Diseño de Zapata

Portico principal 1

PREDIMENSIONAMIENTO DE LA ZAPATA COMBINADA

Capacidad portante del suelo :σ = 0.85 kg/cm²

32.76 tn 71.61 tn 32.38 tn

Za c1 :

Long: 11.95 m

Areas :

32.76 tn = 3.8548.5 tn/m²

71.61 tn = 8.4258.5 tn/m²

32.38 tn = 3.8098.5 tn/m²

3.854 + 8.425 +3.809 = 1.35

a =𝞢𝐴𝑧/𝑙Z1=𝑃_𝑠/𝑐Z2=𝑃_𝑠/𝑐Z3=𝑃_𝑠/𝑐

a =𝞢𝐴𝑧/𝑙 =a =𝞢𝐴𝑧/𝑙

11.95

Area de la zapata combinada :

A = 11.95 m x 1.35 m

DISEÑO DE LA ZAPATA COMBINADA

Carga facturada :

Z1(Tn) Z2 (Tn) Z3 (Tn) total (Tn)1.4D+L 46.98 103.07 46.42 196.47

32.4 89.19 48.58 170.1749.51 89.83 32.27 171.61

Wu = Pu 12.179 tn/m² =Az 11.95 x 1.35

= 1.218 kg/cm²

Ecuacion 1

0.75 0.75

Ecuacion 2

Vc = 1.06 √210 *(2*1195)d ………………………………..(2)

Igualando 1 y 2

0.75

1.25(D+L) +S1.25(D+L) -S

Put =196.47 tn

= 196.47 =

Vu=Put -Wu(d+25)(1195) = 196470 - 1.218(d+25)(1195)………………. (1)

196470 - 1.218(d+25)(1195) = 1.06 √210 *(2*1195)d


d = 5.52 cm

Altura de la zapata :

5.52 +7.5 + 1.27/2 = 13.66 cm

Usar :

30cm

IMAGEN

w = 12.179 11.95 m

w = 145.539 tn/m²

Mu = 145.539 22.013 tn-m2 2

calculo de "d" real :

21.87

Calculo de area de Acero :

Momento último Mu = 22.013 Tn-m.0.90 Materiales:

Ancho sección b = 1,195.00 cm. 4,200 Kg/cm².Peralte sección d = 21.87 cm. 210 Kg/cm².

hz=

h min =

tn/m² x

w * Lu² = x 0 .55² m =

d = 30 -7.5 - 1.27/ 2 =

ρ*bd² fy(1-0.59 ρ fy/f`c ) = Mu/ø

Coeficiente por flexión ø =Fluencia del acero Fy =Resistencia concreto F'c =

Cuantía de acero = 0.0010 Cuantía mínima = 14 0.00330.0028

0.0106

Area de acero As = 86.24 cm². ===> 43.56 N DE VARILLAS

ESPACIAMIENTO :

11.95 -7.5 (2)- 1.59 27.0543.56

viga de cimentacion

136.75 8.5 tn/m²11.95 X 1.35 m²

= 0.85 kg/cm²

Predimensionamiento:

5.575 = 1.285 m semejante 1.30m4

√0.85 kg/cm²

5.575 = 1.54 m semejante 1.55m

4√1.218 kg/cm²

5.575 = 2.004 m semejante 2.05m

} ® El mayor

Cuantía mínima = 0.8*F'c^0.5/Fy =Cuantía balanceada = β₁*0.85*F'c/Fy*(6000/(6000+Fy)

Cuantía máxima = 0.5*ρ balanc.=

ø de 5/8"

USAR : Ø 5/8 @ .27

tn =Ws =𝞢𝑃𝑧/𝐴 =

hs =𝑙𝑛/(4/(√𝑤𝑠)) =

hu =𝑙𝑛/(4/(√𝑤𝑢)) =

hprom =𝑙𝑛/(4/√(𝑤𝑢+𝑤𝑠)) =

4√1.218+0.85kg/cm²

Se usara:h= 1.30m

bw

h

b

0.30≥ bw/2 = 0.25/2 ok

b≤ 4bw = 4*0.25 no cumple

b≤ 1.00 = 1.00 no cumple

calculo del nuevo "b"

