00635C3.92,0.03605

0.00635C3.63,0.03025

0.00635C3.34,0.02445

0.00635C3.05,0.01865

0.00635C2.76,0.01285

0.00635C2.47,0.00705000000000001

0.00635

C2.18,0.00125000000000001

0.00635C1.89,-0.00454999999999999

0.00635C1.6,-0.01035

0.00635C1.31,-0.01615

0.00635C1.02,-0.02195

0.00635C0.73,-0.02775

0.00635C0.44,-0.03355

0.00635C0.15,-0.03935

0.00635C0,0

0.00635C0,0

0.00635C0,0

0.00635C0,0

0.00635C0,0

0.00635C0,0

0.00635C0,0

0.00635C0,0

0.00635C

0,00.00635

C0,0

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0.00635C0,0

0.00635

BARRERA IZQ0000000

VIGA PERIMETRA IZQ0.30.3

0.1750.1750.1250.125

00

acero dist acot acero Temppl pl pl VEREDA IZQ0.03,-0.41665 2.265,-0.41665 0.03,-0.04905 04.5,-0.41665 2.265,-0.61665 0.3,-0.04905 0

2.465,-0.61665 4.5,0.03495 00

acero principal acot pl 0C pl 2.4,-0.00705 04.5,-0.4373 4.38,-0.4373 2.4,0.19295 0

0.0127 4.38,-0.6373 0c pl 04.38,-0.4373 pl 2.18,-0.00125

0.0127 4.26,-0.4373 2.18,0.19295c 4.26,-0.6373 2.5,0.19295 ASFALTO4.26,-0.4373 4.48,-0.6373 0.30

0.0127 4.50c acero Temp ASFALTO 8.704.14,-0.4373 C pl 8.70

0.0127 acot 4.5,0.04765 0.3,0.05 4.50c pl 0.00635 4.5,0.134 0.304.02,-0.4373 4.38,-0.4373 C 8.7,0.05 0.30

0.0127 4.38,-0.6373 4.21,0.04185c 4.155,-0.6373 0.006353.9,-0.4373 C

0.0127 pl 3.92,0.03605c 4.255,-0.4373 0.00635 1 5/8" @ 0.26 m3.78,-0.4373 4.255,-0.6373 C ACERO DISTRIBUCION

0.0127 3.63,0.03025 0.03c 0.00635 4.50

0.00

3.66,-0.4373 C0.0127 3.34,0.02445

c 0.00635 ACERO TEMPERATURA3.54,-0.4373 C dtext 0.03

0.0127 3.05,0.01865 0.30c 0.00635 1 5/8" @ 0.26 m 4.503.42,-0.4373 C

0.0127 2.76,0.01285c 0.006353.3,-0.4373 C

0.0127 2.47,0.00705000000000001c 0.006353.18,-0.4373 C

0.0127 2.18,0.00125000000000001c 0.006353.06,-0.4373 C

0.0127 1.89,-0.00454999999999999c 0.006352.94,-0.4373 C

0.0127 1.6,-0.01035c 0.006352.82,-0.4373 C

0.0127 1.31,-0.01615c 0.006352.7,-0.4373 C

0.0127 1.02,-0.02195c 0.006352.58,-0.4373 C

0.0127 0.73,-0.02775c 0.006352.46,-0.4373 C

0.0127 0.44,-0.03355c 0.006352.34,-0.4373 C

0.0127 0.15,-0.03935c 0.006352.22,-0.4373 C

0.0127 0,0c 0.006352.1,-0.4373 C

0.0127 0,0c 0.006351.98,-0.4373 C

0.0127 0,0c 0.006351.86,-0.4373 C

0.0127 0,0c 0.006351.74,-0.4373 C

0.0127 0,0c 0.006351.62,-0.4373 C

0.0127 0,0c 0.006351.5,-0.4373 C

0.0127 0,0c 0.006351.38,-0.4373 C

0.0127 0,0c 0.006351.255,-0.4373 Cc 0,0

0.0127 0.006351.13,-0.4373 C

0.0127 0,0c 0.006351.005,-0.4373 C

0.0127 0,0c 0.006350.879999999999997,-0.4373 C

0.0127 0,0c 0.006350.754999999999997,-0.4373 C

0.0127 0,0c 0.006350.629999999999997,-0.4373 C

0.0127 0,0c 0.006350.504999999999997,-0.4373 C

0.0127 0,0c 0.006350.379999999999997,-0.4373 C

0.0127 0,0c 0.006350.254999999999997,-0.4373

0.0127c0.129999999999997,-0.4373

0.0127c0,-0.4373

0.0127c0,0

0.0127c0,0

0.0127

c0,0

0.0127c0,0

0.0127c0,0

0.0127c0,0

0.0127c0,0

0.0127c0,0

0.0127c0,0

0.0127c0,0

0.0127c0,0

0.0127c0,0

0.0127c0,0

0.0127c0,0

0.0127c0,0

0.0127c0,0

0.0127c0,0

0.0127c0,0

0.0127c

0,00.0127

c0,0

0.0127c0,0

0.0127c0,0

0.0127c0,0

0.0127c0,0

0.0127c0,0

0.0127c0,0

0.0127c0,0

0.0127c0,0

0.0127c0,0

0.0127c0,0

0.0127c0,0

0.0127

BARRERA DER AREA 0 GRAFICO PUENTE0 0 0 0 0 0.00 00 0 0 0 0 0.30 00 0 0 0 0 4.5 0.0840 0 0 0 0 8.7 00 0 0 0 0 9.00 00 0 0 0 0 9.00 -0.480 0 0 0 0 0.00 -0.48

0.00 0.00VIGA PERIMETRA IZQ VIGA PERIMETRAL DER AREA 0.135

0 8.7 0 2.61 0 FRANJA EXTERIOR0.3 8.7 0.3 2.61 2.6475 1.37 0.500.3 8.825 0.3 10.59 2.6475 1.37 -1.001.2 8.825 1.2 10.59 10.651.2 8.875 1.2 2.6625 10.65 ACOT ACERO PRINCIPAL FI0.3 8.875 0.3 2.6625 2.7 4.38 -0.43730.3 9 0.3 0 2.7 4.38 -0.6373

0 9 0 31.725 31.9954.26 -0.43734.26 -0.6373

VEREDA DER AREA 0 4.48 -0.63730 0 0 0 00 0 0 0 00 0 0 ACOT ACERO PRINCIPAL FE0 0 0 4.38 -0.43730 0 0 4.38 -0.63730 0 0 4.155 -0.63730 0 0 0 00 0 0 0 0 4.255 -0.43730 0 0 0 0 4.255 -0.6373

0.00635ACERO TEMPERATURA

AREA 0.42 0 4.500.05 0.0402 0.225 0 4.21

0.134 0.225 1.1658 0 3.920.05 0 0.435 0 3.63

0 0.7308 0 0 3.340.084 0 0.0252 0 3.05

0 0.015 0 0 2.760.05 1.011 1.851 0 2.47

2.18 2.181.89 1.89

1.6 1.601.31 1.31

1 5/8" @ 0.26 m acotamiento 1.02 1.02ACERO DISTRIBUCION 2.265 -0.41665 0.73 0.73

-0.41665 2.265 -0.61665 0.44 0.44-0.41665 2.465 -0.61665 0.15 0.15

0 0.000 0.00

ACERO TEMPERATURA acotamiento 0 0.00-0.04905 2.4 -0.00705 0 0.00-0.04905 2.4 0.19295 0 0.000.03495 0 0.00

2.18 -0.00125 0 0.002.18 0.19295 0 0.00

2.5 0.19295 0 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.00

0.0127AREA 4.6728 ACERO PRINCIPAL

0 0 4.5 4.5 -0.43730.0252 0 4.38 4.38 -0.4373 -0.12

0 0.7308 4.26 4.26 -0.4373 -0.120 0 4.14 4.14 -0.4373 -0.12

-4.32 0 4.02 4.02 -0.4373 -0.12-4.32 0 3.9 3.9 -0.4373 -0.12

0 0 3.78 3.78 -0.4373 -0.12-8.6148 0.7308 3.66 3.66 -0.4373 -0.12

3.54 3.54 -0.4373 -0.123.42 3.42 -0.4373 -0.12

3.3 3.3 -0.4373 -0.123.18 3.18 -0.4373 -0.123.06 3.06 -0.4373 -0.122.94 2.94 -0.4373 -0.122.82 2.82 -0.4373 -0.12

2.7 2.7 -0.4373 -0.122.58 2.58 -0.4373 -0.122.46 2.46 -0.4373 -0.122.34 2.34 -0.4373 -0.122.22 2.22 -0.4373 -0.12

2.1 2.1 -0.4373 -0.121.98 1.98 -0.4373 -0.121.86 1.86 -0.4373 -0.121.74 1.74 -0.4373 -0.121.62 1.62 -0.4373 -0.12

1.5 1.5 -0.4373 -0.121.38 1.38 -0.4373 -0.12

1.255 1.255 -0.4373 -0.1251.13 1.13 -0.4373 -0.125

1.005 1.005 -0.4373 -0.125ACERO TEMPERATURA 0.88 0.88 -0.4373 -0.125

0.04765 0.755 0.755 -0.4373 -0.1250.04185 0.63 0.63 -0.4373 -0.1250.03605 0.505 0.505 -0.4373 -0.1250.03025 0.38 0.38 -0.4373 -0.1250.02445 0.255 0.255 -0.4373 -0.1250.01865 0.13 0.13 -0.4373 -0.1250.01285 0 0.005 -0.4373 -0.1250.00705 0 -0.12 0 -0.1250.00125 0 -0.245 0 -0.125-0.00455 0 -0.37 0 -0.125-0.01035 0 -0.495 0 -0.125-0.01615 0 -0.62 0 -0.125-0.02195 0 -0.745 0 -0.125-0.02775 0 -0.87 0 -0.125-0.03355 0 -0.995 0 -0.125-0.03935 0 -1.12 0 -0.125

0 0 -1.245 0 -0.1250 0 -1.37 0 -0.1250 0 -1.495 0 -0.1250 0 -1.62 0 -0.1250 0 -1.745 0 -0.1250 0 -1.87 0 -0.1250 0 -1.995 0 -0.1250 0 -2.12 0 -0.1250 0 -2.245 0 -0.1250 0 -2.37 0 -0.1250 0 -2.495 0 -0.1250 0 -2.62 0 -0.1250 0 -2.745 0 -0.1250 0 -2.87 0 -0.1250 0 -2.995 0 -0.1250 0 -3.12 0 -0.125

0 -3.245 0 -0.1250 -3.37 0 -0.1250 -3.495 0 -0.1250 -3.62 0 -0.1250 -3.745 0 -0.1250 -3.87 0 -0.125

INGRESO DE DATOSRECTO ESVIADO

LONGITUD DEL PUENTE = 30.5 mLUZ DE CALCULO = 30 mANCHO DEL CALZADA = 3.6 m 3.60ANCHO LIBRE DEL PUENTE = 7.2 m 7.20NUMERO DE VIAS = 2 ViasANGULO DE ESVIAM = 90 NRO DE VIGAS = 4 uniDESEA ESPACIOS DIFERENTES? (SI/ NOSEPARACION ENTRE EJES VIGAS (S') 1.6 m 1.60

ejes entre vigas entre vigas entre cartelas1ER ESPACIO = 1.5 0.9 m 1.60 1.00 0.702DO ESPACIO = 1.6 1 m 1.60 1.00 0.703ER ESPACIO = 1.6 1 m 1.60 1.00 0.704TO ESPACIO = 1.6 1 m 0.00 0.00 0.00

-2.00 -1.00 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 11.00 12.00

-2

-1

0

1

2

0.00

5TO ESPACIO = 1.5 0.9 m 0.00 0.00 0.004.80 3.00

SEPARACION LIBRE ENTRE VIGAS (S) 1 m 1.00LONGITUD EXTREMA DE VIGAS = 5.40 m ANCHO DE VIGASLOSA ENTRE VIGAS = 0.7 m 0.70 B TEORICO = 0.596 mNRO DE VIGAS DIAFRAGMA = 2 uni ASUMIDO = 0.6 m 0.60ANCHO VIGAS DIAFRAGMA = 0.25 mf'c (Losa) = 280 Kg/cm2 LOSA Fy (Acero corrugado) = 4200 Kg/cm2 t = 0.18 0.2 m

