DISEÑO DE MURO POR GRAVEDAD

DISEÑO DEL DIMENSIONAMIENTO DE MURO DE CONTENCIONPROYECTO :"SUSTITUCION Y AMPLIACION DE INFRAESTRUCTURA Y EQUIPAMIENTO EN LA INSTITUCION EDUCATIVA PUBLICA VERBENAPAMPA DEL DISTRITO DE CHURUBAMBA, PROVINCIA DE HUANUCO"

PROPIETARIO : MUNICIPALIDAD DISTRITAL DE CHURUBAMBA LUGAR : VERBENAPAMPA - CHURUBAMBA-HUANUCOA-HUANUCO FECHA : JULIO DEL 2011

GEOMETRIA DE MURO

0.30

DATOS FISICOS DEL SUELO DE CIMENTACION A H'= S/ 0.00

CAPACIDAD PORTANTE DEL SUELO (d) 1.25 Kg /cm2 5

1.950 T /m3

ANGULO DE FRICCION DEL SUELO (Ø1) 30.00 Grados 1

PROFUNDIDAD DE CIMENTACION (C.) 0.700 m. 4' 6

DATOS FISICOS DEL SUELO DE RELLENO 1

1.950 T/m3

ANGULO DE FRICCION DEL SUELO (Ø2) 30.000 Grados aprox = #DIV/0! 4.0 = aprox.

ANGULO DE RELLENO MÁXIMO (b) 0.000 Grados h 1.60

3

DATOS FISICOS DEL MURO DE CONTENCION H 2.30

PESO ESPECIFICO DEL MURO (W) 2.30 T /m3

FUERZA A LA COMPRESION DEL CONCRETO (F'c) 175.00 Kg /cm2

2 4

VALORES DIMENSIONALES DE LA GEOMETRIA DEL MURO Dimen. Predimen.

CORONA DE MURO A 0.30 0.18 m.

ALTURA TOTAL DEL MURO H 2.30 2.15 m. 1

ALTURA PANTALLA h 1.60 1.88 m. b 0.70 C= 0.700

INCLINACION CUERPO DE MURO EXTERIOR E 0.00 0.19 m.

INCLINACION CUERPO DE MURO INTERIOR I 0.40 0.09 m. 0.30 0.00 0.30 0.40 0.30

PUNTA DE MURO c 0.30 0.18 m. c E A I d

TALON DE MURO d 0.30 0.18 0.30 0.70

BASE LATERAL DE MURO b 0.70 0.27 m. PESO DEL MURO 3.20 TN M N

BASE INFERIOR DE MURO B 1.30 1.29 m. SECCION DEL MURO 1.71 M2 B

BASE DELANTERA DE MURO M 0.30 m. 1.30

BASE TRASERA DE MURO N 0.70 m.

EMPUJES ADICIONALES

HS20

SOBRECARGA 0.00 Kg/m2

FACTORES DE SEGURIDAD A UTILIZARSE EN EL DISEÑO

F. S. AL VOLTEO 2.00

F. S. AL DESLIZAMIENTO 1.50

F.S. AL CORTE, TRACCION Y COMPRESION 2.00

A) CALCULO DEL EMPUJE LATERAL DEL SUELO

Ka = -

SI : COS(b) = -

-

Ka = -

Usar :

Ka = usar esta formula Ka = 0.33

H' = H + N * Tan æ = 2.30 kg/m C = Ka * q * H = 0.00 kg/m

PESO ESPECIFICO DEL SUELO (g1)


COS(b) x COS(b) – ( COS 2(b) – COS 2(Ø)) 1/2

COS(b) + ( COS2(b) – COS2(Ø))1/2

COS2(Ø) =

Para b = 0

TG2(45 - Ø2/2)

G5 q

G4'

Ev

G6 H'

G3 E C = q.Ka.H

G2 G4 Eh

H/2

G1

O

PESOS DEL MURO Y RELLENO EMPUJE ACTIVO SOBRECARGA

A

B



Pa = 1.72 T. = Pah

Pah = Pa x COS(b) 1.72 T.

