Cimentaciones Z. Aislada.xlsx

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UNIVERSIDAD DE HUANUCO E.A.P INGENIERIA CIVIL NOMBRE:

MEZA DOMINGUEZ, MIGUEL ANGEL

DOCENTE:

JERRY MARLON DAVILA MARTEL

GRUPO:

"B"

CURSO:

INGENIERIA DE CIMENTACIONES

PROYECTO:

"MEJORAMIENTO DE LOS SERVICIOS ACADÉMICOS DE EXPERIMENTACIÓN E INVESTIGACIÓN EN LAS CARRERAS DE ENFERMERÍA, OBSTETRICIA, PSICOLOGÍA Y ODONTOLOGÍA DE LA UNHEVAL – HUÁNUCO"

METRADO DE CARGAS - MODULO ENFERMERIA PRIMER NIVEL CARGA MUERTA N°

DESCRIPCIÓN

1

VIGAS

ϪPeso esp. (Kg/m³)

N° DE VECES

LARGO (m)

ANCHO (m)

ALTO (m)

1

7.19

0.3

0.7

2400

2

3.1

0.3

0.7

2400

3124.8

2

7.37

0.3

0.7

2400

7428.96

1

4.27

0.3

0.7

2400

2152.08

2

7.09

0.3

0.7

2400

7146.72

2

2.65

0.3

0.7

2400

2671.2

1

7.18

0.3

0.7

2400

3618.72

1

6.95

0.3

0.7

2400

3502.8

1

5.38

0.3

0.7

2400

2711.52

2

2.39

0.3

0.7

2400

2409.12

1

5.6

0.3

0.7

2400

2822.4

1

5.61

0.3

0.7

2400

2827.44

1

2.89

0.3

0.7

2400

1456.56

1

5.84

0.3

0.4

2400

1681.92

1

2.06

0.3

0.4

2400

593.28

1

5.78

0.3

0.4

2400

1664.64

1

5.98

0.3

0.4

2400

1722.24

1

2.05

0.3

0.4

2400

590.4

1

5.74

0.3

0.4

2400

1653.12

7

4.87

0.3

0.4

2400

9817.92

7

4.88

0.3

0.4

2400

9838.08

7

2.3

0.3

0.2

2400

2318.4

7

0.4

0.6

4

2400

16128

2400

8444.60

0.4

0.7

2400

32256

AREA (m²)

TOTAL (kg)

VIGAS LONGITUDINALES Eje G ÷ 19 y 25

Eje H ÷ 19 y 25

Eje I ÷ 19 y 25

Eje J ÷ 19 y 25

3623.76

VIGAS TRANSVERSALES Ejes 19 - 25 ÷ G y J

2

COLUMNAS C-1 C-2

7

C-3

12

4 4

0.1257

3

4

5

PLACAS Pl-1

1

4

0.64

2400

6144

Pl-2

1

4

0.6925

2400

6648

LOSA(e=0.20) EJE 19 y 20 ÷ G y H

1

39.6882

300

11906.46

EJE 19 y 20 ÷ H y I

1

33.5442

300

10063.26

EJE 19 y 20 ÷ I y J

1

14.4224

300

4326.72

EJE 20 y 21 ÷ G y H

1

15.8387

300

4751.61

EJE 20 y 21 ÷ H y I

1

13.2581

300

3977.43

EJE 20 y 21 ÷ I y J

1

5.5508

300

1665.24

EJE 21 y 22 ÷ G y H

1

39.1608

300

11748.24

EJE 21 y 22 ÷ H y I

1

33.4649

300

10039.47

EJE 21 y 22 ÷ I y J

1

14.3298

300

4298.94

EJE 22 y 23 ÷ G y H

1

40.1916

300

12057.48

EJE 22 y 23 ÷ H y I

1

34.286

300

10285.8

EJE 22 y 23 ÷ I y J

1

14.6641

300

4399.23

EJE 23 y 24 ÷ G y H

1

15.8308

300

4749.24

EJE 23 y 24 ÷ H y I

1

13.2586

300

3977.58

EJE 23 y 24 ÷ I y J

1

5.5555

300

1666.65

EJE 24 y 25 ÷ G y H

1

38.8902

300

11667.06

EJE 24 y 25 ÷ H y I

1

33.2364

300

9970.92

EJE 24 y 25 ÷ I y J

1

14.2383

300

4271.49

2723.625

MUROS MUROS LONGITUDINALES Eje I ÷ 19 y 25

1

5.38

0.15

2.25

1500

2

5.6

0.15

2.25

1500

5670

1

2.89

0.15

2.25

1500

1463.0625

3

4.87

0.24

3.6

1500

18934.56

3

4.88

0.24

3.6

1500

18973.44

4

3.68

0.15

3.15

1500

10432.8

4

2.62

0.15

3.15

1500

7427.7

4

1.05

0.15

3.15

1500

2976.75

P-1

2

1.5

0.01

2.1

1000

63

P-2

8

1.2

0.01

2.1

1000

201.6

V-1

1

2.89

0.006

0.75

2500

32.5125

V-2

2

5.6

0.006

0.75

2500

126

V-3

1

5.38

0.006

0.75

2500

60.525

MUROS TRANSVERSALES Ejes 19 - 25 ÷ G y J

6

7

PUERTAS

VENTANAS

TOTAL =

339905.0760529

SEGUNDO NIVEL CARGA MUERTA N°

1

DESCRIPCIÓN

ϪPeso esp. (Kg/m³)

N° DE VECES

LARGO (m)

ANCHO (m)

ALTO (m)

1

7.19

0.3

0.7

2400

2

3.1

0.3

0.7

2400

3124.8

2

7.37

0.3

0.7

2400

7428.96

1

4.27

0.3

0.7

2400

2152.08

2

7.09

0.3

0.7

2400

7146.72

2

2.65

0.3

0.7

2400

2671.2

1

7.18

0.3

0.7

2400

3618.72

1

6.95

0.3

0.7

2400

3502.8

1

5.38

0.3

0.7

2400

2711.52

2

2.39

0.3

0.7

2400

2409.12

1

5.6

0.3

0.7

2400

2822.4

1

5.61

0.3

0.7

2400

2827.44

1

2.89

0.3

0.7

2400

1456.56

1

5.84

0.3

0.4

2400

1681.92

1

2.06

0.3

0.4

2400

593.28

1

5.78

0.3

0.4

2400

1664.64

1

5.98

0.3

0.4

2400

1722.24

1

2.05

0.3

0.4

2400

590.4

1

5.74

0.3

0.4

2400

1653.12

7

4.87

0.3

0.4

2400

9817.92

7

4.88

0.3

0.4

2400

9838.08

7

2.3

0.3

0.2

2400

2318.4

C-1

7

0.4

0.6

3.85

2400

15523.2

C-2

7

2400

8127.93

C-3

12

2400

31046.4

AREA (m²)

TOTAL (kg)

VIGAS VIGAS LONGITUDINALES Eje G ÷ 19 y 25

Eje H ÷ 19 y 25

Eje I ÷ 19 y 25

Eje J ÷ 19 y 25

3623.76

VIGAS TRANSVERSALES Ejes 19 - 25 ÷ G y J

2

3

COLUMNAS 3.85 0.4

0.7

0.1257

3.85

PLACAS Pl-1

1

3.85

0.64

2400

5913.6

Pl-2

1

3.85

0.6925

2400

6398.7

4

5

LOSA(e=0.20) EJE 19 y 20 ÷ G y H

1

39.6882

300

11906.46

EJE 19 y 20 ÷ H y I

1

33.5442

300

10063.26

EJE 19 y 20 ÷ I y J

1

14.4224

300

4326.72

EJE 20 y 21 ÷ G y H

1

15.8387

300

4751.61

EJE 20 y 21 ÷ H y I

1

13.2581

300

3977.43

EJE 20 y 21 ÷ I y J

1

5.5508

300

1665.24

EJE 21 y 22 ÷ G y H

1

39.1608

300

11748.24

EJE 21 y 22 ÷ H y I

1

33.4649

300

10039.47

EJE 21 y 22 ÷ I y J

1

14.3298

300

4298.94

EJE 22 y 23 ÷ G y H

1

40.1916

300

12057.48

EJE 22 y 23 ÷ H y I

1

34.286

300

10285.8

EJE 22 y 23 ÷ I y J

1

14.6641

300

4399.23

EJE 23 y 24 ÷ G y H

1

15.8308

300

4749.24

EJE 23 y 24 ÷ H y I

1

13.2586

300

3977.58

EJE 23 y 24 ÷ I y J

1

5.5555

300

1666.65

EJE 24 y 25 ÷ G y H

1

38.8902

300

11667.06

EJE 24 y 25 ÷ H y I

1

33.2364

300

9970.92

EJE 24 y 25 ÷ I y J

1

14.2383

300

4271.49

2723.625

MUROS MUROS LONGITUDINALES Eje I ÷ 19 y 25

1

5.38

0.15

2.25

1500

2

5.6

0.15

2.25

1500

5670

1

2.89

0.15

2.25

1500

1463.0625

3

4.87

0.24

3.45

1500

18145.62

3

4.88

0.24

3.45

1500

18182.88

4

3.68

0.15

3.15

1500

10432.8

4

2.62

0.15

3.15

1500

7427.7

4

1.05

0.15

3.15

1500

2976.75

8

1.2

0.01

2.1

1000

201.6

V-1

1

2.89

0.006

0.75

2500

32.5125

V-2

2

5.6

0.006

0.75

2500

126

V-3

1

5.38

0.006

0.75

2500

60.525

MUROS TRANSVERSALES Ejes 19 - 25 ÷ G y J

6

PUERTAS P-2

7

VENTANAS

TOTAL =

335651.8035134

CARGA VIVA

AREA (m²)

ϪPeso esp. (Kg/m²)

AULA 5

75.593

250

18898.25

AULA 6

74.7472

250

18686.8

AULA 7

76.6256

250

19156.4

AULA 8

74.208

250

18552

PASADIZO

133.4092

400

53363.68

TOTAL =

128657.13

TOTAL (kg)

TERCER NIVEL CARGA MUERTA N°

1

DESCRIPCIÓN

ϪPeso esp. (Kg/m³)