MOM NEG -4.15 T-m Rec =BARRERA (SI / NO) NO 0 m 0.00 Elegir diametro para acero principalBASE BARRERA = 0.35 0.35 As princ USAR 1 5/8" @ 0.28 m

As max = 0.090240848 -5.517209614ANCHO VEREDA = 0.8 m 0.80 Elegir diametro para acero temperaturaALTURA VEREDA = 0.25 m As temp USAR 1 3/8" @ 0.39 mANCHO ADICIONAL POR VEREDA= 0 m 0.00ALTURA BARANDA= 1.2 m MOM POS 4.34 T-m Rec =PESO BARANDA = 150 Kg/m Elegir diametro para acero principalANCHO ADICIONAL POR BARANDA= 0.15 m 0.15 As princ USAR 1 5/8" @ 0.28 m

As max = 0.0887370812 2.693058341ANCHO VIGA = 0.3 m 0.30 Elegir diametro para acero distribucionALTURA VIGA SOBRE LOSA = 0.3 m As distr USAR 1 1/2" @ 0.26 m

SOBRECARGA PEATONAL = 0.51 T/m2 LOSA VOLADIZ -2.38 T-m Rec =VEHICULO = HL-93 Elegir diametro para acero principal

As princ USAR 1 1/2"CARPETA ASFALTICA = 0.05 m As max = -0.0746889941 -3.168639142A CARTELA = 0.15 m 0.15 Elegir diametro para acero distribucionB CARTELA = 0.15 m 0.15 As distr USAR 1 1/2"

BOMBEO = 2 %

VOLADIZO DESDE CANTO VIGA = 1.20 m 1.20VOLADIZOS DESDE CARTELA= 1.05 m 1.05VOLADIZOS DESDE EJE DE VIGA= 1.5 m 1.50

DISEO DE LA LOSA (As principal perpendicular al trafico

a) Predimensionamiento de la losaAncho de la viga

b = 0.596 = 0.6

t min = (S + 3000)30

t min = ( 1000 + 3000 ) = 133.3333333333 mm30

t = 0.13333333 = 0.18 m 0.2

SiendoS' = espaciamiento entre ejes de vigasS = Luz libre de losa (mm)L = Luz del puente

B) CRITERIOS LRFD APLICABLES

Resistencia 1 : U = n [(1,25 0,90) DC + (1,50 0,65 ) DW + 1,75 (LL+ IM )]Servicio 1 : U = n [ 1,00 DC + 1,00 DW + 1,00 (LL+ IM )]

NO ES NECESARIO FATIGA EN TABLEROS DE CONCRETO CON VIGAS MULTIPLES

C) MOMENTOS DE FLEXION POR CARGAS

b =0.0157 S' L

C-1) MOMENTO NEGATIVO DE DISEO

1. CARGA MUERTA (DC)

Wlosa = 0.2 x 1 x 2400 = 480 Kg/mcoef

LOSA = 480 1.25 = 0.6 T/M

2. CARGA POR SUPERFICIE DE RODADURA (DW)Wasf = 0.05 x 1 x 2250 = 112.5 Kg/m

CoefASFALTO = 1.5 = 0.17 T/m

CD + DW = 0.77 T/mW LONG PTO APLICAC

MOMENTO EN EL VOLADIZO = LOSA 0.9 1.5 0.75 1.013ASFALTO 0.17 1.20 0.6 0.122TOTAL = 1.134

VIGA 0.60 0.60 0.60 0.60VIGA 2.45 2.45 2.45 2.45 2.45 2.45 2.45 2.45CARTELA B 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15CARTELA A 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15

1.05 0.70 0.70 0.70 1.05LONG = 1.50 1.60 1.60 1.60 1.50

RIG (1/L) = 0.000 0.625 0.625 0.625 0.000COEF DIST = 0 1 0.5 0.5 0.5 0.5 1 0MOM E P = 1.134 -0.164 0.164 -0.164 0.164 -0.164 0.164 -1.134

-0.970 0.000 0.000 0.000 0.000 0.970 0.0000.000 -0.485 0.000 0.000 0.485 0.000 0.0000.000 0.243 0.243 -0.243 -0.243 0.000 0.0000.121 0.000 -0.121 0.121 0.000 -0.121 0.000-0.121 0.061 0.061 -0.061 -0.061 0.121 0.0000.030 -0.061 -0.030 0.030 0.061 -0.030 0.000-0.030 0.045 0.045 -0.045 -0.045 0.030 0.0000.023 -0.015 -0.023 0.023 0.015 -0.023 0.000-0.023 0.019 0.019 -0.019 -0.019 0.023 0.0000.009 -0.011 -0.009 0.009 0.011 -0.009 0.000-0.009 0.010 0.010 -0.010 -0.010 0.009 0.0000.005 -0.005 -0.005 0.005 0.005 -0.005 0.000-0.005 0.005 0.005 -0.005 -0.005 0.005 0.0000.002 -0.003 -0.002 0.002 0.003 -0.002 0.000-0.002 0.003 0.003 -0.003 -0.003 0.002 0.0000.001 -0.001 -0.001 0.001 0.001 -0.001 0.000-0.001 0.001 0.001 -0.001 -0.001 0.001 0.000

CM 0.000 1.134 -1.134 -0.030 0.030 -0.030 0.030 1.134 -1.134

-0.030 -0.276 -0.030 0.269REACCIONES 0.000 1.153 1.342 -0.112 0.615 0.615 -0.112 1.342 1.153

COMBINACION LOSA - BARRERA

POR PESO DE LA BARRERA

ANCHO SUPERIOR = 0.15 m 0.15ANCHO INFERIOR = 0 m 0.00ANCHO INTERMEDIO = -0.325 m -0.33ANCHO DERECHO = 0.175 m A3 0.18ALTURA TOTAL = 0.85 mALTURA INFERIOR = 0.13 mALTURA MEDIA = 0.25 m A5ALTURA SUPERIOR = 0.47 mf'c = 280 A4Fy = 4200 A2

A1

AREA BRAZO MOMA1 0 0.13 = 0.000 1.500 0.000A2 0 0.25 0.5 = 0.000 1.500 0.000A3 0 0.47 = 0.000 1.500 0.000A4 0 0.25 = 0.000 1.500 0.000A5 0 0.47 0.5 = 0.000 1.500 0.000

0.000 0.000

CENTRO DE GRAVEDAD = 0.00 cm0 T/m

PESO = 0 2.4 = 0.00 T/m 1.25 00.00 Kg/m 0.9 0

0 T 0 mBARRERA = 0 T PUNTO APLICACIN = 0.00 m

COEFMOMENTO = 1.25 0 0.00 = 0.00 Tm

COMBINACION LOSA - VIGA PERIMETRALANCHO VIGA = 0.300

VIGA : 0.30 0.3 2.4 = 0.216 T 1.25 0.4575BARANDA (.1 T/m) 0.15 T 0.9 0.3294

0.366 T0.37 T 1.35 m

PESO VP + BAR = 0.366 T PUNTO APLICACIN = 1.35 m

DC 0.675DW 0.1215

COEFMOMENTO = 1.25 0.366 1.35 = 1.414125 Tm

COMBINACION LOSA - VEREDA (sin carga viva)

POR PESO DE LA VEREDA Y BARANDAVEREDA

ANCHO SUPERIOR = 0ANCHO INFERIOR = 0 A2 A1ALTURA TOTAL = 0 A3ALTURA IZQ = 0.15

AREA BRAZO MOMA1 0 0 = 0.000 1.500 0.000A2 0 0.15 = 0.000 1.500 0.000A3 0 -0.15 0.5 = 0.000 1.500 0.000

0.000 0.000

CENTRO DE GRAVEDAD = 0.00 cmPESO = 0.000 2.4 = 0.00 T/m 1.25 0

0.00 Kg/m 0.9 0

0 T 0 mVEREDA = 0 T PUNTO APLICACIN = 0.00 m

PESO DE BARANDA = 0.15 T 0 mBARANDA = 0.15 T PUNTO APLICACIN = 0.000 m

COEFMOMENTO = 1.25 0 0 = 0 Tm

1.25 0.15 0 = 0 Tm0

COMBINACION LOSA - VEREDA (con carga viva)

Wlosa = 0 x 1 x 2400 = 0 Kg/mcoef

LOSA = 0 1.25 = 0

POR PESO DE LA VEREDA Y BARANDAVEREDA

ANCHO SUPERIOR = 0ANCHO INFERIOR = 0 A2 A1ALTURA TOTAL = 0 A3ALTURA IZQ = 0.15

AREA BRAZO MOMA1 0 0 = 0.000 1.500 0.000A2 0 0.15 = 0.000 1.500 0.000A3 0 -0.15 0.5 = 0.000 1.500 0.000

0.000 0.000

CENTRO DE GRAVEDAD = 0.00 cmPESO = 0.000 2.4 = 0.00 T/m 1.25 0

0.00 Kg/m 0.9 0

0 T 0 mVEREDA = 0 T PUNTO APLICACIN = 0.00 m

PESO DE BARANDA = 0.15 T 0 mBARANDA = 0.15 T PUNTO APLICACIN = 0.000 m

0 T 0 mC.V. = 0 T PUNTO APLICACIN = 0.000 m

COEFMOMENTO = 1.25 0 0 = 0 Tm

1.25 0.15 0 = 0 Tm1.5 0.00 0.000 = 0 Tm

0

LONG = 1.50 1.60 1.60 1.60 1.50

RIG (1/L) = 0.000 0.625 0.625 0.625 0.000COEF DIST = 0 1 0.5 0.5 0.5 0.5 1 0MOM E P = 2.548 -0.164 0.164 -0.164 0.164 -0.164 0.164 -2.548

-2.384 0.000 0.000 0.000 0.000 2.384 0.0000.000 -1.192 0.000 0.000 1.192 0.000 0.0000.000 0.596 0.596 -0.596 -0.596 0.000 0.0000.298 0.000 -0.298 0.298 0.000 -0.298 0.000-0.298 0.149 0.149 -0.149 -0.149 0.298 0.0000.075 -0.149 -0.075 0.075 0.149 -0.075 0.000-0.075 0.112 0.112 -0.112 -0.112 0.075 0.0000.056 -0.037 -0.056 0.056 0.037 -0.056 0.000-0.056 0.047 0.047 -0.047 -0.047 0.056 0.0000.023 -0.028 -0.023 0.023 0.028 -0.023 0.000-0.023 0.026 0.026 -0.026 -0.026 0.023 0.0000.013 -0.012 -0.013 0.013 0.012 -0.013 0.000-0.013 0.012 0.012 -0.012 -0.012 0.013 0.0000.006 -0.006 -0.006 0.006 0.006 -0.006 0.000-0.006 0.006 0.006 -0.006 -0.006 0.006 0.0000.003 -0.003 -0.003 0.003 0.003 -0.003 0.000-0.003 0.003 0.003 -0.003 -0.003 0.003 0.000

CM 0.000 2.548 -2.548 -0.313 0.313 -0.313 0.313 2.548 -2.548

-0.313 -0.559 -0.313 1.683REACCIONES 0.000 1.153 2.403 -1.173 0.615 0.615 -1.173 2.403 1.153

MOMENTO CON COEFICIENTE 09=BARRERA 0.9 0.00 0.00 = 0.00 TmVIGA PERIMETRAL 0.9 0.37 1.35 = 0.44 TmVEREDA 0.9 0.00 0.00 = 0.00 Tm

0.9 0.15 0.00 = 0.00 Tm

LONG = 7.80 1.50 1.60 1.60 1.60 1.50

RIG (1/L) = 0.000 0.625 0.625 0.625 0.000COEF DIST = 0.000 1.000 0.500 0.500 0.500 0.500 1.000 0.000MOM E P = 1.579 -0.164 0.164 -0.164 0.164 -0.164 0.164 -1.579

