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CALCULO DE ESTRIBOS DEL PUENTE

Puente CS3 L = 20.25m H = 8m Ancho del tablero = 20.60m N = 40 +

1 1 * L + H = 40 + * 20.5 + 8.50 = 53.63cm = 55cm 4 4

Reacciones de las Vigas 4 vigas  Reacción por Carga Muerta Rviga = 37167 kg RCM =

37167 * 4 = 13516kg / m 11

 Reacción por Carga Viva (sin impacto) 2.25 P * ( Lc − 2.85) Lc

RCV =

Pd = 7258 *1.20 * 1.64 = 14284kg RCV =

2.25 * 14284 * (20.25 − 2.85) = 27615kg / m 20.25

RCV =

27615 * 4 = 10042kg / m 11

Características del Suelo φ = 32° Zona Sísmica = 3 Ao = 0.3g Csh = 0.5 Ao Csv = 2/3 Csh γ = 1.8 t/m3 f = 0.5

Csh = 0.15 Csv = 0.10 Factor de fricción

Suponiendo δ = β = i = 0 (1 − Senφ ) = 0.307 Ka = (1 + Senφ ) Ka = 0.307  Csh   0.5 * Ao  θ = arctag   = arctag    1 − csv   1 − 1 / 3 Ao  Si Ao = 0.30 θ = 9.46° Kas = 0.415 1 E = γ * H 2 * Ka 2

E = 17.68 ton/m

1 E = 1.8* 8 2 * 0.307 2

1 ∆EDa = γ * H 2 ( Kas − Ka )(1 − Csv ) 2 1 ∆EDa = 1.8 * 8 2 (0.415 − 0.307)(1 − 0.1) 2 ∆EDa = 5.60 ton / m

2 M ESTB = 5.60 * * 8 3

M ESTB = 29.87 ton / m

Fuerza de Frenado o Longitudinal

FL = 0.05 * CV

Actuando a 1,83 m sobre el tablero

FL = 0.05(0.952 * 20.25 + 8.17) 2 *

1 11

FL = 0.25ton / m

Viento en la superestructura

W =

0.059 * 20.25 * (1.2 + 1.5) 11

W = 0.29 ton / m

Viento sobre la carga viva

WL =

0.06 * 20.25 11

W = 0.11 ton / m

Figura 1 2 3 4 5 6 7 8

Área(m2) 4.48 3.12 .675 .5 .09 .05 0.71 21.10

Peso (ton/m) 10.75 7.49 1.62 1.2 .22 .12 1.28 37.98

∑ P = 60.66t

XAn ( m ) 2.8 2.15 2.5 2.57 2.87 2.82 2.50 4.135

MA(ton-m/m ) 30.10 16.10 4.05 3.08 .63 .34 3.20 157.05

∑ M = 214.55t − m

∀concreto = 8.92m 3 deconcreto / mlmuro Centro de gravedad del muro 4.48 * ( 0.4 ) + 3.12 * ( 3.64 ) + 0.675 * ( 2.6 ) + 0.5 * ( 7.1) + 0.09 * ( 6.95) + 0.05 * ( 6.6 ) 8.92 = 2.18 m

Ycg MURO = Ycg MURO

Wmuro = 8.92m 3 * 2.4 t

m3

= 21.41t

Diferentes tipos de casos: •

Caso A: Relleno compactado detrás del fuste.

K 0 = 1 − Senφ = 1 − Sen32 = 0.47 1 E = * 1.8 * 8 2 * 0.47 = 27.07 2 1 Z = * 8 = 2.67 3 Mv = 27.07 * 2.67 = 72.19t − m µ = tgφ = tg 32 = 0.66 µ = 0.5 Para ser conservador

F .Sdesl =

Festab Ptotal * µ 60.66 * 0.5 = = = 1.12 Fdesl E 27.07

F .Sdesl ≥ 1.5

No cumple

Festab Ptotal * µ 60.66 * 0.66 = = = 1.49 ≅ 1.5 Fdesl E 27.07 F .Sdesl ≥ 1.5 OK F .Sdesl =

Factor de seguridad al volcamiento: F .Svolc =

Mestab 214.55 = = 2.97 ≥ 1.5 Mvolcantes 72.19

Fuerzas sobre el terreno a=

214.55 − 72.19 = 2.35 60.66

σ max = (4 L − 6a)

σ min = (6a − 2 L)

P L2

P L2

σ max = (4 * 5.6 − 6 * 2.35)

60.66 5.6 2

σ max = 16.05ton / m

σ min = (6 * 2.35 − 2 * 5.6)

60.66 5.6 2

σ min = 5.61 ton / m

2 Los esfuerzos máximos y mínimos no superan al admisible ( σ adm = 20t / m ), el muro

es estable.