0.00

Pav = Pa x SEN(b) - T.

Zona Peso (T) Brazo (m) Brazo (m) Momento (T-m) Momento (T-m)

G1 = b * B * Pm 2.09 0.65 0.35 1.36 0.73 0.62

G2 = 0.5 *E * h * Pm 0.00 0.30 0.00 0.00 0.00 0.94

G3 = A * h * Pm 1.10 0.45 0.15 0.50 0.17

G4 = 0.5 * I * h * Pm 0.74 0.73 0.43 0.54 0.32 0.00

G4' = 0.5 * I * h * Ps 0.62 0.87 0.57 0.54 0.35

G5 = 0.5 * N² * Tan æ * Ps 0.00 1.07 0.77 0.00 0.00 0.00

G6 = d * h * Ps 0.94 1.15 0.85 1.08 0.80 1.10

Pav =PaSen(b) 0.00 0.40 0.10 0.00 0.00 1.72

0.00 0.74

H/3 0.70

TOTALES 5.49 4.01 2.37

2.09

B) CALCULO DEL EMPUJE LATERAL DEL SUELO

* Por Volteo (En la fondo del cimiento)

Calculo de factor de Seguridad: Momento con respecto a la punta (0)

å Pv = 5.49 T

å Me = 4.01 T-m

2.37 T-m

Momento de Volteo (Mv)

Mv = Mv = Pah * H' /3 + C * H/2 = 1.32 T-m B

1.30

Factor de Seguridad (F.S) en A

b

F.S. = å Me / Mv 3.05 >2.00 -YES-

Factor de Seguridad (F.S) en B B/3 B/3 B/3

0.433 0.433 0.433

F.S. = å Me / Mv 1.80 >2.00 THONY te dice -recalcular-X e

* Por Deslizamiento 0.49 0.16

F = 0.90 x TANG (Ø1) 0.52 R

Fr = å Pv x F 2.85 T.

F.S. = Fr / (Pah + C ) = 1.660 >1.5 -YES-

* Ubicación de la Resultante en la Base

X = (åMe - Mv) / åPv > B/3 0.49 > 0.43 -YES-

C) CALCULO DE LA PRESION DEL SUELO

e = B/2 - X 0.16 m.

T /m² 0.73 Kg /cm²

T /m² 0.11 Kg /cm²

qmax = (å Pv / B) +(( å Pv x 6 x e) / B²) 7.33

0.73 < 1.25 -YES-

qmin = (å Pv / B) -(( å Pv x 6 x e) / B²) 1.12

D) VERIFICACION DE CORTE Y TRACCION POR PRESION EN LA PUNTA

Si comparamos la Presion maxima con la Capacidad Portante del Suelo

* Al Corte

b

Y = (qmax x c ) / 3X 1.49 T /m²

T. 1,974.88 Kg. 0.30

q1= qmax - Y 5.84 T /m²

T /m² 0.28 Kg/cm²

V = (q1 x c) + ((qmax - q1) x (c / 2)) 1.97

1.49

Vcac = V / ( b ) 2.82 Kg/cm²

0.49

0.5 x g2 x H'2 x Ka



R

Vcad = 0.53 x Ø x (F'c)½ 5.96 1.47

Donde : Ø = 0.85

F.S. = Vcad / Vcac 21.12 > 2.00 -YES-

T-m 30,743.27 Kg-cm

* A la Traccion

Kg/cm²

M = (( q1 x (c² / 2)) + ((qmax - q1) x (c² / 3 )) 0.31

Kg/cm²

Ftac = ( 6 x M ) / ( b² ) 3.76 T /m² 0.38

Ftad = 1.33 x Ø x (F'c)½ 11.44

Donde : Ø = 0.65

E) VERIFICACION DE ESFUERZOS EN LA INTERSECCION DE MURO CON LA BASE

F.S. = Ftad / Ftac 30.38 > 2.00 -YES-

0.21 T-m 21,275.00 Kg-cm

* A la Traccion

Kg/cm²

M = (Pah x (H/3) - b)) + ((Pav x ((I/h) x (H/3)-b)) +(Wzona4 x I/3)

