zapatas-2

CIMENTACIONES UNIVERSDIDAD NACIONAL DE TRUJILLO

Página 1

DISEÑO DE ZAPATA CONECTADA

Diseñar la zapata conectada que soportara las columnas mostradas en la figura . La capacidad portante admisible del suelo es qa = 1.90 Kg/cm2.

Considere Fy = 4200 kg/cm2 , f'c = 210 kg/cm2 para la cimentación.

DATOS

* qa = 1.90 Kg/cm2

* Df = 1.20 m

* 1.60 Tn/m3

* S/C = 0.20 Tn/m2

* 2.40 Tn/m3

* L = 7.60 m

* f'c = 210 Kg/cm2

* Fy = 4200 Kg/cm2

CARGAS MOMENTOS

PD = 36.00 Ton MD = 5.00 Ton/m

PL = 27.00 Ton ML = 2.00 Ton/m

PE (--->) = -15.00 Ton ME (--->) = -7.00 Ton/m

PE (<---) = 15.00 Ton ME (<---) = 7.00 Ton/m

SECCIÓN 30 x 30 cm

CARGAS MOMENTOS

PD = 54.00 Ton MD = 2.00 Ton/m

PL = 50.00 Ton ML = 1.00 Ton/m

PE (--->) = 10.00 Ton ME (--->) = 5.00 Ton/m

PE (<---) = 10.00 Ton ME (<---) = -5.00 Ton/m

SECCIÓN 40 x 40 cm

A) CARGAS DE GRAVEDAD:

* P1 = 63.00 Ton

* M1 = 7.00 Ton/m

* P2 = 104.00 Ton

* M2 = 3.00 Ton/m

* R = 167.00 Ton

A.1) Dimensiones de la Viga:

* h (m) =L

= 1.086 m7

*h

b (m) = P1

=2 31 x L

* bo = 45 cm ho = ¿?

bo x ho3 = b x h3 ho = 0.91 =

USAR VIGA:

45 x 90 cm

comprobar h=

2

A.2) Dimensión Preliminar de la Zapata Exterior e Interior:

PRESIÓN NETA DEL SUELO qn = 16.40 Tn / m2

ÁREA DE LA ZAPATA EXTERIOR: 1.2 * P1

qn

ɤ relleno =

ɤ concreto =

COLUMNA 1

COLUMNA 2

1.- DIMENSIONAMIENTO EN PLANTA:

b ≥

b ≥

Az 1 =


Página 2

CONSIDERAR:

* T = 2S

S x T =

2S^2 = 4.61

S = 1.50 m

* W u = 0.97 Ton / m

BRAZO PALANCA:

* lv =* Pv =* =

* =

=

* Fy =

=

ZAPATA EXTERIOR ZAPATA INTERIOR

R 1= 4.46 m2 *

R 2

qn qn

* S = 1.50 m * B =

* 2.97 m * B x L =

T = 3.00 m B^2 =

* σ1 = 16.25 Tn / m2 B = L =

* σ2 = 16.25

σ1 ≤ qn

σ2

Cumple

B) CARGAS DE GRAVEDAD + SISMO (-->):


* P1 = 51.00 Ton

* M1 = 1.40 Ton/m

* P2 = 112.00 Ton

* M2 = 7.00 Ton/m

* R = 163.00 Ton

* = 0

= 58.74 Ton

* Fy = 0

COMPROBACIÓN DE ESFUERZOS

Az 1

X PV

∑ M2

R 1

R 2

R 2

Az 1 = Az 2 =

T ≥

∑ M2

R 1


Página 3

= 111.99 Ton

* σ1 = 13.05

≤

* σ2 = 17.92

Cumple

B) CARGAS DE GRAVEDAD + SISMO (<--):


* P1 = 75.00 Ton

* M1 = 12.60 Ton/m

* P2 = 112.00 Ton

* M2 = -1.00 = 1.00 Ton/m

* R = 187.00 Ton

* = 0

= 87.54 Ton

* Fy = 0


= 101.96 Ton

* σ1 = 19.45

≤

* σ2 = 16.31

Cumple

2.1.) COMBINACIÓN:U = 1.4 D + 1.7 L

* PU 1 = 96.30 Ton

* MU 1 = 10.40 Ton/m

* PU 2 = 160.60 Ton

* MU 2 = 4.50 Ton/m

* PU v = 10.82 Ton

* WU v = 1.36 Ton / m

* ∑ M2 = 0

R 1 = 111.23 Ton

* WNU 1 = 74.15 Ton / m

* Fy = 0

R 2 = 156.49 Ton WNU 2 =

R 2 ≤ P 2

Cumple

* Fuerzas Cortantes y Momentos Flectores:

0.00 ≤ X ≤ 0.15

◊ 74.15 x X ( m ) = 0.00

◊ 72.79 x 0.00

◊ 36.40 x ^ 2 0.00

0.15 ≤ X ≤ 1.50

◊ VU x = 72.79 x - 96.30

◊ MU x = 36.40 x ^ 2 - 96.30 ( x - 0.15 ) -

X ( m ) = 0.15 1.50

VU x (Ton) = -85.38 12.89

R 2

R 2 P 2

∑ M2

R 1

R 2

R 2 P 2

2.- DISEÑO DE VIGA DE CONEXIÓN:

WU x =

VU x = VU x (Ton) =

MU x = MU x (Ton /m) =


Página 4

MU x (Ton /m) = -9.58 -58.51

* Momento Máximo :