-1.415 0.000 0.000 0.000 0.000 1.415 0.0000.000 -0.707 0.000 0.000 0.707 0.000 0.0000.000 0.354 0.354 -0.354 -0.354 0.000 0.0000.177 0.000 -0.177 0.177 0.000 -0.177 0.000-0.177 0.088 0.088 -0.088 -0.088 0.177 0.0000.044 -0.088 -0.044 0.044 0.088 -0.044 0.000-0.044 0.066 0.066 -0.066 -0.066 0.044 0.0000.033 -0.022 -0.033 0.033 0.022 -0.033 0.000-0.033 0.028 0.028 -0.028 -0.028 0.033 0.0000.014 -0.017 -0.014 0.014 0.017 -0.014 0.000-0.014 0.015 0.015 -0.015 -0.015 0.014 0.0000.008 -0.007 -0.008 0.008 0.007 -0.008 0.000-0.008 0.007 0.007 -0.007 -0.007 0.008 0.0000.004 -0.004 -0.004 0.004 0.004 -0.004 0.000-0.004 0.004 0.004 -0.004 -0.004 0.004 0.0000.002 -0.002 -0.002 0.002 0.002 -0.002 0.000-0.002 0.002 0.002 -0.002 -0.002 0.002 0.000

CM 0.000 1.579 -1.579 -0.119 0.119 -0.119 0.119 1.579 -1.579

-0.119 -0.365 -0.119 0.714REACCIONES 0.000 1.153 1.676 -0.446 0.615 0.615 -0.446 1.676 1.153

ENVOLVENTE COMBINACION BARRERA - LOSA

MAXIMOS POSITIVOS0 0 1.500 2.548 3.100 -0.030 4.700 -0.030 6.300 2.548

1.500 2.548 1.800 1.862 3.400 -0.180 5.000 0.074 6.600 2.2371.925 1.596 3.525 -0.222 5.125 0.255 6.713 2.1382.050 1.343 3.650 -0.252 5.250 0.449 6.825 2.0492.175 1.101 3.775 -0.270 5.375 0.654 6.938 1.9692.300 0.872 3.900 -0.276 5.500 0.872 7.050 1.8992.425 0.654 4.025 -0.270 5.625 1.101 7.163 1.8392.550 0.449 4.150 -0.252 5.750 1.343 7.275 1.7892.675 0.255 4.275 -0.222 5.875 1.596 7.388 1.7492.800 0.074 4.400 -0.180 6.000 1.862 7.500 1.7183.100 -0.030 4.700 -0.030 6.300 2.548 7.800 1.683

MINIMOS NEGATIVOS0 1.134 -0.313 -0.313 1.134

1.134 0.766 -0.463 0.038 0.8230.633 -0.505 0.087 0.7240.512 -0.535 0.148 0.6350.403 -0.553 0.221 0.5550.306 -0.559 0.306 0.4850.221 -0.553 0.403 0.4250.148 -0.535 0.512 0.3750.087 -0.505 0.633 0.3350.038 -0.463 0.766 0.304

-0.313 -0.313 1.134 0.269

0.000 1.000 2.000 3.000 4.000 5.000 6.000 7.000 8.000 9.000

-1.000-0.5000.0000.5001.0001.5002.0002.5003.000

0.0000.4850.0000.000

2.237 1.718

0.074

1.862

-0.030-0.180 -0.180 -0.030

1.862

0.074

MOM NEG EN CARA D 2.548 -0.030 2.548 2.548MOM POS MAX 0.313 0.559 0.313 0.269

0.000 1.000 2.000 3.000 4.000 5.000 6.000 7.000 8.000 9.000

-1.000-0.5000.0000.5001.0001.5002.0002.5003.000

0.0000.4850.0000.000

2.237 1.718

0.074

1.862

-0.030-0.180 -0.180 -0.030

1.862

0.074

METODO SIMPLIFICADO

CARGA MUERTA (DC)

Mdc = Wlosa S^2 = 0.123 T-m 1.25 = -/+ 0.154 T-m10 -0.154 T-m

CARGA DE ASFALTO (DW)

Mdw = Wasf S^2 = 0.029 T-m 1.5 = -/+ 0.043 T-m10 -0.043 T-m

TOTAL = 0.197-0.197

Carga viva (LL)

DE LA TABLA A4-1

Para S = 1.60 m

M(+) ll+im = 21190 N mmmm

M(+) ll+im = 21190 = 2160.040775 Kg-m = 2.1600407747 T-m9.81 m m

0 7.5 15 16 17 18 19 20M(-) ll+im = 18400 15780 13160 12876 12592 12308 12024 11740

1.88 1.61 1.34 1.31 1.28 1.25 1.23 1.20

Cara de la viga = 30 cm8970

M(-) ll+im = 8970 = 914.3730887 Kg-m = 0.9143730887 T-m9.81 m m

c) CRITERIOS LRFD APLICABLES

RESISTENCIA 1 U= 1.25 DC + 1.50 DW + 1.75 (LL+IM)SERVICIO 1 U= 1.00 DC + 1.00 DW + 1.00 (LL+IM)

d) ESTADO LIMITE DE RESISTENCIA 1

Calculo del acero principal (perpendicular al trafico)


Mu = n ( 1.25 Mdc + 1.50 Mdw + 1.75 Mll+im)

MOMENTOS NEGATIVOS POR CARGAS

CARGA MOM NEG RESISTENCIA 1 MOM POS RESISTENCIA 1COMBINACION DC DW -2.548 0.559METODO SIMPLIFICADO -0.197 -2.548 0.197 0.559CARGA VIVA -0.914 1.750 -1.6001529052 2.1600407747 1.750 3.780071356

-4.148 2.719 4.339

CALCULO DEL ACERO PARA MOMENTO NEGATIVO

Mu = -4.15 T-m

UTILIZANDO As 5/8" RECUBRIMIENTO r = 3 cm

z = 3 + 1.59 = 3.795 cm2

d = 20 cm - 3.795 cm = 16.205 cm


As = Mu = 7.042 cm2 7.042 7.0420.9 Fy (d-a/2)

1.243 1.243 1.243a = As Fy = 1.243 cm 1.243 1.243

f'c b

Usando varilla de 5/8" la separacion sera : s = 2 = 0.28 m7.042

USAR 1 5/8" @ 0.28 mAs maximoUna seccion no sobre reforzada cumple con = c/d

f'c = 280 Kg/cm2 = 27.45905659 Mpa 1 Mpa

fr = 0.63 f'c = 0.63 27.4590565853 = 3.3012875607 Mpa =

S = bh2/6 = 100 x 20 ^2 / 6 = 6666.666667 cm2

b) 1.33 Mu = 1.33 x -4.15 = -5.52 T-m

a) = 2.69305834 T-mb) = -5.52 T-m

Menor valor = -5.5172096 T-m la cantidad de acero calculada 7.042 cm2Mu = -4.15 T-m > -5.517209614 T-m OK

As temperatura

As temp = 0.756 Ag = 0.756 x 200 mm x 1000Fy 420

= 360.0 mm2 = 3.6 cm2

En una capa = 3.6 = 1.8 cm2/capa2

Usando varilla de 3/8" la separacion sera : s = 0.71 = 0.39 m1.8

Smax = 3 t = 3 x 0.2 = 0.6 mSmax = 0.45 m

0.39

USAR 1 3/8" @ 0.39 mCALCULO DEL ACERO PARA MOMENTO POSITIVO

Mu = 4.34 T-m

UTILIZANDO As 5/8" RECUBRIMIENTO r = 2.5 cm

z = 2.5 + 1.59 = 3.295 cm2

d = 20 cm - 3.295 cm = 16.705 cm


As = Mu = 7.141 cm2 7.141 7.1410.9 Fy (d-a/2)

1.26 1.26 1.26a = As Fy = 1.26 cm 1.26 1.26

.85 f'c b

Usando varilla de 5/8" la separacion sera : s = 2 = 0.28 m7.141

USAR 1 5/8" @ 0.28 mAs maximoUna seccion no sobre reforzada cumple con = c/d 2.693058341 T-m OK


% = 3840

II) DISEO DE LA VIGA PRINCIPAL INTERIOR

A) PREDIMENSIONAMIENTO 1.6

h max = 0.070 L

h max = 2.1 =

ASUMIDO 2.8 m

diaframab= 0.25

0.6B) MOMENTOS DE FLEXION POR CARGAS (VIGA INTERIOR)

DIAFRAGMAS

CARGA MUERTA (DC)

CARGAS DISTRIBUIDAS

Wlosa = 0.2 x 1.6 x 2400 = 768 kg/mWviga = 2.6 x 0.6 x 2400 = 3744 kg/mW cartela= 0.15 x 0.15 x 2400 = 54 kg/m

Wdc = 4566 kg/m

Mdc = 4566 x 30 ^2 = 513675 Kg-m8

513.675 T-m

CARGAS PUNTUALES

NUMERO DE VIGAS DIAFRAGMA = 2 UNI

P diaf = 2.45 x 0.25 x 1 x 2400 = 14701.47

LONGITUD DE LAS VIGAS DIAFRAGMALvd = 1 m

SEPARACION DE LAS VIGAS DIAFRAGMASvd = 30 m

CALCULO DEL MOMENTO POR CARGA PUNTUALDIST DIST ACU Ra Rb MOMENTO

VD1 1 1.47 0 0.00 1.47 0 0.000VD2 2 1.47 30 30.00 0 1.47 0.000VD3 0VD4 0VD5 0VD6 0VD7 0VD8 0VD9 0VD10 0VD11 0VD12 0VD13 0VD14 0VD15 0

REACCION TOTAL 1.47 1.47 0.000 T-m

M dc = 513.675 + 0.000 = 513.675 T-m


0.0000.1000.2000.3000.4000.5000.6000.7000.8000.9001.000

Column H

W asf2"= 0.05 x 2250 x 1.6 = 180 Kg/m0.18 T/m

M dw = Wdw L^2 = 20.25 t-m8

CARGA VIVA (LL)

CARGA VIVA (LL)a) camion de diseo (HL-93)

caso 114.8 T

A

Ra= 7.4 T luz = 30 m15 m 15 m

Mmax = 14.8 x 30 = 0 T-m4

caso 2 R= 29.6 T

14.8 T 14.8 T

13.925 2.15 2.15

1.075A

Ra= 13.7393333 T luz = 30 m15 m 15 m

Mmax = 13.925 x 13.7393333 = 0 T-m11.775 x 15.8606667 = 0 T-m

0caso 3posicion de la resultante

33.2 X = 14.8 x 4.3 + 3.6 x 8.6X = 94.6 = 2.84939759 m.

33.2

R= 33.2 T

14.8 T 14.8 T 3.6

X= 2.85 1.4511.425 4.3 4.3

0.73A

Ra= 17.4026667 T luz = 30 m15 m 15 m

Mmax = 15.73 x 17.4026667 - 4.30 x 14.80 = 210.022175117.40 x 11.425 = 198.830708415.80 x 9.97 = 157.5736418

210.0221751caso 1 0caso 2 0caso 3 210.022175

Momento Maximo def = 210.022175 T-mpor camion de diseo

b) Tandem de diseocaso 1 R= 22.4 T

11.2 T 11.2 T

14.7 0.6 0.6 14.1

0.3A

Ra= 10.976 T luz = 30 m15 m 15 m

Mmax = 14.7 x 10.976 = 161.3472 T-mMmax = 14.1 x 11.424 = 161.0784 T-mMmax = 161.3472 T-mcaso 2

11.2 T

A

Ra= 5.6 T luz = 30 m15 m 15 m

Mmax = 11.2 x 30 = 0 T-m4

caso 1 161.3472caso 2 0

Momento Maximo def = 161.3472 T-mpor tandem de diseo

c) Carga de Carril

0.96 T/mA

Ra= 14.4 T luz = 30 m

Mmax = 0.96 x 30 ^2 = 108 T-m8

CAMION DE DISEO 210.022175 T-mTANDEM DE DISEO 161.3472 T-mCARGA DE CARRIL 108 T-m

Mmax(ll+im) = 210.022175 x 1.33 + 108 = 387.3294929 T-m

EL % DE MOMENTO QUE SE DISTRIBUYE EN UNA VIGA INTERIOR ES :

