DISEÑO MURO ARMADO

DISEÑO MUROS DE CONCRETO ARMADO H = 7.10 M 1. DATOS DE ENTRADA DIMENSIONAMIENTO PLANTEADO DEBIDO A RESTRICCIONES Datos de Suelo g1 = f1 =

DEL TERRENO EN AMBOS LADOS g2 = f2 = s suelo = Ka = Kp = μ =

3

tn/m °

1.80 32

3

tn/m 1.80 32 ° kg/cm2 0.80 0.30 3.00 0.45

Datos de muro hz (altura de zapata) B1 (Externa) B2 (central) B3 (interna) L : Ancho de Zapata

= = = = =

1.00 1.8 0.70 0.65 3.15

R1 (Altura de relleno 1) = R2 (Altura de relleno 2) =

Espesor de Muro t1 (sup) = t2 (inf) =

0.30 m 0.70 m

H pantalla =

1.70 m 7.10 m

7.10 m

gconcreto =

2 210 kg/cm 3 4200 kg/cm

f'c = fy =

S/C

m m m m m

3 2.40 tn/m

2 0.30 tn/m

=

2. ANALISIS POR CADA METRO DE LONGITUD W s/c

=

0.30

300

=

E s/c

=

90

8.10

=

M s/c =

729

4.05

=

0.30

1800

90 kg/m 729 kg 2952.45 kg.m

Ka Wa

=

Ea

8.1

4374 kg/m

=

4374

4.05

17714.7 kg

Ma

=

17714.7

2.7

47829.69 kg.m

Wp

=

3.00

1800.00

2.70 =

Ep

=

14580

1.35

=

19683 kg

Mp

=

19683

0.9

=

17714.7 kg.m

Kp 14580 kg/m

3. VERIFICACIONES VERIFICACION DE ESTABILIDAD Zonas 1

L

γ

0.65

7.1

1800

Cargas (kg) 8,307.00

Brazo de Giro (m) 2.83

Momentos (kg.m) 23,467.28

2

0.7

7.1

2400

11,928.00

2.15

25,645.20

3

1.8

1.7

1800

5,508.00

0.90

4,957.20

4

3.15

1

2400

7,560.00

1.58

11,907.00

300

540.00

2.83

1,525.50

2,044.80

1.65

5

H

1.8 ancho

6 columnas extremas

0.3

0.4

7.10

2400

35,887.80 VERIFICACION POR DESPLAZAMIENTO Factu =

Es/c + E a

Fres =

Ep+u x Σ Cargas

Fsd

=

VERIFICACION POR VOLTEO

18443.7 Kg

1.94

35,832.51 Kg >

1.50

CORRECTO

3,373.92 70,876.10

Mact

=

M s/c + Ma

50,782.14 kg.m

Mres

=

Mp + ΣMomentos

Fsv

=

1.74

88,590.80 kg.m >

1.50

CORRECTO

PRESION DEL TERRENO

e=

B Mres Mact  2 P

σ=

ΣP =

35,887.80 kg

MO =

Mres-Mact

d

=

Mo/P

e

= B/2 - d

35887.8 = 1.05

2

37,808.66 kg.m

17032.26667

1.703226667

1.054 m 0.521 m

B/6 =

0.525 m

>

0.521

CORRECTO

4. DISEÑO POR CONCRETO ARMADO

4.1 DISEÑO DE PANTALLA γ

kp wu =

1.8

0.30

Vu =

6901.20

3.55

=

24,499.26 Kg

24499.26 2.36666667

=

57,981.58

Mu =

1800

7.1 =

6,901.20 kg/m

d  Vc =

b x d

0.85

=

0.53

100

x

14.4913767

100

65

=

Vu 24,499.26

42,434.37 >

65

Calculo del acero en pantalla Datos

Momentos en tn.m

h (cm): r (cm): d (cm): b (cm): 2 f'c (Kg/cm ): f: fy (Kg/cm2):

70.00 5 65 100 210 0.9 4200

b (cm) M (tn.m) As (cm2)

100 57.981582 24.70

φ 1" @ 0.30 m + BASTONES DE 5/8" @ 30 r = As bd

=

r min = 0.0018

0.0040 >

Refuerzo Mínimo

Acero colocado:

26.25 cm2

OK!

parte superior = 0.0018 x 100 x 0.3 = parte inferior = 0.0018 x 100 x 0.7 =

5.4 cm2 / m 12.6 cm2 / m

Como la pantalla es de sección variable y asumiendo a = d / 5, ademas As 1 = As2 se obtiene

Kg  Mmax/2= a s x1.7x(5hc)3  6 

f s  K a = tan 2  45   = h 2 sv 

Ka =tg2( 45 - 32/2 ) =

0.307

Lc = hc + d

usar

Lc : tambien 1/3 H pantalla

Utilizado

hc = Lc = Lc =

1.4 2.05 m 2.1 m

=

2.40 m

As = rt bt d Arriba: = 0.0018 x 100 x 30 =

Refuerzo Horizontal 2/3 As 1/3As

2 3

A

st

=

5.4 cm2 / m 3.6

f 1/2" @ 0.30 m

CORRECTO

2 3

A

st

=

1 3

A

st

=

Intermedio:

= 0.0018 x 100 x 50 =

9 cm2 / m

2 3

A

st

=

6

f 1/2" @ 0.25 m

1 3

A

st

=

3

f 3/8" @ 0.25 m

Abajo:

