PRIMERA:

EJEMPLO:

Disear el estribo en voladizo cuya cajuela mide 65cm de ancho y 40cm de alto, la r x n que trasmite la losa del puente es de 400kg/m por concepto de carga muerta y carga viva (s/c), sin incluir impacto. El nivel de cimentacin esta a 6.50m por debajo de la rasante y las caractersticas del terreno son:

= ngulo de friccin interna = 45

Ws = 1650kg/m3

fc = 175 kg/cm2

t = 2 kg/cm2

f = 0.50 (material grueso coef. de friccin)

0.40 (para suelo arcilloso).

T = H/12 = 6.50/12 = 0.54 55 cm

A = H/12 = 55 cm

B = H/2 2H/3

6.50/2 = 3.25

Hacemos B = 3.50

B/3 = 1.17 1.20

CARGAS:

EMPUJE ACTIVO:

H = 0.61m = 1000/1650

Ea = 7079 kg.

F = 0.15R = 0.15 x 4000 = 600 kg.

YF = 6.50 0.40 + 0.025 = 6.125

VERIFICACIN DE ARRANQUE:

MOMENTO FLECTOR EN EL ARRANQUE:

M = Ea y + F YF = 6018 x 2.15 + 600 x 5.575

YF = 5.95 0.40 + 0.025 = 5.575

MA = 16284 kg-m

W = S/C = 0.61, W = 1006.5

CORTANTE EN EL ARRANQUE

V = Ea + F = 6018 + 600 = 6618 kg

ESPESOR EN EL ARRANQUE

Flexin

fc = 0.45fc = 780.75 kg/cm2

fs = 0.5 fy = 2100 kg/cm2

Es = 2.1 x 106Ec = 15000 cfc

J = 1 R/3 = 1 0.273/3 = 0.909

R = (fc j k)/2 = 9.77, b = 100cm

ANCHO MNIMO EN ARRANQUE

d = 7cm = 41 cm + 7 = 48 cm.

= 48cm < 55cm OK!

POR CORTE

se considera as:

v/bd = 0.3fc luego, d = v/(0.3bfc)

d = 6618/(0.3 x 100175) = 16.7cm < 55 OK!

ESTABILIDAD:

Seccin C - C

a) Estribos sin puente y relleno S/C

VOLTEO

W1 = 0.50 x 0.40 x 2.4

= 0.288

W2 = 0.65 x 0.65 x 2.4 x 0.5= 0.507

W3 = 5.55 x 0.30 x 2.4

= 3.996

W4 = 4.90 x 0.25 x 0.5 x 2.4= 1.470

W5 = 3.50 x 0.55 x 2.40

= 4.620

T1 = 5.95 x 1.10 x 1650

= 10.799

T2 = 0.65 x 0.65 x 0.5 x 1.65= 0.348

T3 = 4.90 x 0.45 x 1.65

= 2.235

S/C = 1.10 x 1006.5

= 1.107

28.390

0.55 + 5.95 - 0.25 = 6.30

0.55 + 5.45 - 0.40 = 0.65

Momento

W1 = 3.5 1.10 - 0.15

= 2.25 0.648

W2 = 1.20 + 0.55 + 0.65 / 3

= 1.467 0.997

W3 = 1.20 + 0.55 0.15

= 1.600 6.394

W4 = 1.20 + 2 x 0.25 / 3

= 1.367 2.009

W5 = 3.50 / 2

= 1.73 8.085

T1 = 3.50 0.55

= 2.9531.857

T2 = 1.20 + 0.55 + 2 / 3 x 0.65= 2.183 0.760

T3 = 3.50 + 1.10 0.65 / 2

= 2.07510.904

S/C = 3.50 0.55

= 2.95 3.266

64.920

ESFUERZOS

= 0.81 0.049

( = 64920/28390 = 2287

Xr = 2287 - 0.572 = 1.715

d = B/2 Xr = 3.50/2 1.715 = 0.035m

dmax = B/6 = 0.583 > 0.035 luego OK!

max = 0.86 kg/cm2

< 2

OK!

min = 0.76 kg/cm2

< 2

OK!

b) Estribos con puente y relleno con S/C

F = 600kg YF = 5.575 + 0.55 = 6.125

R = 4000kgVR = 3.50 1.10 0.30 - 0.65/2 = 1.775

FV = 28390 + 4000 = 32390kg

Mb = 64920 + 6000 x 1.775 600 x 6.125 = 68325

FH = Ea +F = 6018 + 600 = 6618

CSV = 68325/(6618 x 3.01) = 3.43 > 2 OK!