VU x = 72.79 x - 96.30

0 = 72.79 x - 96.30

96.30 = 72.79 x

1.32 = x

1.50 ≤ X ≤ 6.50

◊ VU x = 109.19 - 96.30 - 1.36 ( x -

◊ MU x = 109.19 ( x ) - 96.30 ( x - 0.15

- 0.68 ( x - 1.50 ) ^ 2

X ( m ) = 1.50 6.50

VU x (Ton) = 12.89 6.09

MU x (Ton /m) = 23.38 70.82

6.50 ≤ X ≤ 7.75

◊ VU x = 109.19 - 96.30 - 1.36 ( x -

+ 62.59 ( x - 6.50 )

◊ MU x = 109.19 ( x - 0.15 ) - 96.30

- 10.40 - 0.68 ( x - 1.50

31.30 ( x - 6.50 ) ^ 2

X ( m ) = 6.50 7.75

VU x (Ton) = 6.09 82.63

MU x (Ton /m) = 70.82 109.89

7.75 ≤ X ≤ 9.00

◊ VU x = 109.19 - 96.30 - 1.36 ( x -

+ 62.59 ( x - 6.50 ) - 160.60

◊ MU x = 109.19 ( x - 0.15 ) - 96.30

- 10.40 - 0.68 ( x - 1.50

31.30 ( x - 6.50 ) ^ 2 + 4.50

X ( m ) = 7.75 9.00

VU x (Ton) = -77.97 0.27

MU x (Ton /m) = -86.36 -135.99

M máximo =

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00

-100.00

-80.00

-60.00

-40.00

-20.00

0.00

20.00

40.00

60.00

80.00

100.00

DIAGRAMA DE CORTANTES / U = 1.4 D + 1.7 L


Página 5

2.2.) COMBINACIÓN:U = 1.25 (D + L) + E (-->)

* PU 1 = 63.75 Ton

* MU 1 = 1.75 Ton/m

* PU 2 = 140.00 Ton

* MU 2 = 8.75 Ton/m

* PU v = 9.66 Ton

* WU v = 1.22 Ton / m

* ∑ M2 = 0

R 1 = 73.42 Ton

* WNU 1 = 48.95 Ton / m

* Fy = 0

R 2 = 139.99 Ton WNU 2 =

R 2 ≤ P 2

Cumple


0.00 ≤ X ≤ 0.15

◊ 48.95 x X ( m ) = 0.00

◊ 47.73 x 0.00

◊ 23.87 x ^ 2 0.00

0.15 ≤ X ≤ 1.50

◊ VU x = 47.73 x - 63.75

◊ MU x = 23.87 x ^ 2 - 63.75 ( x - 0.15 ) -

X ( m ) = 0.15 1.50

VU x (Ton) = -56.59 7.85

MU x (Ton /m) = -1.21 -34.11

* Momento Máximo :

VU x = 47.73 x - 63.75

0 = 47.73 x - 63.75

63.75 = 47.73 x

1.34 = x

1.50 ≤ X ≤ 6.50

◊ VU x = 71.60 - 63.75 - 1.22 ( x -

◊ MU x = 71.60 ( x ) - 63.75 ( x - 0.15

- 0.61 ( x - 1.50 ) ^ 2

WU x =

VU x = VU x (Ton) =


M máximo =


Página 6

X ( m ) = 1.50 6.50

VU x (Ton) = 7.85 1.78

MU x (Ton /m) = -24.35 -163.04

6.50 ≤ X ≤ 7.75

◊ VU x = 71.60 - 63.75 - 1.22 ( x -

+ 55.99 ( x - 6.50 )

◊ MU x = 71.60 ( x - 0.15 ) - 63.75

- 1.75 - 0.61 ( x - 1.50

28.00 ( x - 6.50 ) ^ 2

X ( m ) = 6.50 7.75

VU x (Ton) = 1.05 70.25

MU x (Ton /m) = 43.66 77.93

7.75 ≤ X ≤ 9.00

◊ VU x = 71.60 - 63.75 - 1.22 ( x -

+ 55.99 ( x - 6.50 ) - 140.00

◊ MU x = 71.60 ( x - 0.15 ) - 63.75

- 1.75 - 0.61 ( x - 1.50

28.00 ( x - 6.50 ) ^ 2 + 8.75

X ( m ) = 7.75 9.00

VU x (Ton) = -70.66 0.24

MU x (Ton /m) = -88.32 -132.71

2.3.) COMBINACIÓN:U = 1.25 (D + L) + E (<--)

* PU 1 = 93.75 Ton

* MU 1 = 15.75 Ton/m

* PU 2 = 140.00 Ton

* MU 2 = 1.25 Ton/m

* PU v = 9.66 Ton

* WU v = 1.22 Ton / m

* ∑ M2 = 0

R 1 = 109.07 Ton

* WNU 1 = 72.71 Ton / m

* Fy = 0

R 2 = 134.34 Ton WNU 2 =

R 2 ≤ P 2

Cumple


0.00 ≤ X ≤ 0.15

◊ 72.71 x X ( m ) = 0.00

◊ 71.50 x 0.00

◊ 35.75 x ^ 2 0.00

0.15 ≤ X ≤ 1.50

WU x =

VU x = VU x (Ton) =



Página 7

◊ VU x = 71.50 x - 93.75

◊ MU x = 35.75 x ^ 2 - 93.75 ( x - 0.15 ) -

X ( m ) = 0.15 1.50

VU x (Ton) = -83.03 13.49

MU x (Ton /m) = -14.95 -61.88

* Momento Máximo :