CASO DE UN CARRIL CARGADO

g = 0.06 + (S/4300)^0.4 x (S/L)^0.3 x (Kg/(Lts^3))^0.1

CALCULO DE (Kg/(Lts^3))^0.1

n = Eviga = 1Elosa

Iviga = 87880000 cm4

Aviga = 15600 cm21.6

eg = 1.4 = 140 cm

0.1

Kg = n(Iviga+Aviga x eq^2) =eq

Kg = 393640000 cm4 1.32.6

entoncesdiaframa

(Kg/L t^3)^0.1 = 1.32278359 b= 0.25

L = 30 mt = 0.2 m 0.6

g = 0.42969964

CASO DE DOS CARRILES CARGADOS

g = 0.075 + (S/2900)^0.6 x (S/L)^0.2 x (Kg/(Lts^3))^0.1

g = 0.5901358 critico se toma

g = 0.42969964g = 0.5901358 0.5901358

Mll+im = 0.5901358 x 387.329493 = 228.5770009834 t-m

C) CRITERIOS LRFD APLICABLESRESISTENCIA 1 U= 1.25 DC + 1.50 DW + 1.75 (LL+IM)SERVICIO 1 U= 1.00 DC + 1.00 DW + 1.00 (LL+IM)FATIGA U= 0.75 (LL+IM)




Mu = n ( 1.25 Mdc + 1.50 Mdw + 1.75 Mll+im)

Mu = 1.25 x 513.675 + 1.5 x 20.25 + 1.75Mu = 1,072.48 T-m

ANCHO EFECTIVO DE LA VIGA T , ES EL MENOR VALOR DE:

L/4 = 30 / 4 = 7.5 m

12 t losa + t viga = 3 m

S = 1.6 m

Entonces b = 1.6 m

1.6

2.6

diaframab= 0.25

0.6

Acero principalNumero del diametro a usar = 8 Numero Acero Area (cm2.) (cm)Recub. = 5 cm 0.05Recub. Lat = 4 cm 0.04 3 3/8" 0.71 0.95 = 1" 4 1/2" 1.29 1.27Area = 5.1 5 5/8" 1.98 1.59Diametro= 2.54 0.0254 6 3/4" 2.85 1.91

8 1" 5.1 2.54Estribos 10 1.1/4" 7.92 3.18Numero del diametro a usar = 4 11 1.3/8" 9.58 3.49

= 1/2"Area = 1.29Diametro= 1.27 0.0127Separacion de barras horizontal= 3.81Separacion de barras horizontal= 1.5" = 3.81 0.0381

1 arreglo de varillas = 3 1 2 2 2 2 2 2rec est 8 1 oo 0 oo 0 oo 0

4 1.27 2.54 0 2.54 2.54 2.54 2.54 2.54 2.542.54 0 0 0 0 0 0 0

Nro de espacios 1 2 3 4Separacion filas =2 arreglo de varillas = 2 2 1 1 1 1 1 1rec est oo 0 o 0 o 0 o 0

4 1.27 2.54 2.54 2.54 0 2.54 0 2.54 00 0 0 0 0 0 0 0

Nro de espacios 1 2 3 4Separacion filas =3 arreglo de varillas = 3 1 2 2 2 2 2 2rec est 8 1 oo 0 oo 0 oo 0

4 1.27 2.54 0 2.54 2.54 2.54 2.54 2.54 2.542.54 0 0 0 0 0 0 0

Nro de espacios 1 2 3 4

SEP ENTRE PAQUETES 7.29 OK 0.07285SEP ENTRE PAQUETES 7.92 OK 0.0792SEP ENTRE PAQUETES 7.29 OK 0.07285

AREA Y YA z = 2184.687 =FILA 1 40.8 7.54 307.632 137.7FILA 1a 10.2 10.08 102.816FILA 2 35.7 16.43 586.551 d = 280 cm -FILA 2a 0 17.7 0FILA 3 40.8 22.78 929.424FILA 3a 10.2 25.32 258.264

137.7 cm2 2184.687 cm3

Fy = 4200 Kg/cm2 Mu = As 0.9 Fy (d-a/2) = 1335.308406 Ton - mf'c = 280 Kg/cm2d = 264.134444 cm a = As Fy = 15.188 cmb = 1.60 m f'c bMu = 1,072.48 T-m c = 17.86823529 cm1 = 0.850

As = 137.7 cm2

As maximoUna seccion no sobre reforzada cumple con = c/d

b) = 1,426.40 T-m

Menor valor = 844.543096 T-m la cantidad de acero calculada 137.7 cm2Mu = 1,072.48 T-m > 844.5430956 T-m OK

USAR 27 1"

ARMADURA DE CONTRACCION Y TEMPERATURA EN CARAS LATERALES

EN EL ALMA DE LA VIGA T

As min = 0.756 Ag/Fy =

As min = 0.756 x 600 x ( 2800 - 200 )4200 / 10.197

As min = 2863.32 mm2 = 28.63 cm2

As min = 28.63 = 14.32 por cara2

Consideraciones

Smax = 3 t = 3 x 0.6 = 1.8 mSmax = 45 cm

Usamos 8 1/2"



Ms = n ( 1.00 Mdc + 1.00 Mdw + 1.00 Mll+im)

Mu = 1 x 513.675 + 1 x 20.25 + 1Mu = 762.50 T-m



f sa = Z

A = = 2 x 14.5955555556 x 60 = 64.869135827

Z = 30000 N/mmZ = 30000 x 1.0197 = 30591 kg/cm

luego

f sa = 30591 Kg/cm = 3115.354168552 Kg/cm2( 14.5955556 cm x 64.8691358

f sa

160 cm

yEN

264.13 278.73c

14.60 (fs/n)

60


Ast = n x As =7.94300452 x 137.7 = 1093.751721856 cm2


160 y (y/2) = 1093.75172 ( 264.1344444 - y)80 y^2 + 1093.75172 y - 288897.5034126 = 0

y = -1093.7517 + 1196292.829 + 92447201.092160

y = 53.6450321

y = -67.316929


I = Ast (ds - y)^2 + by^3/3

I = 56693089.5 cm4

Luego

fs = Ms c n = 762.502001 x 100000 x 210.49 x 7.943004516I 56693089.51403

= 2248.67105 Kg/cm2 < 2520 OK


PARA EL DISEO POR FATIGA, CON n = nd nr n1 = 1


1.- CARGA DE FATIGA

Se calcula con un camion de diseo, con una separacion constante de 9.00 m entre los ejes de 14.8 t

caso 114.8 T

A

Ra= 7.4 T luz = 30 m15 m 15 m

Mmax = 14.8 x 30 = 0 T-m4

caso 2aposicion de la resultante

18.4 X = 3.6 x 4.3X = 15.48 = 0.841304348 m.

18.4

R= 18.4 T

14.8 T 3.6 T

X= 0.84 3.4614.579

4.30.42

ARa= 8.942 T luz = 30 m15 m 15 m

Mmax = 14.58 x 8.942 = 130.368528311.12 x 9.458 = 105.1791283

130.3685283

caso 2b R= 29.6 T

14.8 T 14.8 T

12.75 4.5 4.5

2.25A

Ra= 12.58 T luz = 30 m15 m 15 m

Mmax = 12.75 x 12.58 = 0 T-m8.25 x 17.02 = 0 T-m

0

caso 3posicion de la resultante

33.2 X = 14.8 x 9 + 3.6 x 13.3X = 181.08 = 5.454216867 m.

33.2

R= 33.2 T

14.8 T 14.8 T 3.6

X= 5.45 3.557.773 9 4.3

1.77A

Ra= 18.562 T luz = 30 m15 m 15 m

Mmax = 16.77 x 18.562 - 9.00 x 14.80 = 178.138413318.56 x 7.773 = 144.280413314.64 x 8.93 = 130.6750133

178.1384133

caso 1 0caso 2a 130.368528caso 2b 0caso 3 178.138413


CONSIDERANDO EL ANCHO EFECTIVO PARA UN SOLO CARRILCARGADO (ELIMINADO EL FACTOR DE PRESENCIA MULTIPLE 1.2) Y IM= 0.15(TABLA 3,6,2,1,-,1)

Mfat = 1.00 x 0.75 x 1.15 x 178.138413253 x E

Mfat = 153.644381 x 0.43 = 55.02 T-m/m1.2

2.- SECCION FISURADASE UTILIZA LA SECCION FISURADA SI LA SUMA DE ESFUERZOS DEBIDO A CARGAS PERMANENTES NO MAYORADAS MAS 1.5 VECES LA CARGA DE FATIGA, DAN POR RESULTADOUNA TENSION DE TRACCION MAYOR QUE 0.25 f'c


f trac = 0.25 f'c = 1.31003475 MPa

f trac = 13.3584243 Kg/cm2


M' fat = 1 x 513.675 + 1 x 20.25 + 1.5

M' fat = 616.45 T-m

f fat = Mfat = 616.45 x 100000 = 29.49 Kg/cm2S 2090666.667

Como f fat = 29.49 Kg/cm2 > 13.3584243083 Kg/cm2 se usara seccion agrietada

3.- VERIFICACION DE ESFUERZOSEsfuerzo en el refuerzo debido a la carga viva

As = 27 1" = 137.7 cm2

jd = d - y/3 = 264.134444 - 53.64503207 = 246.25276709 cm revision agrietamiento3

= 55.02 100000 = 162.25024726 Kg/cm2As (jd) 137.7 246.2527671


El esfuerzo mnimo es el esfuerzo por carga viva mnimo combinado con el esfuerzopor carga permanente

El momento por carga muerta para la viga interior es:

MDL = MDC + MDW = 513.675 + 20.25 = 533.925 T-m


f LL = Mfat

= 533.93 100000 = 1574.5816895 Kg/cm2As (jd) 137.7 246.2527671

Por ser viga simplemente apoyada, el esfuerzo por carga viva mnimo es cero.

Luego, el esfuerzo mnimo es:

f min = 0 + 1574.58169 = 1574.581689466 Kg/cm2

El esfuerzo mximo es el esfuerzo por carga viva mximo combinado con el esfuerzopor cargas permanentes:

f max = 162.250247 + 1574.58169 = 1736.831936721 Kg/cm2

El rango de esfuerzos es: f = fmx fmn = 162.2502472551 Kg/cm2

El rango lmite es:

f 162.2502472551 Kg/cm2 OK

f DL = MDL

CALCULO DE LA VIGA EXTERIOR

C) MOMENTOS DE FLEXION POR CARGAS

7.4 Ton 7.4 Ton 7.4

0.60.6 1.8 1.2

0.3 Xpara calculo de 0.9

0.15 0 losa voladizo0.15 0.25

0.300.18

0.150.15

UBICACIN DE RUEDASRUEDA IZQ PEATONAL 1.05

0.6 0.05 0 00.6 1.05 0 0 0.6 1

RUEDA DER 0 0 1.22.4 0.05 0 02.4 1.05 0 0

0 00 0 1.50 1.600 0

Carga Muerta (DC) :PESO BRAZO

Plosa = 0.18 x 1.2 x 2400 = 518.4 Kg/m 0.6

Pbarrera = 1 x 1 x 0 = 0 Kg/m 1.2Pvereda 0.15 x 0 x 2400 = 0 Kg/m 1.575

0.25 x 0 x 2400 = 0 Kg/m 1.50.1 x 0 x 2400 = 0 Kg/m 1.55

Pbaranda = 1 x 1 x 0 = 0 Kg/m 1.525Viga perim = 0.3 x 0.55 x 2400 = 396 Kg/m 1.65

914.4 Kg/m

Mdc =

Carga por supeficie de rodadura (DW)

Wasf = 0.05 x 0.9 x 2250 = 101.25 Kg/m

Mdw = 101.25 x 0.45 = 0.0455625 T-m

Carga viva (LL)