= 0.0018 x 100 x 70 =

2 3

A

st

1 3

A

st

12.6 cm2 / m

=

8.4

f 5/8" @ 0.25 cm

=

4.2

f 1/2" @ 0.30 m

36f = 36 x 1.91 = f 3/4" @ 0.30 m

Acero de montaje:

f 3/8" @ 0.30 m

1.8

68.76 < S

Smax = 30 cm

4.1 DISEÑO DE ZAPATA DISEÑO DE LA PUNTA

wu =

1.67

σ= 17032.27 =

Mu =

28443.88534

1.62 =

Vu

=

Wu ( B3-d) =

 Vc = b x d =

28443.88534 kg 46079.09 kg.m 25599.50 kg

0.85

0.53

100 x

14.4913767

100

90

=

58,755.29 >

25,599.50 CORRECTO

90

=

58,755.29 >

-6,651.00 CORRECTO

90

Datos

Momentos en tn.m

h (cm): r (cm): d (cm): b (cm): 2 f'c (Kg/cm ): f: fy (Kg/cm2):

100.00 10 90 100 210 0.9 4200


100 46.08 13.79

Se coloca acero en doble malla : f 5/8" @ 0.25 m

Acero colocado :

en doble malla

DISEÑO DEL TALON

Wu =

1.5 x hz x γ + 1.8 x γ x R1 =

Vu

Wu ( B3-d) =

=

 Vc =

-6651 kg

0.85

b x d =

100 x

Mu =

Wu x B3xB3/ 2

0.53

Asmin zapata :

14.4913767

100

90 =

5620.095

Datos h (cm): r (cm): d (cm): b (cm): f'c (Kg/cm2): f: fy (Kg/cm2):

26604 Kg/m

Momentos en tn.m 100.00 10 90 100 210 0.9 4200

0.0018

En cada cara :


100

9 cm2

100.00 =

100 5.62 1.66

=

18

cm2

f 5/8" @ 0.25 m

Refuerzo transversal As temp = 0.0018 x 100 x 100 = En cada cara

18 9

f 5/8" @ 0.30 m

DISEÑO MUROS DE CONCRETO ARMADO H = 6.50 M 1. DATOS DE ENTRADA

DIMENSIONAMIENTO PLANTEADO DEBIDO A RESTRICCIONES DEL TERRENO EN AMBOS LADOS Datos de Suelo

g1 = f1 =

g2 = f2 = s suelo = Ka = Kp = μ =

3

tn/m °

1.80 32

tn/m3 1.80 32 ° kg/cm2 0.80 0.30 3.00 0.45


= = = = =

1.00 1.8 0.55 0.5 2.85



0.30 m 0.55 m

H pantalla =

1.7 m 6.5 m

6.50 m

gconcreto =

2

210 kg/cm 3 4200 kg/cm

f'c = fy =

S/C

m m m m m

3

2.40 tn/m

2 0.30 tn/m

=


=

0.30

300

=

E s/c

=

90

7.50

=

M s/c =

675

3.75

=

0.30

1800

90 kg/m 675 kg 2531.25 kg.m

Ka Wa

=

Ea

7.5

4050 kg/m

=

4050

3.75

15187.5 kg

Ma

=

15187.5

2.5

37968.75 kg.m

Wp

=

3.00

1800.00

2.70 =

Ep

=

14580

1.35

=

19683 kg

Mp

=

19683

0.9

=

17714.7 kg.m

Kp 14580 kg/m

3. VERIFICACIONES VERIFICACION DE ESTABILIDAD

Zonas 1

L

γ

0.5

6.5

1800

Cargas (kg) 5850

0.55

6.5

2400

8580

3

1.8

1.7

1800

4

2.85

1

2400

5

1.8

2

H

300

2.6

Momentos (kg.m) 15210

2.075

17803.5

5508

0.9

4957.2

6840

1.425

9747

540

2.60

27318 VERIFICACION POR DESPLAZAMIENTO Factu =

Es/c + E a

Fres =

Ep+u x Σ Cargas

Fsd

=

15862.5 Kg

2.02

31,976.10 Kg >

1.50

CORRECTO

Brazo de Giro (m)

1404 49121.7

VERIFICACION POR VOLTEO Mact

=

M s/c + Ma

40,500.00 kg.m

Mres

=

Mp + ΣMomentos

66,836.40 kg.m

Fsv

=

1.65

>

1.50

CORRECTO

PRESION DEL TERRENO

e=


σ=

ΣP =

27,318.00 kg

MO =

Mres-Mact

d

=

Mo/P

e

= B/2 - d

27318 = 0.96

2

26,336.40 kg.m

14168.09291

1.416809291

0.964 m 0.461 m

B/6 =

0.475 m

>

0.461

CORRECTO



kp wu =

1.8

0.30

1800

6.5 =

6,318.00 kg/m

Vu =

6318.00

3.25

=

20,533.50 Kg

Mu =

20533.5 2.16666667

=

44,489.25

d  Vc =

b x d

0.85

=

0.53

100

x

14.4913767

100

50

=

Vu 20,533.50 CORRECTO

32,641.83 >

50


Momentos en tn.m

h (cm): r (cm): d (cm): b (cm): f'c (Kg/cm2): f: 2 fy (Kg/cm ):

55.00 5 50 100 210 0.9 4200


100 44.48925 25.01

φ 1" @ 0.30 m + BASTONES DE 5/8" @ 30 r = As bd

=

r min = 0.0018

0.0053 >

Refuerzo Mínimo

Acero colocado:

26.25 cm2

OK!