ESFUERZOS

( = 68325/32390 = 2.11

S = 6618(3.01)/32390 = 0.62

Xr = r s = 2.11 0.62 = 1.49

d = 3.5/2 1.49 = 0.26

dmax = B/6 = 0.583 > 0.26 OK!

ESFUERZOS TRASMITIDOS

.

max = 1.34> 2

OK!

min = 0.52> 2

OK!

DISEO DE LA PANTALLA: (Clculo del acero)

d = 55 7 = 48

5/8 (2cm2) = 1 5/8 @ 11cm

3/4 (2.85cm2) = 1 3/4 @ 16cm

CHEQUEO POR ADHERENCIA

E0 nec = V/(Mjd) = 6618/(15.97 x 0.909 x 48) = 9.50cm

E0 Mu = 9.5

3/4 = 5.98cm

Eo disponibilidad de 1m de c/muro:

(100/16 + 1)(5.98) = 41.86 > 9.5

OK!

LONGITUD DE DESARROLLO:

ACERO DE REPARTO

Acero repar. Vert.

= 0.0015 x 100 x 48 = 7.2 cm2 5/8 @27 1/5 @ .

Acero repar. Horiz.

= 0.0025 x 100 x 48 = 12 cm2 5/8 @17

DISEO DE REPARTO:

CASO I

W = pr + pp + S/C

W = 1650 x 5.95 + 2400x 0.5 + 1000

W = 12017.50 kg/m2

(min = 0.76

(max - (min = 0.10

a/1.75 = 0.10/3.50 ; a = 0.05

(a = 0.810

b/2.3 = 0.10/3.50 ; b = 0.066

(b = 0.826

CLCULO DEL MOMENTO EN EL INICIO DEL TALN (D)

CORTANTE A UNA DISTANCIA d/2

= (48 7)/2 = 0.804

(a = 0.76 + (0.1 x 1.545)/3.5 = 0.804

V = w l2 ((a2 - (min)l2/2

= 12017.5 x 1.545 0.5 (7600 + 8040)1.545

= 18567.037 12081.9 = 6485.14 = 6485

CASO II

(min = 0.520 kg/cm2= 5200 kg/m/m de ancho

(max = 1.340 kg/cm2= 13400 kg/m/m de ancho

(a = 0.520 + 1.75 (1.34 0.52)/3.50 = 0.92510 kg/cm2

= 9210 kg/m por metro de ancho

CORTANTE

V = 12017.5 X 1.5454 0.5(8820 + 5200) = 11557 kg-m

DISEO DEL ACERO DEL TALN

Utilizamos los valores ms encontrados: (esfuerzos de trabajo).

VERIFICACIN DEL PERALTE

Tomamos: d = 48 7 = 41

OK!

CLCULO DEL ACERO

Utilizamos dc = 10cm, d = 40

As = 16.31 cm2 5/8 1.98cm2 1 3/8 @ 11.2cm

CHEQUEO POR ADHERENCIA

LONGITUD DE DESARROLLO

Ld = fs D/4u = (2100 x 5/8 x 2.54)/(4 x 19.17) = 43.5 cm

ARMADURA DE REPARTO

As min = 0.0015 x 48 x 100 = 7.2 cm2

As rep y temp = 0.0025 x 48 x 100 = 12cm2

0.0015 x 48 x 100 = 7.2 cm2

DISEO DE LA JUNTA

Cargas verticales: slo pas propio de base hacia abajo y r x n del terreno hacia arriba, no se considera empuje pasivo.

W = 0.55 x 2400 = 1320 kg/cm2

CASO A:

(max = 0.860 kg/cm2

(b = 0.826 kg/cm2 (calculado en taln)

(min = 0.760 kg/cm2

MOMENTO:

M = Wl2/2 - l2/6 (2(max + (b)

= 1320 1.202/2 - 1.202/6 (2 x 8600 + 8260) = -5160.40

M = -5160.4

CORTANTE:

d/2 = 40/2 = 20

l = 1.20 0.20 = 1.00

(b = 0.760 + (0.86 0.76)(3.5 1)/3.5 = 0.831

V = 1320 x 1.0 0.5(8600 + 8310) x 1.00 =

V = -7135.0 kg (hacia arriba)

CASO B:

(max = 1.345 kg/cm2

(b = 0.52 + 1.0 x (1.34 0.52)/3.5 = 0.754 kg/cm2

(min = 0.52 kg/cm2

MOMENTO:

M = w l2/2 - l2/6 (2(max + (b)

M = 1320 x 1.202/2 1.202/6(2 x 13400 + 7540)

= -7291.20 (hacia arriba)

CORTANTE:

(b = 0.52 + (1.34 0.52)(3.5 1)/3.50 = 1.106

V = 1320 x 1 0.5(13400 + 7540)

= -9150 kg (hacia arriba)

VERIFICACIN DEL PERALTE:

(adoptado)

CHEQUEO POR CORTE TALN

d = V/(0.32b(fc) = 11557/(0.3 x 100(175) = 29.1

= 29.41 < 40

OK!