N° DE VECES

LARGO (m)

ANCHO (m)

ALTO (m)

1

7.19

0.3

0.7

2400

2

3.1

0.3

0.7

2400

3124.8

2

7.37

0.3

0.7

2400

7428.96

1

4.27

0.3

0.7

2400

2152.08

2

7.09

0.3

0.7

2400

7146.72

2

2.65

0.3

0.7

2400

2671.2

1

7.18

0.3

0.7

2400

3618.72

1

6.95

0.3

0.7

2400

3502.8

1

5.38

0.3

0.7

2400

2711.52

2

2.39

0.3

0.7

2400

2409.12

1

5.6

0.3

0.7

2400

2822.4

1

5.61

0.3

0.7

2400

2827.44

1

2.89

0.3

0.7

2400

1456.56

1

5.84

0.3

0.4

2400

1681.92

1

2.06

0.3

0.4

2400

593.28

1

5.78

0.3

0.4

2400

1664.64

1

5.98

0.3

0.4

2400

1722.24

1

2.05

0.3

0.4

2400

590.4

1

5.74

0.3

0.4

2400

1653.12

7

4.87

0.3

0.4

2400

9817.92

7

4.88

0.3

0.4

2400

9838.08

7

2.3

0.3

0.2

2400

2318.4

C-1

7

0.4

0.6

3.85

2400

15523.2

C-2

7

2400

8127.93

C-3

12

2400

31046.4

AREA (m²)

TOTAL (kg)

VIGAS VIGAS LONGITUDINALES Eje G ÷ 19 y 25

Eje H ÷ 19 y 25

Eje I ÷ 19 y 25

Eje J ÷ 19 y 25

3623.76

VIGAS TRANSVERSALES Ejes 19 - 25 ÷ G y J

2

3

COLUMNAS 3.85 0.4

0.7

0.1257

3.85

PLACAS Pl-1

1

3.85

0.64

2400

5913.6

Pl-2

1

3.85

0.6925

2400

6398.7

4

5

LOSA(e=0.20) EJE 19 y 20 ÷ G y H

1

39.6882

300

11906.46

EJE 19 y 20 ÷ H y I

1

33.5442

300

10063.26

EJE 19 y 20 ÷ I y J

1

14.4224

300

4326.72

EJE 20 y 21 ÷ G y H

1

15.8387

300

4751.61

EJE 20 y 21 ÷ H y I

1

13.2581

300

3977.43

EJE 20 y 21 ÷ I y J

1

5.5508

300

1665.24

EJE 21 y 22 ÷ G y H

1

39.1608

300

11748.24

EJE 21 y 22 ÷ H y I

1

33.4649

300

10039.47

EJE 21 y 22 ÷ I y J

1

14.3298

300

4298.94

EJE 22 y 23 ÷ G y H

1

40.1916

300

12057.48

EJE 22 y 23 ÷ H y I

1

34.286

300

10285.8

EJE 22 y 23 ÷ I y J

1

14.6641

300

4399.23

EJE 23 y 24 ÷ G y H

1

15.8308

300

4749.24

EJE 23 y 24 ÷ H y I

1

13.2586

300

3977.58

EJE 23 y 24 ÷ I y J

1

5.5555

300

1666.65

EJE 24 y 25 ÷ G y H

1

38.8902

300

11667.06

EJE 24 y 25 ÷ H y I

1

33.2364

300

9970.92

EJE 24 y 25 ÷ I y J

1

14.2383

300

4271.49

2723.625

MUROS MUROS LONGITUDINALES Eje I ÷ 19 y 25

1

5.38

0.15

2.25

1500

2

5.6

0.15

2.25

1500

5670

1

2.89

0.15

2.25

1500

1463.0625

3

4.87

0.24

3.45

1500

18145.62

3

4.88

0.24

3.45

1500

18182.88

2

3.68

0.15

3.15

1500

5216.4

3

2.62

0.15

3.15

1500

5570.775

3

1.05

0.15

3.15

1500

2232.5625

1

4.88

0.15

3.15

1500

3458.7

2

4.07

0.15

3.15

1500

5769.225

1

3.32

0.15

3.15

1500

2353.05

1

5.84

0.15

3.15

1500

4139.1

P-2

5

1.2

0.01

2.1

1000

126

P-6

3

0.8

0.006

2.1

1000

30.24000

V-1

1

2.89

0.006

0.75

2500

32.5125

V-2

2

5.6

0.006

0.75

2500

126

V-3

1

5.38

0.006

0.75

2500

60.525

V-8

1

2.63

0.006

0.9

2500

35.505

MUROS TRANSVERSALES Ejes 19 - 25 ÷ G y J

6

7

PUERTAS

VENTANAS

TOTAL =

343544.5110134

CARGA VIVA

AREA (m²)

ϪPeso esp. (Kg/m²)

SALA DE COMPUTO

75.593

250

18898.25

LABORATORIO DE ENFERMERIA CLINICA

62.5826

300

18774.78

DEPOSITO (LABORATORIO DE ENFERMERIA CLINICA)

11.7906

300

3537.18

TOTAL (kg)

LABORATORIO DE NIÑO

40.2075

300

12062.25

DEPOSITO (LABORATORIO DEL NIÑO)

9.7898

300

2936.94

LABORATORIO DE NEONATOLOGIA

36.8851

300

11065.53

LABORATORIO DE MUJER

74.208

300

22262.4

DEPOSITO (LABORATORIO DE LA MUJER)

7.9176

300

2375.28

PASADIZO

116.7896

400

46715.84

TOTAL =

138628.45

CUARTO NIVEL CARGA MUERTA N°

DESCRIPCIÓN

1

VIGAS

ϪPeso esp. (Kg/m³)

N° DE VECES

LARGO (m)

ANCHO (m)

ALTO (m)

1

7.19

0.3

0.7

2400

2

3.1

0.3

0.7

2400

3124.8

2

7.37

0.3

0.7

2400

7428.96

1

4.27

0.3

0.7

2400

2152.08

1

7.09

0.3

0.7

2400

3573.36

1

2.65

0.3

0.7

2400

1335.6

1

5.38

0.3

0.7

2400

2711.52

2

2.39

0.3

0.7

2400

2409.12

1

5.6

0.3

0.7

2400

2822.4

1

5.61

0.3

0.7

2400

2827.44

1

2.89

0.3

0.7

2400

1456.56

1

5.84

0.3

0.4

2400

1681.92

1

2.06

0.3

0.4

2400

593.28

1

5.78

0.3

0.4

2400

1664.64

1

5.98

0.3

0.4

2400

1722.24

1

2.05

0.3

0.4

2400

590.4

1

5.74

0.3

0.4

2400

1653.12

4

4.87

0.3

0.4

2400

5610.24

4

4.88

0.3

0.4

2400

5621.76

3

10.35

0.3

0.8

2400

17884.8

7

2.3

0.3

0.2

2400

2318.4

C-1

4

0.4

0.6

4.15

C-2

7

C-3

12

AREA (m²)

TOTAL (kg)

VIGAS LONGITUDINALES Eje G ÷ 19 y 25

Eje H ÷ 19 y 25

Eje I ÷ 19 y 25

Eje J ÷ 19 y 25

3623.76

VIGAS TRANSVERSALES Ejes 19 - 25

2

3

4

÷GyJ

COLUMNAS 4.15 0.4

0.7

0.1257

4.15

2400

9561.6

2400

8761.27

2400

33465.6

PLACAS Pl-1

1

4.15

0.64

2400

6374.4

Pl-2

1

4.15

0.6925

2400

6897.3

LOSA(e=0.20) EJE 19 y 20 ÷ G y H

1

39.6882

300

11906.46

EJE 19 y 20 ÷ H y I

1

33.5442

300

10063.26

EJE 19 y 20 ÷ I y J

1

14.4224

300

4326.72

EJE 20 y 21 ÷ G y H

1

15.8387

300

4751.61

EJE 20 y 21 ÷ H y I

1

13.2581

300

3977.43

EJE 20 y 21 ÷ I y J

1

5.5508

300

1665.24

EJE 21 y 22 ÷ G y I

1

74.7472

300

22424.16

EJE 21 y 22 ÷ I y J

1

14.3298

300

4298.94

5

EJE 22 y 23 ÷ G y I

1

76.6256

300

22987.68

EJE 22 y 23 ÷ I y J

1

14.6641

300

4399.23

EJE 23 y 24 ÷ G y I

1

29.8616

300

8958.48

EJE 23 y 24 ÷ I y J

1

5.5555

300

1666.65

EJE 24 y 25 ÷ G y I

1

74.208

300

22262.4

EJE 24 y 25 ÷ I y J

1

14.2383

300

4271.49

480.9375

MUROS MUROS LONGITUDINALES Eje I ÷ 19 y 25

1

0.75

0.15

2.85

1500

1

0.64

0.15

0.95

1500

136.8

1

4.2

0.15

3.35

1500

3165.75

2

4.87

0.24

3.35

1500

11746.44

2

4.88

0.24

3.35

1500

11770.56

1

2.92

0.1

3.35

1500

1467.3

1

0.4

0.1

3.35

1500

201

1

4.87

0.15

3.35

1500

3670.7625

1

4.88

0.15

3.35

1500

3678.3

1

8.55

0.15

2.75

1500

5290.3125

1

1.4

0.15

2.75

1500

866.25

1

3.3

0.15

2.75

1500

2041.875

1

0.95

0.15

2.75

1500

587.8125

1

1.35

0.15

2.75

1500

835.3125

P-4

3

0.9

0.078125

2.1

1000

442.96875

P-7

2

1.8

0.01

3.35

1000

120.6

P-7-A

1

1.5

0.01

3.35

1000

50.25

P-7-B

1

1.2

0.01

2.1

1000

25.2

P-8

3

0.8

0.006

2.1

1000

30.24

P-8-A

1

0.8

0.078125

2.1

1000

131.25

V-9

1

1.09

0.008

3.35

2500

73.03

V-10

2

0.7

0.008

3.35

2500

93.8

V-11

4

0.64

0.008

3.35

2500

171.52

V-12

1

0.75

0.008

0.5

2500

7.5

V-13

1

0.64

0.006

0.95

2500

9.12

M-1

1

2.39

0.008

3.35

2500

160.13

M-2

1

3.38

0.008

3.35

2500

226.46

M-3

1

2.68

0.008

3.35

2500

179.56

M-4

1

3.2

0.008

3.35

2500

214.4

M-5

1

2

0.008

3.35

2500

134

M-6

1

3.3

0.008

3.35

2500

221.1

M-7

1

4.98

0.008

3.35

2500

333.66

MUROS TRANSVERSALES Ejes 19 - 25 ÷ G y J

6

7

8

PUERTAS

VENTANAS

MAMPARAS

TOTAL =

314390.5248423

CARGA VIVA

AREA (m²)