HL-93P = 7.4 Ton SEPARACION MINIMA ENTRE LLANTA Y BARRERA O VEREDA = 0.3 m

E = 1140 + 0.833 X = 1889.7 mm = 1.8897 m

X = DISTANCIA ENTRE LA CARGA Y EL PUNTO DE APOYO (mm)

X = 900 mm

El momento del eje de rueda vehicular distribuido en un ancho E=1.27m,afectado por el factor de presencia mltiple (m=1.2), y el incremento por cargadinmica (I=0.33) es:

M ll + im = 7.4 1.2 1.33 0.6 = 3.7499285601 T-m1.8897

Brazo = 0.6 mM ll+im = 3.74992856 Ton - m

COLISION VEHICULAR (CT)

Rw = -18.25612188

0.85 Lc + 2H = 2.196579496 + 2 0.85= 3.896579496 m

Mct

Mct = -16.761385 0.85 = -3.656329195 T - m3.8965795

adicional por impacto en veredaM = 750 Kg x 0.25 m = 0.1875 T-m

PEATONALPpeat = 0 Ton/m2brazo = 1.575M peatonal = 0 Ton - m

Mtotal = 0.09359937 Ton - m

CALCULO DEL ACERO PARA MOMENTO NEGATIVOMOMENTO TOTAL

c) CRITERIOS LRFD APLICABLES

RESISTENCIA 1 U= 1.25 DC + 1.50 DW + 1.75 (LL+IM)SERVICIO 1 U= 1.00 DC + 1.00 DW + 1.00 (LL+IM)

d) ESTADO LIMITE DE RESISTENCIA 1

Calculo del acero principal (perpendicular al trafico)


Mu = n ( 1.25 Mdc + 1.50 Mdw + 1.75 Mll+im)

Mu = 1.25 x 0.96444 + 1.5 x 0.0455625 + 1.75Mu = 7.84 T-m

Para el Estado Lmite de Evento Extremo II, con n= nDnRnI=1:

Mu = n[1.25 MDC + 1.50 MDW + 1.00 MCT ] (Tabla 3.4.1-1)

Mu = 1.25 x 0.96444 + 1.5 x 0.0455625 + 1Mu = -2.38 T-m

UTILIZANDO As 1/2" RECUBRIMIENTO r = 5 cm

z = 5 + 1.27 = 5.635 cm2

d = 18 cm - 5.635 cm = 12.365 cm

Fy = 4200 Kg/cm2f'c = 280 Kg/cm2d = 12.365 cmb = 1.00 mMu = (2.38) T-m1 = 0.850

As = Mu = -4.446 cm2 -4.446 -4.446CASO EXT 1 Fy (d-a/2)

-0.785 -0.785 -0.785

a = As Fy = -0.785 cm -0.785 -0.785 f'c b

Usando varilla de 1/2" la separacion sera : s = 1.29 = -0.290148448 m-4.446

USAR 1 1/2" @ -0.295 m.


como :

c = a / 1 = -0.785 / 0.85 = -0.9235294118 cmd = 12.365 cm

c / d = -0.07468899 -3.168639142 T-m OK


% = 3840

% = 3840 = 3840 = 121.4314621505 % entonces 67 % S 1000

As rep = 67.00 x -4.446 = -2.98 cm2

Usando varilla de 1/2" la separacion sera : s = 1.29 = -0.43 m -2.98

USAR 1 1/2" @ -0.44 m.

II) DISEO DE LA VIGA PRINCIPAL EXTERIOR

A) PREDIMENSIONAMIENTO 1.6

h max = 2.8 m

diaframab= 0.25

0.6B) MOMENTOS DE FLEXION POR CARGAS (VIGA EXTERIOR)

TOMANDO VIGAS DIAFRAGMA EN APOYOS Y EN CENTRO DE LUZ

CARGA MUERTA (DC)

CARGAS DISTRIBUIDAS

Plosa = 0.18 x 1.6 x 2400 = 691.2 Kg/mPviga = 2.62 x 0.6 x 2400 = 3772.8 Kg/mPcartela = 0.15 x 0.15 x 2400 = 54 Kg/mPbarrera = 1 x 1 x 0 = 0 Kg/mPvereda 0.15 x 0 x 2400 = 0 Kg/m

0.28 x 0 2400 = 0 Kg/mViga Peri = 0.30 x 0.3 x 2400 = 108 Kg/mPbaranda = 1 x 1 x 150 = 150 Kg/m

4776 Kg/m

Mdc = 4776 x 30 ^2 = 537300 Kg-m8

537.3 T-m

CARGAS PUNTUALES

NUMERO DE VIGAS DIAFRAGMA = 2 UNI

P diaf = 2.47 x 0.25 x 0.5 x 2400 = 7410.741

LONGITUD DE LAS VIGAS DIAFRAGMALvd = 0.5 m

SEPARACION DE LAS VIGAS DIAFRAGMASvd = 30 m

CALCULO DEL MOMENTO POR CARGA PUNTUALPESO DIST DIST ACU Ra Rb MOMENTO

VD1 1 0.741 0 0.00 0.741 0 0.000VD2 2 0.741 30 30.00 0 0.741 0.000VD3 0VD4 0VD5 0VD6 0VD7 0VD8 0VD9 0VD10 0VD11 0VD12 0VD13 0VD14 0VD15 0

REACCION TOTAL 0.741 0.741 0.000 T-m

0.0000.1000.2000.3000.4000.5000.6000.7000.8000.9001.000

Column H

M dc = 537.3 + 0.000 = 537.3 T-m


W asf2"= 0.05 x 2250 x 1.6 = 180 Kg/m0.18 T/m

M dw = Wdw L^2 = 20.25 t-m8

CARGA VIVA (LL)

Mmax(ll+im) = 387.329493 T-m

EL % DE MOMENTO QUE SE DISTRIBUYE EN UNA VIGA INTERIOR ES :

CASO DE UN CARRIL CARGADO

REGLA DE MOMENTOS

0.5 2.20 1.10.5 0.40 0.20.5 0 00.5 0 0

1.3Ra 1.3 = 0.8125 P

1.6

Factor de presencia multiple para 1 carril = 1.2g = 0.8125 1.2 = 0.975

CASO DE DOS CARRILES CARGADOS

de = 1.20 m

e = 0.77 + de/2800 =

e = 1.19857143

g int = 0.5901358

g = 0.5901358 1.19857143 = 0.7073199114

CASO PUENTES DE VIGA Y LOSA CON DIAFRAGMAS RIGIDAMENTE CONECTADOS

UN CARRIL CARGADO

Nl = NUMERO DE CARRILES CARGADOS = 1 2Nb = NUMERO DE VIGAS = 4e = EXCENTRICIDAD DEL CAMION DE DISEO O CARGA DE CARRIL RESPECTO AL CENTRO DE GRAVEDAD DEL CONJUNTO DE VIGASe = 2.1

-0.9Xext = Distancia horizontal desde el centro de gravedad del conjunto de vigas hasta la viga exterior

2.7x = distancia horizontal desde el centro de gravedad del conjunto de vigas hasta cada viga

x1 = 2.4x2 = 0.80x3 = 0.00

R = 1 + 2.7 2.1 = 0.692968754 2 2.4 2 0.8 2

DOS CARRILES CARGADOS

g = 0.8315625

R = 2 + 2.7 2.1 -0.9 = 0.7531254 2 2.4 2 0.8 2

PRESENCIA MULTIPLE 1

g = R = 1 0.753125 = 0.753125

FACTOR DE DISTRIBUCION CRITICO =

g = 0.975g = 0.70731991g = 0.8315625g = 0.753125

g = 0.975

Mll+im = 0.975 x 387.329493 = 377.6462555614 t-m

C) CRITERIOS LRFD APLICABLESRESISTENCIA 1 U= 1.25 DC + 1.50 DW + 1.75 (LL+IM)SERVICIO 1 U= 1.00 DC + 1.00 DW + 1.00 (LL+IM)FATIGA U= 0.75 (LL+IM)




Mu = n ( 1.25 Mdc + 1.50 Mdw + 1.75 Mll+im)

Mu = 1.25 x 537.3 + 1.5 x 20.25 + 1.75Mu = 1,362.88 T-m

ANCHO EFECTIVO DE LA VIGA T , ES EL MENOR VALOR DE:

L/4 = 30 / 4 = 7.5 m

12 t losa + t viga = 2.76 m

S = 2.3 m

Entonces b = 2.3 m

2.3

2.62

diaframab= 0.25

0.6

Acero principalNumero del diametro a usar = 8 Numero Acero Area (cm2.) (cm)Recub. = 5 cm 0.05Recub. Lat = 4 cm 0.04 3 3/8" 0.71 0.95 = 1" 4 1/2" 1.27 1.27Area = 5.1 5 5/8" 1.98 1.59Diametro= 2.54 0.0254 6 3/4" 2.85 1.91

8 1" 5.1 2.54Estribos 10 1.1/4" 7.92 3.18Numero del diametro a usar = 4 11 1.3/8" 9.58 3.49

= 1/2"Area = 1.27Diametro= 1.27 cm 0.0127Separacion de barras horizontal= 3.81 cm 0.0381Separacion de barras horizontal= 1.5" = 3.81 0.0381

1 arreglo de varillas = 4 2 2 2 2 2 2 2rec est 88 2 oo 0 oo 0 oo 0

4 1.27 2.54 2.54 2.54 2.54 2.54 2.54 2.54 2.542.54 2.54 0 0 0 0 0 0

Nro de espacios 1 2 3 4Separacion filas =2 arreglo de varillas = 2 2 1 1 1 1 1 1rec est oo 0 o 0 o 0 o 0

4 1.27 2.54 2.54 2.54 0 2.54 0 2.54 00 0 0 0 0 0 0 0


Separacion filas =3 arreglo de varillas = 4 2 2 2 2 2rec est 88 2 oo 0 oo 0 oo 0

4 1.27 2.54 2.54 2.54 2.54 2.54 2.54 2.54 2.542.54 2.54 0 0 0 0 0 0


SEP ENTRE PAQUETES 6.02 OK 0.06015SEP ENTRE PAQUETES 7.92 OK 0.0792SEP ENTRE PAQUETES 6.02 OK 0.06015

AREA Y YA z = 2390.319 =FILA 1 51 7.54 384.54 158.1FILA 1a 20.4 10.08 205.632FILA 2 35.7 16.43 586.551 d = 280 cm -FILA 2a 0 17.7 0FILA 3 30.6 22.78 697.068FILA 3a 20.4 25.32 516.528

158.1 cm2 2390.319 cm3

Fy = 4200 Kg/cm2 Mu = As 0.9 Fy (d-a/2) = 1546.73081 Ton - mf'c = 280 Kg/cm2d = 264.880968 cm a = As Fy = 12.13 cmb = 2.30 m f'c bMu = 1,362.88 T-m c = 14.27058824 cm1 = 0.850

As = 158.1 cm2


como :

c = a / 1 = 12.13 / 0.85 = 14.270588235 cmd = 264.880968 cm

c / d = 0.05387548

a) = 1214.0307 T-mb) = 1,812.63 T-m

Menor valor = 1214.0307 T-m la cantidad de acero calculada 158.1 cm2Mu = 1,362.88 T-m > 1214.0307 T-m OK

USAR 31 1"

ARMADURA DE CONTRACCION Y TEMPERATURA EN CARAS LATERALES

EN EL ALMA DE LA VIGA T

As min = 0.756 Ag/Fy =

As min = 0.756 x 600 x ( 2800 - 180 )4200 / 10.197

As min = 2885.34 mm2 = 28.85 cm2

As min = 28.85 = 14.43 por cara2

Consideraciones

Smax = 3 t = 3 x 0.6 = 1.8 mSmax = 45 cm

Usamos 8 1/2"



Ms = n ( 1.00 Mdc + 1.00 Mdw + 1.00 Mll+im)