CHEQUEO POR CORTE TALN

d = 9150/(0.32 x 100(175) = 23.05 < 40cm

OK!

REFUERZO PRINCIPAL:

As = M/fs j d = (7291 x 1000)/(2100 x 0.909 x 40)

= 9.55 cm2 1/2" = 1 1/2" @ 0.13

Asmin = 0.0015 x 48 x 100 = 7.2cm2 < 9.55OK!

Asrepart = 0.00025 x 48 x 100 = 12.0cm2 1/2 @0.10

CHEQUEO POR ADHERENCIA:

u = 2.3(175/1.27 = 23.96

(nec = 11557/(23.96 x 0.909 x 40) = 13.26

Edisp = (100/10 + 1)( x 1.27 = 43.9 > 13.26 OK!

LONGITUD DE DESARROLLO:

Ld = fs d/4u = (2100 x 1.27)/(4 x 23.96) = 27.83cm

Se tomar Ld = 35cm.

3.50

0.55

1.20

1.75

0.55

B

C

B

C

6.50

0.30

0.65

0.30

0.40

Ea = cwh (h + 2h)

2

C = 1 Sen 45 = 0.171

1 + Sen 45

y = h(h + 3h) = 6.5(6.5 + 3 x 0.61) = 2.33 m.

3(h + 2h) 3(6.5 + 2 x 0.61)

Ea = 0.717 x 1650 x 650 ( 6.5 + 2 x 0.61)

2

Yb = 5.95(5.95 + 3 x 0.61) = 2.15

3(5.95 + 2 x 0.01)

Eab = 0.171 x 1650 x 5.95 (5.95 + 2(0.61)) = 6018kg

2

0.40

S/C

T2

2.15 = y

0.55

Ea

T3

T1

W2

W1

3.50

1.20

1.75

0.55

B

C

B

C

5.95

0.30

0.65

0.30

F

0.65

se considera.

YF

0.55

n = 2.10 x 106 = Es = 10.5

15000175 Ec

R = 1 = 0.273

1 + Fs .

n fc

S = 6018(2.15 + 0.55) = 0.572

28390

= 0.11 x 28390 0.06 x 28390 x 3.5

350 3.502

CSD = 28390 x 0.5 = 2.36 > 2 OK!

6018

CSV = 64920 . = 4 > 2 OK!

6018(2.15 + 0.55)

H = 6018(2.15 + 0.55)+ 600(6.125) = 3.01

6018 + 600

= 0.01 x 32390 0.06 x 32390 x 0.26 = 0.93 0.41

3.503.502

M = 2.3fc = 2.3175 = 15.97

D x 2.54

As = 16284.00 = 17.77 cm2/metro de muro

2100 x 0.909 x 48

As = Ms .

fs j d

Lsd = Fs D = 2100 x 1.587 = 52cm (anclaje en ciment.)

4u 4 x 15.97

sS2

1/2" @ 17

5/8 @ 17

1.20

0.55

1.75

2.05

1.545

a

(max=0.86

C

D

l

E

B

A

W

(min = 0.76

MD = W l2 l2 (2(min + (a = 1 l2 (w 2((min + (a))

2 6 2 6

(a = 0.520 + 1.545(1.34 0.52) = 0.882

350

MD = 1 x l.752 (12017.5 (2 x 5200 + 93100)) = 13397 kg-m

2 6

MD = 1 x l.752 (12017.5 (2 x 7600 + 8100)) = 12455 kg-m

2 6

As = M = 12455 x 100 = 16.31 cm

fs j d 2100 x 0.909 x 40

(disp = ( 100 + 1 )( (1.59) = 49.57 cm >> 16.58 cmOK!

11.2

(NEC = 11557 = 16.58 cm

19.17 x 0.909 x 40

(NEC = V con u = 2.3(fc = 2.3(175 = 19.17

u j d D (5/8 x 2.54)

_1057500550.unknown

_1057500691.unknown

_1057514899.unknown

_1057516457.unknown

_1057500641.unknown

_1057500125.unknown