DATOS:

f´c = 210 Kg/cm²

fy = 4200 Kg/cm²

sT = 2.2 Kg/m²

Ko = 5000 Tn/m³

NPT = 0.25 m

Df = 1.7 m

S/C = 400 kg/m²

PD = 40.0 Tn PD = 60.0 Tn PD = 45.0 Tn

PL = 25.0 Tn PL = 35.0 Tn PL = 30.0 Tn

MDx = 2.8 Tn - m MDx = 2.0 Tn - m MDx = 3.2 Tn - m

MLx = 1.4 Tn - m MLx = 1.2 Tn - m MLx = 1.8 Tn - m

MDy = 2.2 Tn - m MDy = 2.1 Tn - m MDy = 2.4 Tn - m

MLy = 1.5 Tn - m MLy = 1.3 Tn - m MLy = 1.7 Tn - m

0.40 C1 0.40 C2 0.40 C3

5.00 m 6.00 m

12.20 m

0.45 m

1.00

m 0.40 m

1.40 m

SOLUCIÓN:

Verificación de la Rigidez:

VIGA DE CIMENTACIÓN FLEXIBLE O FLOTANTE

Columna 1 Columna 2 Columna 3

Lm = 5.90 m

Kc = 2.2*K750*((b+300)/2*b))²

Kc = 4054.85 Ton/m

I = 0.0611 m⁴

1.75*(4*E*I/Kc*b)¼ = 5.44 m

Lm = 5.90 > 5.44 \ Cimentación Flexible

Cálculo de la Elástica:

L = (4*E*I/Kc*b)¼

L = 3.11 m

M1 M2 M3

P1 P2 P3

0.2 5.40 m 6.40 m 0.2

Para P1: fig.

lL = 0.06

lR = 3.86 GT-15 0.06 3.86

Para P2:

lL = 1.80

lR = 2.12 GT-25 1.80 2.12

Para P3:

lL = 3.86

lR = 0.06 GT-15 3.86 0.06

Para M1:

lL = 0.06

lR = 3.86 GT-26 0.06 3.86

Para M2:

lL = 1.80

lR = 2.12 GT-27 1.80 2.12

Para M3:

lL = 3.86

lR = 0.06 GT-26 3.86 0.06

Determinación de los Coeficientes de esfuerzos del Terreno:

P1 P2

0.2 5.40 m 6.40

1 2 3 4 5

Debido a:

s1 = s7 0.00 0.00

s2 l = 0.00 l = 1.74 l =

2.00 0.04

s = 29.85 s = 0.87 s =

s3 l = 0.87 l = 0.87 l =

0.40 0.31

s = 5.97 s = 6.76 s =

s4 l = 1.74 l = 0.00 l =

-0.15 0.53

s = -2.24 s = 11.56 s =

s5 l = 2.77 l = 1.03 l =

-0.15 0.30

s = -2.24 s = 6.55 s =

s6 l = 3.79 l = 2.06 l =

0.00 -0.10

s = 0.00 s = -2.18 s =

Determinación de los Coeficientes de Momentos de Flexión:

Debido a:

M1 = M7 0.00 0.00

M2 l = 0.00 l = 1.74 l =

0.00 -0.01

M = 0.00 M = -2.95 M =

M3 l = 0.87 l = 0.87 l =

-0.31 -0.005

M = -62.67 M = -1.48 M =

M4 l = 1.74 l = 0.00 l =

-0.15 0.25

M = -30.33 M = 73.87 M =

M5 l = 2.77 l = 1.03 l =

-0.05 0.01

M = -10.11 M = 2.95 M =

M6 l = 3.79 l = 2.06 l =

0.00 -0.004

P1

GT-15 GT-25 GT-15

P2 P3

P1 P2 P3

M = 0.00 M = -1.18 M =

Determinación de los Coeficientes de Esfuerzos Cortantes:

Debido a:

V1 = V7 0.00 0.00

V2 l = 0.00 l = 1.74 l =

-1.00 0.04

V = -65.00 V = 3.80 V =

V3 l = 0.87 l = 0.87 l =

0.13 -0.10

V = 8.45 V = -9.50 V =

V4 l = 1.74 l = 0.00 l =

0.20 0.50

V = 13.00 V = 47.50 V =

V5 l = 2.77 l = 1.03 l =

0.00 0.00

V = 0.00 V = 0.00 V =

V6 l = 3.79 l = 2.06 l =

0.00 0.00

V = 0.00 V = 0.00 V =

Determinación del Refuerzo Longitudinal:

Punto 2:

Mu = 8708.79 Kg-m

d = 90.75 cm

a = 18.15 cm

b = 45 cm

ab = 0.01

As = 2.82

Asmin = 0.7*(f´c/fy)*bw*d

Asmin = 9.86 cm²

USAR : 2 Φ Nº 6 +

\ As = 9.66 cm2

Punto 3:

P1 P2 P3

Mu = 51089.51 Kg-m

d = 90.75 cm

a = 18.15 cm

b = 140.00 cm

ab = 0.03

As = 16.55

USAR : 6 Φ Nº 6

\ As = 17.10 cm2

Punto 4:

Mu = 26801.31 Kg-m

d = 90.75 cm

a = 18.15 cm

b = 45.00 cm

ab = 0.05

As = 8.68

Asmin = 0.7*(f´c/fy)*bw*d

Asmin = 9.86 cm²

USAR : 2 Φ Nº 6 +

\ As = 9.66 cm2

Punto 5:

Mu = 70665.63 Kg-m

d = 90.75 cm

a = 18.15 cm

b = 140.00 cm

ab = 0.04

As = 22.89

USAR : 3 Φ Nº 8 +

\ As = 23.75 cm2

Punto 5:

Mu = 13193.82 Kg-m

d = 90.75 cm

a = 18.15 cm

b = 45.00 cm

ab = 0.02

As = 4.27

Asmin = 0.7*(f´c/fy)*bw*d

Asmin = 9.86 cm²

USAR : 2 Φ Nº 6 +

\ As = 9.66 cm2

Determinación de los Coeficientes de esfuerzos del Terreno:

P3

m 0.2

6 7

0.00 0.00 0.00 0.00

3.79 l = 0.00 l = 1.74 l = 3.79

0.00 -2.00 -1.50 0.00

0.00 s = -1.93 s = -1.10 s = 0.00

2.93 l = 0.87 l = 0.87 l = 2.93

-0.15 0.20 0.40 0.10

-2.58 s = 0.19 s = 0.29 s = 0.11

2.06 l = 1.74 l = 0.00 l = 2.06

-0.20 0.40 -0.20 0.35

-3.44 s = 0.39 s = -0.15 s = 0.40

1.03 l = 2.77 l = 1.03 l = 1.03

0.40 0.20 -0.75 0.25

6.89 s = 0.19 s = -0.55 s = 0.29

0.00 l = 3.79 l = 2.06 l = 0.00

2.00 0.05 -1.50 -2.00

34.45 s = 0.05 s = -1.10 s = -2.30

0.00 0.00 0.00 0.00

3.79 l = 0.00 l = 1.74 l = 3.79

0.00 1.00 0.00 -0.09

0.00 M = 13.06 M = 0.00 M = -1.40

2.93 l = 0.87 l = 0.87 l = 2.93

0.02 0.79 0.08 -0.10

3.50 M = 10.32 M = 0.80 M = -1.56

2.06 l = 1.74 l = 0.00 l = 2.06

-0.10 0.125 0.31 0.12

-23.33 M = 1.63 M = 3.09 M = 1.87

1.03 l = 2.77 l = 1.03 l = 1.03

-0.30 -0.10 0.00 0.50

-69.98 M = -1.31 M = 0.00 M = 7.78

0.00 l = 3.79 l = 2.06 l = 0.00

0.00 -0.09 0.00 1.00

M3

GT-15 GT-26 GT-27 GT-26

P3 M1 M2

M3P3 M1 M2

0.00 M = -1.18 M = 0.00 M = 15.55

0.00 0.00 0.00 0.00

3.79 l = 0.00 l = 1.74 l = 0.02

0.00 0.10 -0.75 -0.09

0.00 V = 0.42 V = -2.40 V = -0.45

2.93 l = 0.87 l = 0.87 l = 2.93

0.00 -0.62 -0.22 0.00

0.00 V = -2.60 V = -0.70 V = 0.00

2.06 l = 1.74 l = 0.00 l = 2.06

0.15 -0.35 -0.30 -0.29

11.25 V = -1.47 V = -0.96 V = -1.45

1.03 l = 2.77 l = 1.03 l = 1.03

0.14 -0.04 0.00 -0.63

10.50 V = -0.17 V = 0.00 V = -3.15

0.00 l = 3.79 l = 2.06 l = 0.00

-1.00 0.02 0.00 0.10

-95.00 V = 0.08 V = 0.00 V = 0.50

cm

cm2

2 Φ Nº 5

M3P3 M1 M2

cm

cm2

cm

cm2

2 Φ Nº 5

cm

cm2

3 Φ Nº 6

cm

cm2

2 Φ Nº 5

TOTAL

0

27.70

10.75

6.52

11.12

28.92

TOTAL

0

8.71

-51.09

26.80

-70.67

27.70

10.75

6.52

11.12

28.92

8.71

51.09

26.80

13.19

13.19

TOTAL

0

-63.63

-4.36

67.87

7.18

-94.42

63.63

94.42

4.36

67.87

7.18

6.00

3Ø3/4"3Ø1"3Ø3/4"

2Ø3/4"+2Ø5/8"

2

.45 .455.00 .45

2Ø3/4"+2Ø5/8"

3Ø3/4" 1

1 2

6.00

3Ø3/4"3Ø1"3Ø3/4"

2Ø3/4"+2Ø5/8"

2

.45 .455.00 .45

2Ø3/4"+2Ø5/8"

3Ø3/4" 1

1 2

27.70

10.75

6.52

11.12

28.92

8.71

51.09

26.80

13.19

63.63

94.42

4.36

67.87

7.18

6.00

3Ø3/4"3Ø1"3Ø3/4"

2Ø3/4"+2Ø5/8"

2

.45 .455.00 .45

2Ø3/4"+2Ø5/8"

3Ø3/4" 1

1 2

6.00

3Ø3/4"3Ø1"3Ø3/4"

2Ø3/4"+2Ø5/8"

2

.45 .455.00 .45

2Ø3/4"+2Ø5/8"

3Ø3/4" 1

1 2

6.00

3Ø3/4"3Ø1"3Ø3/4"

2Ø3/4"+2Ø5/8"

2

.45 .455.00 .45

2Ø3/4"+2Ø5/8"

3Ø3/4" 1

1 2

6.00

3Ø3/4"3Ø1"3Ø3/4"

2Ø3/4"+2Ø5/8"

2

.45 .455.00 .45

2Ø3/4"+2Ø5/8"

3Ø3/4" 1

1 2