Kg/cm²

Ftac = ( 6 x M ) / ( b² ) 1.82 T /m² 0.18

Ftad = 1.33 x Ø x (F'c)½ 11.44

Donde : Ø = 0.65

F.S. = Ftad / Ftac 62.71 > 2.00 -YES-



GEOMETRIA DE MURO

0.20



1.950 T /m3




1.950 T/m3



3




2 4








TALON DE MURO d 0.20 0.13 0.20 0.60





EMPUJES ADICIONALES

HS20







Ka = -

SI : COS(b) = -

-

Ka = -

Usar :






COS(b) + ( COS2(b) – COS2(Ø))1/2

COS2(Ø) =

Para b = 0

TG2(45 - Ø2/2)

G5 q

G4'

Ev

G6 H'

G3 E C = q.Ka.H

G2 G4 Eh

H/2

G1

O


A

B



Pa = 0.83 T. = Pah


0.00



G1 = b * B * Pm 0.69 0.50 0.30 0.35 0.21 0.51

G2 = 0.5 *E * h * Pm 0.00 0.20 0.00 0.00 0.00 0.51

G3 = A * h * Pm 0.60 0.30 0.10 0.18 0.06

G4 = 0.5 * I * h * Pm 0.60 0.53 0.33 0.32 0.20 0.00

G4' = 0.5 * I * h * Ps 0.51 0.67 0.47 0.34 0.24

G5 = 0.5 * N² * Tan æ * Ps 0.00 0.80 0.60 0.00 0.00 0.00

G6 = d * h * Ps 0.51 0.90 0.70 0.46 0.35 0.60

Pav =PaSen(b) 0.00 0.32 0.12 0.00 0.00 0.83

0.00 0.60

H/3 0.47

TOTALES 2.90 1.64 1.06

0.69




å Pv = 2.90 T

å Me = 1.64 T-m

1.06 T-m


Mv = Mv = Pah * H' /3 + C * H/2 = 0.44 T-m B

1.00


b

F.S. = å Me / Mv 3.69 >2.00 -YES-


0.333 0.333 0.333

F.S. = å Me / Mv 2.38 >2.00 -YES-X e


F = 0.90 x TANG (Ø1) 0.52 R

Fr = å Pv x F 1.51 T.

F.S. = Fr / (Pah + C ) = 1.811 >1.5 -YES-


X = (åMe - Mv) / åPv > B/3 0.41 > 0.33 -YES-


e = B/2 - X 0.09 m.

T /m² 0.44 Kg /cm²

T /m² 0.14 Kg /cm²


0.44 < 1.25 -YES-




* Al Corte

b

Y = (qmax x c ) / 3X 0.72 T /m²

T. 815.48 Kg. 0.20

q1= qmax - Y 3.72 T /m²

T /m² 0.27 Kg/cm²

V = (q1 x c) + ((qmax - q1) x (c / 2)) 0.82

0.72

Vcac = V / ( b ) 2.72 Kg/cm²

0.41

0.5 x g2 x H'2 x Ka



R

Vcad = 0.53 x Ø x (F'c)½ 5.96 1.24

Donde : Ø = 0.85

F.S. = Vcad / Vcac 21.92 > 2.00 -YES-

T-m 8,394.24 Kg-cm

* A la Traccion

Kg/cm²

M = (( q1 x (c² / 2)) + ((qmax - q1) x (c² / 3 )) 0.08

Kg/cm²

Ftac = ( 6 x M ) / ( b² ) 5.60 T /m² 0.56

Ftad = 1.33 x Ø x (F'c)½ 11.44

Donde : Ø = 0.65


F.S. = Ftad / Ftac 20.44 > 2.00 -YES-

0.27 T-m 27,386.67 Kg-cm

* A la Traccion

Kg/cm²


Kg/cm²

Ftac = ( 6 x M ) / ( b² ) 2.74 T /m² 0.27

Ftad = 1.33 x Ø x (F'c)½ 11.44

Donde : Ø = 0.65

F.S. = Ftad / Ftac 41.76 > 2.00 -YES-



GEOMETRIA DE MURO

0.30



1.950 T /m3




1.950 T/m3



3




2 4








TALON DE MURO d 0.30 0.23 0.30 1.00





EMPUJES ADICIONALES

HS20







Ka = -

SI : COS(b) = -

-

Ka = -

Usar :






