Muro de Contencion Con Contrafuerte

DISEÑO DE MURO DE CONTENCION CON CONTRAFUERTE DISEÑAR EL MURO DE CONTENCION

S/C t1

1.00 m

h1

h

hp

h2

h3

hz

t2

B2

B1 B

DATOS H1 (m) H2 (m) H3 (m) N.F. (m) = h´1 φ1 (º) φ2 (º) φ3 (º) Ý 1 (Tn/m3) Ý 2 (Tn/m3) Ý 3 (Tn/m3) σt (Tn/m2) S/C (Tn/m2) FSD FSV Contrafuertes f´c (Kg/cm3) Ý´concreto (Kg/cm3) fy (Kg/cm3)

CONSTRUCTORA CGR INGENIERIA CONSTRUCCION SAC TACNA - PERU

CASO 05 1.5 3.5 3.5 1 28 22 20 1.7 1.8 1.9 30 0 1.5 1.75 SI 210 2400 4200

ELIZABEHT G. ZEBALLOS HUAMANI ING. CIVIL CIP 124611

DISEÑO DE MURO DE CONTENCION CON CONTRAFUERTE CALCULO DE PRESIONES :

Coeficiente de empuje activo (Ka): Ka =

1 − sen  1 + sen 

donde: Ka1 = 0.361 º Ka2 = 0.455 º Ka3 = 0.490 º

hs/c = S/C/Y1 S/C = 0.000 m Ýh2O = 1.00 tn/m3 m = 0.7

P1 = Ka1*Ý1*hS/C

P1 = 0.00 tn-m2

P2 = Ka1*Ý1*(h`1+hS/C)

P2 = 0.92 tn-m2

Ý1` = Ý1-m*ÝH2O Ý1` = 1.00 tn/m3 he1= Wtotal/Ý1` he1 =(S/C+Ý1*h1`)/Ý1` he1 = 1.700 m P3 = Ka1*Ý1`(he1+(h1-h1`))+Ýh2O*(h1-h1`)

P3 = 1.29 tn-m2

Ý2` = Ý2-m*ÝH2O Ý2` = 1.10 tn/m3 he2= Wtotal/Ý2` he2 = (S/C+Ý1*h1)/Ý2` he2 = 2.318 m P4 = Ka2*Ý2`(he2+h2)+Ýh2O*h2

P4 = 6.41 tn-m2

Ý3` = Ý3-m*ÝH2O Ý3` = 1.20 tn/m3 he3= Wtotal/Ý3` he3 = (S/C+Ý1*h1+Ý2*h2)/Ý3` he3 = 7.375 m P5 = Ka3*Ý3`*(he3+h3)+Ýh2O*h3

CONSTRUCTORA CGR INGENIERIA CONSTRUCCION SAC TACNA - PERU

P5 = 9.89 tn-m2

ELIZABEHT G. ZEBALLOS HUAMANI ING. CIVIL CIP 124611

DISEÑO DE MURO DE CONTENCION CON CONTRAFUERTE

P1 =0.00tn-m

1 P2 =0.92 tn-m P3 = 1.29 tn-m

0,5

3,5

P4 = 6.41 tn-m

3,5

P5 = 9.89 tn-m

EFECTO

Empuje Activo

Total

FUERZA (Tn) 1/2*0.92*1 0.460 Tn (0.92+1.29)/2*0.5 0.554 Tn (1.29+6.41)/2*3.5 13.486 Tn (6.41+7.60)/2*3.5 28.536 Tn 43.036 Tn

BRAZO PALANCA 1/3*1+7.5 7.833 m

MOMENTO 0.460*7.833 3.605 Tn-m 0.554*7.236 4.006 Tn-m 13.486*4.412 65.576 Tn-m 28.536*0.972 46.384 Tn-m 119.572 Tn-m

(0.92*0.5*0.5/2+(1.29-0.92)*0.5/2*0.5/3)/((0.92+1.29)/2*0.5)+7

7.236 m (1.29*3.5^2/2+(6.41-1.29)*3.5^2/6)/((1.29+6.41)/2*3.5)+3.5

4.863 m (6.41*3.5^2/2+(7.6-6.41)*3.5^2/6)/(6.41+7.6)/2*3.5)