VU x = 71.50 x - 93.75

0 = 71.50 x - 93.75

93.75 = 71.50 x

1.31 = x

1.50 ≤ X ≤ 6.50

◊ VU x = 107.24 - 93.75 - 1.22 ( x -

◊ MU x = 107.24 ( x ) - 93.75 ( x - 0.15

- 0.61 ( x - 1.50 ) ^ 2

X ( m ) = 1.50 6.50

VU x (Ton) = 13.49 7.42

MU x (Ton /m) = 15.11 54.64

6.50 ≤ X ≤ 7.75

◊ VU x = 107.24 - 93.75 - 1.22 ( x -

+ 53.74 ( x - 6.50 )

◊ MU x = 107.24 ( x - 0.15 ) - 93.75

- 15.75 - 0.61 ( x - 1.50

26.87 ( x - 6.50 ) ^ 2

X ( m ) = 6.50 7.75

VU x (Ton) = 6.69 73.07

MU x (Ton /m) = 70.83 105.05

7.75 ≤ X ≤ 9.00

◊ VU x = 107.24 - 93.75 - 1.22 ( x -

+ 53.74 ( x - 6.50 ) - 140.00

◊ MU x = 107.24 ( x - 0.15 ) - 93.75

- 15.75 - 0.61 ( x - 1.50

26.87 ( x - 6.50 ) ^ 2 - 1.25

X ( m ) = 7.75 9.00

VU x (Ton) = -67.83 0.24

MU x (Ton /m) = -71.20 -113.82

2.4.) COMBINACIÓN:U = 0.90 (D ) + E (-->)

* PU 1 = 17.40 Ton

* MU 1 = 2.50 Ton/m

* PU 2 = 58.60 Ton

* MU 2 = 6.80 Ton/m

* PU v = 6.95 Ton

* WU v = 0.87 Ton / m

* ∑ M2 = 0

R 1 = 23.26 Ton

M máximo =


Página 8

* WNU 1 = 15.50 Ton / m

* Fy = 0

R 2 = 59.70 Ton WNU 2 =


0.00 ≤ X ≤ 0.15

◊ 15.50 x X ( m ) = 0.00

◊ 14.63 x 0.00

◊ 7.31 x ^ 2 0.00

0.15 ≤ X ≤ 1.50

◊ VU x = 14.63 x - 17.40

◊ MU x = 7.31 x ^ 2 - 17.40 ( x - 0.15 ) -

X ( m ) = 0.15 1.50

VU x (Ton) = -15.21 4.54

MU x (Ton /m) = -2.34 -9.53

* Momento Máximo :

VU x = 14.63 x - 17.40

0 = 14.63 x - 17.40

17.40 = 14.63 x

1.19 = x

1.50 ≤ X ≤ 6.50

◊ VU x = 21.94 - 17.40 - 0.87 ( x -

◊ MU x = 21.94 ( x ) - 17.40 ( x - 0.15

- 0.44 ( x - 1.50 ) ^ 2

X ( m ) = 1.50 6.50

VU x (Ton) = 4.54 0.17

MU x (Ton /m) = -99.59 -482.30

6.50 ≤ X ≤ 7.75

◊ VU x = 21.94 - 17.40 - 0.87 ( x -

+ 23.88 ( x - 6.50 )

◊ MU x = 21.94 ( x - 0.15 ) - 17.40

- 2.50 - 0.44 ( x - 1.50

11.94 ( x - 6.50 ) ^ 2

X ( m ) = 6.50 7.75

VU x (Ton) = -2.26 28.93

MU x (Ton /m) = 18.71 33.60

7.75 ≤ X ≤ 9.00

◊ VU x = 21.94 - 17.40 - 0.87 ( x -

+ 23.88 ( x - 6.50 ) - 58.60

◊ MU x = 21.94 ( x - 0.15 ) - 17.40

- 2.50 - 0.44 ( x - 1.50

11.94 ( x - 6.50 ) ^ 2 - 6.80

X ( m ) = 7.75 9.00

WU x =

VU x = VU x (Ton) =


M máximo =


Página 9

VU x (Ton) = -32.71 0.17

MU x (Ton /m) = -46.45 -65.57

2.5.) COMBINACIÓN:U = 0.90 (D ) + E (<--)

* PU 1 = 47.40 Ton

* MU 1 = 11.50 Ton/m

* PU 2 = 58.60 Ton

* MU 2 = 3.20 Ton/m

* PU v = 6.95 Ton

* WU v = 0.87 Ton / m

* ∑ M2 = 0

R 1 = 56.40 Ton

* WNU 1 = 37.60 Ton / m

* Fy = 0

R 2 = 56.56 Ton WNU 2 =

R 2 ≤ P 2

Cumple


0.00 ≤ X ≤ 0.15

◊ 37.60 x X ( m ) = 0.00

◊ 36.72 x 0.00

◊ 18.36 x ^ 2 0.00

0.15 ≤ X ≤ 1.50

◊ VU x = 36.72 x - 47.40

◊ MU x = 18.36 x ^ 2 - 47.40 ( x - 0.15 ) -

X ( m ) = 0.15 1.50

-41.89 7.69

-11.09 -34.17

* Momento Máximo :

VU x = 36.72 x - 47.40

0 = 36.72 x - 47.40

47.40 = 36.72 x

1.29 = x

1.50 ≤ X ≤ 6.50

◊ VU x = 55.09 - 47.40 - 0.87 ( x -

◊ MU x = 55.09 ( x ) - 47.40 ( x - 0.15

- 0.44 ( x - 1.50 ) ^ 2

X ( m ) = 1.50 6.50

7.69 3.31

-58.87 -275.88

6.50 ≤ X ≤ 7.75

◊ VU x = 55.09 - 47.40 - 0.87 ( x -

WU x =

VU x = VU x (Ton) =


VU x (Ton) =

MU x (Ton /m) =

M máximo =

VU x (Ton) =

MU x (Ton /m) =


Página 10

+ 22.62 ( x - 6.50 )

