Diseño de Zapatas Combinadas

Vconexion -1 Vcon -9

Vconexion -2

Vconexion -3

Vconexion -4

Vconexion -5

Vconexion -6

Vconexion -7

Vconexion -8

Vcon-10

Vcon-11

Vcon-12

Vcon-14

Vcon-13

Vcon-15

Vco

n -1

7

Vc -1

8

Vc -1

9

Vco

n -2

1

Vcon-16

3.75m 2.70m 3.23m

Vc -2

2

Vc -2

3

Vatad-2

Vatad-5

Vatad-4

Vatad-3

Vatad-1

Vatad-6

Vatad

o-2

2

Vata-2

3

Vat-2

4

Vat-2

5

Vatad

o-2

6

Vatad

0-1

7

Vata-1

8

Vata-1

3

Vata-8

Va-1

2

Va-7

Vat-1

9

Vat-1

4

Vat-9

V

at-10

Vat-1

5

Vat-2

0

Vatad

0-2

1

Va1

6

Va-1

1

Placa

Placa

3.25m

2.60m

2.95m

2.90m

2.95m

3.25m

2.60m

Zcom

b -

Zcom

b -

M1 M2

1 -0.08489 0.20687

2 0.0388 0.30119

3 0.17812 0.29722

4 0.00865 0.20688

5 -0.0138 0.20731

6 -0.17614 0.2969

7 -0.04187 0.3047

8 0.08192 0.20743

9 -0.02686 0.04183

9 -0.03556 0.0116

10 -0.14 -0.20525

11 0.09403 -0.26051

12 0.03268 -0.15644

13 -0.04061 -0.15618

14 -0.10133 -0.26057

15 0.13723 -0.20655

16 0.02649 0.04202

16 0.03486 0.01186

17 0.02123 0.03275

18 0.01322 0.01824

19 0.03795 -0.07558

20 -0.04447 -0.07575

21 -0.10133 -0.26057

22 0.01451 0.01585

23 -0.20443 0.03149

24 0.05218 -0.02307

Carga Muerta

25 0.06291 -0.16137

26 0.03904 -0.07359

27 -0.04361 -0.07372

28 -0.05993 -0.1612

29 -0.07191 0.01026

30 0.1897 0.02744

2.70m

3.15m

2.95m

2.90m

2.95m

2.70m

3.15m

1

9

2 3

2 1 0

2 4

17

3

1 1

2 5 1 8

4

1 2

2 6 1 9

5

1 3

2 7 2 0

6

1 4

2 8 2 1

7

1 5

2 9 2

2

8

3 0

1 6

b

h 1 2

M1 M2

-0.00475 0.0408

-0.00586 0.06602

0.0228 0.0755

-0.00044 0.07548

-0.00187 0.0755

-0.02303 0.07528

0.00377 0.06646

0.00281 0.04087

-0.00406 0.01049

-0.00811 0.00623

-0.04235 -0.05635

0.0067 -0.06647

0.00499 -0.06451

-0.00787 -0.0645

-0.00986 -0.06648

0.04 -0.05734

0.00367 0.01049

0.0075 0.00628

0.00648 0.01351

-0.00396 -0.00194

0.01049 -0.01593

-0.01313 -0.01594

0.00331 -0.00232

0.00102 0.00653

-0.03233 0.02366

0.0006 -0.01612

Carga Viva

0.00357 -0.03348

0.00579 -0.01396

-0.00824 -0.01395

-0.00391 -0.03338

-0.00331 -0.00292

0.02865 0.02256

M1

b h

1 35 50 25.63 2.73 -0.0849

2 35 50 28.63 3.5 0.0388

3 35 50 37.25 4.94 0.1781

4 35 50 30.3 4.63 0.0087

5 35 50 30.36 4.63 -0.0138

6 35 50 37.56 4.92 -0.1761