COS(b) + ( COS2(b) – COS2(Ø))1/2

COS2(Ø) =

Para b = 0

TG2(45 - Ø2/2)

G5 q

G4'

Ev

G6 H'

G3 E C = q.Ka.H

G2 G4 Eh

H/2

G1

O


A

B



Pa = 2.55 T. = Pah


0.00



G1 = b * B * Pm 1.84 0.80 0.50 1.47 0.92 1.57

G2 = 0.5 *E * h * Pm 0.00 0.30 0.00 0.00 0.00 1.35

G3 = A * h * Pm 1.59 0.45 0.15 0.71 0.24

G4 = 0.5 * I * h * Pm 1.85 0.83 0.53 1.54 0.99 0.00

G4' = 0.5 * I * h * Ps 1.57 1.07 0.77 1.67 1.20

G5 = 0.5 * N² * Tan æ * Ps 0.00 1.27 0.97 0.00 0.00 0.00

G6 = d * h * Ps 1.35 1.45 1.15 1.95 1.55 1.59

Pav =PaSen(b) 0.00 0.40 0.10 0.00 0.00 2.55

0.00 1.85

H/3 0.87

TOTALES 8.19 7.35 4.90

1.84




å Pv = 8.19 T

å Me = 7.35 T-m

4.90 T-m


Mv = Mv = Pah * H' /3 + C * H/2 = 2.38 T-m B

1.60


b

F.S. = å Me / Mv 3.09 >2.00 -YES-


0.533 0.533 0.533

F.S. = å Me / Mv 2.06 >2.00 -YES-X e


F = 0.90 x TANG (Ø1) 0.52 R

Fr = å Pv x F 4.26 T.

F.S. = Fr / (Pah + C ) = 1.671 >1.5 -YES-


X = (åMe - Mv) / åPv > B/3 0.61 > 0.53 -YES-


e = B/2 - X 0.19 m.

T /m² 0.88 Kg /cm²

T /m² 0.14 Kg /cm²


0.88 < 1.25 -YES-




* Al Corte

b

Y = (qmax x c ) / 3X 1.45 T /m²

T. 2,428.48 Kg. 0.30

q1= qmax - Y 7.37 T /m²

T /m² 0.49 Kg/cm²

V = (q1 x c) + ((qmax - q1) x (c / 2)) 2.43

1.45

Vcac = V / ( b ) 4.86 Kg/cm²

0.61

0.5 x g2 x H'2 x Ka



R

Vcad = 0.53 x Ø x (F'c)½ 5.96 1.82

Donde : Ø = 0.85

F.S. = Vcad / Vcac 12.27 > 2.00 -YES-

T-m 37,516.51 Kg-cm

* A la Traccion

Kg/cm²

M = (( q1 x (c² / 2)) + ((qmax - q1) x (c² / 3 )) 0.38

Kg/cm²

Ftac = ( 6 x M ) / ( b² ) 9.00 T /m² 0.90

Ftad = 1.33 x Ø x (F'c)½ 11.44

Donde : Ø = 0.65


F.S. = Ftad / Ftac 12.70 > 2.00 -YES-

1.54 T-m 153,615.00 Kg-cm

* A la Traccion

Kg/cm²


Kg/cm²

Ftac = ( 6 x M ) / ( b² ) 9.22 T /m² 0.92

Ftad = 1.33 x Ø x (F'c)½ 11.44

Donde : Ø = 0.65

F.S. = Ftad / Ftac 12.41 > 2.00 -YES-

DISEÑO DEL DIMENSIONAMIENTO DE MURO DE CONTENCIONPROYECTO :