◊ MU x = 55.09 ( x - 0.15 ) - 47.40

- 11.50 - 0.44 ( x - 1.50

11.31 ( x - 6.50 ) ^ 2

X ( m ) = 6.50 7.75

0.89 30.50

34.64 47.51

7.75 ≤ X ≤ 9.00

◊ VU x = 55.09 - 47.40 - 0.87 ( x -

+ 22.62 ( x - 6.50 ) - 58.60

◊ MU x = 55.09 ( x - 0.15 ) - 47.40

- 11.50 - 0.44 ( x - 1.50

11.31 ( x - 6.50 ) ^ 2 - 3.20

X ( m ) = 7.75 9.00

-31.14 0.17

-28.94 -47.08

VU x (Ton) =

MU x (Ton /m) =

VU x (Ton) =

MU x (Ton /m) =


Página 11

DISEÑO DE ZAPATA CONECTADA

REFUERZO

4Ø

3/4 "

REFUERZO

4Ø

1 "

0.27 m

0.90 m

45 cm

= 4.61 m2


Página 12

S = 1.52 cm

7.95 m7.727 Ton3.775 m

0

73.14 Ton

0

101.59 Ton

≤

Cumple

ZAPATA INTERIOR

= 6.19 m2

L

6.19

6.19

2.50 m

Tn / m2

≤ qn

Cumple


P 2


Página 13

Tn / m2 Cumple

Tn / m2 Cumple


Tn / m2 Cumple

Tn / m2 Cumple

62.59 Ton / m

0.15

10.92

0.82

10.40


Página 14

-59.65 Ton / m

L (m) L (m)

1.50 ) 0.00 0.00 0.00 0.00

) - 10.40 0.01 0.73 0.00 0.01

0.02 1.46 0.01 0.02

0.03 2.18 0.03 0.03

0.04 2.91 0.06 0.04

0.05 3.64 0.09 0.05

0.06 4.37 0.13 0.06

0.07 5.10 0.18 0.07

0.08 5.82 0.23 0.08

0.09 6.55 0.29 0.09

1.50 ) 0.10 7.28 0.36 0.10

0.11 8.01 0.44 0.11

0.12 8.74 0.52 0.12

( x - 0.15 ) 0.13 9.46 0.62 0.13

) ^ 2 + 0.14 10.19 0.71 0.14

0.15 10.92 0.82 0.15

0.15 -85.38 -9.58 0.15

0.20 -81.74 -13.76 0.20

0.25 -78.10 -17.76 0.25

0.30 -74.46 -21.57 0.30

0.35 -70.82 -25.20 0.35

0.40 -67.18 -28.65 0.40

0.45 -63.54 -31.92 0.45

1.50 ) 0.50 -59.90 -35.01 0.50

0.55 -56.26 -37.91 0.55

0.60 -52.62 -40.63 0.60

( x - 0.15 ) 0.65 -48.98 -43.17 0.65

) ^ 2 + 0.70 -45.34 -45.53 0.70

0.75 -41.70 -47.71 0.75

0.80 -38.07 -49.70 0.80

0.85 -34.43 -51.51 0.85

0.90 -30.79 -53.14 0.90

0.95 -27.15 -54.59 0.95

1.00 -23.51 -55.86 1.00

1.05 -19.87 -56.94 1.05

1.10 -16.23 -57.84 1.10

1.15 -12.59 -58.57 1.15

1.20 -8.95 -59.10 1.20

1.25 -5.31 -59.46 1.25

1.30 -1.67 -59.63 1.30

1.35 1.97 -59.63 1.35

1.40 5.61 -59.44 1.40

1.45 9.25 -59.07 1.45

1.50 12.89 -58.51 1.50

1.50 12.89 23.38 1.50

1.75 12.55 26.56 1.75

2.00 12.21 29.66 2.00

2.25 11.87 32.67 2.25

2.50 11.53 35.59 2.50

2.75 11.19 38.43 2.75

3.00 10.85 41.18 3.00

3.25 10.51 43.85 3.25

3.50 10.17 46.44 3.50

V UX M UX

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00

-100.00

-80.00

-60.00

-40.00

-20.00

0.00

20.00

40.00

60.00

80.00

100.00

DIAGRAMA DE CORTANTES / U = 1.4 D + 1.7 L


Página 15

3.75 9.83 48.94 3.75

4.00 9.49 51.35 4.00

4.25 9.15 53.68 4.25

4.50 8.81 55.93 4.50

4.75 8.47 58.09 4.75

5.00 8.13 60.16 5.00

5.25 7.79 62.15 5.25

5.50 7.45 64.05 5.50

5.75 7.11 65.87 5.75

6.00 6.77 67.61 6.00

6.25 6.43 69.26 6.25

6.50 6.09 70.82 6.50

6.50 6.09 54.44 6.50

6.75 21.39 57.88 6.75

7.00 36.70 65.14 7.00

7.25 52.01 76.23 7.25

7.50 67.32 91.15 7.50

7.75 82.63 109.89 7.75

7.75 -77.97 -86.36 7.75

8.00 -62.32 -103.94 8.00

8.25 -46.67 -117.69 8.25

8.50 -31.03 -127.62 8.50

8.75 -15.38 -133.72 8.75

9.00 0.27 -135.99 9.00

55.99 Ton / m

0.15

7.16

0.54

1.75

-34.76 Ton / m

1.50 )

) - 1.75

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00

-80.00

-60.00

-40.00

-20.00

0.00

20.00

40.00

60.00

80.00

DIAGRAMA DE CORTANTES / U = 1.25 (D + L) + E (-->)