1.625 m

M = 119.57 tn-m Mu = 1.6*M Mu = 191.315 Tn-m

C.G. = M/P =119.572/43.036 Yg = 2.778 m

DIMENSIONAMIENTO DE LA PANTALLA: Calculo de t1: t1 >= 0.25m t1 = 0.300 m Calculo de t2: b = 1.000 m ρ = 0.004 m φ = 0.900 m

43.036 tn-m2

Yg = 2.778 m

w = ρ*fy/f´c w = 0.08 Mu = φ*b*d^2*f`c*w(1-0.59w) 191.315*10^5 = 0.9*100*d^2*210*0.08*(1-0.59*0.08) d = 115.239 cm t2 = d +rec +Øb/2 t2 = 1.200 m Usar:

CONSTRUCTORA CGR INGENIERIA CONSTRUCCION SAC TACNA - PERU

asumiendo: Ø Nº3 = 1.590 cm

t2 = 1.30 m

d = 1.25 m

ELIZABEHT G. ZEBALLOS HUAMANI ING. CIVIL CIP 124611

DISEÑO DE MURO DE CONTENCION CON CONTRAFUERTE Verificación por Corte: 9.89 Tn/m2

8.848 Tn/m2 6.41 Tn/m2

43.036Tn 43.036Tn

1,05

2,45

Y

3,5

P..(1.05) = (9.89-6.41)/3.5*2.45+6.41 P..(1.05) = 8.649 Tn/m2 Y = 43.036- (8.848+9.89)/2*1.05 Y = 31.428 Tn/m

Vud = 1.6*Vd Vud = 50.284 Tn/m

Vc = 0.53*f´c^1/2*b*d Vc = 96.163 Tn/m

ΦVc = 0.85*80.802 ΦVc = 81.738 Tn/m ok¡ cumple

ΦVc >= Vud DIMENSIONAMIENTO DE LA ZAPATA: hz = t2 +5cm hz = 1.35 m h = hz + hp h = 9.85 m Dimensionamiento por estabilidad al deslizamiento: P = (9.89-6.41)/3.5*4.65+6.41 P = 11.24 tn-m2 P1 =0.00tn-m 1 0,5

P2 =0.92 tn-m P3 = 1.29 tn-m

3,5

P4 = 6.41 tn-m

3,5

P5 = 9.89 tn-m 1.35

P6 = 11.24 tn-m

EFECTO

Empuje Activo

Total

FUERZA (Tn) 1/2*0.92*1 0.460 Tn (0.92+1.29)/2*0.5 0.554 Tn (1.29+6.41)/2*3.5 13.486 Tn (6.41+7.60)/2*3.5 28.536 Tn (9.89+11.24)/2*1.35 14.264 Tn 57.300 Tn

CONSTRUCTORA CGR INGENIERIA CONSTRUCCION SAC TACNA - PERU

BRAZO PALANCA 1/3*1+8.85

9.183 m (0.92*0.5^2/2+(1.29-0.92)*0.5^2/6)/((0.92+1.29)/2*0.5)+8.35

8.586 m (1.29*3.5^2/2+(6.41-1.29)*3.5^2/6)/((1.29+6.41)/2*3.5)+4.85

6.213 m (6.41*3.5^2/2+(7.6-6.41)*3.5^2/6)/((6.41+7.6)/2*3.5)+1.35

2.975 m (9.89*1.35^2/2+(11.24-9.89)*1.35^2/6)/((9.89+11.24)/2*1.35)

0.661 m

MOMENTO 0.460*7.833 4.227 Tn-m 0.554*7.236 4.754 Tn-m 13.486*4.412 83.782 Tn-m 28.536*0.972 84.908 Tn-m 14.264*0.661 9.424 Tn-m 187.095 Tn-m