PROPIETARIO : LUGAR : FECHA : JULIO DEL 2011

GEOMETRIA DE MURO

0.30



1.950 T /m3




1.950 T/m3



3




2 4








TALON DE MURO d 1.60 0.58 1.60 4.60





EMPUJES ADICIONALES

HS20







Ka = -

SI : COS(b) = -

-

Ka = -

Usar :






COS(b) + ( COS2(b) – COS2(Ø))1/2

COS2(Ø) =

Para b = 0

TG2(45 - Ø2/2)

G5 q

G4'

Ev

G6 H'

G3 E C = q.Ka.H

G2 G4 Eh

H/2

G1

O


A

B



Pa = 15.47 T. = Pah


0.00



G1 = b * B * Pm 13.46 3.25 1.65 43.73 22.20 17.55

G2 = 0.5 *E * h * Pm 0.00 1.60 0.00 0.00 0.00 18.72

G3 = A * h * Pm 4.14 1.75 0.15 7.24 0.62

G4 = 0.5 * I * h * Pm 20.70 2.90 1.30 60.03 26.91 0.00

G4' = 0.5 * I * h * Ps 17.55 3.90 2.30 68.45 40.37

G5 = 0.5 * N² * Tan æ * Ps 0.00 4.97 3.37 0.00 0.00 0.00

G6 = d * h * Ps 18.72 5.70 4.10 106.70 76.75 4.14

Pav =PaSen(b) 0.00 -0.18 -1.78 0.00 0.00 15.47

0.00 20.70

H/3 2.23

TOTALES 74.57 286.15 166.85

13.46




å Pv = 74.57 T

å Me = 286.15 T-m

166.85 T-m


Mv = Mv = Pah * H' /3 + C * H/2 = 35.59 T-m B

6.50


b

F.S. = å Me / Mv 8.04 >2.00 -YES-


2.167 2.167 2.167

F.S. = å Me / Mv 4.69 >2.00 -YES-X e

* Por Deslizamiento 3.36 -0.11

F = 0.90 x TANG (Ø1) 0.52 R

Fr = å Pv x F 38.75 T.

F.S. = Fr / (Pah + C ) = 2.504 >1.5 -YES-


X = (åMe - Mv) / åPv > B/3 3.36 > 2.17 -YES-


e = B/2 - X -0.11 m.

T /m² 1.03 Kg /cm²

T /m² 1.26 Kg /cm²


1.03 < 1.25 -YES-




* Al Corte

b

Y = (qmax x c ) / 3X 1.64 T /m²

T. 15,176.71 Kg. 1.60

q1= qmax - Y 8.67 T /m²

T /m² 1.69 Kg/cm²

V = (q1 x c) + ((qmax - q1) x (c / 2)) 15.18

1.64

Vcac = V / ( b ) 16.86 Kg/cm²

3.36

0.5 x g2 x H'2 x Ka



R

Vcad = 0.53 x Ø x (F'c)½ 5.96 10.08

Donde : Ø = 0.85

F.S. = Vcad / Vcac 3.53 > 2.00 -YES-

T-m 1,249,021.73 Kg-cm

* A la Traccion

Kg/cm²

M = (( q1 x (c² / 2)) + ((qmax - q1) x (c² / 3 )) 12.49

Kg/cm²

Ftac = ( 6 x M ) / ( b² ) 92.52 T /m² 9.25

Ftad = 1.33 x Ø x (F'c)½ 11.44

Donde : Ø = 0.65


F.S. = Ftad / Ftac 1.24 > 2.00 THONY te dice -recalcular-

42.36 T-m 4,236,255.00 Kg-cm

* A la Traccion

Kg/cm²


Kg/cm²

Ftac = ( 6 x M ) / ( b² ) 77.02 T /m² 7.70

Ftad = 1.33 x Ø x (F'c)½ 11.44

Donde : Ø = 0.65

F.S. = Ftad / Ftac 1.48 > 2.00 THONY te dice -recalcular-



GEOMETRIA DE MURO

0.20



1.950 T /m3




1.950 T/m3



3




2 4








TALON DE MURO d 0.30 0.18 0.30 0.90





EMPUJES ADICIONALES

HS20







Ka = -

SI : COS(b) = -

-

Ka = -

Usar :