ϪPeso esp. (Kg/m²)

ADMINISTRACION DE ENFERMERIA

114.0416

250

28510.4

DEPOSITO

20.8378

250

5209.45

TOTAL (kg)

DEPOSITO

20.8378

250

5209.45

COCINETA

12.6256

250

3156.4

PROSCENIO

45.236

300

13570.8

SALA DE CONFERENCIAS

191.9415

300

57582.45

PASADIZO

84.4783

400

33791.32

AZOTEA

525.1993

100

52519.93

TOTAL =

194340.75

RESUMEN NIVELES

CARGA MUERTA

CARGA VIVA

339905.076052849

0

2DO NIVEL

335651.803513367

128657.13

464308.933513368

3ER NIVEL

343544.511013368

138628.45

482172.961013368

4TO NIVEL

314390.524842331

194340.75

508731.274842331

SUB TOTAL DE CARGAS

1333491.91542192

461626.33

1795118.24542192

1ER NIVEL

CARGA TOTAL DE LA INFRAESTRUCTURA MODULO ENFERMERIA

Ps 339905.076052849

1795118.25

KG

1795.12

TN

AREA 1 AREA 2 AREA 3 AREA 4 AREA 5 AREA 6 AREA 7 AREA 8 AREA 9 AREA 10 AREA 11 AREA 12 AREA 13 AREA 14 AREA 15 AREA 16 AREA 17 AREA 18 AREA 19 AREA 20 AREA 21 AREA 22 AREA 23 AREA 24 AREA 25 AREA 26 AREA 27 AREA 28

m2 5.1956 14.0477 21.1997 11.645 15.917 28.773 18.9913 6.8761 6.9408 19.3154 29.2357 16.1635 22.0929 39.9367 26.4979 9.9886 6.9154 19.377 29.2872 16.1756 11.8434 21.3192 13.8996 6.8543 5.1233 18.3451 27.894 14.8294

Total =

484.6804

CALCULO DE LA CARGA NETA Cn = Peso Total Area Total

Cn = 1795.12 484.6804 Cn = 3.7037

CALCULO DE CARGA EN CADA COLUMNA Columna =

Area x Cn

Tn 19.24 52.03 78.52 43.13 58.95 106.57 70.34 25.47 25.71 71.54 108.28 59.87 81.83 147.91 98.14 36.99 25.61 71.77 108.47 59.91 43.86 78.96 51.48 25.39 18.98 67.95 103.31 54.92

c-2 c-3 c-1 c-3 c-3 c-1 c-3 c-2 c-2 c-3 c-1 c-3 c-3 c-1 c-3 c-2 c-2 c-3 c-1 c-3 c-3 c-1 c-3 c-2 c-2 p-2 c-1 p-1 Total =

1795.12

CÁLCULO DE MOMENTOS Y EXCENTRICIDADES COLUMNA TIPO C-2 (Area Tributaria 1) En el Plano Columna Viga x Viga y Losa

y

1.55 m

Peso (Tn) 4.7816 3.4330 0.6624 6.2347

CARGAS PUNTUALES EN X 4.7816

14.5477

x y

CM=

x

Pasadizo

3.4330

1.49 m 1.69 m

15.1117 8.3130

3.38 m

3.38 m CV= Ps=

8.3130 CM+CV =

23.4247 CARGAS PUNTUALES EN Y

CM CV

Veces 1 4 4 4

EJE X Columna Losa Viga Pasadizo

Largo (m)

Veces 1 4 4 4

EJE Y Columna Losa Viga Pasadizo

Largo (m)

Alto (m) 15.85

2.98

Area (m²) 0.1257 5.1956 0.12 5.1956

ϪP.e (Tn/m³) 2.4 0.3 2.4 0.4

Peso (Tn) 4.7816 6.2347 3.4330 8.3130

C.g 0 1.49 1.69 1.49

Area (m²) 0.1257 5.1956 0.06 5.1956

ϪP.e (Tn/m³) 2.4 0.3 2.4 0.4

Peso (Tn) 4.7816 6.2347 0.6624 8.3130

C.g 0 0.575 0.775 0.575

4.7816

14.5477

0.6624

y 0.575 m

CM CV

My= ∑ Wx * X1

Ҽx= My P

Mx= ∑ Wy * Y1

1.15

Alto (m) 15.85

My= (4.78*0.0) + (6.23*1.49) + (3.43*1.69) +(8.31*1.49) My= 27.4777 Ҽx= 27.4777 23.4247 Ҽx= 1.1730

Mx= (4.78*0.0) + (6.23*0.58) + (0.66*0.78) +(8.31*.575) Mx= 8.8783

0.75 m 1.55 m

UBICACIÓN DEL PUNTO DE LA EXCENTRICIDAD Y

1.1730 0.3790

Ҽy= Mx P

Ҽy= 8.8783 23.4247

X

Ҽy= 0.3790

CÁLCULO DE MOMENTOS Y EXCENTRICIDADES COLUMNA TIPO C-3 (Area Tributaria 2) y

En el Plano Columna Viga x Viga y Losa Muro x Muro y

3.99m

x

Peso 10.6512 5.7456 3.4733 16.8572 4.6524 12.1219

CARGAS PUNTUALES EN X

Sala Com. Adm. Enf. Pasadizo Aula

53.5017

CV=

10.6512 2.3232 2.3232 7.6032 4.6464

0.3240

x 0.67 m 1.425 m 1.775 m

1.35 m CM=

16.8960

3.55 m Ps=

CM

CV

CM

CV

Veces 1 4 4 3 1 2 1 1 4

EJE X Largo (m) Columna Losa Viga 2.85 Muro 2.85 Muro 0.64 Aula Sala de Computo Adm. Enf. Pasadizo

Alto (m) 15.85

Veces 1 4 4 4 4 4 2 1 1 4

EJE Y Largo (m) Columna Losa Losa Viga 1.15 Viga 2.44 Muro 2.44 Aula Sala de Computo Adm. Enf. Pasadizo

Alto (m) 15.85

Area (m²) 0.28 14.0477 0.21

2.25 2.25 9.2928 9.2928 9.2928 4.752 Area (m²) 0.28 9.2928 4.752 0.06 0.12

3.45 9.2928 9.2928 9.2928 4.752

CM+CV =

70.3977

ϪP.e (Tn/m³) 2.4 0.3 2.4 0.225 0.225 0.25 0.25 0.25 0.4

Peso (Tn) 10.6512 16.8572 5.7456 4.3284 0.3240 4.6464 2.3232 2.3232 7.6032

C.g 0 1.425 1.775 1.775 0.67 1.425 1.425 1.425 1.425

ϪP.e (Tn/m³) 2.4 0.3 0.3 2.4 2.4 0.36 0.25 0.25 0.25 0.4

Peso (Tn) 10.6512 11.1514 5.7024 0.6624 2.8109 12.1219 4.6464 2.3232 2.3232 7.6032

C.g 0 1.32 -0.675 -0.775 1.42 1.42 1.32 1.32 1.32 -0.675

33.7532 10.0740

3.55 m

CARGAS PUNTUALES EN Y 13.3056

0.6624

10.6512

20.4442 14.9328

y - 0.675 m

1.32 m

- 0.775 m

1.42 m 3.99m

UBICACIÓN DEL PUNTO DE LA EXCENTRICIDAD Y

0.9403 My= ∑ Wx * X1

Mx= ∑ Wy * Y1 0.5497 My= 66.1969

Mx= 38.6962

X

Ҽx= My P

Ҽx= 66.1969 70.3977 Ҽx= 0.9403

Ҽy= Mx P

Ҽy= 38.6962 70.3977 Ҽy= 0.5497

CÁLCULO DE MOMENTOS Y EXCENTRICIDADES COLUMNA TIPO C-1 (Area Tributaria 3) En el Plano Columna Viga x Viga y Losa Muro y

5.48 2.74

CM= 3.85

CV

CM

CV

EJE X Largo (m) Columna Losa Viga 3.35 Aula Sala de Computo Adm. Enf.

Alto (m) 15.85

Veces EJE Y Largo (m) Columna 1 Losa 4 Losa 4 Viga 2.44 4 Viga 2.44 4 Muro 2.44 4 Muro 2.44 4 2 Aula 1 Sala de Computo 1 Adm. Enf.