Página 16

1.50 )

( x - 0.15 )

) ^ 2 +

L (m) L (m)

1.50 ) 0.00 0.00 0.00 0.00

0.01 0.71 0.00 0.01

0.02 1.43 0.01 0.02

( x - 0.15 ) 0.03 2.14 0.03 0.03

) ^ 2 + 0.04 2.86 0.06 0.04

0.05 3.57 0.09 0.05

0.06 4.29 0.13 0.06

0.07 5.00 0.18 0.07

0.08 5.72 0.23 0.08

0.09 6.43 0.29 0.09

0.10 7.15 0.36 0.10

0.11 7.86 0.44 0.11

0.12 8.58 0.52 0.12

0.13 9.29 0.62 0.13

0.14 10.01 0.71 0.14

0.15 10.72 0.82 0.15

0.15 -83.03 -9.58 0.15

0.20 -79.45 -13.76 0.20

0.25 -75.88 -17.76 0.25

0.30 -72.30 -21.57 0.30

0.35 -68.73 -25.20 0.35

0.40 -65.15 -28.65 0.40

0.45 -61.58 -31.92 0.45

0.50 -58.00 -35.01 0.50

0.55 -54.43 -37.91 0.55

0.60 -50.85 -40.63 0.60

0.65 -47.28 -43.17 0.65

0.70 -43.70 -45.53 0.70

0.75 -40.13 -47.71 0.75

53.74 Ton / m 0.80 -36.55 -49.70 0.80

0.85 -32.98 -51.51 0.85

0.90 -29.40 -53.14 0.90

0.95 -25.83 -54.59 0.95

1.00 -22.25 -55.86 1.00

1.05 -18.68 -56.94 1.05

1.10 -15.10 -57.84 1.10

1.15 -11.53 -58.57 1.15

1.20 -7.96 -59.10 1.20

1.25 -4.38 -59.46 1.25

0.15 1.30 -0.81 -59.63 1.30

10.72 1.35 2.77 -59.63 1.35

0.80 1.40 6.34 -59.44 1.40

1.45 9.92 -59.07 1.45

1.50 13.49 -58.51 1.50

1.50 13.49 23.38 1.50

V UX M UX


Página 17

1.75 13.19 26.56 1.75

15.75 2.00 12.89 29.66 2.00

2.25 12.58 32.67 2.25

2.50 12.28 35.59 2.50

2.75 11.97 38.43 2.75

3.00 11.67 41.18 3.00

3.25 11.37 43.85 3.25

3.50 11.06 46.44 3.50

3.75 10.76 48.94 3.75

4.00 10.46 51.35 4.00

4.25 10.15 53.68 4.25

-63.15 Ton / m 4.50 9.85 55.93 4.50

4.75 9.54 58.09 4.75

5.00 9.24 60.16 5.00

5.25 8.94 62.15 5.25

1.50 ) 5.50 8.63 64.05 5.50

) - 15.75 5.75 8.33 65.87 5.75

6.00 8.03 67.61 6.00

6.25 7.72 69.26 6.25

6.50 7.42 70.82 6.50

6.50 7.42 70.82 6.50

6.75 20.55 72.30 6.75

7.00 33.68 73.69 7.00

7.25 46.81 76.23 7.25

7.50 59.94 91.15 7.50

7.75 73.07 109.89 7.75

7.75 -67.83 109.89 7.75

8.00 -53.49 0.00 8.00

1.50 ) 8.25 -40.06 0.00 8.25

8.50 -26.63 0.00 8.50

8.75 -13.19 0.00 8.75

( x - 0.15 ) 9.00 0.24 0.00 9.00

) ^ 2 +

1.50 )

( x - 0.15 )

) ^ 2 +

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00

-100.00

-80.00

-60.00

-40.00

-20.00

0.00

20.00

40.00

60.00

80.00

100.00

DIAGRAMA DE CORTANTES / U = 1.25 (D + L) + E (<--)

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00

-40.00

-30.00

-20.00

-10.00

0.00

10.00

20.00

30.00

40.00

DIAGRAMA DE CORTANTES / U = 0.90 (D) + E (-->)


Página 18

23.88 Ton / m

0.15

2.19

0.16

2.50

L (m)