Promedio:

b =1.35+ 1

= 1.1752

PRESION DEL TERRENO

q = Wu * b

q = 14.310 Tn/m2

MOMENTO CAUSADO POR LA PRESION

SE LE CONSIDERA

H = 0.75 m


1.30

ACERO SUPERIOR


Ancho sección b = 117.50 cm. 4,200 Kg/cm².Peralte sección d = 67.78 cm. 210 Kg/cm².

Cuantía de acero = 0.0011

As = P * b * d

As = 8.76 cm2

USAR :

ACERO INFERIOR





2 Ø 1"


As = P * b * d

As = 15.27 cm2

N° DE BARRAS:

15.27 12.02 varillas1.27

ESPACIAMIENTO:

Es = 117.5-7.5(2)-1.27 = 8.42 cm

12.02

ACERO SUPERIOR




As = P * b * d

As = 8.76 cm2

USAR :

Portico 2



USAR : Ø 1/2 @ 8 cm


2 Ø 1"

34.24 tn 73.67 tn 39.48 tn

Za c1 :

Long: 11.95 m

Areas :

34.24 tn = 4.0288.5 tn/m²

73.67 tn = 8.6678.5 tn/m²

39.48 tn = 4.6458.5 tn/m²

4.028 + 8.667 +4.645 = 1.4511.95


A = 11.95 m x 1.45 m




Carga facturada :


35.93 91.57 55.84 183.3449.66 92.61 42.85 185.12

Wu = Pu 12.259 tn/m² =Az 11.95 x 1.45

1.2259 kg/cm²

Ecuacion 1

0.75 0.75

Ecuacion 2

Vc = 1.06 √210 *(2*1195)d ………………………………..(2)

Igualando 1 y 2

0.75

d = 6.062 cm


6.062 +7.5 + 1.27/2 = 14.20 cm

Usar :

30cm

1.25(D+L) +S1.25(D+L) -S

Put =212.42 tn

= 212.42 =

Vu=Put -Wu(d+25)(1195) = 212420 - 1.2259(d+25)(1195)………………. (1)

212420 - 1.2259(d+25)(1195) = 1.06 √210 *(2*1195)d

hz=

h min =

IMAGEN

w = 12.259 11.95 m

w = 146.497 tn/m²

Mu = 146.497 26.369 tn-m2 2


21.87 cm





0.0106


ESPACIAMIENTO :

11.95 -7.5 (2)- 1.59 27.0543.56

tn/m² x

w * Lu² = x 0 .60² m =

d = 30 -7.5 - 1.27/ 2 =

ρ*bd² fy(1-0.59 ρ fy/f`c ) = Mu/ø


} ® El mayor



ø de 5/8"

USAR : Ø 5/8 @ .27

viga de cimentacion Predimensionamiento:

147.39 8.5 tn/m²11.95 X 1.45 m²

= 0.85 kg/cm²


5.575 = 1.285 m semejante 1.30m4

√0.85 kg/cm²

5.575 = 1.54 m semejante 1.55 m

4√1.2259 kg/cm²

5.575 = 2.008 m semejante 2.05 m

4√1.2259+0.85kg/cm²

Se usara:h= 1.30m

bw

h


hs =𝑙𝑛/(4/(√𝑤𝑠)) =

hu =𝑙𝑛/(4/(√𝑤𝑢)) =


b

0.30≥ bw/2 = 0.25/2 ok


b≤ 1.00 = 1.00 se usara

Promedio:

b =1.45+ 1

= 1.2252

PRESION DEL TERRENO

q = Wu * b

q = 15.017 Tn/m2


SE CONSIDERA :

H = 0.75 m

ACERO SUPERIOR

Momento último Mu = 23.270 Tn-m.