Mu = 1 x 537.3 + 1 x 20.25 + 1Mu = 935.20 T-m



f sa = Z

bw = ANCHO DEL ALMA = 60 cm

31

A = = 2 x 13.8490322581 x 60 = 53.6091571331

Z = 30000 N/mmZ = 30000 x 1.0197 = 30591 kg/cm

luego

f sa = 30591 Kg/cm = 3378.372542373 Kg/cm2( 13.8490323 cm x 53.60915713

f sa

n = Es = 7.94300452Ec

160 cm

yEN

264.88 278.73c

13.85 (fs/n)

60


Ast = n x As =7.94300452 x 158.1 = 1255.789013983 cm2


160 y (y/2) = 1255.78901 ( 264.8809677 - y)80 y^2 + 1255.78901 y - 332634.6093035 = 0

y = -1255.789 + 1577006.048 + 106443074.98160

y = 57.1092621

y = -72.806625


I = Ast (ds - y)^2 + by^3/3

I = 64145126.3 cm4

Luego

fs = Ms c n = 935.196256 x 100000 x 207.77 x 7.943004516I 64145126.25517

= 2406.08136 Kg/cm2 < 2520 OK


PARA EL DISEO POR FATIGA, CON n = nd nr n1 = 1


1.- CARGA DE FATIGA

Tomando momento de viga interior


CONSIDERANDO EL ANCHO EFECTIVO PARA UN SOLO CARRILCARGADO (ELIMINADO EL FACTOR DE PRESENCIA MULTIPLE 1.2) Y IM= 0.15(TABLA 3,6,2,1,-,1)

Mfat = 1.00 x 0.75 x 1.15 x 178.138413253 x E

Mfat = 153.644381 x 0.71 = 90.56 T-m/m1.2

2.- SECCION FISURADASE UTILIZA LA SECCION FISURADA SI LA SUMA DE ESFUERZOS DEBIDO A CARGAS PERMANENTES NO MAYORADAS MAS 1.5 VECES LA CARGA DE FATIGA, DAN POR RESULTADOUNA TENSION DE TRACCION MAYOR QUE 0.25 f'c


f trac = 0.25 f'c = 1.31003475 MPa

f trac = 13.3584243 Kg/cm2


M' fat = 1 x 537.3 + 1 x 20.25 + 1.5

M' fat = 693.39 T-m

f fat = Mfat = 693.39 x 100000 = 23.07 Kg/cm2S 3005333.333

Como f fat = 23.07 Kg/cm2 > 13.3584243083 Kg/cm2 se usara seccion agrietada

3.- VERIFICACION DE ESFUERZOSEsfuerzo en el refuerzo debido a la carga viva

As = 31 1" 0 = 158.1 cm2

jd = d - y/3 = 264.880968 - 57.1092621 = 245.84454704 cm revision agrietamiento3

= 90.56 100000 = 233.00158287 Kg/cm2As (jd) 158.1 245.844547

f LL = Mfat


El esfuerzo mnimo es el esfuerzo por carga viva mnimo combinado con el esfuerzopor carga permanente

El momento por carga muerta para la viga interior es:

MDL = MDC + MDW = 537.3 + 20.25 = 557.55 T-m


= 557.55 100000 = 1434.4696709 Kg/cm2As (jd) 158.1 245.844547

f DL = MDL

Por ser viga simplemente apoyada, el esfuerzo por carga viva mnimo es cero.

Luego, el esfuerzo mnimo es:

f min = 0 + 1434.46967 = 1434.469670898 Kg/cm2

El esfuerzo mximo es el esfuerzo por carga viva mximo combinado con el esfuerzopor cargas permanentes:

f max = 233.001583 + 1434.46967 = 1667.471253764 Kg/cm2

El rango de esfuerzos es: f = fmx fmn = 233.0015828656 Kg/cm2

El rango lmite es:

f 233.0015828656 Kg/cm2 OK

MODELO PROPUESTO

0-0.325

0.15 0.175

0.477 3/8"

0.85

1 1/2"0.25 @ 0.17

0.13 asf = 0.05

0.2LOSA

A) Resistencia en flexin alrededor de un eje vertical a la barrera (Mw)

0-0.325

0.15 0.175

0.075 d1

0.1975-0.038 0.47

A1 d2 0.85

0.19751 1/2"

0.25 @ 0.17 A2d3

4 3/8"d4 0.13 asf = 0.05 A3

0.2LOSA

SECCION A1

z = recub + + /2 = 2 2.54 + 2.54 + 3 2.542 8 2

z = 6.82625

di = 7.5 cmd2 = -3.84308511 - 6.82625 = -10.6693351064 cmd3 = -17.5 - 6.82625 = -24.32625 cm

d = d1 + d2 + d3 = -9.165195035 cm3

As = 2.5 x 3/8" = 2.5 0.71 = 1.775 cm2

a = As Fy / (.85 x f'c x b) = 1.775 4200 = 0.6664580726 cm0.85 280 47

= 1 (caso eventos extremos, AASHTO 1.3.2.1 )

Mu = As Fy (d - a/2) = 1 1.775 4200 ( -9.1651950355 - 0.6664580732

Mu = -70810.7515 Kg - cm = -0.7081075 T - m

SECCION A2

d3 = -24.32625 cmd4 = 0 - 6.82625 = -6.82625 cm

d = d3 + d4 = -15.57625 cm2

As = 1 x 3/8" = 1 0.71 = 0.71 cm2

a = 0.71 4200 = 0.5011764706 cm0.85 280 25

Mu = 1 0.71 4200 ( -15.57625 - 0.5011764706 )2

Mu = -47195.6316 Kg - cm = -0.4719563 T - m

SECCION A3

d4 = -6.82625 cm

As = 0.5 x 3/8" = 0.5 0.71 = 0.355 cm2

a = 0.355 4200 = 0.4819004525 cm0.85 280 13

Mu = 1 0.355 4200 ( -6.82625 - 0.4819004525 )2

Mu = -10537.1955 Kg - cm = -0.105372 T - m

Momento Total

Mw = -0.70810751 + -0.4719563 + -0.1053719554 =

Mw = -1.28543579 T - m

B) Resistencia en flexin alrededor de un eje paralelo al eje longitudinal del puente (Mc)

Se calcula de acuerdo a las lneas de rotura con el momento de flexin negativo.ste produce esfuerzos de tensin en la cara inclinada de la barrera, determinandoel refuerzo de la barrera para esa cara.

Utilizando 1 1/2 @ 0.17m, considerando fajas de 1m de ancho:

As = 1.29 cm2Sep = 0.17 m

As = 7.58823529 cm2/m

SECCION A1

z = recub + /2 = 2 2.54 + 2.542 2

z = 5.715

d = -9.55808511 cm

a = As Fy / (.85 x f'c x b) = 7.58823529 4200 = 1.339100346 cm

0.85 280 100


Mu = As Fy (d - a/2) = 1 7.588235294 4200 ( -9.5580851064 - 1.3391003462

Mu = -325960.753 Kg - cm = -3.2596075 T - m

SECCION A2

d = -17.5 + 0 - 5.715 = -14.465 cm2

a = As Fy / (.85 x f'c x b) = 7.58823529 4200 = 1.339100346 cm0.85 280 100


Mu = As Fy (d - a/2) = 1 7.588235294 4200 ( -14.465 - 1.3391003462

Mu = -482347.017 Kg - cm = -4.8234702 T - m

SECCION A2

d = 0 - 5.715 = -5.715 cm

a = As Fy / (.85 x f'c x b) = 7.58823529 4200 = 1.339100346 cm0.85 280 100


Mu = As Fy (d - a/2) = 1 7.588235294 4200 ( -5.715 - 1.339100346

2Mu = -203479.37 Kg - cm = -2.0347937 T - m

EL MOMENTO PROMEDIO ES

Mc = -3.25960753 47 + -4.823470167 25 + -2.0347936963 1385

Mc = -3.53224266 T - m

C) Longitud crtica de la lnea de rotura (Lc) segn el patrn de falla

Siendo:Lt = longitud de distribucin longitudinal de la fuerza de impacto Ft = 1.07 m para el nivel TL-4 (Tabla A13.2-1)H = altura de la barrera = 0.85 mMb= resistencia flexional adicional en la parte superior del muro = 0Mw= resistencia flexional del muro respecto de su eje vertical = -1.2854357861 T - mMc= resistencia flexional de los muros en voladizo respecto de un eje paralelo al eje longitudinal del puente = -3.5322426583 T - mLc = longitud crtica de la lnea de rotura en el patrn de falla

Lc = 2.1965795 m

D) Resistencia nominal a la carga transversal Rw

Siendo:Ft = 240,000N para el nivel TL-4 = 24.47 T (Tabla A13.2-1)Rw = resistencia del parapeto

Rw = -18.2561219 > Ft = 24.47 T REVISE

E) Transferencia de cortante entre la barrera y la losa

Cortante actuante:

Vct = Rw / (Lc + 2H) = -18.256122 = -4.6851660272 T/M2.1965795 + 1.7

Cortante resistente:

Para concretos vaciados en diferente momento

Acv = rea de corte en contacto = 0 100 = 0 cm2Avf = rea del dowel en el plano de corte= 11/[email protected] (en razn de que slouna pata est anclada) = 1.29 cm2 / 0.17 m = 7.5882352941 cm2 / mc = factor de cohesin (5.8.4.2) = 0.52 Mpa = 5.3 Kg/cm2 (caso 3) = 0.6 = 0.6 1 = 0.6 (caso 3)f'c = 280 Kg/cm2Fy = 4200 Kg/cm2Pc = fuerza de compresin permanente perpendicular al plano de cortepeso de la baranda = 0 Kg

En 1 m de ancho de barrera se tendra :

Vn = 5.3 0 + 0.6 ( 7.5882352941 4200 + 0Vn = 19122.3529 Kg

19.1223529 Ton

Vn = 0.2 280 0 = 0 Kg.= 0 Ton

Vn = 5.5 0 0.10197 = 0 Kg.

fac conversion 0 Ton

Vn = 19.1223529 Ton Vct = -4.6851660272 Ton/m OK

F) Chequeo del Dowel

La armadura por corte debe satisfacer en interfases entre hormign de losas yvigas, por unidad de longitud de viga:

Avf >= .35 bv / Fy

Siendo:bv = ancho de la interfase = 0 mmFy = 4200 Kg/cm2 = 411.8793 Mpa

fact conver 10.1971621

Avf = 0.35 0 1000 mm = 0 mm2 / m411.8793 1000 mm

= 0 cm2 / m

1 1/2" @ 0.17 = 7.5882352941 cm2 / m > 0 OK

G) Longitud de anclaje

100 db / (f'c ^.5) =

db = 1/2" = 12.7 mmf'c = 280 Kg/cm2 = 27.45862 MPa

100 12.7 = 242.3619106 mm27.45862 ^ .5

= 24.23619106 cm

Considerando que el recubrimiento lateral perpendicular al plano del gancho esmayor o igual que 64mm, la longitud bsica de anclaje se afectar por el factor 0.7(5.11.2.4.2).

0.7 24.2361911 = 16.9653337424 cm

16.9653337 >= 10.16 y 15 cm OK

Se dispone para la longitud de desarrollo slo de 15 cm, lo cual no essatisfactorio. Sin embargo, considerando que cuando hay ms armadura quela requerida la longitud bsica de desarrollo disminuye segn la relacin

As provista

7.58823529 15 = 6.70918304 cm216.9653337

La longitud bsica de anclaje (hb) para una barra terminada en gancho es:

hb =

hb =

dh = .7 hb =

La longitud de anclaje dh no debe ser menor que 8db 15cm (5.11.2.4.1)

dh =

As requerida x hb =

As requerida =

Se necesita recalcular la capacidad de la barreraSe usara esta area para hacer el recalculo

a = As Fy / (.85 x f'c x b) = 6.70918304 4200 = 1.1839734776 cm0.85 280 100


Mc,I = As Fy (d - a/2) = 1 6.70918304 4200 ( -9.5580851064 - 1.1839734782

Mc,I = -286014.497 Kg - cm = -2.860145 T - m

Mc,II = As Fy (d - a/2) = 1 6.70918304 4200 ( -14.465 - 1.1839734782

Mc,II = -424284.336 Kg - cm = -4.2428434 T - m

Mc,III = As Fy (d - a/2) = 1 6.70918304 4200 ( -5.715 - 1.1839734782

Mc,II = -177721.86 Kg - cm = -1.7772186 T - m

entonces

Mc = -2.86014497 0.47 + -4.242843363 0.25 + -1.7772185954 0.130.85

Mc = -3.10119694 T - m

Lc = 2.29704493 m

Rw = -16.7613851 > Ft = 24.47 T REVISE

Con lo que la longitud de desarrollo ldh=15cm, es adecuada. Las barras terminadasen gancho deben adems extenderse 12db+4db=16(1.27)= 20.32 cm

(C5.11.2.4.1)

Diseo por Corte (viga interior)

Seccin crtica por corte cerca al apoyo extremoDe acuerdo al Art. 5.8.3.2, cuando la reaccin en direccin del cortante aplicadointroduce compresin en la regin extrema, la seccin crtica por corte se localizacon el mayor valor de 0.5dvcot o dv, desde la cara interna del apoyo.