ELIZABEHT G. ZEBALLOS HUAMANI ING. CIVIL CIP 124611

DISEÑO DE MURO DE CONTENCION CON CONTRAFUERTE

Yg = 3.265 m

Ha = P = 57.300 Tn Mº = 187.095 Tn-m DATOS: Ým = f= Ka = Ýs = FSD = FSV =

2.00 tn-m3 0.6 0.490 º 1900 kg/m3 1.5 1.75

Dimensionamiento por estabilidad al Deslizamiento: Hr = f*Pm Hr = f*Ým*B1*H Ha = 57.3 T/m

Pm

9.85 m

Ha = 57.30 Tn/m

Hr / Ha >= FSD = 1.5 B1 >= 57.3*1.5/(0.6*2*9.85) B1 >= 7.27 m

3.265 m

Hr

Usar :

B1 =

B1

7.30 m

Dimensionamiento por estabilidad al Volteo: Aplicando Mº en "A" Mo = Ha*Yg Mo = 57.3*3.625 Mo = 187.095 Tn-m

9.85 m

Mr = Pm*(B2+B1/2) Mr = Ým*B1*H*(B2+B1/2

Ha = 57.30 Tn/m Pm`

3.265 m

A

Mr / Mo >= FSV = 1.75 (2.0*7.3*9.85*(B2+7.3/2))/187.095 >= 1.75 B2 >= -1.37 m

B2

pero: B2mín = H/10 = 0.99 m Usar :

B2 = 1.00 m

Entonces: B = B1+B2 B = 8.30 m condición:

0.5H = Vud

ok conforme ¡

Refuerzo Transversal: As temp. = 0.0018*b*t As temp. = 24.300 cm2

Ø Nº8 = A Nº8 =

s = 20.864 cm As montaje = 36*( Øb) As montaje = 57.240 cm2

2.540 cm 5.070 cm2 usar: Ø Nº8 @ 0.20m

Ø Nº5 = A Nº5 =

1.590 cm 1.980 cm2 usar: Ø Nº5 @ 0.50m

CONSTRUCTORA CGR INGENIERIA CONSTRUCCION SAC TACNA - PERU

ELIZABEHT G. ZEBALLOS HUAMANI ING. CIVIL CIP 124611

DISEÑO DE MURO DE CONTENCION CON CONTRAFUERTE

DISEÑO DE LA PANTALLA: Contrafuerte

-As

Franjas Horizontales L/3

L`

L

L/3

+As

L = 3.20m

P -As

3L/8

P` = 57.300 Tn L = 3.500 m P = P`/L*(L-3L/8) P = 35.813 Tn Acero Horizontal: Momentos para el diseño: (+)M = PL^2/16 (+)M = 27.42 tn-m

(-)M = PL^2/12 (-)M = 36.56 tn-m

Para (+)Mº : (+)M = 27.42 tn-m donde: As = Mu/(φ*fy*(d-a/2)) a = As*fy/(0.85*f´c*b) a = d/5 = a= a= a=

25.041 cm 1.515 cm 1.371 cm 1.371 cm

As = As = As = As =

6.437 cm2 5.829 cm2 5.825 cm2 5.825 cm2

φ = 0.9 fy = 4200 Kg/cm2 f´c = 210 Kg/cm2 d = 125.205 cm b = 100.000 cm Ø Nº8 = 2.540 cm A Nº8 = 5.070 cm2

As = 5.825 cm2 As mín = 0.0018*b*d As mín = 22.537 cm2 s = 22.496 cm usar: Ø Nº8 @ 0.22m

CONSTRUCTORA CGR INGENIERIA CONSTRUCCION SAC TACNA - PERU

ELIZABEHT G. ZEBALLOS HUAMANI ING. CIVIL CIP 124611

DISEÑO DE MURO DE CONTENCION CON CONTRAFUERTE Para (+)Mº : (-)M = 36.56 tn-m donde: As = Mu/(φ*fy*(d-a/2)) a = As*fy/(0.85*f´c*b) a = d/5 = a= a= a=