0.90 Materiales:Ancho sección b = 122.50 cm. 4,200 Kg/cm².

Peralte sección d = 67.78 cm. 210 Kg/cm².



As = P * b * d

As = 9.13 cm2

USAR :

ACERO INFERIOR

Momento último Mu = 40.870 Tn-m.

0.90 Materiales:Ancho sección b = 122.50 cm. 4,200 Kg/cm².

Peralte sección d = 68.41 cm. 210 Kg/cm².


As = P * b * d

As = 15.92 cm2

N° DE BARRAS:

15.92 12.54 varillas1.27

ESPACIAMIENTO:

Es = 122.5-7.5(2)-1.27 = 8.47 cm

12.54

2 Ø 1"


ACERO SUPERIOR




As = P * b * d

As = 8.76 cm2

USAR :

Portico 3



37.33 tn 81.34 tn 41.5 tn

Za c1 :

USAR : Ø 1/2 @ 8 cm


2 Ø 1"

Long: 11.95 m

Areas :

37.33 tn = 4.3928.5 tn/m²

81.34 tn = 9.5698.5 tn/m²

41.5 tn = 4.8828.5 tn/m²

4.392 + 9.569 +4.882 = 1.57711.95


A = 11.95 m x 1.577 m


Carga facturada :


38.96 102.16 60.01 201.1354.36 101.19 43.75 199.3

1.25(D+L) +S1.25(D+L) -S



Wu = Pu 12.273 tn/m² =Az 11.95 x 1.577

1.2273 kg/cm²

Ecuacion 1

0.75 0.75

Ecuacion 2

Vc = 1.06 √210 *(2*1195)d ………………………………..(2)

Igualando 1 y 2

0.75

d = 6.71 cm


6.71 +7.5 + 1.27/2 = 14.85 cm

Usar :

30cm

w = 12.273 11.95 m

w = 146.664 tn/m²

Put =231.27 tn

= 231.27 =

Vu=Put -Wu(d+25)(1195) = 231270 - 1.2273(d+25)(1195)………………. (1)

231270 - 1.2273(d+25)(1195) = 1.06 √210 *(2*1195)d

hz=

h min =

tn/m² x

Mu = 146.664 31.944 tn-m2 2


21.87 cm





0.0106


ESPACIAMIENTO :

11.95 -7.5 (2)- 1.59 27.0543.56


160.17 8.5 tn/m²11.95 X 1.577 m²

w * Lu² = x 0 .66² m =

d = 30 -7.5 - 1.27/ 2 =

ρ*bd² fy(1-0.59 ρ fy/f`c ) = Mu/ø


} ® El mayor



ø de 5/8"

USAR : Ø 5/8 @ .27


= 0.85 kg/cm²


5.575 = 1.285 m semejante 1.30m4

√0.85 kg/cm²

5.575 = 1.54 m semejante 1.55 m

4√1.2273 kg/cm²

5.575 = 2.009 m semejante 2.05 m

4√1.2273+0.85kg/cm²

Se usara:h= 1.30 m

bw

h

b

0.30≥ bw/2 = 0.25/2 ok


b≤ 1.00 = 1.00 se usara

Ws =𝞢𝑃𝑧/𝐴 =

hs =𝑙𝑛/(4/(√𝑤𝑠)) =

hu =𝑙𝑛/(4/(√𝑤𝑢)) =


Promedio:

b =1.45+ 1

= 1.2252

PRESION DEL TERRENO

q = Wu * b

q = 0.000 Tn/m2


SE CONSIDERA :H = 0.75 m

ACERO SUPERIOR




As = P * b * d

As = 8.30 cm2

USAR :

ACERO INFERIOR


2 Ø 1"




As = P * b * d

As = 15.08 cm2

N° DE BARRAS:

15.08 11.87 varillas1.27

ESPACIAMIENTO:

Es = 122.5-7.5(2)-1.27 = 8.95 cm

11.87

ACERO SUPERIOR





USAR : Ø 1/2 @ 9 cm


a =𝞢𝐴𝑧/𝑙Z1=𝑃_𝑠/𝑐

As = P * b * d

As = 7.96 cm2

USAR : 8.5 tn/m²

6.004 +14.458 +8.406 = 0.00011.95


A = 11.95 m x 2.416 m


Carga facturada :


54.83 154.96 102.02 311.8172.75 152.26 76.61 301.62

353640 kg

Wu = Pu #DIV/0! tn/m² =Az 11.95 x 2.416

#DIV/0! kg/cm²

Ecuacion 1

0.75 0.75

Ecuacion 2

2 Ø 1"

1.25(D+L) +S1.25(D+L) -S

Put =353.64 tn =

= 353.64 =

Vu=Put -Wu(d+25)(1195) = 353640 - 1.2251(d+25)(1195)………………. (1)

Z2=𝑃_𝑠/𝑐Z3=𝑃_𝑠/𝑐


Vc = 1.06 √210 *(2*1195)d ………………………………..(2)

Igualando 1 y 2

0.75

d = #DIV/0! cm


10.93 +7.5 + 1.27/2 = #DIV/0! cm

Usar :

30cm

w = #DIV/0! 11.95 m

w = #DIV/0! tn/m²

Mu = #DIV/0! #DIV/0! tn-m2 2


21.87 cm


353640 - 1.2251(d+25)(1195) = 1.06 √210 *(2*1195)d

hz=

h min =

tn/m² x

w * Lu² = x 1.083² m =

d = 30 -7.5 - 1.27/ 2 =

ρ*bd² fy(1-0.59 ρ fy/f`c ) = Mu/ø


0 #DIV/0! tn/m²11.95 X 2.416 m²

= #DIV/0! kg/cm²



5.575 = #DIV/0! m semejante 1.30m4

√0.85 kg/cm²

5.575 = #DIV/0! m semejante 1.55 m

4√1.2251 kg/cm²

5.575 = #DIV/0! m semejante 2.05 m

4√1.2251+0.85kg/cm²

Se usara:h= 1.30 m

bw

h

b

0.30≥ bw/2 = 0.25/2 ok


b≤ 1.00 = 1.00 se usara

hs =𝑙𝑛/(4/(√𝑤𝑠)) =

hu =𝑙𝑛/(4/(√𝑤𝑢)) =


Portico 5



Za c1 :

Long: 11.95 m

Areas :

37.56 tn = 4.4198.5 tn/m²

4.64 tn = 0.5468.5 tn/m²

68.27 tn = 8.0328.5 tn/m²

4.509 tn = 0.5308.5 tn/m²

19.57 tn = 2.3028.5 tn/m²

4.419 +0.546 +8.032+0.530+2.30= 1.32511.95


A = 11.95 m x 1.325 m


Carga facturada :



Z4=𝑃_𝑠/𝑐Z5=𝑃_𝑠/𝑐

Z1(Tn) Z2 (Tn) Z3 (Tn) Z4 (Tn) Z5 (Tn)1.4D+L 54.6 6.85 100.62 7.24 27.81

42.47 3.37 84.69 6.84 28.86

51.44 5.23 86 5.4 20.06

197120 kg

Wu = Pu 12.453 tn/m² =Az 11.95 x 1.325

1.2453 kg/cm²

Ecuacion 1

0.75 0.75

Ecuacion 2

Vc = 1.06 √210 *(2*1195)d ………………………………..(2)

Igualando 1 y 2

0.75

d = 5.51 cm


5.51 +7.5 + 1.27/2 = 13.65 cm

Usar :