Alto (m) 15.85

My= ∑ Wx * X1 Ҽx= My P

Mx= ∑ Wy * Y1

Sala Com. Adm. Enf. Aula

5.2999 5.2999 10.5999

71.1884

CV=

21.1997

CM+CV =

Area (m²) 0.24 21.1997 0.21 21.1997 21.1997 21.1997

ϪP.e (Tn/m³) 2.4 0.3 2.4 0.25 0.25 0.25

Peso (Tn) 9.1296 25.4396 6.7536 10.5999 5.2999 5.2999

Area (m²) 0.24 10.5985 10.5985 0.12 0.12

ϪP.e (Tn/m³) 2.4 0.3 0.3 2.4 2.4 0.36 0.36 0.25 0.25 0.25

Peso (Tn) 9.1296 12.7182 12.7182 2.8109 2.8109 12.1219 12.1219 10.5999 5.2999 5.2999

3.45 3.45 21.1997 21.1997 21.1997

CARGAS PUNTUALES EN X 25.4396

46.6393

6.7536

x 1.725 m 1.925 m

92.3881

3.85

C.g 0 1.725 1.925 1.725 1.725 1.725

C.g

CARGAS PUNTUALES EN Y 14.9328 12.7182

14.9328 12.7182

y

0 1.37 -1.37 1.52 -1.52 1.52 -1.52

0 0 0

9.1296

- 1.37 m

1.37 m

- 1.52 m

1.52 m 5.48

UBICACIÓN DEL PUNTO DE LA EXCENTRICIDAD Y

My= 93.4535 Ҽx= 93.4535 92.3881 Ҽx= 1.0115

Mx= 0.0000

Ҽx= 1.0115 Ҽy= 0.0000

CM

Veces 1 4 4 2 1 1

Ps=

Peso 9.1296 6.7536 5.6218 25.4396 24.2438

X

Ҽy= Ҽy= Mx P

Ҽy= 0.0000 92.3881 Ҽy= 0.0000

CÁLCULO DE MOMENTOS Y EXCENTRICIDADES COLUMNA TIPO C-3 (Area Tributaria 4) En el Plano Columna Viga x Viga y Losa Muro y

2.84

CM= 4.3

CM

CV

Ps=

Veces 1 4 4 2 1 1

EJE X Largo (m) Columna Losa Viga 3.6 Aula Sala de Computo Adm. Enf.

Alto (m) 15.85

Veces 1 4 4 4 2 1 1

EJE Y Largo (m) Columna Losa Viga 2.44 Muro 2.44 Aula Sala de Computo Adm. Enf.

Alto (m) 15.85

Peso 10.6512 7.2576 2.8109 13.9740 12.1219

Sala Com. Adm. Enf. Aula

2.9113 2.9113 5.8225

46.8156

CV=

11.6450

CM+CV =

CARGAS PUNTUALES EN X 10.6512

25.6190

x 1.8 m 2.15 m

58.4606

Area (m²) 0.28 11.645 0.21 11.645 11.645 11.645

ϪP.e (Tn/m³) 2.4 0.3 2.4 0.25 0.25 0.25

Peso (Tn) 10.6512 13.9740 7.2576 5.8225 2.9113 2.9113

C.g 0 1.8 2.15 1.8 1.8 1.8

Area (m²) 0.28 11.645 0.12

ϪP.e (Tn/m³) 2.4 0.3 2.4 0.36 0.25 0.25 0.25

Peso (Tn) 10.6512 13.9740 2.8109 12.1219 5.8225 2.9113 2.9113

C.g 0 -1.22 -1.42 -1.42 -1.22 -1.22 -1.22

7.2576

4.3

CARGAS PUNTUALES EN Y 14.9328 25.6190

10.6512

y

CM

CV

3.45 11.645 11.645 11.645

- 1.22 m - 1.42 m 2.84

UBICACIÓN DEL PUNTO DE LA EXCENTRICIDAD My= ∑ Wx * X1 Ҽx= My P

My= 61.7180

Y

Ҽx= 61.7180 58.4606 Ҽx= 1.0557

X -0.8974 1.0557

Mx= ∑ Wy * Y1 Ҽy= Mx

Mx= -52.4598 Ҽy= -52.4598

P

58.4606 Ҽy= -0.8974

CÁLCULO DE MOMENTOS Y EXCENTRICIDADES COLUMNA TIPO C-3 (Area Tributaria 5) En el Plano Columna Viga x Viga y Losa Muro y

2.84

Peso 10.6512 10.3824 2.8109 19.1004 2.6366

CARGAS PUNTUALES EN X Sala Com. Adm. Enf. Aula Pasadizo

2.8045 2.8045 5.6090 6.4752

45.5814

CV=

17.6932

2.8045

7.2576

21.8751

10.6512

12.9504

3.1248

x CM= 3.95

CM

CV

CM

CV

Veces 1 4 4 4 4 2 1 1 3 Veces 1 4 4 3 2 1 1 3

1.9 5.85 EJE X Largo (m) Columna Losa Losa Viga 3.6 Viga 1.55 Aula Sala de Computo Adm. Enf. Pasadizo EJE Y Largo (m) Columna Losa Viga 2.44 Muro 1.24 Aula Sala de Computo Adm. Enf. Pasadizo

My= ∑ Wx * X1 Ҽx= My P

Ps= Alto (m) 15.85

Alto (m) 15.85

Area (m²) 0.28 11.218 5.396 0.21 0.21 11.218 11.218 11.218 5.396 Area (m²) 0.28 15.917 0.12

3.15 11.218 11.218 11.218 5.396

ϪP.e (Tn/m³) 2.4 0.3 0.3 2.4 2.4 0.25 0.25 0.25 0.4 ϪP.e (Tn/m³) 2.4 0.3 2.4 0.225 0.25 0.25 0.25 0.4

CM+CV = Peso (Tn) 10.6512 13.4616 6.4752 7.2576 3.1248 5.6090 2.8045 2.8045 6.4752 Peso (Tn) 10.6512 19.1004 2.8109 2.6366 5.6090 2.8045 2.8045 6.4752

- 1.025 m - 1.975 m - 2.15 m

63.2746 C.g 0 -1.975 0.95 -2.15 1.125 -1.975 -1.975 -1.025 0.95 C.g 0 -1.22 -1.42 -2.02 -1.22 -1.22 -1.22 -1.22

5.85

CARGAS PUNTUALES EN Y 2.6366

2.8109 36.7936

10.6512

y - 1.22 m - 1.42 m - 2.02 m 2.84

UBICACIÓN DEL PUNTO DE LA EXCENTRICIDAD

My= -45.8635 Ҽx= -45.8635 63.2746 Ҽx= -0.7248

0.95 m 1.125 m

Y

X -0.8567 -0.7248

Mx= ∑ Wy * Y1

Mx= -54.2055

Ҽy= Mx P

Ҽy= -54.2055 63.2746 Ҽy= -0.8567

CÁLCULO DE MOMENTOS Y EXCENTRICIDADES COLUMNA TIPO C-1 (Area Tributaria 6) En el Plano Columna Viga x Viga y Losa Muro y

5.48 2.74 3.6

0.4

Peso 9.1296 9.8784 2.3424 34.5276 13.8348

CARGAS PUNTUALES EN X Sala Com. Adm. Enf. Aula Pasadizo

5.2060 5.2060 10.4120 13.1520

69.7128

CV=

33.9760

7.2576

CM

CV

CM

CV

Veces 1 4 4 4 4 2 1 1 4

EJE X Largo (m) Columna Losa Losa Viga 3.6 Viga 1.3 Aula Sala de Computo Adm. Enf. Pasadizo

Alto (m) 15.85

Veces 1 4 4 4 4 4 2 1 1 4

EJE Y Largo (m) Columna Losa Viga 2.44 Viga 2.44 Muro 2.44 Muro 2.44 Aula Sala de Computo Adm. Enf. Pasadizo

Alto (m) 15.85

CM+CV =

103.6888

Area (m²) 0.24 20.824 8.22 0.21 0.21 20.824 20.824 20.824 8.22

ϪP.e (Tn/m³) 2.4 0.3 0.3 2.4 2.4 0.25 0.25 0.25 0.4

Peso (Tn) 9.1296 24.9888 9.8640 7.2576 2.6208 10.4120 5.2060 5.2060 13.1520

C.g 0 -1.9 0.75 -2 0.85 -1.9 -1.9 -1.9 0.75

Area (m²) 0.24 28.773 0.12 0.12

ϪP.e (Tn/m³) 2.4 0.3

Peso (Tn) 9.1296 34.5276 1.1712 1.1712 6.9174 6.9174 10.4120 5.2060 5.2060 13.1520

C.g 0 0 -1.52 1.52 -1.52 1.52 0 0 0 0

3.15 3.15 20.824 20.824 20.824 8.22

0.225 0.225 0.25 0.25 0.25 0.4

23.0160

- 1.90 m - 2.00 m

5.3 Ps=

9.1296

2.6208

x

1.3 CM=

45.8128

0.75 m 0.85 m

5.3

CARGAS PUNTUALES EN Y 8.0886

9.1296

8.0886

y 1.52 m - 1.52 m 5.48

UBICACIÓN DEL PUNTO DE LA EXCENTRICIDAD Y

My= ∑ Wx * X1

Mx= ∑ Wy * Y1 X My= -82.0698

Ҽx= My P

Ҽx= -82.0698 103.6888 Ҽx= -0.7915

-0.7915

Mx= 0.0000 Ҽy= Mx P

Ҽy= 0.0000 103.6888 Ҽy= 0.0000

CÁLCULO DE MOMENTOS Y EXCENTRICIDADES COLUMNA TIPO C-3 (Area Tributaria 7) En el Plano Columna Viga x Viga y Losa Muro y

2.84

Peso 10.6512 10.3824 2.8109 0.0000 2.6366

CARGAS PUNTUALES EN X Sala Com. Adm. Enf. Aula Pasadizo

2.8045 2.8045 5.6090 6.4752

26.4810

CV=

17.6932

2.8045

7.2576

21.8751

10.6512

12.9504

3.1248

x CM= 3.95

CM

CV

CM

CV

Veces 1 4 4 4 4 2 1 1 3 Veces 1 4 4 3 2 1 1 3

1.9 5.85 EJE X Largo (m) Columna Losa Losa Viga 3.6 Viga 1.55 Aula Sala de Computo Adm. Enf. Pasadizo EJE Y Largo (m) Columna Losa Viga 2.44 Muro 1.24 Aula Sala de Computo Adm. Enf. Pasadizo

My= ∑ Wx * X1 Ҽx= My P

Ps= Alto (m) 15.85

Alto (m) 15.85

Area (m²) 0.28 11.218 5.396 0.21 0.21 11.218 11.218 11.218 5.396 Area (m²) 0.28 0 0.12

3.15 11.218 11.218 11.218 5.396

ϪP.e (Tn/m³) 2.4 0.3 0.3 2.4 2.4 0.25 0.25 0.25 0.4 ϪP.e (Tn/m³) 2.4 0.3 2.4 0.225 0.25 0.25 0.25 0.4

CM+CV = Peso (Tn) 10.6512 13.4616 6.4752 7.2576 3.1248 5.6090 2.8045 2.8045 6.4752 Peso (Tn) 10.6512 0.0000 2.8109 2.6366 5.6090 2.8045 2.8045 6.4752