269.0404444Seccion critica por cortante

= 4512.5 12.5

Determinacin del peralte efectivo por corte (Art. 5.8.2.9)_x0001_ = 45 (procedimiento simplificado, Art. 5.8.3.4)

dv = peralte de corte efectivo = de - a/2 = 264.1344444 - 15.188 = 256.54044442

no menor que el 0.90de= 0.9 x 264.1344444 = 237.721 cm okmayor valor de 0.72h = 0.72 x 280 = 201.6 cm

La seccin crtica por corte se ubica desde el eje del apoyo en:

12.5 + 256.540444 = 269.0404444444 cm

A la distancia de 2.69040444 mCarga muerta (DC)Con wDC=155 4566 Kg/my Pdiaf = 1470 Kg

Vdc= 56.9406133 T

1470 Kg1470 Kg

15 152.690

4566 Kg/mA

Ra= 70695 Kg luz = 30 m

684902205

Superficie de rodadura (DW) 70695Con wDW= 0.18VDW = 2.2157272 T

a) Camin de DiseoV= 27.0692857 T

14.8 T 14.8 T 3.6 T

2.690 4.3 4.3

A

Ra= 27.0692857 T luz = 30 m

b) Tandem de DiseoV= 19.9431647 T

11.2 T 11.2 T

2.690 1.2 26.11

A

Ra= 19.9431647 T luz = 30 m

c) Carga de carril

V= 11.8172117 T

2.690

A

Ra= 14.4 T luz = 30 m

Luego VLL+IM= 47.8193618 T

Distribucin en viga interior:Caso de un carril cargado:

g = 0.36 + S (Tabla 4.6.2.2.3a-1)7600

g = 0.36 + 1600 = 0.57052631587600

Caso de dos carriles cargados:

g = 0.2 + S - (S/10700) 2 (Tabla 4.6.2.2.3a-1)3600

g = 0.2 + 1600 - ( 1600 ) 2 = 0.622084413 CRITICO3600 10700

VLL+IM= 0.62208441 x 47.8193618 = 29.747679602 T29747.67960196 Kg

Para el Diseo por Estado Lmite de Resistencia I, con n= nDnRnI=1:

Vu = n[1.25 VDC + 1.50 VDW + 1.75 V(LL+IM)] (Tabla 3.4.1-1)

Vu = 1.25 x 56.9406133 + 1.5 x 2.2157272 + 1.75Cortante actuante : Vu = 126.5577967

Cortante resistente : Vr = Vn (5.8.2.1-2) = 0.9 (5.5.4.2)

siendo Vn el menor de:Vn = Vc+Vs+ Vp (5.8.3.3.-1)Vn = 0.25 fc bv dv + Vp (5.8.3.3-2)

Donde:

Cortante resistente concreto

Vc = 0.53 f'c bv dv

Vc = 0.53 x 280 ^.5 x 60 x 256.5404444

Vc = 136509.218 kg siendo bv = ancho del alma= 30 0.6 CM

Cortante resistente acero:

Asumiendo una separacion de 15 cm con barras de 1/2" 1.29 cm2

Vs = Av Fy dv / s

Vs = 2.58 x 4200 x 256.5404444444 = 185324.8170667 Kg15

donde:

Componente fuerza pretensado Vp=0

Cortante nominal resistente

El menor valor de Vn

Vn = 136509.218 + 185324.817 + 0 = 321834.0349623 kgVn = 0.25 x 280 x 60 x 256.5404444444 = 1077469.867

Luego Vn = 321834.035 kg

Cortante resistente total

Vr = Vn = 0.9 (Vn) = 289650.631 kg > 126557.7967368 kg ok

Refuerzo transversal mnimo

Av = 0.27 f'c bv s =Fy

0.96813517 cm2 < 2.58 cm2 ok

Espaciamiento mximo del refuerzo transversal

vu = Vu - Vp = Vp = 0 bv dv

vu = 126.557797 = 9.1356468475 Kg/cm20.9 60 256.540444

Tambin:si vu < 0.125fc smx= 0.8dv = 0.125fc smx= 0.4dv

-2.00 -1.00 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 11.00 12.00

-2

-1

0

1

2

0.00

ALTURA DE VIGASH TEORICO = 2.100 mASUMIDO = 2.8 m

3 cm5 5/8"

OKOK

3

2.5 cm5 5/8"

OKOK

4

5 cm4 1/2"

@ -0.295 m.OKOK

4@ -0.435 m.

0.00 0.000.00 0.00 0.00 0.000.00 0.00 0.00 0.000.00 0.00 0.00 0.00

0.00 0.000.00 0.00

0.000 0.0000 0 0 0

0.000 0.000 0.000 0.0000.000 0.000 0.0000.000 0.000 0.0000.000 0.000 0.0000.000 0.000 0.0000.000 0.000 0.0000.000 0.000 0.0000.000 0.000 0.0000.000 0.000 0.0000.000 0.000 0.0000.000 0.000 0.0000.000 0.000 0.0000.000 0.000 0.0000.000 0.000 0.0000.000 0.000 0.0000.000 0.000 0.0000.000 0.000 0.0000.000 0.000 0.000

0.000 0.000 0.000 0.000 0.000

0.269 0.0000.000 0.000 0.000 0.000 0.000

0.00 0.00

0.000 0.0000 0 0 0

0.000 0.000 0.000 0.0000.000 0.000 0.0000.000 0.000 0.0000.000 0.000 0.0000.000 0.000 0.0000.000 0.000 0.0000.000 0.000 0.0000.000 0.000 0.0000.000 0.000 0.0000.000 0.000 0.0000.000 0.000 0.0000.000 0.000 0.0000.000 0.000 0.0000.000 0.000 0.0000.000 0.000 0.0000.000 0.000 0.0000.000 0.000 0.0000.000 0.000 0.000

0.000 0.000 0.000 0.000 0.000

1.683 0.0000.000 0.000 0.000 0.000 0.000

0.00 0.00

0.000 0.0000.000 0.000 0.000 0.0000.000 0.000 0.000 0.0000.000 0.000 0.0000.000 0.000 0.0000.000 0.000 0.0000.000 0.000 0.0000.000 0.000 0.0000.000 0.000 0.0000.000 0.000 0.0000.000 0.000 0.0000.000 0.000 0.0000.000 0.000 0.0000.000 0.000 0.0000.000 0.000 0.0000.000 0.000 0.0000.000 0.000 0.0000.000 0.000 0.0000.000 0.000 0.0000.000 0.000 0.000

0.000 0.000 0.000 0.000 0.000

0.714 0.0000.000 0.000 0.000 0.000 0.000

0.000 0.0000.000 0.0000.000 0.0000.000 0.0000.000 0.0000.000 0.0000.000 0.0000.000 0.0000.000 0.0000.000 0.0000.000 0.000

0.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.000

0.000 1.000 2.000 3.000 4.000 5.000 6.000 7.000 8.000 9.000

-1.000-0.5000.0000.5001.0001.5002.0002.5003.000

0.0000.4850.0000.000

2.237 1.718

0.074

1.862

-0.030-0.180 -0.180 -0.030

1.862

0.074

0.000 0.000 T-M0.269 0.000 T-M

-0.15

0.000 1.000 2.000 3.000 4.000 5.000 6.000 7.000 8.000 9.000

-1.000-0.5000.0000.5001.0001.5002.0002.5003.000

0.0000.4850.0000.000

2.237 1.718

0.074

1.862

-0.030-0.180 -0.180 -0.030

1.862

0.074

-0.15

21 22 22.5 23 24 2511456 11172 11030 10892.66667 10618 10343.333

1.17 1.14 1.12 1.11 1.08 1.05

316.205 20

7.042 7.042 7.042 7.042 7.04 6.988

1.243 1.243 1.243 1.242 1.233 11.243 1.243 1.243 1.243 1.242 1.233

10.197 kg/cm2

33.66322926 kg/cm2

resiste

mm =

16.705 20

2.5

7.141 7.141 7.141 7.141 7.138 7.083

1.26 1.26 1.26 1.26 1.25 11.26 1.26 1.26 1.26 1.26 1.25

10.197 kg/cm2

33.66322926 kg/cm2

resiste

0.2

0.15

0.152.45 2.8

0.15

KgTn

0.0000.1000.2000.3000.4000.5000.6000.7000.8000.9001.000

Column H

11.775

Bt

15.8606666667

T

9.97

Bt

15.7973333333

T-mT-mT-m

Bt

11.424 T

Bt

Bt

0.2

0.15

0.152.8

0.15

x 228.58 =

0.2

0.15 lopez-777hottmail.com

0.152.8

0.15

3 1 0 0 0 08 1 0 0

2.54 0 0 0 0 02.54 0 0 0 0 0

0 0 0

2 2 0 0 0 0oo 0 0 0

2.54 2.54 0 0 0 00 0 0 0 0 0

0 0 0

3 1 0 0 0 08 1 0 0

2.54 0 0 0 0 02.54 0 0 0 0 0

0 0 0

15.86555556 cm

15.86555556 cm = 264.1344444 cm

OK, PERO REVISE SI HAY DEMAS

FUNCIONA COMO VIGA T

10.197 kg/cm2

33.66322926 kg/cm2

resiste

x 228.58 =

cm2

x 228.58 =

Bt

11.12

Bt

9.458

T-mT-m

8.25

Bt

17.02

T8.93

Bt

14.638

T-mT-mT-m

x 55.02

Ton 7.4 Ton

1.8

0.6

MOMENTO311.04

00000

653.4964.44 Kg - m

0.96444 Ton - m

x 3.7499285601 =

x -3.656329195

5

12.365 18

-4.446 -4.446 -4.446 -4.447 -4.436 -4.781

-0.785 -0.785 -0.785 -0.783 -0.844 1

-0.785 -0.785 -0.785 -0.785 -0.783 -0.844

10.197 kg/cm2

33.66322926 kg/cm2

resiste

0.18

0.15

0.152.47 2.8

0.15

KgTn

0.0000.1000.2000.3000.4000.5000.6000.7000.8000.9001.000

Column H

EXCENTRICIDAD DEL CAMION DE DISEO O CARGA DE CARRIL RESPECTO AL CENTRO DE GRAVEDAD DEL CONJUNTO DE VIGAS

x 377.65 =

0.18

0.15

0.152.8

0.15

ARREGLO DE VARILLAS01 o 2.54 02 oo 2.54 2.543 8 2.54 04 88 2.54 2.545 8o 2.54 2.546 o8 2.54 0

4 2 0 0 0 088 2 0 0

2.54 2.54 0 0 0 02.54 2.54 0 0 0 0

0 0 0

2 2 0 0 0 0oo 0 0 0

2.54 2.54 0 0 0 00 0 0 0 0 0

0 0 0

4 2 0 0 0 088 2 0 0

2.54 2.54 0 0 0 02.54 2.54 0 0 0 0

0 0 0

15.11903226 cm

15.11903226 cm = 264.8809677 cm

OK, PERO REVISE SI HAY DEMAS

FUNCIONA COMO VIGA T

10.197 kg/cm2

33.66322926 kg/cm2

resiste

x 377.65 =

cm2

x 377.65 =

x 90.56

1470 Kg

B

-70695 T

18.71

B

6.1307142519 T

B

2.4568353185 T

B14.4 T

x 29.747679602

VEREDA IZQ VEREDA DER BARRERA IZQ BARRERA DER0 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 00 0 0 0 VIGA PERIMETRA IZQ VIGA PERIMETRAL DER0 0 0 0 0.3 0 7.5 0