30cm

1.25(D+L) +S

1.25(D+L) -S

Put =197.12 tn =

= 197.12 =

Vu=Put -Wu(d+25)(1195) = 197120 - 1.2453(d+25)(1195)………………. (1)

197120 - 1.2453(d+25)(1195) = 1.06 √210 *(2*1195)d

hz=

h min =

w = 12.453 11.95 m

w = 148.812 tn/m²

Mu = 148.812 21.536 tn-m2 2


21.87 cm


tn/m² x

w * Lu² = x 0.538² m =

d = 30 -7.5 - 1.27/ 2 =

ρ*bd² fy(1-0.59 ρ fy/f`c ) = Mu/ø


134.549 8.50 tn/m²11.95 X 1.325 m²

= 0.85 kg/cm²


5.575 = 1.285 m semejante 1.30m4

√0.85 kg/cm²

5.575 = 1.56 m semejante 1.60 m

4√1.2453 kg/cm²

5.575 = 2.017 m semejante 2.05 m

4√1.2453+0.85kg/cm²

Se usara:h= 1.30 m

bw

h


hs =𝑙𝑛/(4/(√𝑤𝑠)) =

hu =𝑙𝑛/(4/(√𝑤𝑢)) =


b

0.30≥ bw/2 = 0.25/2 ok


b≤ 1.00 = 1.00 se usara

Portico 6



28.72 tn 58.17 tn 28.08 tn

Za c1 :

Long: 11.95 m

Areas :

28.72 tn = 3.3798.5 tn/m²

58.17 tn = 6.8448.5 tn/m²

28.08 tn = 3.3048.5 tn/m²

6.004 +14.458 +8.406 = 1.13211.95


A = 11.95 m x 1.132 m


Carga facturada :




29.19 73.87 42.57 145.6342.61 71.55 27.64 141.8

165180 kg

Wu = Pu 12.212 tn/m² =Az 11.95 x 1.132

1.2212 kg/cm²

Ecuacion 1

0.75 0.75

Ecuacion 2

Vc = 1.06 √210 *(2*1195)d ………………………………..(2)

Igualando 1 y 2

0.75

d = 4.44 cm


4.44 +7.5 + 1.27/2 = 12.57 cm

Usar :

30cm

1.25(D+L) +S1.25(D+L) -S

Put =165.18 tn =

= 165.18 =

Vu=Put -Wu(d+25)(1195) = 165180 - 1.2212(d+25)(1195)………………. (1)

165180 - 1.2212(d+25)(1195) = 1.06 √210 *(2*1195)d

hz=

h min =

w = 12.212 11.95 m

w = 145.935 tn/m²

Mu = 145.935 14.191 tn-m2 2


21.87 cm


tn/m² x

w * Lu² = x 0.441² m =

d = 30 -7.5 - 1.27/ 2 =

ρ*bd² fy(1-0.59 ρ fy/f`c ) = Mu/ø


114.97 8.5 tn/m²11.95 X 1132 m²

= 0.85 kg/cm²


5.575 = 1.285 m semejante 1.30m4

√0.85 kg/cm²

5.575 = 1.54 m semejante 1.55 m

4√1.2212 kg/cm²

5.575 = 2.006 m semejante 2.05 m

4√1.22512+0.85kg/cm²

Se usara:h= 1.30 m

bw

h


hs =𝑙𝑛/(4/(√𝑤𝑠)) =

hu =𝑙𝑛/(4/(√𝑤𝑢)) =


b

0.30≥ bw/2 = 0.25/2 ok


b≤ 1.00 = 1.00 se usara

m²

m²

m²

m

1.218 kg/cm²

c/Fy*(6000/(6000+Fy)

m²

m²

m²

m

c/Fy*(6000/(6000+Fy)

m²

m²

m²

m

c/Fy*(6000/(6000+Fy)

m²

m²

m

m²

m²

m²

m²

m²

m

total (Tn)

197.12

166.23

168.13

m²

m²

m²

m

Diseño de Zapata

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