- 1.025 m - 1.975 m - 2.15 m

44.1742 C.g 0 1.975 0.95 -2.15 1.125 -1.975 1.975 -1.025 0.95 C.g 0 -1.22 -1.42 -2.02 -1.22 -1.22 -1.22 -1.22

0.95 m 1.125 m

5.85

CARGAS PUNTUALES EN Y 2.6366

2.8109 17.6932

10.6512

y - 1.22 m - 1.42 m - 2.02 m 2.84

UBICACIÓN DEL PUNTO DE LA EXCENTRICIDAD

My= 40.5432

Y

Ҽx= 40.5432 44.1742 Ҽx= 0.9178

0.9178 -0.6996

X

Mx= ∑ Wy * Y1 Ҽy= Mx P

Mx= -30.9030 Ҽy= -30.9030 44.1742 Ҽy= -0.6996

CÁLCULO DE MOMENTOS Y EXCENTRICIDADES COLUMNA TIPO C-2 (Area Tributaria 8) En el Plano Columna Viga x Viga y Losa

1.55

Peso 4.7816 4.6541 0.6624 8.2513

CARGAS PUNTUALES EN X

Pasadizo

11.0018

18.3494

CV=

11.0018

3.4445

13.8446

4.7816

5.4250

1.2096

x CM= 3.19

1.25

Ps=

CM+CV =

- 1.595 m - 1.695 m

29.3512

0.625 m 0.725 m

4.44 4.44

CM

CV

Veces 1 4 4 4 4 4 4

EJE X Columna Losa Losa Viga Viga Pasadizo Pasadizo

Largo (m)

Alto (m) 15.85

2.99 1.05

Area (m²) 0.1257 4.9445 1.9375 0.12 0.12 4.9445 1.9375

ϪP.e (Tn/m³) 2.4 0.3 0.3 2.4 2.4 0.4 0.4

Peso (Tn) 4.7816 5.9334 2.3250 3.4445 1.2096 7.9112 3.1000

C.g 0 -1.595 0.625 -1.695 0.725 -1.595 0.625

CARGAS PUNTUALES EN Y 4.7816

19.2531

0.6624

y 0.575 m 0.775 m

CM CV

Veces 1 4 4 4

EJE Y Columna Losa Viga Pasadizo

Largo (m)

My= ∑ Wx * X1 Ҽx= My P

Mx= ∑ Wy * Y1

1.15

Alto (m) 15.85

Area (m²) 0.1257 6.8761 0.06 6.8761

ϪP.e (Tn/m³) 2.4 0.3 2.4 0.4

My= -23.6529

Peso (Tn) 4.7816 8.2513 0.6624 11.0018

C.g 0 0.575 0.775 0.575

1.55

UBICACIÓN DEL PUNTO DE LA EXCENTRICIDAD

Ҽx= -23.6529 29.3512 Ҽx= -0.8059

Y

Mx= 11.5839 -0.8059

Ҽy= Mx

Ҽy= 11.5839

P

29.3512 Ҽy= 0.3947

0.3947

X

CÁLCULO DE MOMENTOS Y EXCENTRICIDADES COLUMNA TIPO C-2 (Area Tributaria 9) En el Plano Columna Viga x Viga y Losa

1.55

Peso 4.7816 4.7462 0.6624 8.3290

CARGAS PUNTUALES EN X

Pasadizo

11.1053

18.5192

CV=

11.1053

1.2211

5.4684

4.7816

14.1484

3.5251

x CM= 1.26

3.26

Ps=

CM+CV =

- 0.63 m - 0.73 m

29.6245

1.63 m 1.73 m

4.52 4.52

CM

CV

Veces 1 4 4 4 4 4 4

EJE X Columna Losa Losa Viga Viga Pasadizo Pasadizo

Largo (m)

Alto (m) 15.85

1.06 3.06

Area (m²) 0.1257 1.9530 5.053 0.12 0.12 1.953 5.053

ϪP.e (Tn/m³) 2.4 0.3 0.3 2.4 2.4 0.4 0.4

Peso (Tn) 4.7816 2.3436 6.0636 1.2211 3.5251 3.1248 8.0848

C.g 0 -0.63 1.63 -0.73 1.73 -0.63 1.63

CARGAS PUNTUALES EN Y 4.7816

19.4342

0.6624

y 0.575 m 0.775 m

CM CV

Veces 1 4 4 4

EJE Y Largo (m) W Columna W Losa W Viga 1.15 Pasadizo

My= ∑ Wx * X1 Ҽx= My P

Mx= ∑ Wy * Y1

Alto (m) 15.85

Area (m²) 0.1257 6.9408 0.06 6.9408

ϪP.e (Tn/m³) 2.4 0.3 2.4 0.4

My= 24.8238 Ҽx= 24.8238 29.6245 Ҽx= 0.8379

Peso (Tn) 4.7816 8.3290 0.6624 11.1053

C.g 0 0.575 0.775 0.575

1.55

UBICACIÓN DEL PUNTO DE LA EXCENTRICIDAD Y

Mx= 11.6880 0.8379

Ҽy= Mx

Ҽy= 11.6880

P

29.6245 Ҽy= 0.3945

0.3945

X

CÁLCULO DE MOMENTOS Y EXCENTRICIDADES COLUMNA TIPO C-1 (Area Tributaria 11) En el Plano Columna Viga x Viga y Losa Muro y

5.48 2.74 1.3

0.4

Peso 9.1296 9.9792 2.3424 35.0828 13.8348

Aula Lab.Enf. Adm. Enf. Deopsito Pasadizo

10.5490 6.3294 2.0550 5.2745 9.8640

CARGAS PUNTUALES EN X

70.3688

CV=

34.0719

2.6208

- 0.75 m - 0.85 m

5.35 Ps=

CM

CV

Veces 1 4 4 4 4 2 1 1 1 3

EJE X Columna Losa Losa Viga Viga Aula Lab.Enf. Adm. Enf. Deopsito Pasadizo

Largo (m)

Veces 1 4 4 4 4 4 2 1 1

EJE Y Columna Losa Viga Viga Muro Muro Aula Lab.Enf. Adm. Enf.

Largo (m)

Alto (m) 15.85

1.3 3.65

CM+CV =

104.4407

Area (m²) 0.24 8.22 21.098 0.21 0.21 21.098 21.098 8.22 21.098 8.22

ϪP.e (Tn/m³) 2.4 0.3 0.3 2.4 2.4 0.25 0.3 0.25 0.25 0.4

Peso (Tn) 9.1296 9.8640 25.3176 2.6208 7.3584 10.5490 6.3294 2.0550 5.2745 9.8640

C.g 0 -0.75 1.925 -0.85 2.025 1.925 1.925 -0.75 1.925 -0.75

Area (m²) 0.24 29.2357 0.12 0.12

ϪP.e (Tn/m³) 2.4 0.3

Peso (Tn) 9.1296 35.0828 1.1712 1.1712 6.9174 6.9174 10.5490 6.3294 2.0550

C.g 0 0 -1.52 1.52 -1.52 1.52 0 0 0

9.1296

47.4705

7.3584

x

3.65 CM=

21.7830

1.925 m 2.025 m 5.35

CARGAS PUNTUALES EN Y 8.0886

9.1296

8.0886

y 1.52 m - 1.52 m 5.48

CM

CV

2.44 2.44 2.44 2.44

Alto (m) 15.85

3.15 3.15 21.098 21.098 8.22

0.225 0.225 0.25 0.3 0.25

UBICACIÓN DEL PUNTO DE LA EXCENTRICIDAD Y

CV 1 3

Deopsito Pasadizo

21.098 8.22

0.25 0.4

5.2745 9.8640

0 0

X 0.8399

My= ∑ Wx * X1

Mx= ∑ Wy * Y1 My= 87.7165

Ҽx= My P

Ҽx= 87.7165 104.4407 Ҽx= 0.8399

Mx= 0.0000 Ҽy= Mx P

Ҽy= 0.0000 104.4407 Ҽy= 0.0000

CÁLCULO DE MOMENTOS Y EXCENTRICIDADES COLUMNA TIPO C-3 (Area Tributaria 12) En el Plano Columna Viga x Viga y Losa Muro y

2.84

1.9

4.03

CM=

5.93

CM

CV

CM

CV

Ps=

Veces 1 4 4 4 4 2 1 1 1 3

EJE X Columna Losa Losa Viga Viga Aula Lab. Enfer. Adm. Enf. Deposito Pasadizo

Largo (m)

Veces 1 4 4 1 3 2 1 1 1 3

EJE Y Columna Losa Viga Muro Muro Aula Lab. Enfer. Adm. Enf. Deposito Pasadizo

Largo (m)

Alto (m) 15.85

1.55 3.68

2.44 2.44 1.24

Alto (m) 15.85

Peso 10.6512 10.5437 2.8109 19.3962 4.3659

Lab. Enf. Adm. Enf. Deposito Pasadizo

5.7226 3.4336 1.3490 2.8613 6.4752

47.7679

CV=

19.8417

CM+CV =

CARGAS PUNTUALES EN X Aula

ϪP.e (Tn/m³) 2.4 0.3 0.3 2.4 2.4 0.25 0.3 0.25 0.25 0.4

Peso (Tn) 10.6512 6.4752 13.7342 3.1248 7.4189 5.7226 3.4336 1.3490 2.8613 6.4752

C.g 0 -0.95 2.015 -1.125 2.19 2.015 2.015 -0.95 2.015 -0.95

Area (m²) 0.28 16.1635 0.12

ϪP.e (Tn/m³) 2.4 0.3 2.4 0.225 0.225 0.25 0.3 0.25 0.25 0.4

Peso (Tn) 10.6512 19.3962 2.8109 1.7294 2.6366 5.7226 3.4336 1.3490 2.8613 6.4752