0.00 0.00 0.00 0.00 0.00

0.01 0.37 0.00 0.00 0.00

-10.24 Ton / m 0.02 0.73 0.00 0.00 0.00

0.03 1.10 0.01 -0.01 0.01

0.04 1.47 0.01 -0.01 0.01

0.05 1.84 0.02 -0.02 0.02

1.50 ) 0.06 2.20 0.03 -0.03 0.03

) - 2.50 0.07 2.57 0.04 -0.04 0.04

0.08 2.94 0.05 -0.05 0.05

0.09 3.31 0.06 -0.06 0.06

0.10 3.67 0.07 -0.07 0.07

0.11 4.04 0.09 -0.09 0.09

0.12 4.41 0.11 -0.11 0.11

0.13 4.77 0.12 -0.12 0.12

0.14 5.14 0.14 -0.14 0.14

0.15 5.51 0.16 -0.16 0.16

1.50 ) 0.15 -41.89 -2.34 2.34 -2.34

0.20 -40.06 -3.08 3.08 -3.08

0.25 -38.22 -3.78 3.78 -3.78

( x - 0.15 ) 0.30 -36.38 -4.45 4.45 -4.45

) ^ 2 + 0.35 -34.55 -5.08 5.08 -5.08

0.40 -32.71 -5.68 5.68 -5.68

0.45 -30.87 -6.24 6.24 -6.24

0.50 -29.04 -6.76 6.76 -6.76

0.55 -27.20 -7.25 7.25 -7.25

0.60 -25.37 -7.70 7.70 -7.70

0.65 -23.53 -8.11 8.11 -8.11

0.70 -21.69 -8.49 8.49 -8.49

0.75 -19.86 -8.83 8.83 -8.83

1.50 ) 0.80 -18.02 -9.13 9.13 -9.13

0.85 -16.18 -9.40 9.40 -9.40

0.90 -14.35 -9.63 9.63 -9.63

( x - 0.15 ) 0.95 -12.51 -9.82 9.82 -9.82

) ^ 2 + 1.00 -10.68 -9.98 9.98 -9.98

1.05 -8.84 -10.10 10.10 -10.10

1.10 -7.00 -10.18 10.18 -10.18

1.15 -5.17 -10.23 10.23 -10.23

V UX M UX


Página 19

1.20 -3.33 -10.24 10.24 -10.24

1.25 -1.49 -10.21 -10.21 10.21

1.30 0.34 -10.15 -10.15 10.15

1.35 2.18 -10.05 -10.05 10.05

1.40 4.01 -9.91 -9.91 9.91

1.45 5.85 -9.74 -9.74 9.74

1.50 7.69 -9.53 -9.53 9.53

1.50 7.69 -99.59 -99.59 99.59

1.75 7.47 -118.21 -118.21 118.21

2.00 7.25 -136.88 -136.88 136.88

2.25 7.03 -155.60 -155.60 155.60

2.50 6.81 -174.38 -174.38 174.38

2.75 6.59 -193.22 -193.22 193.22

3.00 6.37 -212.11 -212.11 212.11

3.25 6.16 -231.05 -231.05 231.05

3.50 5.94 -250.05 -250.05 250.05

3.75 5.72 -269.10 -269.10 269.10

4.00 5.50 -288.21 -288.21 288.21

4.25 5.28 -307.38 -307.38 307.38

4.50 5.06 -326.59 -326.59 326.59

4.75 4.84 -345.87 -345.87 345.87

22.62 Ton / m 5.00 4.63 -365.19 -365.19 365.19

5.25 4.41 -384.57 -384.57 384.57

5.50 4.19 -404.01 -404.01 404.01

5.75 3.97 -423.50 -423.50 423.50

6.00 3.75 -443.05 -443.05 443.05

6.25 3.53 -462.65 -462.65 462.65

6.50 3.31 -482.30 -482.30 482.30

6.50 0.89 34.64 34.64 -34.64

6.75 8.75 36.15 36.15 -36.15

7.00 14.19 39.01 39.01 -39.01

7.25 19.62 43.24 43.24 -43.24

7.50 25.06 48.83 48.83 -48.83

7.75 30.50 47.51 47.51 -47.51

0.15 7.75 -31.14 -28.94 -28.94 28.94

5.51 8.00 -22.45 -35.29 -35.29 35.29

0.41 8.25 -16.79 -40.27 -40.27 40.27

8.50 -11.14 -43.90 -43.90 43.90

8.75 -5.48 -46.17 -46.17 46.17

9.00 0.17 -47.08 -47.08 47.08

11.50

-34.98 Ton / m

1.50 )

) - 11.50

1.50 )

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00

-50.00

-40.00

-30.00

-20.00

-10.00

0.00

10.00

20.00

30.00

40.00

DIAGRAMA DE CORTANTES / U = 0.90 (D) + E (<--)


Página 20

( x - 0.15 )

) ^ 2 +

1.50 )

( x - 0.15 )

) ^ 2 +


Página 21


Página 22


Página 23


Página 24

0.00 0.00

0.48 0.00

0.95 0.01

1.43 0.02

1.91 0.04

2.39 0.06

2.86 0.09

3.34 0.12

3.82 0.15

4.30 0.19

4.77 0.24

5.25 0.29

5.73 0.34

6.21 0.40

6.68 0.47

7.16 0.54

-56.59 -1.21

-54.20 -3.98

-51.82 -6.63

-49.43 -9.16

-47.04 -11.58

-44.66 -13.87

-42.27 -16.04

-39.88 -18.10

-37.50 -20.03

-35.11 -21.85

-32.72 -23.54

-30.34 -25.12

-27.95 -26.57

-25.56 -27.91

-23.18 -29.13

-20.79 -30.23

-18.40 -31.21

-16.02 -32.07

-13.63 -32.81

-11.24 -33.43

-8.86 -33.94

-6.47 -34.32

-4.08 -34.58

-1.70 -34.73

0.69 -34.75

3.08 -34.66

5.46 -34.44

7.85 -34.11

7.85 -24.35

7.55 -28.82

7.24 -35.11

6.94 -41.47

6.64 -47.91

6.33 -54.43

6.03 -61.02

5.72 -67.69

5.42 -74.43

V UX M UX


Página 25

5.12 -81.25

4.81 -88.15

4.51 -95.12

4.21 -102.32

3.90 -109.44

3.60 -116.49

3.29 -123.77

2.99 -131.12

2.69 -138.55

2.38 -146.05

2.08 -153.63

1.78 -161.29

1.78 32.92

15.47 35.07

29.17 40.65

42.86 49.65

56.56 62.08

70.25 77.93

-69.75 -88.32

-55.75 -104.04

-41.75 -116.35

-27.75 -125.22

-13.76 -130.68

0.24 -132.71

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00

-80.00

-60.00

-40.00

-20.00

0.00

20.00

40.00

60.00

80.00

DIAGRAMA DE CORTANTES / U = 1.25 (D + L) + E (-->)