25.041 cm 2.020 cm 1.832 cm 1.831 cm

As = As = As = As =

8.583 cm2 7.787 cm2 7.782 cm2 7.782 cm2

φ = 0.9 fy = 4200 Kg/cm2 f´c = 210 Kg/cm2 d = 125.205 cm b = 100.000 cm Ø Nº8 = 2.540 cm A Nº8 = 5.070 cm2

As = 7.782 cm2 As mín = 0.0018*b*d As mín = 22.537 cm2 s = 22.496 cm usar: Ø Nº8 @ 0.22m Acero Vertical:

+M +As

-M L /3

-A s

Momentos para el diseño: (-)M = 0.06*P`*L (-)M = 12.03 tn-m

(+)M = (-)M/4 (+)M = 3.01 tn-m

Para (-)Mº : (-)M = 12.03 tn-m donde: As = Mu/(φ*fy*(d-a/2)) a = As*fy/(0.85*f´c*b) a = d/5 = a= a= a=

25.041 cm 0.665 cm 0.030 cm 0.018 cm

As = As = As = As =

2.825 cm2 2.549 cm2 2.543 cm2 2.543 cm2

φ = 0.9 fy = 4200 Kg/cm2 f´c = 210 Kg/cm2 d = 125.205 cm b = 100.000 cm Ø Nº8 = 2.540 cm A Nº8 = 5.070 cm2

As = 2.543 cm2 As mín = 0.0018*b*d As mín = 22.537 cm2 s = 22.496 cm

CONSTRUCTORA CGR INGENIERIA CONSTRUCCION SAC TACNA - PERU

usar: Ø Nº8 @ 0.22m

ELIZABEHT G. ZEBALLOS HUAMANI ING. CIVIL CIP 124611

DISEÑO DE MURO DE CONTENCION CON CONTRAFUERTE Para (+)Mº : (+)M = 3.01 tn-m donde: As = Mu/(φ*fy*(d-a/2)) a = As*fy/(0.85*f´c*b) As = 0.706 cm2 As = 0.636 cm2 As = 0.636 cm2

a = d/5 = 25.041 cm a = 0.166 cm a = 0.150 cm

φ = 0.9 fy = 4200 Kg/cm2 f´c = 210 Kg/cm2 d = 125.205 cm b = 100.000 cm Ø Nº8 = 2.540 cm A Nº8 = 5.070 cm2

As = 0.636 cm2 As mín = 0.0018*b*d As mín = 22.537 cm2 s = 22.496 cm usar: Ø Nº8 @ 0.22m

DISEÑO DE LOS CONTRAFUERTES: Por Flexión:

Mu

?

hp

As

PhpL

t2/2 jd

Tu Tu Cos? d

CONSTRUCTORA CGR INGENIERIA CONSTRUCCION SAC TACNA - PERU

ELIZABEHT G. ZEBALLOS HUAMANI ING. CIVIL CIP 124611

DISEÑO DE MURO DE CONTENCION CON CONTRAFUERTE TOMANDO DATOS ANTERIOERES: P1 =0.00tn-m

1 P2 =0.92 tn-m P3 = 1.29 tn-m

0,5

3,5

P4 = 6.41 tn-m

3,5

P5 = 9.89 tn-m

FUERZA (Tn) 1/2*0.92*1 0.460 Tn (0.92+1.29)/2*0.5 0.554 Tn (1.29+6.41)/2*3.5 13.486 Tn (6.41+7.60)/2*3.5 28.536 Tn 43.036 Tn

EFECTO

Empuje Activo

Total

BRAZO PALANCA 1/3*1+7.5 7.833 m (0.92*0.5*0.5/2+(1.29-0.92)*0.5/2*0.5/3)/((0.92+1.29)/2*0.5)+7

7.236 m (1.29*3.5^2/2+(6.41-1.29)*3.5^2/6)/((1.29+6.41)/2*3.5)+3.5

4.863 m (6.41*3.5^2/2+(7.6-6.41)*3.5^2/6)/(6.41+7.6)/2*3.5)

1.625 m

M = 119.572 Tn-m V = 31.428 Tn/m ? = 35.22º

Yg = tp/2 = cos ? = tg ? =

MOMENTO 0.460*7.833 3.605 Tn-m 0.554*7.236 4.006 Tn-m 13.486*4.412 65.576 Tn-m 28.536*0.972 46.384 Tn-m 119.572 Tn-m