COS(b) + ( COS2(b) – COS2(Ø))1/2

COS2(Ø) =

Para b = 0

TG2(45 - Ø2/2)

G5 q

G4'

Ev

G6 H'

G3 E C = q.Ka.H

G2 G4 Eh

H/2

G1

O


A

B



Pa = 1.50 T. = Pah


0.00



G1 = b * B * Pm 2.25 0.70 0.40 1.58 0.90 0.85

G2 = 0.5 *E * h * Pm 0.00 0.30 0.00 0.00 0.00 0.85

G3 = A * h * Pm 0.67 0.40 0.10 0.27 0.07

G4 = 0.5 * I * h * Pm 1.00 0.70 0.40 0.70 0.40 0.00

G4' = 0.5 * I * h * Ps 0.85 0.90 0.60 0.76 0.51

G5 = 0.5 * N² * Tan æ * Ps 0.00 1.10 0.80 0.00 0.00 0.00

G6 = d * h * Ps 0.85 1.25 0.95 1.06 0.81 0.67

Pav =PaSen(b) 0.00 0.27 -0.03 0.00 0.00 1.50

0.00 1.00

H/3 0.65

TOTALES 5.62 4.37 2.68

2.25




å Pv = 5.62 T

å Me = 4.37 T-m

2.68 T-m


Mv = Mv = Pah * H' /3 + C * H/2 = 1.08 T-m B

1.40


b

F.S. = å Me / Mv 4.06 >2.00 -YES-


0.467 0.467 0.467

F.S. = å Me / Mv 2.49 >2.00 -YES-X e


F = 0.90 x TANG (Ø1) 0.52 R

Fr = å Pv x F 2.92 T.

F.S. = Fr / (Pah + C ) = 1.943 >1.5 -YES-


X = (åMe - Mv) / åPv > B/3 0.59 > 0.47 -YES-


e = B/2 - X 0.11 m.

T /m² 0.60 Kg /cm²

T /m² 0.21 Kg /cm²


0.60 < 1.25 -YES-




* Al Corte

b

Y = (qmax x c ) / 3X 1.02 T /m²

T. 1,639.22 Kg. 0.30

q1= qmax - Y 4.95 T /m²

T /m² 0.23 Kg/cm²

V = (q1 x c) + ((qmax - q1) x (c / 2)) 1.64

1.02

Vcac = V / ( b ) 2.34 Kg/cm²

0.59

0.5 x g2 x H'2 x Ka



R

Vcad = 0.53 x Ø x (F'c)½ 5.96 1.76

Donde : Ø = 0.85

F.S. = Vcad / Vcac 25.45 > 2.00 -YES-

T-m 25,352.85 Kg-cm

* A la Traccion

Kg/cm²

M = (( q1 x (c² / 2)) + ((qmax - q1) x (c² / 3 )) 0.25

Kg/cm²

Ftac = ( 6 x M ) / ( b² ) 3.10 T /m² 0.31

Ftad = 1.33 x Ø x (F'c)½ 11.44

Donde : Ø = 0.65


F.S. = Ftad / Ftac 36.84 > 2.00 -YES-

0.23 T-m 22,513.85 Kg-cm

* A la Traccion

Kg/cm²


Kg/cm²

Ftac = ( 6 x M ) / ( b² ) 1.69 T /m² 0.17

Ftad = 1.33 x Ø x (F'c)½ 11.44

Donde : Ø = 0.65

F.S. = Ftad / Ftac 67.73 > 2.00 -YES-

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DISEÑO DE MURO POR GRAVEDAD