Página 26

0.00 0.00

0.15 0.00

0.29 0.01

0.44 0.02

0.59 0.04

0.73 0.06

0.88 0.09

1.02 0.12

1.17 0.15

1.32 0.19

1.46 0.24

1.61 0.29

1.76 0.34

1.90 0.40

2.05 0.47

2.19 0.54

-15.21 -1.21

-14.47 -3.98

-13.74 -6.63

-13.01 -9.16

-12.28 -11.58

-11.55 -13.87

-10.82 -16.04

-10.09 -18.10

-9.35 -20.03

-8.62 -21.85

-7.89 -23.54

-7.16 -25.12

-6.43 -26.57

-5.70 -27.91

-4.97 -29.13

-4.23 -30.23

-3.50 -31.21

-2.77 -32.07

-2.04 -32.81

-1.31 -33.43

-0.58 -33.94

0.16 -34.32

0.89 -34.58

1.62 -34.73

2.35 -34.75

3.08 -34.66

3.81 -34.44

4.54 -34.11

4.54 -22.60

V UX M UX


Página 27

4.33 -28.82

4.11 -35.11

3.89 -41.47

3.67 -47.91

3.45 -54.43

3.23 -61.02

3.01 -67.69

2.79 -74.43

2.58 -81.25

2.36 -88.15

2.14 -95.12

1.92 -102.17

1.70 -109.29

1.48 -116.49

1.26 -123.77

1.04 -131.12

0.83 -138.55

0.61 -146.05

0.39 -153.63

0.17 -161.29

-2.26 -161.29

5.92 #VALUE!

11.67 -176.83

17.42 -184.71

23.17 -192.67

28.93 #VALUE!

-29.67 -203.20

-23.70 #VALUE!

-17.73 #VALUE!

-11.76 #VALUE!

-5.79 #VALUE!

0.17 #VALUE!

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00

-100.00

-80.00

-60.00

-40.00

-20.00

0.00

20.00

40.00

60.00

80.00

100.00

DIAGRAMA DE CORTANTES / U = 1.25 (D + L) + E (<--)

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00

-40.00

-30.00

-20.00

-10.00

0.00

10.00

20.00

30.00

40.00

DIAGRAMA DE CORTANTES / U = 0.90 (D) + E (-->)


Página 28


Página 29

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00

-50.00

-40.00

-30.00

-20.00

-10.00

0.00

10.00

20.00

30.00

40.00

DIAGRAMA DE CORTANTES / U = 0.90 (D) + E (<--)


Página 30

2.1 DISEÑO POR FLEXION

Mu= 59.65 Tn-mf´c= 210 Kg/cm2fy= 4200 Kg/cm2

1° TanteoAs= 21.9186079102 cm2a= 11.4607100184 cm2

2° Tanteo a= 11.46071As= 21.2487856881 cm2a= 11.1104761768 cm2

Ø 1"= N= 4.16642857 5 BARRAS

bmin= 36.02 cm OKAs= 25.5 cm2d= 82.78 cm ρ= 0.007

Ø Mn- = 73.37 Tn-m Ø Mn+ = 45.56 Tn-ma-= 13.33 cma+= 8.0 cm

Ø Mn+ ≥Ø Mn-/2

Ø Mn= 45.56 Tn-m

Ø Mn+ ≥Ø Mn-/2

3.DISEÑO POR CORTANTE3.1. DISEÑO POR RESISTENCIA

A) SISMO

Wu=ln= 5 mb= 45d= 82.78As= 15.3 cm2 As= 25.5 cm2fs= 5.25 ton/cm2 a= 16.67

a= 10 cm

Mpr1= 62.48 ton-m Mpr2= 99.67 ton-m

Ve= 32.428452

B) SISMO

Mpr1= 62.48 ton-m Mpr2= 99.67 ton-mVe= 32.428452

ZAPATAS AISLADAS

COLUMNA 1 COLUMNA 230X30 40X40

PD= 36 Tn PD= 54 TnPL= 27 Tn PL= 50 TnMD= 5 Tn-m MD= 2 Tn-mML= 2 Tn-m ML= 1 Tn-mPE= -15 Tn PE= 10 TnME= -7 Tn-m ME= 5 Tn-mPE= 15 Tn PE= 10 TnME= 7 Tn-m ME= -5 Tn-m

f´c= 210 Kg/cm2fy= 4200 Kg/cm2

qa= 1.9 Kg/cm2Df= 1.2 ms/c= 0.2 Tn/m2

Ȣ= 2 Tn/m2

1. DIMENSIONAMIENTO EN PLANTA

1.1 POR GRAVEDAD

qn= 16.4 Tn/m2P1= 63 Tn P2= 104 TnM1= 7 Tn-m M2= 3 Tn-m

S= 1.50 m B= 2.50 mT= 3.00 m L= 2.50 m

ơmax1= 16.25 Tn/m3 correcto ơmax2= 16.25 Tn/m3

4 Ø 3/4" 4 Ø 1"

1.1 POR CARGAS DE G+S

a. D+L+E ͢͢

qn= 22.67 Tn/m2P1= 51 Tn P2= 112 TnM1= 1.4 Tn-m M2= 7 Tn-m

S= 1.50 m B= 2.50 mT= 3.00 m L= 2.50 m


b. D+L+E ͢͢

P1= 75 Tn P2= 112 TnM1= 12.6 Tn-m M2= -1 Tn-m

S= 1.50 m B= 2.50 mT= 3.00 m L= 2.50 m


A. CALCULO DE LA DISTRIBUCION DE PRESIONESZAPATA 1

COMBINACION PU MU ơu1 ơu2

1.4D+1.7L 79.1 10.4 8.3333 26.82 0.13147914 17.578 9.24441.25(D+L)+E 63.75 1.75 12.611 15.72 0.02745098 14.167 1.55561.25(D+L)+E 93.75 15.75 6.8333 34.83 0.168 20.833 140.9D+E 17.4 -2.5 1.6444 6.089 -0.14367816 3.8667 2.22220.9D+E 47.4 11.5 0.3111 20.76 0.24261603 10.533 10.222