7 35 50 28.78 3.5 -0.0419

8 35 50 25.63 2.71 0.0819

-0.0269

-0.0356

10 35 50 44.24 7.62 -0.1400

11 35 50 44.24 8.2 0.0940

12 35 50 38.6 7.65 0.0327

13 35 50 38.75 7.65 -0.0406

14 35 50 44.73 8.21 -0.1013

15 35 50 44.85 7.61 0.1372

0.0265

0.0349

17 25 85 45.02 8.95 0.0212

18 35 50 37.74 7.1 0.0132

19 35 50 35.01 6.72 0.0380

20 35 50 35.15 6.72 -0.0445

21 35 50 37.86 7 -0.1013

22 25 85 44.25 8.45 0.0145

23 35 50 29.58 3.1 -0.2044

24 35 50 35.37 5.47 0.0522

25 35 50 30.2 4.62 0.0629

26 35 50 24.81 4.19 0.0390

27 35 50 24.84 4.18 -0.0436

28 35 50 30.14 4.52 -0.0599

29 35 50 34.38 5 -0.0719

30 35 50 28.99 2.96 0.1897

16 25 270 60 18

9 25 270 60 18

Carga Muerta

COLUMNADIMENSIONES

PCM (tn) PCV (tn) MxCM (tn-m)

M2 M1 M2

0.2069 -0.0048 0.0408

0.3012 -0.0059 0.0660

0.2972 0.0228 0.0755

0.2069 -0.0004 0.0755

0.2073 -0.0019 0.0755

0.2969 -0.0230 0.0753

0.3047 0.0038 0.0665

0.2074 0.0028 0.0409

0.0418 -0.0041 0.0105 1

0.0116 -0.0081 0.0062 2

-0.2053 -0.0424 -0.0564

-0.2605 0.0067 -0.0665

-0.1564 0.0050 -0.0645

-0.1562 -0.0079 -0.0645

-0.2606 -0.0099 -0.0665

-0.2066 0.0400 -0.0573

0.0420 0.0037 0.0105 1

0.0119 0.0075 0.0063 2

0.0328 0.0065 0.0135

0.0182 -0.0040 -0.0019

-0.0756 0.0105 -0.0159

-0.0758 -0.0131 -0.0159

-0.2606 0.0033 -0.0023

0.0159 0.0010 0.0065

0.0315 -0.0323 0.0237

-0.0231 0.0006 -0.0161

-0.1614 0.0036 -0.0335

-0.0736 0.0058 -0.0140

-0.0737 -0.0082 -0.0140

-0.1612 -0.0039 -0.0334

0.0103 -0.0033 -0.0029

0.0274 0.0287 0.0226

Carga Muerta Carga Viva

MyCM (tn-m) MxCV (tn-m) MyCV (tn-m)

Columna 8

Datosσadm = 1 kg/cm2 PCM = 25.63 Tn

L ejes de col = 2.6 m PCV = 2.71 Tn

f'c = 210 kg/cm2 MCM = 0.21

fy = 4200 kg/cm2 MCV = 0.04

Factor

CM = 1.4

CV = 1.7

50

40

Cargas de Servicio

Coumna 1 Coumna 2

Ps = 28 Tn Ton Ps = 32 Tn

Ms = 0.2483 Ton-m Ms = 0.37

qneto = 0.9 kg/cm2

Zapata Combinada -1

Az = 80826.67

Adoptamos

L = 350

B = 235

2.60m

X = 1.38

28.3Ton 60.6Ton 32.3Ton

5.1Ton-m

3.50m

𝑨𝒓𝒆𝒂 =𝟏. 𝟐 (𝑷𝟏 + 𝑷𝟐)

𝒒𝒏𝒆𝒕𝒐

P1 P2

R

X

q2

q1

2.60m

X = 1.39

40.5Ton 86.7Ton 46.2Ton

7.5Ton-m

0.00m

40489.0Kg 46242.0Kg

Pu1 Pu2

Ru

X

q2

q1

qu=

0.25m 2.60m 0.65m

DFC (Kg) 40574.7

7110.9

12821.0

-33378.1 -5667.3

Vmax = 40575

27753.8

DFC (Kg)