C.g 0 -1.22 -1.42 -1.42 -2.02 -1.22 -1.22 -1.22 -1.22 -1.22

11.4452 11.4452 5.396 11.4452 5.396

14.2994

10.6512

25.7517

7.4189

x - 0.95 m -1.125 m

67.6095

Area (m²) 0.28 5.396 11.4452 0.21 0.21 11.4452 11.4452 5.396 11.4452 5.396

3.15 3.15

3.1248

2.015 m 2.19 m 5.93

CARGAS PUNTUALES EN Y 2.6366

4.5402 39.2379

10.6512

y - 1.22 m - 1.42 m - 2.02 m 2.84

UBICACIÓN DEL PUNTO DE LA EXCENTRICIDAD Y

X My= ∑ Wx * X1

Mx= ∑ Wy * Y1 My= 51.0372

-0.8822 Mx= -59.6431

0.7549

Ҽx= My P

Ҽx= 51.0372 67.6095 Ҽx= 0.7549

Ҽy= Mx P

Ҽy= -59.6431 67.6095 Ҽy= -0.8822

CÁLCULO DE MOMENTOS Y EXCENTRICIDADES COLUMNA TIPO C-3 (Area Tributaria 13) En el Plano Columna Viga x Viga y Losa Muro y

2.84

4.03

4.03

CM=

8.06

CM

CV

CM

CV

Ps=

Veces 1 4 4 4 4 2 1 1 1

EJE X Columna Losa Losa Viga Viga Aula Lab. Enfer. Lab. Niño Proscenio

Largo (m)

Veces 1 4 4 3 2 1 1 1

EJE Y Columna Losa Viga Muro Aula Lab. Enfer. Adm. Enf. Proscenio

Largo (m)

My= ∑ Wx * X1

Alto (m) 15.85

3.68 3.68

2.44 2.44

Alto (m) 15.85

Peso 10.6512 14.8378 2.8109 26.5115 8.3009

Aula Lab. Enfer. Lab. Niño Proscenio

11.0465 3.4336 3.4336 6.6279

63.1122

CV=

24.5414

CM+CV =

CARGAS PUNTUALES EN X

ϪP.e (Tn/m³) 2.4 0.3 0.3 2.4 2.4 0.25 0.3 0.3 0.3

Peso (Tn) 10.6512 13.7342 13.7342 7.4189 7.4189 11.0465 3.4336 3.4336 6.6279

C.g 0 -2.015 2.015 -2.19 2.19 0 -2.015 2.015 0

Area (m²) 0.28 22.0929 0.12

ϪP.e (Tn/m³) 2.4 0.3 2.4 0.36 0.25 0.3 0.3 0.3

Peso (Tn) 10.6512 26.5115 2.8109 8.3009 5.7226 3.4336 3.4336 3.4336

C.g 0 -1.22 -1.42 -1.42 -1.22 -1.22 -1.22 -1.22

11.4452 11.4452 11.4452 11.4452

Mx= ∑ Wy * Y1

17.1678

10.6512

17.1678

7.4189

x - 2.015 m -2.19 m

87.6536

Area (m²) 0.28 11.4452 11.4452 0.21 0.21 22.0929 11.4452 11.4452 22.0929

3.15

7.4189

2.015 m 2.19 m 8.06

CARGAS PUNTUALES EN Y 11.1118 42.5348

10.6512

y - 1.22 m - 1.42 m 2.84

UBICACIÓN DEL PUNTO DE LA EXCENTRICIDAD Y

X

-0.7720

My= 0.0000 Ҽx= My P

Mx= -67.6711 Ҽx= 0.0000 87.6536 Ҽx= 0.0000

Ҽy= Mx P

Ҽy= -67.6711 87.6536 Ҽy= -0.7720

CÁLCULO DE MOMENTOS Y EXCENTRICIDADES COLUMNA TIPO C-1 (Area Tributaria 14) En el Plano Columna Viga x Viga y Losa Muro y

5.48 2.74

3.65

3.65

CM=

7.3

CM

CV

CM

Ps=

Veces 1 4 4 3 3 2 1 1 1

EJE X Columna Losa Losa Viga Viga Aula Lab. Enfer. Lab. Niño Proscenio

Largo (m)

Veces 1 4 4 4 3 3

EJE Y Columna Losa Viga Viga Muro Muro

Largo (m)

Alto (m) 11.7

3.65 3.65

2.44 2.44 2.44 2.44

Alto (m) 11.7

3.15 3.15

Peso 6.7392 11.0376 5.6218 47.9240 16.6018

Aula Lab. Enfer. Lab. Niño Proscenio

19.9684 6.0006 6.0006 11.9810

87.9244

CV=

43.9506

CM+CV =

CARGAS PUNTUALES EN X 5.5188

30.0030

ϪP.e (Tn/m³) 2.4 0.3 0.3 2.4 2.4 0.25 0.3 0.3 0.3

Peso (Tn) 6.7392 24.0024 24.0024 5.5188 5.5188 19.9684 6.0006 6.0006 11.9810

C.g 0 -1.825 1.825 -1.925 1.925 0 -1.825 1.825 0

Area (m²) 0.24 39.9367 0.12 0.12

ϪP.e (Tn/m³) 2.4 0.3 2.4 2.4 0.36 0.36

Peso (Tn) 6.7392 47.9240 2.8109 2.8109 8.3009 8.3009

C.g 0 0 -1.52 1.52 1.52 -1.52

30.0030

5.5188

x - 1.825 m - 1.925 m

131.8749

Area (m²) 0.24 20.0020 20.0020 0.21 0.21 39.9367 20.0020 20.0020 39.9367

6.7392

1.825 m 1.925 m 7.3

CARGAS PUNTUALES EN Y 11.1118

6.7392

11.1118

y 1.52 m

- 1.52 m 5.48

UBICACIÓN DEL PUNTO DE LA EXCENTRICIDAD

2 1 1 1

CV

Aula Lab. Enfer. Adm. Enf. Proscenio

20.0020 20.0020 20.0020 20.0020

0.25 0.3 0.3 0.3

10.0010 6.0006 6.0006 6.0006

0 0 0 0

Y

X My= ∑ Wx * X1

Mx= ∑ Wy * Y1 My= 0.0000

Ҽx= My P

Mx= 0.0000 Ҽx= 0.0000 131.8749 Ҽx= 0.0000

Ҽy= Mx P

Ҽy= 0.0000 131.8749 Ҽy= 0.0000

CÁLCULO DE MOMENTOS Y EXCENTRICIDADES COLUMNA TIPO C-2 (Area Tributaria 16) En el Plano Columna Viga x Viga y Losa

1.55

Peso 4.7816 6.9350 0.6624 11.9863

CARGAS PUNTUALES EN X

Pasadizo

15.9818

24.3654

CV=

15.9818

3.4906

14.0182

4.7816

13.8446

x CM= 3.23

3.19

Ps=

CM+CV =

- 1.615 m - 1.715 m

40.3471

1.595 m 1.695 m

6.42 6.42

CM

CV

Veces 1 4 4 4 4 4 4

EJE X Columna Losa Losa Viga Viga Pasadizo Pasadizo

Largo (m)

Alto (m) 15.85

3.03 2.99

Area (m²) 0.1257 5.0065 4.9445 0.12 0.12 5.0065 4.9445

ϪP.e (Tn/m³) 2.4 0.3 0.3 2.4 2.4 0.4 0.4

Peso (Tn) 4.7816 6.0078 5.9334 3.4906 3.4445 8.0104 7.9112

C.g 0 -1.615 1.595 -1.715 1.695 -1.615 1.595

CARGAS PUNTUALES EN Y 4.7816

27.9681

0.6624

y 0.575 m 0.775 m

Veces EJE Y Largo (m) 1 W Columna CM

Alto (m) 15.85

Area (m²) 0.1257

ϪP.e (Tn/m³) 2.4

Peso (Tn) 4.7816

C.g 0

1.55

3.4445

CM CV

4 4 4

W Losa W Viga Pasadizo

9.9886 0.06 9.9886

1.15

My= ∑ Wx * X1

0.3 2.4 0.4

11.9863 0.6624 15.9818

0.575 0.775 0.575

My= -0.7052

Ҽx= My P

UBICACIÓN DEL PUNTO DE LA EXCENTRICIDAD

Ҽx= -0.7052 40.3471 Ҽx= -0.0175

Mx= ∑ Wy * Y1

Y

Mx= 16.5950 -0.0175

Ҽy= Mx P

Ҽy= 16.5950 40.3471 Ҽy= 0.4113

0.4113

X

CÁLCULO DE MOMENTOS Y EXCENTRICIDADES COLUMNA TIPO C-2 (Area Tributaria 17) En el Plano Columna Viga x Viga y Losa

1.55

Peso 4.7816 4.7002 0.6624 8.2985

CARGAS PUNTUALES EN X

Pasadizo

11.0646

18.4427

CV=

11.0646

3.4560

13.8880

4.7816

5.5552

x CM= 3.2

1.28

Ps=

CM+CV =

- 1.6 m - 1.7 m

29.5073

0.64 m 0.74 m

4.48 4.48

CM

CV

Veces 1 4 4 4 4 4

EJE X Columna Losa Losa Viga Viga Pasadizo

Largo (m)

3 1.08

Alto (m) 15.85

Area (m²) 0.1257 4.96 1.984 0.12 0.12 4.96

ϪP.e (Tn/m³) 2.4 0.3 0.3 2.4 2.4 0.4

Peso (Tn) 4.7816 5.9520 2.3808 3.4560 1.2442 7.9360

C.g 0 -1.6 0.64 -1.7 0.74 -1.6

CARGAS PUNTUALES EN Y 4.7816

y

19.3631

0.6624

1.2442

CV

4

Pasadizo

1.984

0.4

3.1744

0.64

0.575 m 0.775 m

CM CV

Veces 1 4 4 4

EJE Y Columna Losa Viga Pasadizo

Largo (m)

My= ∑ Wx * X1 Ҽx= My P

Mx= ∑ Wy * Y1

1.15

Alto (m) 15.85

Area (m²) 0.1257 6.9154 0.06 6.9154

ϪP.e (Tn/m³) 2.4 0.3 2.4 0.4

My= -23.6200

Peso (Tn) 4.7816 8.2985 0.6624 11.0646

C.g 0 0.575 0.775 0.575

1.55

UBICACIÓN DEL PUNTO DE LA EXCENTRICIDAD

Ҽx= -23.6200 29.5073 Ҽx= -0.8005

Y

Mx= 11.6472 -0.8005

Ҽy= Mx P

Ҽy= 11.6472 29.5073 Ҽy= 0.3947

0.3947

X

CÁLCULO DE MOMENTOS Y EXCENTRICIDADES COLUMNA TIPO C-3 (Area Tributaria 19) En el Plano Columna Viga x Viga y Losa Muro x Muro y