2.78 m 65.00cm 0.817 0.706

Tu = Mu / (cos?(d-tp/2)) As = Tu/(0.9*fy)

SECCION ANALIZADA Mu (Tn-m) Vu (Tn/m) d (cm) Tu (Tn) As (cm2) Nº varillas

A UN TERCIO DE LA ALTURA 121.936 Tn-m 32.049 Tn-m 7*567/850+30-6 490.67 cm 35.062 Tn 9.28 cm2 2 Nº8

EN LA BASE 119.572 Tn-m 31.428 Tn/m 730-6 724.00 cm 22.209 Tn 5.88 cm2 3 Nº5

AL CENTRO 182.904 Tn-m 48.074 Tn-m 7*425/850+30-6 374.00 cm 72.451 Tn 19.17 cm2 4 Nº8

En un contrafuerte no puede haber espaciamiento de 20cm, por lo que se le aumenta a 35cm El refuerzo transversal se calcula de acuerdo a las reacciones que esta ejerce sobre la pantalla vertical: Tu = 3/2*M h = 35

donde M = 12.03 tn-m Tu = 2.235 Tn As = 0.59 cm2 s=

CONSTRUCTORA CGR INGENIERIA CONSTRUCCION SAC TACNA - PERU

0.18 cm

Asmín = 0.002*100*35 Asmin= 7.00 cm2 Usar Nº4 @ 0 .18cm

ELIZABEHT G. ZEBALLOS HUAMANI ING. CIVIL CIP 124611

DISEÑO DE MURO DE CONTENCION CON CONTRAFUERTE Por Cortante: t1

?

d t2

Tu

La distacia critica para un contrafuerte se ubica a 0.15Ln: d = 52.50 cm SECCION ANALIZADA Mu (Tn-m) Vui (Tn/m)

EN LA BASE 119.572 Tn-m 31.428 Tn/m 730-6 724.00 cm 31.171 Tn/m 30.242 Tn/m no cumple

d (cm) Vu (Tn/m) 0.75*Vc (Tn/m) 0.75*Vc > Vu Avmin Vs Φb s

A UN TERCIO DE LA ALTURA 121.936 Tn-m 32.049 Tn-m 7*567/850+30-6 490.67 cm 31.643 Tn-m 30.242 Tn-m no cumple

AL CENTRO 182.904 Tn-m 48.074 Tn-m 7*425/850+30-6 374.00 cm 47.235 Tn-m 30.242 Tn-m no cumple

9.45 cm2 20.051 Tn-m 1/2" 13.97 cm

9.45 cm2 41.417 Tn-m

Entonces calculamos el acero por cortante: 9.45 cm2 18.880 Tn/m 14.83 cm

6.76 cm

Por Tracción de la pantalla(refuerzo horizontal) Contrafuerte

-As

L

Contrafuerte L

L

Datos: Tu = 1.6*PL Tu = 241.003 Tn As = Tu/(φ*fy)

CONSTRUCTORA CGR INGENIERIA CONSTRUCCION SAC TACNA - PERU

P = 43.036 Tn L = 3.50 m φ = 0.9 As = 63.76 cm2

ELIZABEHT G. ZEBALLOS HUAMANI ING. CIVIL CIP 124611

DISEÑO DE MURO DE CONTENCION CON CONTRAFUERTE

Por Tracción de la zapata (refuerzo vertical): Contrafuerte L

L

L

-As

-As

Zapata Posterior

Datos: Wu = 26.24 tn/m Tu = Wu*L Tu = 91.826 Tn As = Tu/(φ*fy) s = 20.87 cm2

As = 24.29 cm2 Φb Nº8 = 5.07 cm2 Usar Nº8 @.20

CONSTRUCTORA CGR INGENIERIA CONSTRUCCION SAC TACNA - PERU

ELIZABEHT G. ZEBALLOS HUAMANI ING. CIVIL CIP 124611