5.4 cm2 / m 9.9 cm2 / m


Kg  Mmax/2= a s x1.7x(5hc)3  6 

f s  K a = tan 2  45   = h 2 sv 

Ka =tg2( 45 - 32/2 ) =

0.307

Lc = hc + d

usar


Utilizado

hc = Lc = Lc =

1.282 1.78 m 1.8 m

=

2.20 m



2 3

A

st

=

5.4 cm2 / m 3.6

f 1/2" @ 0.30 m

2 3

A

st

=

1 3

A

st

=

Intermedio:

= 0.0018 x 100 x 42.5 =

2 3

A

st

1 3

A

st

Abajo:

7.65 cm2 / m

=

5.1

f 1/2" @ 0.25 m

=

2.55

f 3/8" @ 0.25 m

= 0.0018 x 100 x 55 =

2 3

A

1 3

A

9.9 cm2 / m

st

=

6.6

f 5/8" @ 0.25 cm

st

=

3.3

f 1/2" @ 0.30 m

36f = 36 x 1.91= f 3/4" @ 0.30 m

Acero de montaje:

f 3/8" @ 0.30 m

1.8

68.76 < S

Smax = 30 cm


1.67

σ= 14168.09 =

23660.71515

1.62 =

wu = Mu = Vu

=

Wu ( B3-d) =

 Vc = b x d =

23660.71515 kg 38330.36 kg.m 21294.64 kg

0.85

0.53

100 x

14.4913767

100

90

=

58,755.29 >

21,294.64 CORRECTO

90

=

58,755.29 >

-9,864.00 CORRECTO

90

Datos

Momentos en tn.m

h (cm): r (cm): d (cm): b (cm): f'c (Kg/cm2): f: fy (Kg/cm2):

100.00 10 90 100 210 0.9 4200

b (cm) M (tn.m) 2 As (cm )

100 38.33 11.44


Acero colocado :

en doble malla

DISEÑO DEL TALON

Wu =

1.5 x hz x γ + 1.8 x γ x R1 =

24660 Kg/m

Vu

Wu ( B3-d) =

-9864 kg

=

 Vc =

0.85

b x d =

100 x

Mu =

Wu x B3xB3/ 2

0.53

Asmin zapata :

100

90 =

3082.5

Datos h (cm): r (cm): d (cm): b (cm): f'c (Kg/cm2): f: 2 fy (Kg/cm ):

14.4913767

Momentos en tn.m 100.00 10 90 100 210 0.9 4200

0.0018

En cada cara :


100

9 cm2

100.00 =

100 3.0825 0.91

=

18

cm2

f 5/8" @ 0.25 m


18 9

f 5/8" @ 0.30 m



g1 = f1 =

g2 = f2 = s suelo = Ka = Kp = μ =

3

tn/m °

1.80 32

tn/m3 1.80 32 ° kg/cm2 0.80 0.30 3.00 0.45


= = = = =

0.80 1.8 0.45 0.5 2.75



0.30 m 0.45 m

H pantalla =

1.7 m 5.1 m

5.10 m

gconcreto =

2

210 kg/cm 3 4200 kg/cm

f'c = fy =

S/C

m m m m m

3

2.40 tn/m

2 0.30 tn/m

=


=

0.30

300

=

E s/c

=

90

5.90

=

M s/c =

531

2.95

=

0.30

1800

3186

2.95

90 kg/m 531 kg 1566.45 kg.m

Ka Wa

=

Ea

=

5.9

3186 kg/m 9398.7 kg

Ma

=

9398.7 1.96666667

18484.11 kg.m

Wp

=

3.00

1800.00

2.50 =

Ep

=

13500

1.25

=

16875 kg

Mp

=

16875 0.83333333

=

14062.5 kg.m

Kp 13500 kg/m


Zonas 1

L

γ

0.5

5.1

1800

Cargas (kg) 4590

0.45

5.1

2400

5508

3

1.8

1.7

1800

4

2.75

0.8

2400

5

1.8

2

H

300

2.5


2.025

11153.7

5508

0.9

4957.2

5280

1.375

7260

540

2.50


Es/c + E a

Fres =

Ep+u x Σ Cargas

Fsd

=

9929.7 Kg

2.67

26,516.70 Kg >

1.50

CORRECTO

Brazo de Giro (m)

1350 36195.9


=

M s/c + Ma

20,050.56 kg.m

Mres

=

Mp + ΣMomentos

50,258.40 kg.m

Fsv

=

2.51

>

1.50

CORRECTO

PRESION DEL TERRENO

e=

ΣP =

B Mres Mact  21,426.00 kg 2 P

MO =

Mres-Mact

d

=

Mo/P

e

= B/2 - d

σ=

21426 = 1.41

2

30,207.84 kg.m

7598.581626

0.759858163

1.410 m -0.035 m

B/6 =

0.45833333 m

>

-0.035

CORRECTO



kp wu =

1.8

0.30

1800

5.1 =

4,957.20 kg/m

Vu =

4957.20

2.55

=

12,640.86 Kg

Mu =

12640.86

1.7

=

21,489.46

0.85

0.53

d  Vc =

b x d

=

100

x

14.4913767

100

40

=


26,113.46 >

40


Momentos en tn.m


45.00 5 40 100 210 0.9 4200


100 21.49 14.86

φ 3/4" @ 0.30 m + BASTONES DE 5/8" @ 30 r = As bd

=

r min = 0.0018

0.0044 >

Refuerzo Mínimo

Acero colocado:

17.45 cm2

OK!