-12821.0

-46199.1 -18488.2

-5710.1

Vmax = 46199

DMF (Kg-m) -20585.9

𝒘𝒍^𝟐

𝟖

888.9 6008.7

Mmax = 20586

Diseño por Flexión

B = 235.00 cm Mact =h = 40.00 cm

d = 32.00 cm a =f'c = 210.00 kg/cm2

fy = 4200.00 kg/cm2 As =

Asmin =

Cortante

B = 235.00 cm

h = 40.00 cm Vc =

d = 32.00 cm Vmax =

f'c = 210 kg/cm2

fy = 4200 kg/cm2 Av =

ø Estribo = 1/2 pulg Vs =Área varilla = 1.27 cm2

S =

Smax =

5 @ 5cm, 5 @ 10, R@ 15

Corte por Punzonadob= 50.00 cm 1) Vn =

h= 35.00 cm 2) Vn =

m= 66 cm 3) Vn =n= 67 cm

Bc= 1.429 ≤ 2 Valores de α

F'c= 210 kg/cm2 Centrada

ρo= 199 cm Bordeα = 30 Borde Esquina

Corte por Flexión Se analiza para 1 m de ancho

qu = 1.210 Kg/cm2 Vact =

d = 32.00 cm Vc=

f'c = 210 kg/cm2

Lv = 100.0 cm Mact =d = 52 cm

f'c = 210 kg/cm2 a =

fy = 4200 kg/cm2 En 100 cmb = 100 cm As =

Asmin =


h= 35.00 cm 2) Vn =

m= 102 cm 3) Vn =n= 87 cm



ρo= 378 cm Bordeα = 40 Centrada Esquina




d = 32.00 cm Vc=

f'c = 210 kg/cm2

Lv = 100.0 cm Mact =d = 52 cm

f'c = 210 kg/cm2 a =


Asmin =


Columna 7

Ton PCM = 28.78 Tn Ton Columna 1

Ton PCV = 3.50 Tn Ton b =

Ton-m MCM = 0.30 Ton-m h =

Ton-m MCV = 0.07 Ton-m

Columna 2

b =

h =

R 50

Cargas ultimas

Coumna 1

Ton Pu = 40.489

Ton-m Mu = 0.359881

Zapata Combinada -1

2.60

2.85

cm2

cm Area = 82250 Conforme

cm

e = 0.084 m

m M = 5.12 Ton-m

q1 = 0.844 Kg/cm2

q2 = 0.630 Kg/cm2

CUMPLE

𝒒𝟏, 𝟐 = (𝑷𝟏 + 𝑷𝟐)

𝑩 ∗ 𝑳+ (𝟏 ±

𝟔 ∗ 𝒆

𝑳

< Qneto

e = 0.086 m

m M = 7.48 Ton-m

q1 = 1.210 Kg/cm2

q2 = 0.899 Kg/cm2

𝒒𝟏, 𝟐 = (𝑷𝟏 + 𝑷𝟐)

𝑩 ∗ 𝑳+ (𝟏 ±

𝟔 ∗ 𝒆

𝑳

Qmayor

28443.420 Kg/m

Kg

Kg

Kg-m

20585.93 Kg-cm

0.04 Usar : N° Varillas:

0.17 cm2 Usar acero mínimo

16.92 cm2

2.85

49093.31 Kg No necesita estribos, colocar mínimos

46199.12 Kg d/2 16.00

S = 30 30.00

2.53 cm2 s cal 64.75

5258.60 Kg

64.75 cm So = 16.00

16.00 cm

5 @ 5cm, 5 @ 10, R@ 15

119596.29 Kg

97817.95 Kg ØVn = 144525 Vu=

170029.06 Kg

40

30

20

8230 Kg Ok, cumple

20891 Kg

605179 Kg-cm

0.730 Varilla :

Cantidad : 3.101 cm2 Separacion:

7.20 cm2 Usar acero mínimo 3 ø

1.97

369155.88 Kg

301933.05 Kg ØVn = 490458 Vu=

577009.52 Kg

40

30

20

8230 Kg Ok, cumple

ACERO DISPONIBLE (cm² )

20891 Kg

605179 Kg-cm

0.730 Varilla :



1.97

50 cm

35 cm

50 cm

35 cm

Coumna 2

Ton Pu = 46.242 Ton

Ton-m Mu = 0.539562 Ton-m

CUMPLE

1.210 Kg/cm2

3/46

0.25d 8.00

So ( 2d ) = 8db 20.32

30 30.00

s cal 64.75

So = 30.000

35137 --> Cumple por Punzonamiento

5/8 1/2" 5/8" 3/4" 1" 1¼"

ø 4 6.00 1.97 2.85 5.06 7.9125.00 cm 12.00 3.94 5.70 10.12 15.82

18.00 5.91 8.55 15.18 23.73



5/8

ø 4 25.00 cm

3/8 1/2

0.71 1.26

1.42 2.52

2.13 3.78

2.84 5.04

3.55 6.30

4.26 7.56

5.68 10.08


5/8 3/4 1 1¼

1.97 2.85 5.06 7.91

3.94 5.70 10.12 15.82

5.91 8.55 15.18 23.73

7.88 11.40 20.24 31.64

9.85 14.25 25.30 39.55

11.82 17.10 30.36 47.46

15.76 22.80 40.48 63.28


Columna 1

Datosσadm = 1 kg/cm2 PCM = 25.63 Tn

L ejes de col = 2.6 m PCV = 2.73 Tn

f'c = 210 kg/cm2 MCM = 0.21

fy = 4200 kg/cm2 MCV = 0.04

Factor

CM = 1.4

CV = 1.7

50

40

Cargas de Servicio

Coumna 1 Coumna 2

Ps = 28 Tn Ton Ps = 32 Tn

Ms = 0.2477 Ton-m Ms = 0.37

qneto = 0.9 kg/cm2

Zapata Combinada -1

Az = 80653.33

Adoptamos

L = 350

B = 235

2.60m

X = 1.38

28.4Ton 60.5Ton 32.1Ton

4.9Ton-m

3.50m

𝑨𝒓𝒆𝒂 =𝟏. 𝟐 (𝑷𝟏 + 𝑷𝟐)

𝒒𝒏𝒆𝒕𝒐

P1 P2

R

X

q2

q1

2.60m

X = 1.38

40.5Ton 86.6Ton 46.0Ton

7.2Ton-m

0.00m

40523.0Kg 46032.0Kg

Pu1 Pu2

Ru

X

q2

q1

qu=

0.25m 2.60m 0.65m

DFC (Kg) 39954.6

7059.4

12277.2

-33463.6 -6077.4

Vmax = 39955

27677.4

DFC (Kg)