•

Caso B: Estribo Cargado

GRUPO I GRUPO (I) = D, L, CF, E, B, ST B=Flotación

D=Muerta L=Viva CF=Fuerza centrifuga (curva) E=Empuje ST=Flujo de agua (corriente)

F .Svolc =

214.55 + (13.52 + 10.04) * (1.87 + 0.25) = 7.48 17.68 * 2

F .Sdesl =

(60.66 + 13.52 + 10.04)0.5 = 2.38 17.68

F .Svolc = 7.48 > 1.5

F .Sdesl = 2.38 ≥ 1.5

Fuerza sobre el terreno: a=

214.55 + (13.52 + 10.04 ) * 2.12 − 17.68 * 2 = 2.72 60.66 + 13.52 + 10.04

σ max = (4 L − 6a)

P L2

σ max = (4 * 5.6 − 6 * 2.72)

σ min = (6a − 2 L)

5.6 2

σ max = 16.33 ton / m ≤ 20

P L2

σ min = (6 * 2.72 − 2 * 5.6)

GRUPO II

( 60.66 + 13.52 + 10.04)

( 60.66 + 13.52 + 10.04) 5.6 2

σ min = 13.75 ton / m ≤ 20

GRUPO (II) = D + E + B + SF + W F .Svolc =

214.55 + 13.52 * 2.12 = 6.27 17.68 * 2 + 0.29 * 8 + 0.11 * 9.83

F .Svolc = 6.27 > 1.5 F .Sdesl =

(60.66 + 13.52) * 0.5 = 2.05 17.68 + 0.29 + 0.11

F .Sdesl = 2.05 ≥ 1.5

Fuerza sobre el terreno: (214.55 + 13.52 * 2.12) − (17.68 * 2 + 0.29 * 8 + 0.11 * 9.83) = 2.76 60.66 + 13.52

a=

σ max

P = ( 4 L − 6a ) 2 L

σ max = (4 * 5.6 − 6 * 2.76)

60.66 + 13.52 = 13.81ton / m 5.6 2

σ max = 13.81 ≤ 1.25 * 20

σ min

P = (6a − 2 L ) 2 L

σ max = (6 * 2.76 − 2 * 5.6)

60.66 + 13.52 = 12.68ton / m 5.6 2

σ max = 12.68 ≤ 1.25 * 20

GRUPO III GRUPO (III) = D, L, E, 0.3W, WL, LF F .Svolc =

214.55 + 13.52 * 2.12 + 10.04 * 2.12 = 6.68 ≥ 1.5 17.68 * 2 + 0.29 * 8 * 0.3 + 0.11 * 9.83 + 0.25 * 9.83

F .Sdesl =

(60.66 + 13.52 + 10.04) * 0.5 = 2.32 ≥ 1.5 17.68 + 0.3 * 0.29 + 0.11 + 0.25

Fuerza sobre el terreno:

a=

214.55 + 13.52 * 2.12 + 10.04 * 2.12 − (17.68 * 2 + 0.29 * 8 * 0.3 + 0.11 * 9.83 + 0.25 * 9.83) 60.66 + 13.52 + 10.04

a = 2.67 m

σ max = (4 L − 6a)

P L2

σ max = (4 * 5.6 − 6 * 2.67)

60.66 + 13.52 + 10.04 5.6 2

σ max = 17.13 ton / m ≤ 1.25 * 20

σ min

σ min = (6 * 2.67 − 2 * 5.6)

P = (6 a − 2 L ) 2 L

60.66 + 13.52 + 10.04 5.6 2

σ max = 12.94 ton / m ≤ 1.25 * 20 GRUPO VII GRUPO VII: D, E, SF, EQ Wse = 159674 Kg Sse = 159674 * 0.15 = 23951 23.951 = 2.34 10.25 Wmuro = 8.92m 3 * 2.4 t

m3

= 21.41t

Smuro = 21.4 * 0.15 = 3.21 1. Sin el sismo vertical F .Sdesl =

(60.66 + 13.52) * 0.5 = 1.30 ≤ 1.5 17.68 + 5.60 + 3.21 + 2.34

F .Svolc =

214.55 + 13.52 * 2.12 = 3.18 ≥ 1.5 17.68 * 2 + 5.60 * 4 + 3.21 * 2.18 + 2.34 * 5

a=

( 214.55 + 13.52 * 2.12) − (17.68 + 5.60 * 4 + 3.21 * 2.18 + 2.34 * 5) = 2.48 60.66 + 13.52

60.66 + 13.52 ( 4 * 5.6 − 6 * 2.48) = 17.79 ≤ 1.33 * 20 5.6 2 60.66 + 13.52 ( 6 * 2.48 − 2 * 5.6) = 8.70 ≤ 1.33 * 20 = 5.6 2

σ max = σ min

1 b = 2.48 ⇒ b = 7.44 3 b * σ max ∑V = 2 ∑ V = 60.66 + 13.52 = 74.18 7.44 * σ max 74.18 = 2 σ max = 19.94 NOTA 1.30