5.4 cm2 / m 8.1 cm2 / m


f sh Kg  2 3 = tan 45   = Mmax/2= a s x1.7x(5hK ) c a 2   sv  6  Ka =tg2( 45 - 32/2 ) =

0.307

Lc = hc + d

usar


Utilizado

hc = Lc = Lc =

1.006 1.41 m 1.5 m

=

1.70 m



2 3

A

st

=

5.4 cm2 / m 3.6

f 1/2" @ 0.30 m

2 3 1

3

Intermedio:

2 3 1

3

Abajo:

2 3 1

3

A

st

=

A

st

=

= 0.0018 x 100 x 37.5 =

6.75 cm2 / m

A

st

=

4.5

st

=

2.25

A

= 0.0018 x 100 x 45 =

st

=

2.7

st

=

A

A

f 1/2" @ 0.25 m f 3/8" @ 0.25 m

8.1 cm2 / m 5.4

36f = 36 x 1.59 = f 5/8" @ 0.25m

Acero de montaje:

f 3/8" @ 0.30 m

1.8

f 5/8" @ 0.25 cm f 1/2" @ 0.30 m

57.24 < S


1.67

σ= 7598.58 =

12689.63132

1.62 =

wu = Mu = Vu

=

Wu ( B3-d) =

 Vc = b x d =

12689.63132 kg 20557.20 kg.m 13958.59 kg

0.85

0.53

100 x

14.4913767

100

70

=

45,698.56 >

13,958.59 CORRECTO

70

=

45,698.56 >

-3,880.80 CORRECTO

70

Datos

Momentos en tn.m


80.00 10 70 100 210 0.9 4200


100 20.56 7.87


Acero colocado :

en doble malla

DISEÑO DEL TALON

Wu =

1.5 x hz x γ + 1.8 x γ x R1 =

Vu

Wu ( B3-d) =

=

 Vc =

0.85

b x d =

100 x

Mu =

Wu x B3xB3/ 2

0.53

14.4913767

100

70 =

2425.5

Datos

Momentos en tn.m


Asmin zapata :

19404 Kg/m -3880.8 kg

80.00 10 70 100 210 0.9 4200

0.0018

En cada cara :


100

7.2 cm2

80.00 =

100 2.4255 0.92

=

14.4

cm2

f 5/8" @ 0.30m


14.4 7.2

f 5/8" @ 0.30 m

DISEÑO MUROS DE CONCRETO ARMAD H = 5.10 M 1. DATOS DE ENTRADA

Datos de Suelo g1 = f1 =

g2 = f2 = s suelo = Ka = Kp = μ =

tn/m3 °

1.80 32

1.80 32 0.80 0.30 3.00 0.45


= = = = =


f'c = fy =

S/C

=

2 210 kg/cm 3 4200 kg/cm

0.80 1.8 0.45 0.5 2.75

m m m m m

1.1 m 5.1 m


0.30 0.45

H pantalla =

5.10

gconcreto =

2.40

2 0.30 tn/m


=

0.30

E s/c

=

90

M s/c =

531

Ka Wa

=

0.30

Ea

=

3186

Ma

=

9398.7

Wp

=

3.00

Ep

=

10260

Mp

=

9747

Kp


Zonas 1

L

γ

H 0.5

5.1

1800

2

0.45

5.1

2400

3

1.8

1.1

1800

4

2.75

0.8

2400

5

1.8

300

VERIFICACION POR DESPLAZAMIENTO Factu =

Es/c + E a

Fres =

Ep+u x Σ Cargas

Fsd

=

9929.7 Kg

1.86

18,513.90 Kg >

1.50


=

M s/c + Ma

20,050.56 kg.m

Mres

=

Mp + ΣMomentos

40,619.40 kg.m

Fsv

=

2.03

PRESION DEL TERRENO

e=


>

1.50

e=


ΣP =

19,482.00 kg

MO =

Mres-Mact

d

=

Mo/P

e

= B/2 - d

20,568.84 kg.m 1.056 m 0.319 m

B/6 =

0.45833333 m

>



kp wu =

1.8

0.30

1800

5.1 =

Vu =

4957.20

2.55

=

Mu =

12640.86

1.7

=

0.85

0.53

d  Vc =

b x d

=

100

x

14.4913767

100

40

40


Momentos en tn.m


45.00 5 40 100 210 0.9 4200


100 21.49 14.86

φ 3/4" @ 0.30 m + BASTONES DE 5/8" @ 30 r = As bd

Refuerzo Mínimo

=

0.0044 >

r min = 0.0018


Como la pantalla es de sección variable y asumiendo a = d / 5, ademas As1 = As2 se obtiene

Kg  Mmax/2= a s x1.7x(5hc)3  6 

f s  K a = tan 2  45   = h 2 sv 

Ka =tg2( 45 - 32/2 ) =

0.307

Lc = hc + d

usar


Utilizado

hc = Lc = Lc =

1.006 1.41 m 1.5 m

=

1.70 m



2 3

A

st

=

3.6

1 3

A

st

=

1.8

Intermedio:

= 0.0018 x 100 x 37.5 =

2 3

A

st

=

4.5

1 3

A

st

=

2.25

Abajo:

Acero de montaje:

= 0.0018 x 100 x 45 =

2 3

A

st

=

5.4

1 3

A

st

=

2.7

36f = 36 x 1.59 = f 5/8" @ 0.25m

57.24 < S


wu =

1.67

σ= 9226.29 =

Mu =

15407.91073

1.62 =

Vu

=

24960.82 kg.m

Wu ( B3-d) =

 Vc = b x d =

15407.91073 kg

16948.70 kg 0.85

0.53

100 x

14.4913767

100

70

70

Datos

Momentos en tn.m


80.00 10 70 100 210 0.9 4200


100 24.96 9.59


Acero colocado :

en doble malla

DISEÑO DEL TALON

Wu =

1.5 x hz x γ + 1.8 x γ x R1 =

Vu

Wu ( B3-d) =

=

 Vc =

-3880.8 kg 0.85

b x d =

100 x

Mu =

Wu x B3xB3/ 2

0.53

14.4913767

100

70

Datos h (cm): r (cm): d (cm): b (cm): f'c (Kg/cm2): f:

19404 Kg/m

=

2425.5 Momentos en tn.m

80.00 10 70 100 210 0.9


100 2.4255 0.92

70

fy (Kg/cm2):

Asmin zapata :

4200

0.0018

En cada cara :