0.3 0.3 7.5 0.3ASFALTO 0.175 0.3 7.625 0.3

0.30 0.05 0.175 1.5 7.625 1.53.90 0.122 0.125 1.5 7.675 1.57.50 0.05 0.125 0.3 7.675 0.3

0 0.3 7.8 0.30 0 7.8 0

SI Numero AceroNO

3 3/8"1 4 1/2"2 5 5/8"3 6 3/4"4 8 1"5 10 1.1/4"6 11 1.3/8"

VIGA INTERIOR VIGA EXTERIORM DC = 513.675 T-m g = 0.5901358022 M DC = 537.3 T-mM DW = 20.25 t-m M LL+IM = 228.57700098 t-m M DW = 20.25 t-m

Mu = 1072.48 T-m Mu = 1,362.88 T-m

Acero Principal Nro = 8 1" Acero Principal Nro = 8Recub = 5 cm Recub = 5Recub lateral = 4 cm Recub lateral = 4Estribos 4 1/2" Estribos 4

ARREGLO DE ACERO As = 137.7 cm2 ARREGLO DE ACERO As =8 oo oo oo 8 d = 264.13 cm 88 oo oo oo 88 d =oo o o o oo a = 15.19 cm oo o o o oo a =8 oo oo oo 8 c = 17.87 cm 88 oo oo oo 88 c =

FUNCIONA COMO VIGA T FUNCIONA COMO VIGA TTOTAL VAR = 27 1" TOTAL VAR = 31 MOM RES = 1335.31 Ton - m OK, PERO REVISE SI HAY DEMAS MOM RES = 1,546.73 Ton - m

As max = 0.06764826

FISURACION 2248.67 Kg/cm2 < 2520 OK FISURACION 2406.08 Kg/cm2 162.2502472551 OK

0.000 1.000 2.000 3.000 4.000 5.000 6.000 7.000 8.000 9.000

-0.400

-0.200

0.000

0.200

0.400

0.600

0.800

1.000

1.200

1.400

1.5 1.6 0.125 1.6 0.125 1.6 0.125 1.5 0.1131.500 1.134 3.100 -0.030 4.700 -0.030 6.300 1.1341.800 0.766 3.400 -0.180 5.000 0.038 6.600 0.8231.925 0.633 3.525 -0.222 5.125 0.087 6.713 0.7242.050 0.512 3.650 -0.252 5.250 0.148 6.825 0.6352.175 0.403 3.775 -0.270 5.375 0.221 6.938 0.5552.300 0.306 3.900 -0.276 5.500 0.306 7.050 0.4852.425 0.221 4.025 -0.270 5.625 0.403 7.163 0.4252.550 0.148 4.150 -0.252 5.750 0.512 7.275 0.3752.675 0.087 4.275 -0.222 5.875 0.633 7.388 0.3352.800 0.038 4.400 -0.180 6.000 0.766 7.500 0.304

1.500 3.100 -0.030 4.700 -0.030 6.300 1.134 7.800 0.269

0.000 1.000 2.000 3.000 4.000 5.000 6.000 7.000 8.000 9.000

-0.400

-0.200

0.000

0.200

0.400

0.600

0.800

1.000

1.200

1.400

0.000 1.000 2.000 3.000 4.000 5.000 6.000 7.000 8.000 9.000

-1.000-0.5000.0000.5001.0001.5002.0002.5003.000

1.5 1.6 0.125 1.6 0.125 1.6 0.125 1.5 0.1131.500 2.548 3.100 -0.313 4.700 -0.313 6.300 2.5481.800 1.862 3.400 -0.463 5.000 0.074 6.600 2.2371.925 1.596 3.525 -0.505 5.125 0.255 6.713 2.1382.050 1.343 3.650 -0.535 5.250 0.449 6.825 2.0492.175 1.101 3.775 -0.553 5.375 0.654 6.938 1.9692.300 0.872 3.900 -0.559 5.500 0.872 7.050 1.8992.425 0.654 4.025 -0.553 5.625 1.101 7.163 1.8392.550 0.449 4.150 -0.535 5.750 1.343 7.275 1.7892.675 0.255 4.275 -0.505 5.875 1.596 7.388 1.7492.800 0.074 4.400 -0.463 6.000 1.862 7.500 1.718

1.500 3.100 -0.313 4.700 -0.313 6.300 2.548 7.800 1.683

0.000 1.000 2.000 3.000 4.000 5.000 6.000 7.000 8.000 9.000

-0.500

0.000

0.500

1.000

1.500

2.000

1.50 1.60 0.125 1.6 0.125 1.6 0.125 1.5 0.1131.500 1.579 3.100 -0.119 4.700 -0.119 6.300 1.5791.800 1.110 3.400 -0.269 5.000 0.049 6.600 1.2671.925 0.936 3.525 -0.311 5.125 0.140 6.713 1.1682.050 0.773 3.650 -0.341 5.250 0.243 6.825 1.0792.175 0.623 3.775 -0.359 5.375 0.357 6.938 1.0002.300 0.484 3.900 -0.365 5.500 0.484 7.050 0.9302.425 0.357 4.025 -0.359 5.625 0.623 7.163 0.8702.550 0.243 4.150 -0.341 5.750 0.773 7.275 0.8202.675 0.140 4.275 -0.311 5.875 0.936 7.388 0.7792.800 0.049 4.400 -0.269 6.000 1.110 7.500 0.748

1.500 3.100 -0.119 4.700 -0.119 6.300 1.579 7.800 0.714

0.000 1.000 2.000 3.000 4.000 5.000 6.000 7.000 8.000 9.000

-0.500

0.000

0.500

1.000

1.500

2.000

LINEA DE PESO VIGA PERIMETRAL BRAZO DE PALANCA

0.1 -0.15 -0.5

-0.7 0.00 -0.5

26 27 28 29 30 45 60 cm10068.667 9794 9519.33333 9244.667 8970 5910 4290 N mm

1.03 1.00 0.97 0.94 0.91 0.60 0.44 mm

ARREGLO DE VARILLAS01 o 2.54 0 1 02 oo 2.54 2.54 2 03 8 2.54 0 1 14 88 2.54 2.54 2 25 8o 2.54 2.54 2 16 o8 2.54 0 2 1

est rec Y0 0 8 2.54

0 2 2.540 0 1.27 4 29.140 0 7.29

43.81

0 0 7 2.540 0 0

0 0 1.27 4 31.680 0 7.92

43.81

0 0 8 2.540 2 2.54

0 0 1.27 4 29.140 0 7.29

4

TOTAL VARILLAS 27

VIGA INTERIOR ESTRIBO ACERO 1a ACERO 1b2.80 -2.80 2.84 -2.75 -2.7246 2.8654 -2.7246 0 0

COORDENADAS 3.36 -2.75 ACERO 1c ACERO 1d3.36 -0.05 -2.6992 2.8654 -2.6992 0 02.84 -0.05 -2.69922.84 -2.75

ESTRIBO ACERO 9a ACERO 9b2.8527 -2.7373 -2.6357 2.8654 -2.6357 2.8908 -2.63573.3473 -2.7373 ACERO 9c ACERO 9d3.3473 -0.0627 0 0 0 0 02.8527 -0.0627 -2.63572.8527 -2.7373

ACERO 17a ACERO 17b2.8654 -2.5722 0 0

ACERO 17c ACERO 17d0 0 0 0

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

1 02 01 12 22 12 1

est rec Y0 0 10 2.54

0 4 2.540 0 1.27 4 24.060 0 6.02

43.81

0 0 7 2.540 0 0

0 0 1.27 4 31.680 0 7.92

4

3.810 0 6 2.54

0 4 2.540 0 1.27 4 24.060 0 6.02

4

TOTAL VARILLAS 31

VIGA EXTERIOR ESTRIBO ACERO 1a ACERO 1b1.2 -2.8 1.24 -2.75 -2.7246 1.2654 -2.7246 1.2908 -2.7246

1.76 -2.75 ACERO 1c ACERO 1d1.76 -0.05 -2.6992 1.2654 -2.6992 1.2908 -2.69921.24 -0.05 -2.69921.24 -2.75

ESTRIBO ACERO 9a ACERO 9b1.2527 -2.7373 -2.6357 1.2654 -2.6357 1.2908 -2.63571.7473 -2.7373 ACERO 9c ACERO 9d1.7473 -0.0627 0 0 0 0 01.2527 -0.0627 -2.63571.2527 -2.7373

ACERO 17a ACERO 17b1.2654 -2.5722 1.2908 -2.5722

ACERO 17c ACERO 17d0 0 1.2908 -2.5468

VIGAS DIAFRAGMA 1 GRAFICO PUENTE1.80 -2.6 0.00 0

2.8 -2.6 0.30 03.9 0.072

VIGAS DIAFRAGMA 2 7.5 03.4 -2.6 7.80 04.4 -2.6 7.80 -0.2 7.80 -3.00

7.80 -0.2 7.80 -3.00VIGAS DIAFRAGMA 3 7.80 -0.20

5 -2.6 7.80 -0.20 7.8 -3.006 -2.6 7.80 -0.20 7.80 -3.00

7.80 -0.20VIGAS DIAFRAGMA 4 7.80 -0.20

0 -2.6 7.80 -0.200 -2.6 7.80 -0.20

7.80 -0.20 7.8 -3.00VIGAS DIAFRAGMA 5 7.80 -0.20 6.30 -3.00

0 -2.6 7.80 -0.200 -2.6 7.80 -0.20

6.75 -0.206.60 -0.356.60 -2.80 6.3 -3.00

Area (cm2.) (cm) 6.00 -2.80 4.70 -3.006.00 -0.35

0.71 0.95 5.85 -0.201.29 1.27 5.15 -0.20

2 1.59 5.00 -0.352.85 1.91 5.00 -2.80 4.7 -3.005.1 2.54 4.40 -2.80 3.10 -3.00

7.92 3.18 4.40 -0.359.58 3.49 4.25 -0.20

3.55 -0.203.40 -0.35

3.40 -2.80 3.1 -3.002.80 -2.80 1.50 -3.002.80 -0.352.65 -0.201.95 -0.20

g = 0.975 1.80 -0.35M LL+IM = 377.64626 t-m 1.80 -2.80 1.5 -3.00

1.20 -2.80 0.00 -3.001.20 -0.351.05 -0.20

1" 0.00 -0.20cmcm

0

158.1 cm2264.88 cm

12.13 cm14.27 cm

FUNCIONA COMO VIGA T1"OK, PERO REVISE SI HAY DEMAS

0.42 OK1214.0307 OK

2520 OK

0.000 1.000 2.000 3.000 4.000 5.000 6.000 7.000 8.000 9.000

-0.400

-0.200

0.000

0.200

0.400

0.600

0.800

1.000

1.200

1.400

0 0.0000.000 0.0000.000 0.0000.000 0.0000.000 0.0000.000 0.0000.000 0.0000.000 0.0000.000 0.0000.000 0.0000.000 0.0000.000 0.000

0.000 1.000 2.000 3.000 4.000 5.000 6.000 7.000 8.000 9.000

-0.400

-0.200

0.000

0.200

0.400

0.600

0.800

1.000

1.200

1.400

0.000 1.000 2.000 3.000 4.000 5.000 6.000 7.000 8.000 9.000

-1.000-0.5000.0000.5001.0001.5002.0002.5003.000

0 0.0000.000 0.0000.000 0.0000.000 0.0000.000 0.0000.000 0.0000.000 0.0000.000 0.0000.000 0.0000.000 0.0000.000 0.0000.000 0.000

0.000 1.000 2.000 3.000 4.000 5.000 6.000 7.000 8.000 9.000

-0.500

0.000

0.500

1.000

1.500

2.000

diseño puente viga

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