5.48 2.74 3.6

0.4

1.3

5.3

CM=

Peso 9.1296 7.4088 2.3424 35.1446 0.6581 10.3761

Aula Lab. Niño Pasadizo Deposito Sala Conf. Pasadizo

10.4120 6.2472 1.6440 1.2330 8.7862 6.5760

65.0597

CV=

34.8984

Ҽx= My P Ҽx= -77.1803 99.9580 Ҽx= -0.7721 CARGAS PUNTUALES EN X

5.4432 Ps=

CM

CV

CM

CV

Veces 1 4 4 3 3 1 2 1 1 1 1 2

EJE X Columna Losa Losa Viga Viga Muro Aula Lab. Niño Pasadizo Deposito Sala Conf. Pasadizo

Largo (m)

Veces 1 4 4 4 3 3 2 1 1 1 1 2

EJE Y Columna Losa Viga Viga Muro Muro Aula Lab. Niño Pasadizo Deposito Sala Conf. Pasadizo

Largo (m)

3.6 1.3 1.3

Alto (m) 15.85

Area (m²) 0.24 20.824 8.22 0.21 0.21

2.25 20.824 20.824 4.11 4.11 29.2872 8.22

2.44 2.44 2.44 2.44

Alto (m) 15.85

Area (m²) 0.24 29.2872 0.12 0.12

3.15 3.15 20.824 20.824 4.11 4.11 29.2872 8.22

CM+CV =

41.6480

8.7862 9.1296

19.3170

2.6237

99.9580

ϪP.e (Tn/m³) 2.4 0.3 0.3 2.4 2.4 0.225 0.25 0.3 0.4 0.3 0.3 0.4

Peso (Tn) 9.1296 24.9888 9.8640 5.4432 1.9656 0.6581 10.4120 6.2472 1.6440 1.2330 8.7862 6.5760

C.g 0 -1.7 0.55 -2 0.85 0.85 -1.7 -1.7 0.55 0.55 -0.95 0.55

ϪP.e (Tn/m³) 2.4 0.3

Peso (Tn) 9.1296 35.1446 1.1712 1.1712 5.1881 5.1881 10.4120 6.2472 1.6440 1.2330 8.7862 6.5760

C.g 0 0 -1.52 1.52 -1.52 1.52 0 0 -1.37 1.37 0 0

0.225 0.225 0.25 0.3 0.4 0.3 0.3 0.4

Ҽy= Mx P Ҽy= -0.5631 99.9580 Ҽy= -0.0056

-0.95 m

x

- 1.70 m - 2.00 m

0.55 m 0.85 m

5.3 CARGAS PUNTUALES EN Y 1.6440 6.3593

1.2330 6.3593

9.1296

y -1.37 m - 1.52 m

1.37 m 1.52 m

5.48 UBICACIÓN DEL PUNTO DE LA EXCENTRICIDAD Y

-0.7721 -0.0056

X

My= ∑ Wx * X1

Mx= ∑ Wy * Y1

My= -77.1803

Mx= -0.5631

CÁLCULO DE MOMENTOS Y EXCENTRICIDADES COLUMNA TIPO C-3 (Area Tributaria 20) En el Plano Columna Viga x Viga y Losa Muro y

2.84

Peso 10.6512 10.5638 4.0992 19.4107 2.9201

Aula Deposito Lab. Niño Sala Conf. Pasadizo

5.7368 3.4421 1.6188 4.8527 4.3168

CARGAS PUNTUALES EN X

47.6450

CV=

19.9672

7.4390

22.9472 4.8527

10.6512

12.4108

3.1248

x 4.04

1.9

CM=

5.94

CM

CV

CM

CV

Ps=

Veces 1 4 4 4 4 2 1 1 1 2

EJE X Columna Losa Losa Viga Viga Aula Lab. Niño Deposito Sala Conf. Pasadizo

Largo (m)

Veces 1 4 3 1 2 1 2 1 1 1

EJE Y Columna Losa Viga Viga Muro Muro Aula Lab. Niño Deposito Sala Conf.

Largo (m)

Alto (m) 15.85

3.69 1.55

2.44 2.44 1.24 1.64

Alto (m) 15.85

CM+CV =

67.6122

Area (m²) 0.28 11.4736 5.3960 0.21 0.21 11.4736 11.4736 5.3960 16.1756 5.3960

ϪP.e (Tn/m³) 2.4 0.3 0.3 2.4 2.4 0.25 0.3 0.3 0.3 0.4

Peso (Tn) 10.6512 13.7683 6.4752 7.4390 3.1248 5.7368 3.4421 1.6188 4.8527 4.3168

C.g 0 -2.02 0.95 -2.195 1.125 -2.02 -2.02 0.95 -1.07 0.95

Area (m²) 0.28 16.1756 0.12 0.24

ϪP.e (Tn/m³) 2.4 0.3 2.4 3.4 0.225 0.225 0.25 0.3 0.3 0.3

Peso (Tn) 10.6512 19.4107 2.1082 1.9910 1.7577 1.1624 5.7368 3.4421 1.6188 4.8527

C.g 0 -1.22 -1.42 -1.42 -2.02 -1.82 -1.22 -1.22 -1.22 -1.22

3.15 3.15 11.4736 11.4736 5.3960 16.1756

- 1.07 m - 2.02 m

0.95 m 1.125 m

- 2.195 m 5.94

CARGAS PUNTUALES EN Y

1.7577

1.1624 4.0992 39.3779

10.6512

y - 1.22 m - 1.42 m - 1.82 m - 2.02 m 2.84

UBICACIÓN DEL PUNTO DE LA EXCENTRICIDAD Y

CV 2

Pasadizo

5.3960

My= ∑ Wx * X1

0.4

4.3168

-1.22

Mx= ∑ Wy * Y1

X -0.8804

My= -52.5687

Mx= -59.5279 -0.7775

Ҽx= My P

Ҽx= -52.5687 67.6122 Ҽx= -0.7775

Ҽy= Mx P

Ҽy= -59.5279 67.6122 Ҽy= -0.8804

CÁLCULO DE MOMENTOS Y EXCENTRICIDADES COLUMNA TIPO C-3 (Area Tributaria 21) En el Plano Columna Viga x Viga y Losa Muro y

2.84

Peso 10.6512 Aula 7.4390 Lab. Mujer 2.8109 Sala Conf. 14.2121 Deposito 3.4871 Pasadizo

CARGAS PUNTUALES EN X 3.5358 2.1215 3.5530 1.6188 4.3168

3.1248

12.4108

10.6512

3.553 14.1432

4.3142

x 1.9

2.49

CM=

4.39

CM

CV

CM

Ps=

Veces 1 4 4 4 4 2 1 1 1 2

EJE X Largo (m) Columna Losa Losa Viga 1.55 Viga 2.14 Aula Lab. Mujer Sala Conf. Deposito Pasadizo

Alto (m) 15.85

Veces 1 4 4 1 2

EJE Y Columna Losa Viga Muro Muro

Alto (m) 15.85

Largo (m)

2.44 2.44 1.24

3.15 3.15

38.6003 CM+CV =

CV=

15.1459

- 0.95 m -1.125 m

53.7462

Area (m²) 0.28 5.396 7.0716 0.21 0.21 7.0716 7.0716 11.843 5.396 5.396

ϪP.e (Tn/m³) 2.4 0.3 0.3 2.4 2.4 0.25 0.3 0.3 0.3 0.4

Peso (Tn) 10.6512 6.4752 8.4859 3.1248 4.3142 3.5358 2.1215 3.5530 1.6188 4.3168

C.g 0 -0.95 1.245 -1.125 1.42 1.245 1.245 0.295 -0.95 -0.95

Area (m²) 0.28 11.8434 0.12

ϪP.e (Tn/m³) 2.4 0.3 2.4 0.225 0.225

Peso (Tn) 10.6512 14.2121 2.8109 1.7294 1.7577

C.g 0 -1.22 -1.42 -1.42 -2.02

0.295 m 1.245 m 1.42 m 4.39

CARGAS PUNTUALES EN Y 1.7577

4.5402 27.9264

10.6512

y - 1.22 m - 1.42 m - 2.02 m 2.84

2 1 1 1 2

CV

Aula Lab. Mujer Sala Conf. Deposito Pasadizo

7.0716 7.0716 5.396 7.0716 5.396

0.25 0.3 0.3 0.3 0.4

3.5358 2.1215 1.6188 2.1215 4.3168

-1.22 -1.22 -1.22 -1.22 -1.22

UBICACIÓN DEL PUNTO DE LA EXCENTRICIDAD Y

X My= ∑ Wx * X1

Mx= ∑ Wy * Y1

-0.8199

My= 9.4770 Ҽx= My P

0.1763

Mx= -44.0679 Ҽx= 9.4770 53.7462 Ҽx= 0.1763

Ҽy= Mx P

Ҽy= -44.0679 53.7462 Ҽy= -0.8199

CÁLCULO DE MOMENTOS Y EXCENTRICIDADES COLUMNA TIPO C-1 (Area Tributaria 22) En el Plano Columna Viga x Viga y Losa Muro y

5.48 2.74 1.32

0.4

Peso 9.1296 7.1366 2.3424 25.5830 13.8348

Aula Lab.Enf. Adm. Enf. Deopsito Pasadizo

6.6308 3.9785 2.0824 3.3154 9.9955

CARGAS PUNTUALES EN X

58.0265

CV=

26.0026

2.6611

CM=

- 0.76 m - 0.86 m

3.94 Ps=

CM

CV

Veces 1 4 4 4 4 2 1 1 1 3

EJE X Columna Losa Losa Viga Viga Aula Lab.Enf. Adm. Enf. Deopsito Pasadizo

Largo (m)

1.32 2.22

Alto (m) 15.85

Area (m²) 0.24 8.3296 13.2616 0.21 0.21 13.2616 13.2616 8.33 13.2616 8.33

ϪP.e (Tn/m³) 2.4 0.3 0.3 2.4 2.4 0.25 0.3 0.25 0.25 0.4

CM+CV =

Peso (Tn) 9.1296 9.9955 15.9139 2.6611 4.4755 6.6308 3.9785 2.0824 3.3154 9.9955

9.1296

84.0291

C.g 0 -0.76 1.21 -0.86 1.31 1.21 1.21 -0.76 1.21 -0.76

29.8386

x

2.22

.