100

7.2 cm2

80.00 =

=

14.4 f 5/8" @ 0.30m


14.4 7.2

f 5/8" @ 0.30 m

CRETO ARMADO

DIMENSIONAMIENTO PLANTEADO DEBIDO A RESTRICCIONES DEL TERRENO EN AMBOS LADOS tn/m3 ° kg/cm2

m m

m

tn/m3

300

=

5.90

=

2.95

=

1800 2.95

5.9

90 kg/m 531 kg 1566.45 kg.m

3186 kg/m 9398.7 kg

1.96666667

18484.11 kg.m

1800.00

1.90 =

0.95

=

9747 kg

0.63333333

=

6173.1 kg.m

Cargas (kg) 4590

10260 kg/m

2.5


5508

2.025

11153.7

3564

0.9

3207.6

5280

1.375

7260

540

2.50

1350

19482

CORRECTO

CORRECTO

Brazo de Giro (m)

34446.3

S DE 5/8" @ 30

σ=

19482 = 1.06

2

9226.29385

0.922629385

0.319

CORRECTO

4,957.20 kg/m 12,640.86 Kg 21,489.46

=

26,113.46 >

Acero colocado:

OK!

5.4 cm2 / m 8.1 cm2 / m


17.45 cm2

5.4 cm2 / m f 1/2" @ 0.30 m

2.834645669 35.27777778

f 3/8" @ 0.30 m

2.535211268 39.44444444

6.75 cm2 / m f 1/2" @ 0.25 m

3.543307087 28.22222222

f 3/8" @ 0.25 m

3.169014085 31.55555556

8.1 cm2 / m f 5/8" @ 0.25 cm

2.713567839 36.85185185

f 1/2" @ 0.30 m

2.125984252 47.03703704

=

45,698.56 >

16,948.70 CORRECTO

=

45,698.56 >

-3,880.80 CORRECTO

cm2

8" @ 0.30m

8" @ 0.30 m

pulg 3/8 1/2 5/8 3/4 1

cm

area 0.95 1.27 1.59 1.91 2.54

0.71 1.27 1.99 2.87 5.07



g1 = f1 =

g2 = f2 = s suelo = Ka = Kp = μ =

3

tn/m °

1.80 32

tn/m3 1.80 32 ° kg/cm2 0.80 0.30 3.00 0.45


= = = = =

0.60 0.7 0.30 0.5 1.50



0.30 m 0.30 m

H pantalla =

1 m 3.5 m

3.50 m

gconcreto =

2

210 kg/cm 3 4200 kg/cm

f'c = fy =

S/C

m m m m m

3

2.40 tn/m

2 0.30 tn/m

=


=

0.30

300

=

E s/c

=

90

4.10

=

369 kg

90 kg/m

M s/c =

369

2.05

=

756.45 kg.m

0.30

1800

2214

2.05

Ka Wa

=

Ea

=

4.1

2214 kg/m 4538.7 kg

Ma

=

4538.7 1.36666667

6202.89 kg.m

Wp

=

3.00

1800.00

1.60 =

Ep

=

8640

0.8

=

6912 kg

Mp

=

6912 0.53333333

=

3686.4 kg.m

Kp 8640 kg/m


Zonas 1

L

2

γ

0.5

H 3.5

1800

Cargas (kg) 3150


Momentos (kg.m) 3937.5

0.3

3.5

2400

2520

0.85

2142

3

0.7

1

1800

1260

0.35

441

4

1.50

0.6

2400

2160

0.75

1620

5

1.8

540

1.25

300


Es/c + E a

Fres =

Ep+u x Σ Cargas

Fsd

=

4907.7 Kg

2.29

11,245.50 Kg >

1.50

CORRECTO

675 8815.5


=

M s/c + Ma

Mres

=

Mp + ΣMomentos

6,959.34 kg.m

Fsv

=

1.80

12,501.90 kg.m >

1.50

CORRECTO

PRESION DEL TERRENO

e=

ΣP =

B Mres Mact  9,630.00 kg 2 P

MO =

Mres-Mact

d

=

Mo/P

e

= B/2 - d

σ=

9630 = 0.58

2

5,542.56 kg.m

8365.890491

0.836589049

0.576 m 0.174 m

B/6 =

0.25 m

>

0.174

CORRECTO



kp wu =

1.8

0.30

Vu =

3402.00

1.75

=

5,953.50 Kg

5953.5 1.16666667

=

6,945.75

Mu =

1800

3.5 =

3,402.00 kg/m

d  Vc =

b x d

0.85

=

0.53

100

x

14.4913767

100

25

=

16,320.91 >

Vu 5,953.50

25


Momentos en tn.m


30.00 5 25 100 210 0.9 4200


100 6.95 7.62

φ 5/8" @ 0.25 m r = As bd

=

r min = 0.0018

0.0040 >

Refuerzo Mínimo

Acero colocado:

9.95 cm2

OK!