-12277.2

-45740.8 -18354.6

-5217.8

Vmax = 45741

DMF (Kg-m) -20437.1

𝒘𝒍^𝟐

𝟖

882.4 5965.2

Mmax = 20437


B = 235.00 cm Mact =h = 40.00 cm

d = 32.00 cm a =f'c = 210.00 kg/cm2

fy = 4200.00 kg/cm2 As =

Asmin =

Cortante

B = 235.00 cm

h = 40.00 cm Vc =

d = 32.00 cm Vmax =

f'c = 210 kg/cm2

fy = 4200 kg/cm2 Av =

ø Estribo = 1/2 pulg Vs =Área varilla = 1.27 cm2

S =

Smax =

5 @ 5cm, 5 @ 10, R@ 15


h= 35.00 cm 2) Vn =

m= 66 cm 3) Vn =n= 67 cm



ρo= 199 cm Bordeα = 30 Borde Esquina



d = 32.00 cm Vc=

f'c = 210 kg/cm2

Lv = 100.0 cm Mact =d = 52 cm

f'c = 210 kg/cm2 a =


Asmin =


h= 35.00 cm 2) Vn =

m= 102 cm 3) Vn =n= 87 cm



ρo= 378 cm Bordeα = 40 Centrada Esquina




d = 32.00 cm Vc=

f'c = 210 kg/cm2

Lv = 100.0 cm Mact =d = 52 cm

f'c = 210 kg/cm2 a =


Asmin =


Columna 2

Ton PCM = 28.63 Tn Ton Columna 1

Ton PCV = 3.50 Tn Ton b =

Ton-m MCM = 0.30 Ton-m h =

Ton-m MCV = 0.07 Ton-m

Columna 2

b =

h =

R 50

Cargas ultimas

Coumna 1

Ton Pu = 40.523

Ton-m Mu = 0.359097

Zapata Combinada -1

2.60

2.85

cm2

cm Area = 82250 Conforme

cm

e = 0.081 m

m M = 4.90 Ton-m

q1 = 0.838 Kg/cm2

q2 = 0.633 Kg/cm2

CUMPLE

𝒒𝟏, 𝟐 = (𝑷𝟏 + 𝑷𝟐)

𝑩 ∗ 𝑳+ (𝟏 ±

𝟔 ∗ 𝒆

𝑳

< Qneto

e = 0.083 m

m M = 7.16 Ton-m

q1 = 1.202 Kg/cm2

q2 = 0.903 Kg/cm2

𝒒𝟏, 𝟐 = (𝑷𝟏 + 𝑷𝟐)

𝑩 ∗ 𝑳+ (𝟏 ±

𝟔 ∗ 𝒆

𝑳

Qmayor

28237.771 Kg/m

Kg

Kg

Kg-m

20437.09 Kg-cm

0.04 Usar : N° Varillas:


16.92 cm2

2.85

49093.31 Kg No necesita estribos, colocar mínimos

45740.76 Kg d/2 16.00

S = 30 30.00

2.53 cm2 s cal 72.15

4719.35 Kg

72.15 cm So = 16.00

16.00 cm

5 @ 5cm, 5 @ 10, R@ 15

119596.29 Kg

97817.95 Kg ØVn = 144525 Vu=

170029.06 Kg

40

30

20

8171 Kg Ok, cumple

20891 Kg

600804 Kg-cm

0.724 Varilla :


7.20 cm2 Usar acero mínimo 3 ø

1.97

369155.88 Kg

301933.05 Kg ØVn = 490458 Vu=

577009.52 Kg

40

30

20

8171 Kg Ok, cumple


20891 Kg

600804 Kg-cm

0.724 Varilla :



1.97

50 cm

35 cm

50 cm

35 cm

Coumna 2

Ton Pu = 46.032 Ton

Ton-m Mu = 0.5339 Ton-m

CUMPLE

1.202 Kg/cm2

3/46

0.25d 8.00

So ( 2d ) = 8db 20.32

30 30.00

s cal 72.15

So = 30.000


5/8 1/2" 5/8" 3/4" 1" 1¼"

ø 4 6.00 1.97 2.85 5.06 7.9125.00 cm 12.00 3.94 5.70 10.12 15.82

18.00 5.91 8.55 15.18 23.73



5/8

ø 4 25.00 cm

3/8 1/2

0.71 1.26

1.42 2.52

2.13 3.78

2.84 5.04

3.55 6.30

4.26 7.56

5.68 10.08


5/8 3/4 1 1¼

1.97 2.85 5.06 7.91

3.94 5.70 10.12 15.82

5.91 8.55 15.18 23.73

7.88 11.40 20.24 31.64

9.85 14.25 25.30 39.55

11.82 17.10 30.36 47.46

15.76 22.80 40.48 63.28


Documents

Diseño de Zapatas Combinadas