ZAPATA 2COMBINACION PU MU ơu1 ơu2

1.4D+1.7L 127.3 4.5 18.64 22.1 0.03534957 20.368 1.7281.25(D+L)+E 140 8.75 19.04 25.76 0.0625 22.4 3.361.25(D+L)+E 140 -1.25 21.92 22.88 -0.00892857 22.4 0.480.9D+L 58.6 6.8 6.7648 11.99 0.11604096 9.376 2.61120.9D+L 58.6 -3.2 8.1472 10.6 -0.05460751 9.376 1.2288

ZAPATA 1 ZAPATA 2 ơu average= 23.7222222 Tn/m2 ơu average= 23.84 Tn/m2ơu 1= 29.2777778 Tn/m2 ơu2 = 24.8 Tn/m2

ZAPATA 1B. CALCULO DEL ESPESOR DE LA ZAPATA POR FLEXION

1.- Wu= 87.833 Tn/mMu= 21.519 Tn-m

6.3292

2.-Wu= 43.917 Tn/mMu= 52.755 Tn-m

31.032

Considerando 0.004w= 0.08

bd ^2= 366192.319 cm3b= 3.00 md= 34.937674 cmhz= 44.937674 cmNO menor a 25db= 47.75

hz= 50 cmd= 40 cm

C. COMPROBAR hz POR CORTANTE ACCION DE VIGA

ØVn=ØVc = 78.3403827 TnVud= 70.2666667 OK

D. COMPROBAR hz POR CORTANTE ACCION DE LOSA(PUNZONAM

ơu 1= 29.2777778 Tn/m2X= 70 cmY= 70 cmVu= 79.4038889 Tn

ρ =

ØVc ≥ Vud

Punzonamiento 1.622.08285714

bo= 210 cm 1.06αs= 30βc= 1 ØVn= 109.7 OK

E. VERIFICACION POR APLASTAMIENTO DEL CONCRE

e.1 APLASTAMIENTO DEL CONCRETO DE LA COLUMNA 3

ØPnb= 187.425 Tn OK1.5

e.2 APLASTAMIENTO DEL CONCRETO DE LA ZAPATA

ØPnb= 568.488172 Tn224.91 Tn

ØPnb= 224.91 Tn OK y=0.50

A1= 900A2= 23000

F. CALCULO DEL REFUERZO

αf= 0.042372880.0051544

As= 61.8528398 cm2S= Ø 5/8"= 9.60343942 cm Ø 3/4"= 13.8231325 cm

Ø 1"= 12.3195637 cm

hz min= 30 cmUsar

G. VERIFICANDO LONGITUD DE DESARROLLO

Cb menor= 8.46 cm15 cm

Cb+Ktr =4.42931937db usar 2.5

ρ =

1 Ø 1"@0.30

��/(√(2 ) )&�´� ∗��∗�

ld= 84.133 > 30 cmld= 85 cmldisponible= 102.5 cm > ldOK

correcto

correcto

correcto

ZAPATA 2B. CALCULO DEL ESPESOR DE LA ZAPATA POR FLEXION

1.- Wu= 62 Tn/mMu= 37.51 Tn-m

2.-Wu= 62 Tn/mMu= 37.51 Tn-m

Considerando 0.004w= 0.08

bd ^2= 260371.548 cm3b= 2.50 md= 32.2720652 cmhz= 42.2720652 cmNO menor a 25db= 63.5

hz= 65 cmd= 55 cm

C. COMPROBAR hz POR CORTANTE ACCION DE VIGA

ØVn=ØVc = 89.7650218 TnVud= 34.1 OK

D. COMPROBAR hz POR CORTANTE ACCION DE LOSA(PUNZONAMIENTO)

ơu2 = 24.8 Tn/m2X= 85 cmY= 85 cmVu= 122.082 Tn

Punzonamiento

bo= 340 cm

ρ =

ØVc ≥ Vud

��/(√(2 ) )&�´� ∗��∗�

αs= 40βc= 1 ØVn= 244.160859

E. VERIFICACION POR APLASTAMIENTO DEL CONCRETO

e.1 APLASTAMIENTO DEL CONCRETO DE LA COLUMNA

ØPnb= 333.2 Tn OK

e.2 APLASTAMIENTO DEL CONCRETO DE LA ZAPATA

ØPnb= 1299.48 Tn399.84 Tn

ØPnb= 399.84 Tn OK

F. CALCULO DEL REFUERZO

αf= 0.042372880.00133314

As= 18.3306893 cm2S= Ø 5/8"= 27.0038945 cm Ø 3/4"= 38.8692421 cm

Ø 1"= 34.6413596 cm

hz min= 30 cmUsar

G. VERIFICANDO LONGITUD DE DESARROLLO

Cb menor=

Cb+Ktr =db

ρ =

1 Ø 1"@0.30

ld= 84.132793 > 30ld= 85 cmldisponible= 102.5 cm > ld

B. CALCULO DEL ESPESOR DE LA ZAPATA POR FLEXION

D. COMPROBAR hz POR CORTANTE ACCION DE LOSA(PUNZONAMIENTO)

1.622.28705882

1.06

OK

2.6

2.6

y=0.55

A1= 1600A2= 67600

8.77 cm15 cm

3.45275591usar 2.5

cm

OK

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