5.4 cm2 / m 5.4 cm2 / m



0.307

Lc = hc + d

usar


Utilizado

hc = Lc = Lc =

0.69 0.94 m 1.00 m

=

1.00 m



2 3

A

st

=

5.4 cm2 / m 3.6

f 3/8" @ 0.25 m

CORRECTO

2 3 1

3

Intermedio:

A

st

=

A

st

=

= 0.0018 x 100 x 30 =

2 3 1

3

Abajo:

5.4 cm2 / m

A

st

=

3.6

st

=

1.8

A

= 0.0018 x 100 x 30 =

2 3 1

st

=

1.8

st

=

A

A

3

f 3/8" @ 0.25 m f 3/8" @ 0.25 m

5.4 cm2 / m 3.6

36f = 36 x 1.27 = f 1/2" @ 0.25m

Acero de montaje:

f 3/8" @ 0.25 m

1.8

f 1/2" @ 0.30 cm f 1/2" @ 0.30 m

45.72 < S


1.67

σ= 8365.89 =

13971.03712

0.245 =

wu = Mu = Vu

=

Wu ( B3-d) =

 Vc = b x d =

13971.03712 kg 3422.90 kg.m 2794.21 kg

0.85

0.53

100 x

14.4913767

100

50

=

32,641.83 >

2,794.21 CORRECTO

50

=

32,641.83 >

0.00 CORRECTO

50

Datos

Momentos en tn.m


60.00 10 50 100 210 0.9 4200


100 3.42 1.82


Acero colocado :

en doble malla

DISEÑO DEL TALON

Wu =

1.5 x hz x γ + 1.8 x γ x R1 =

Vu

Wu ( B3-d) =

=

 Vc =

0 kg

0.85

b x d =

100 x

Mu =

Wu x B3xB3/ 2

0.53

14.4913767

100

50 =

1687.5

Datos

Momentos en tn.m


Asmin zapata :

13500 Kg/m

60.00 10 50 100 210 0.9 4200

0.0018

En cada cara :


100

5.4 cm2

60.00 =

100 1.6875 0.89

=

10.8 f 1/2" @ 0.25m


10.8 5.4

f 1/2" @ 0.25m

cm2



g2 = f2 = s suelo = Ka = Kp = μ =

3

tn/m °

1.80 32

tn/m3 1.80 32 ° kg/cm2 0.80 0.30 3.00 0.45


= = = = =

0.50 0.45 0.25 0.5 1.20



0.25 m 0.25 m

H pantalla =

0.4 m 2.2 m

2.20 m

gconcreto =

2

210 kg/cm 3 4200 kg/cm

f'c = fy =

S/C

m m m m m

3

2.40 tn/m

2 0.30 tn/m

=


=

0.30

300

=

E s/c

=

90

2.70

=

243 kg

90 kg/m

M s/c =

243

1.35

=

328.05 kg.m

0.30

1800

Ka Wa

=

Ea

2.7

1458 kg/m

=

1458

1.35

1968.3 kg

Ma

=

1968.3

0.9

1771.47 kg.m

Wp

=

3.00

1800.00

0.90 =

Ep

=

4860

0.45

=

2187 kg

Mp

=

2187

0.3

=

656.1 kg.m

Kp 4860 kg/m


Zonas 1

L

γ

0.5

H 2.2

1800

Cargas (kg) 1980



2

0.25

2.2

2400

1320

0.575

759

3

0.45

0.4

1800

324

0.225

72.9

4

1.20

0.5

2400

1440

0.6

864

5

1.8

540

0.95

300


Es/c + E a

Fres =

Ep+u x Σ Cargas

Fsd

=

2211.3 Kg

2.13

4,708.80 Kg >

1.50

CORRECTO

513 4089.9


=

M s/c + Ma

2,099.52 kg.m

Mres

=

Mp + ΣMomentos

4,746.00 kg.m

Fsv

=

2.26

>

1.50

CORRECTO

PRESION DEL TERRENO

e=

ΣP =

B Mres Mact  5,604.00 kg 2 P

MO =

Mres-Mact

d

=

Mo/P

e

= B/2 - d

σ=

5604 = 0.47

2

2,646.48 kg.m

5933.318219

0.593331822

0.472 m 0.128 m

B/6 =

0.2 m

>

0.128

CORRECTO



kp wu =

1.8

0.30

1800

2.2 =

2,138.40 kg/m

Vu =

2138.40

1.1

=

2,352.24 Kg

Mu =

2352.24 0.73333333

=

1,724.98

d  Vc =

b x d

0.85

=

0.53

100

x

14.4913767

100

20

=

13,056.73 >

20


Momentos en tn.m


25.00 5 20 100 210 0.9 4200


φ 3/8" @ 0.25 m r = As bd

=

100 1.72 2.31

Acero colocado:

r min = 0.0018

0.0018000 >

Refuerzo Mínimo

3.55 cm2

OK!


4.5 cm2 / m 4.5 cm2 / m



0.307

Lc = hc + d

usar


Utilizado

hc = Lc = Lc =

0.434 0.63 m 0.65 m

=

0.65 m



2 3

A

st

=

4.5 cm2 / m 3

f 3/8" @ 0.30 m

Vu 2,352.24

CORRECTO

2 3 1

3

Intermedio:

2 3 1

3

Abajo:

A

st

=

A

st

=

= 0.0018 x 100 x 25 =

4.5 cm2 / m

A

st

=

3

st

=

1.5

A

= 0.0018 x 100 x 25 =

2 3 1

st

=

1.5

st

=

A

A

3

f 3/8" @ 0.30 m f 3/8" @ 0.30 m

4.5 cm2 / m 3

36f = 36 x0.71 = f 3/8" @ 0.30m

Acero de montaje:

f 3/8" @ 0.30 m

1.5

f 3/8" @ 0.30 m f 3/8" @ 0.30 m

34.2 < S


1.67

σ= 5933.32 =

9908.641426

0.10125 =

wu = Mu = Vu

=

Wu ( B3-d) =

 Vc = b x d =

9908.641426 kg 1003.25 kg.m 495.43 kg

0.85

0.53

100 x

14.4913767

100

40

=

26,113.46 >

495.43 CORRECTO

40

=

26,113.46 >

892.80 CORRECTO

40

Datos

Momentos en tn.m


50.00 10 40 100 210 0.9 4200


100 1.00 0.66


Acero colocado :

en doble malla

DISEÑO DEL TALON

Wu =

1.5 x hz x γ + 1.8 x γ x R1 =

8928 Kg/m

Vu

Wu ( B3-d) =

892.8 kg

=

 Vc =

0.85

b x d =

100 x

Mu =

Wu x B3xB3/ 2

0.53

100

40 =

1116

Datos

Momentos en tn.m


Asmin zapata :

14.4913767

50.00 10 40 100 210 0.9 4200

0.0018

En cada cara :


100

4.5 cm2

50.00 =

100 1.116 0.74

=

9 f 1/2" @ 0.25m


9 4.5

f 1/2" @ 0.30m

cm2



g2 = f2 = s suelo = Ka = Kp = μ =

3

tn/m °

1.80 32

tn/m3 1.80 32 ° kg/cm2 0.80 0.30 3.00 0.45


= = = = =

0.30 0.3 0.20 0.3 0.80



0.20 m 0.20 m

H pantalla =

0.3 m 1.7 m

1.70 m

gconcreto =

2

210 kg/cm 3 4200 kg/cm

f'c = fy =

S/C

m m m m m

3

2.40 tn/m

2 0.30 tn/m

=


=

0.30

300

=

E s/c

=

90

2.00

=

180 kg

90 kg/m

M s/c =

180

1

=

180 kg.m

Ka Wa

=

0.30

1800

Ea

1

2

1080 kg/m

=

1080

Ma

=

1080 0.66666667

1080 kg

Wp

=

3.00

1800.00

0.60 =

Ep

=

3240

0.3

=

972 kg

Mp

=

972

0.2

=

194.4 kg.m

720 kg.m

Kp 3240 kg/m


Zonas 1

L

γ

0.3

1.7

1800

Cargas (kg) 918



0.2

1.7

2400

816

0.4

326.4

3

0.3

0.3

1800

162

0.15

24.3

4

0.80

0.3

2400

576

0.4

230.4

5

1.8

540

0.65

2

H

300


Es/c + E a

Fres =

Ep+u x Σ Cargas

Fsd

=

1260 Kg

1.85

2,327.40 Kg >

1.50

CORRECTO

351 1528.8


=

M s/c + Ma

Mres

=

Mp + ΣMomentos

900.00 kg.m

Fsv

=

1.91

1,723.20 kg.m >

1.50

CORRECTO

PRESION DEL TERRENO

e=

ΣP =

B Mres Mact  3,012.00 kg 2 P

MO =

Mres-Mact

d

=

Mo/P

e

= B/2 - d

σ=

3012 = 0.27

2

823.20 kg.m

5510.291545

0.551029155

0.273 m 0.127 m

B/6 =

0.13333333 m

>

0.127

CORRECTO



kp wu =

1.8

0.30

1800

1.7 =

Vu =

1652.40

0.85

=

Mu =

1404.54 0.56666667

=

1,652.40 kg/m 1,404.54 Kg 795.91

d  Vc =

b x d

0.85

=

0.53

100

x

14.4913767

100

15

=

9,792.55 >

15


Momentos en tn.m


20.00 5 15 100 210 0.9 4200


φ 3/8" @ 0.30 m r = As bd

=

100 0.80 1.42

Acero colocado:

r min = 0.0018

0.0019000 >

Refuerzo Mínimo

2.84 cm2

OK!


3.6 cm2 / m 3.6 cm2 / m



0.307

Lc = hc + d

usar


Utilizado

hc = Lc = Lc =

0.335 0.49 m 0.50 m

=

0.50 m



2 3

A

st

=

3.6 cm2 / m 2.4

f 3/8" @ 0.30 m

Vu 1,404.54

CORRECTO

2 3 1

3

Intermedio:

2 3 1

3

Abajo:

A

st

=

A

st

=

= 0.0018 x 100 x 20 =

3.6 cm2 / m

A

st

=

2.4

st

=

1.2

A

= 0.0018 x 100 x 20 =

2 3 1

st

=

1.2

st

=

A

A

3

f 3/8" @ 0.30 m f 3/8" @ 0.30 m

3.6 cm2 / m 2.4

36f = 36 x0.71 = f 3/8" @ 0.30m

Acero de montaje:

f 3/8" @ 0.30 m

1.2

f 3/8" @ 0.30 m f 3/8" @ 0.30 m

34.2 < S


1.67

σ= 5510.29 =

9202.18688

0.045 =

wu = Mu = Vu

=

Wu ( B3-d) =

 Vc = b x d =

9202.18688 kg 414.10 kg.m 920.22 kg

0.85

0.53

100 x

14.4913767

100

20

=

13,056.73 >

920.22 CORRECTO

100

20

=

13,056.73 >

658.80 CORRECTO

20

Datos

Momentos en tn.m


30.00 10 20 100 210 0.9 4200


100 0.41 0.55

Se coloca acero en una malla : f 1/2" @ 0.25 m

Acero colocado :

Una malla

DISEÑO DEL TALON

Wu =

1.5 x hz x γ + 1.8 x γ x R1 =

6588 Kg/m

Vu

Wu ( B3-d) =

658.8 kg

=

 Vc =

0.85

b x d =

100 x

Mu =

Wu x B3xB3/ 2

0.53

20 =

296.46

Datos

Momentos en tn.m


Asmin zapata :

14.4913767

30.00 10 20 100 210 0.9 4200

0.0018

en una malla


100

6.35 cm2

30.00 =

100 0.29646 0.39

=

5.4 f 1/2" @ 0.25m

Refuerzo transversal As temp = 0.0018 x 100 x 30 =

5.4

f 1/2" @ 0.30m

cm2

DISEÑO MUROS DE CONCRETO ARMAD H = 1.30 M 1. DATOS DE ENTRADA


g2 = f2 = s suelo = Ka = Kp = μ =

tn/m3 °

1.80 32

1.80 32 0.80 0.30 3.00 0.45


= = = = =


f'c = fy =

S/C

=

2 210 kg/cm 3 4200 kg/cm

0.30 0.25 0.15 0.3 0.70

m m m m m

0.3 m 1.3 m


0.15 0.15

H pantalla =

1.30

gconcreto =

2.40

2 0.30 tn/m


=

0.30

E s/c

=

90

M s/c =

144

Ka Wa

=

0.30

Ea

=

864

Ma

=

691.2

Wp

=

3.00

Ep

=

3240

Mp

=

972

Kp


Zonas 1

L

γ

H 0.3

1.3

1800

2

0.15

1.3

2400

3

0.25

0.3

1800

4

0.70

0.3

2400

5

1.8

300

VERIFICACION POR DESPLAZAMIENTO Factu =

Es/c + E a

Fres =

Ep+u x Σ Cargas

Fsd

=

835.2 Kg

2.43

2,029.05 Kg >

1.50


=

M s/c + Ma

483.84 kg.m

Mres

=

Mp + ΣMomentos

Fsv

=

2.53

PRESION DEL TERRENO

e=


1,222.88 kg.m >

1.50

e=


ΣP =

2,349.00 kg

MO =

Mres-Mact

d

=

Mo/P

e

= B/2 - d

739.04 kg.m 0.315 m 0.035 m

B/6 =

0.11666667 m

>



kp wu =

1.8

0.30

1800

1.3 =

Vu =

1263.60

0.65

=

Mu =

821.34

0.43333333

=

0.85

0.53

d  Vc =

b x d

=

100

x

14.4913767

100

10

Acero colocado:

2.84

10


Momentos en tn.m


15.00 5 10 100 210 0.9 4200


φ 3/8" @ 0.30 m r = As bd

Refuerzo Mínimo

=

0.0028000 >

100 0.36 0.95

r min = 0.0018


Como la pantalla es de sección variable y asumiendo a = d / 5, ademas As1 = As2 se obtiene

Kg  Mmax/2= a s x1.7x(5hc)3  6 

f s  K a = tan 2  45   = h 2 sv 

Ka =tg2( 45 - 32/2 ) =

0.307

Lc = hc + d

usar


Utilizado

hc = Lc = Lc =

0.256 0.36 m 0.40 m

=

0.40 m



2 3

A

st

=

1.8

1 3

A

st

=

0.9

Intermedio:

= 0.0018 x 100 x 15 =

2 3

A

st

=

1.8

1 3

A

st

=

0.9

Abajo:

Acero de montaje:

= 0.0018 x 100 x 15 =

2 3

A

st

=

1.8

1 3

A

st

=

0.9

36f = 36 x0.71 = f 3/8" @ 0.30m

34.2 < S


wu =

1.67

σ= 3733.11 =

Mu =

6234.297205

0.03125 =

Vu

=

194.82 kg.m

Wu ( B3-d) =

 Vc = b x d =

6234.297205 kg

311.71 kg 0.85

0.53

100 x

14.4913767

100

20

100

20

20

Datos

Momentos en tn.m


30.00 10 20 100 210 0.9 4200


100 0.19 0.26

Se coloca acero en una malla : f 1/2" @ 0.25 m

Acero colocado :

Una malla

DISEÑO DEL TALON

Wu =

1.5 x hz x γ + 1.8 x γ x R1 =

5292 Kg/m

Vu

Wu ( B3-d) =

529.2 kg

=

 Vc =

0.85

b x d =

100 x

Mu =

Wu x B3xB3/ 2

14.4913767

20

Datos h (cm): r (cm): d (cm): b (cm): f'c (Kg/cm2): f:

0.53

=

238.14 Momentos en tn.m

30.00 10 20 100 210 0.9


100 0.23814 0.32

fy (Kg/cm2):

Asmin zapata :

4200

0.0018

en una malla

100

6.35 cm2

30.00 =

=

5.4 f 1/2" @ 0.25m

Refuerzo transversal As temp = 0.0018 x 100 x 30 =

5.4

f 1/2" @ 0.30m

CRETO ARMADO

tn/m3 ° kg/cm2

m m

m

tn/m3

300

=

1.60

=

144 kg

0.8

=

115.2 kg.m

1800 0.8

1.6

90 kg/m

864 kg/m 691.2 kg

0.53333333

368.64 kg.m

1800.00

0.60 =

3240 kg/m

0.3

=

972 kg

0.2

=

194.4 kg.m

Cargas (kg) 702



468

0.325

152.1

135

0.125

16.875

504

0.35

176.4

540

0.55

297

2349

CORRECTO

CORRECTO

1028.475

σ=

2349 = 0.31

2

3733.112099

0.37331121

0.035

CORRECTO

1,263.60 kg/m 821.34 Kg 355.91

=

6,528.37 >

cm2

OK!

2.7 cm2 / m 2.7 cm2 / m

Vu 821.34

CORRECTO

2.7 cm2 / m f 3/8" @ 0.30 m

1.417322835 70.55555556

f 3/8" @ 0.30 m

1.267605634 78.88888889

2.7 cm2 / m f 3/8" @ 0.30 m

1.417322835 70.55555556

f 3/8" @ 0.30 m

1.267605634 78.88888889

2.7 cm2 / m f 3/8" @ 0.30 m

0.904522613 110.5555556

f 3/8" @ 0.30 m

0.708661417 141.1111111

=

13,056.73 >

311.71 CORRECTO

=

13,056.73 >

529.20 CORRECTO

2" @ 0.25m

2" @ 0.30m

cm2

pulg 3/8 1/2 5/8 3/4 1

cm

area 0.95 1.27 1.59 1.91 2.54

0.71 1.27 1.99 2.87 5.07

DISEÑO MURO ARMADO

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