22.0734

1.21 m 1.31 m 3.94

CARGAS PUNTUALES EN Y 8.0886

9.1296

8.0886

y 1.52 m - 1.52 m 5.48

4.4755

CM

CV

Veces 1 4 4 4 4 4 2 1 1 1 3

EJE Y Columna Losa Viga Viga Muro Muro Aula Lab.Enf. Adm. Enf. Deopsito Pasadizo

Largo (m)

2.44 2.44 2.44 2.44

Alto (m) 15.85

Area (m²) 0.24 21.3192 0.12 0.12

3.15 3.15 13.2616 13.2616 8.3296 13.2616 8.3296

ϪP.e (Tn/m³) 2.4 0.3

0.225 0.225 0.25 0.3 0.25 0.25 0.4

Peso (Tn) 9.1296 25.5830 1.1712 1.1712 6.9174 6.9174 6.6308 3.9785 2.0824 3.3154 9.9955

C.g 0 0 -1.52 1.52 -1.52 1.52 0 0 0 0 0

UBICACIÓN DEL PUNTO DE LA EXCENTRICIDAD Y

X 0.2726

My= ∑ Wx * X1

Mx= ∑ Wy * Y1 My= 22.9033

Ҽx= My P

Mx= 0.0000

Ҽx= 22.9033 84.0291 Ҽx= 0.2726

Ҽy= Mx P

Ҽy= 0.0000 84.0291 Ҽy= 0.0000

CÁLCULO DE MOMENTOS Y EXCENTRICIDADES COLUMNA TIPO C-2 (Area Tributaria 24) En el Plano Columna Viga x Viga y Losa

1.55

Peso 4.7816 4.6426 0.6624 8.2252

CARGAS PUNTUALES EN X

Pasadizo

10.9669

18.3117

CV=

10.9669

1.2557

5.5986

4.7816

13.6276

x CM= 1.29

3.14

Ps=

CM+CV =

- 0.645 m - 0.745 m

29.2786

1.57 m 1.67 m

4.43 4.43

CM

CV

Veces 1 4 4 4 4 4

EJE X Columna Losa Losa Viga Viga Pasadizo

Largo (m)

1.09 2.94

Alto (m) 15.85

Area (m²) 0.1257 1.9995 4.867 0.12 0.12 1.9995

ϪP.e (Tn/m³) 2.4 0.3 0.3 2.4 2.4 0.4

Peso (Tn) 4.7816 2.3994 5.8404 1.2557 3.3869 3.1992

C.g 0 -0.645 1.57 -0.745 1.67 -0.645

CARGAS PUNTUALES EN Y 4.7816

y

19.1920

0.6624

3.3869

CV

4

Pasadizo

4.867

0.4

7.7872

1.57

0.575 m 0.775 m

CM CV

Veces 1 4 4 4

EJE Y Largo (m) W Columna W Losa W Viga 1.15 Pasadizo

Alto (m) 15.85

Area (m²) 0.1257 6.8543 0.06 6.8543

My= ∑ Wx * X1

ϪP.e (Tn/m³) 2.4 0.3 2.4 0.4

Peso (Tn) 4.7816 8.2252 0.6624 10.9669

C.g 0 0.575 0.775 0.575

1.55

My= 22.5048

Ҽx= My P

UBICACIÓN DEL PUNTO DE LA EXCENTRICIDAD

Ҽx= 22.5048 29.2786 Ҽx= 0.7686

Mx= ∑ Wy * Y1

Y

Mx= 11.5488 0.7686

Ҽy= Mx P

Ҽy= 11.5488 29.2786 Ҽy= 0.3944

0.3944

X

CÁLCULO DE MOMENTOS Y EXCENTRICIDADES COLUMNA TIPO C-2 (Area Tributaria 25) y

1.55 m

En el Plano Columna Viga x Viga y Losa

Peso (Tn) 4.7816 3.3984 0.6624 6.1480

CARGAS PUNTUALES EN X 3.3984

14.3452

x y

CM=

x

Pasadizo

1.475 m 1.675 m

14.9904 8.1973

3.35 m

3.35 m CV= Ps=

8.1973 CM+CV =

23.1877 CARGAS PUNTUALES EN Y

4.7816

CM CV

Veces 1 4 4 4

EJE X Columna Losa Viga Pasadizo

Largo (m)

Veces 1 4 4 4

EJE Y Columna Losa Viga Pasadizo

Largo (m)

Alto (m) 15.85

2.95

Area (m²) 0.1257 5.1233 0.12 5.1233

ϪP.e (Tn/m³) 2.4 0.3 2.4 0.4

Peso (Tn) 4.7816 6.1480 3.3984 8.1973

C.g 0 1.475 1.675 1.475

Area (m²) 0.1257 5.1233 0.06 5.1233

ϪP.e (Tn/m³) 2.4 0.3 2.4 0.4

Peso (Tn) 4.7816 6.1480 0.6624 8.1973

C.g 0 0.575 0.775 0.575

4.7816

14.3452

0.6624

y 0.575 m

CM CV

My= ∑ Wx * X1

Alto (m) 15.85

1.15

1.55 m

My= (4.78*0.0) + (6.23*1.49) + (3.43*1.69) +(8.31*1.49) My= 26.8515

Ҽx= My P

Mx= ∑ Wy * Y1

0.75 m

UBICACIÓN DEL PUNTO DE LA EXCENTRICIDAD

Ҽx= 26.8515 23.1877 Ҽx= 1.1580

Y

Mx= (4.78*0.0) + (6.23*0.58) + (0.66*0.78) +(8.31*.575) Mx= 8.7619

1.1580 0.3779

Ҽy= Mx P

Ҽy= 8.7619 23.1877 Ҽy= 0.3779

CÁLCULO DE MOMENTOS Y EXCENTRICIDADES COLUMNA TIPO C-1 (Area Tributaria 27)

5.48 2.74

En el Plano Columna Viga x Viga y Losa Muro y CM=

Peso 9.1296 5.0652 5.6218 Aula 33.4728 Lab. Mujer 24.2438 Sala Conf.

13.9470 6.9735 6.9735

77.5332

27.8940

CV=

CARGAS PUNTUALES EN X 33.4728

61.3668

x -2.35 m -2.55 m

5.0652

X

5.1

CV

CM

CV

EJE X Largo (m) Columna Losa Viga 3.35 Aula Lab. Mujer Sala Conf.

Alto (m) 15.85

Veces EJE Y Largo (m) Columna 1 Losa 4 Losa 4 Viga 2.44 4 Viga 2.44 4 Muro 2.44 4 Muro 2.44 4 2 Aula 1 Lab. Mujer 1 Sala Conf.

Alto (m) 15.85

My= ∑ Wx * X1 Ҽx= My P

Mx= ∑ Wy * Y1 Ҽy= Mx P

CM+CV =

Area (m²) 0.24 27.894 0.21 27.894 27.894 27.894

ϪP.e (Tn/m³) 2.4 0.3 2.4 0.25 0.25 0.25

Peso (Tn) 9.1296 33.4728 5.0652 13.9470 6.9735 6.9735

Area (m²) 0.24 13.9740 13.9740 0.12 0.12

ϪP.e (Tn/m³) 2.4 0.3 0.3 2.4 2.4 0.36 0.36 0.25 0.25 0.25

Peso (Tn) 9.1296 16.7688 16.7688 2.8109 2.8109 12.1219 12.1219 13.9470 6.9735 6.9735

3.45 3.45 27.894 27.894 27.894

105.4272

5.1

C.g 0 -2.35 -2.55 -2.35 -2.35 -2.35

C.g

CARGAS PUNTUALES EN Y 14.9328 16.7688

14.9328 16.7688

y

0 1.37 -1.37 1.52 -1.52 1.52 -1.52

0 0 0

9.1296

- 1.37 m

1.37 m

- 1.52 m

1.52 m 5.48

UBICACIÓN DEL PUNTO DE LA EXCENTRICIDAD Y

My= -157.1282 Ҽx= -157.1282 105.4272 Ҽx= -1.4904

Mx= 0.0000 Ҽy= 0.0000 105.4272 Ҽy= 0.0000

Ҽx= -1.4904 Ҽy= 0.0000

CM

Veces 1 4 3 2 1 1

Ps=

X

CÁLCULO DE MOMENTOS Y EXCENTRICIDADES COLUMNA TIPO C-2-1 CÁLCULO DE EXCENTRICIDADES COLUMNAS TIPO C-2-1 8132.7 Tn 1718.47 Tn CV

CÁLCULO DE CM 8132.7 1173.21 x 22.9075 CÁLCULO DE CV 1718.47 1173.2121 x 22.9075

CM

ÁREA TRIBUTARI A

22.9075

AREA TOTA 1173.2121

5.9500 3.8500

T S

m2 m2 m m

x

=

158.79

x

=

33.554

S'=S-2e1= T'=T-2e2=

0.88 4.03

CÁLCULO DE ÁREA REDUCIDA Y e2

C-2-1

S'

C-2-1

e 1

T= 5.95

X

P T'

S= 3.85 UBICACIÓN DEL PUNTO DE LA EXCENTRICIDAD T= 5.95 Y CÁLCULO DE LAS EXCENTRICIDADES EJE X 192.35

CÁLCULO DE LAS EXCENTRICIDADES EJE Y 192.35 0.96

2.98

2.98

Ray

1.925 RBy

∑▒ 〖� � =� 〗

∑▒ 〖� � =� 〗

Mizq. = Mder. =

Cálculo de las reacciones

RBy

96.17

RAy = 96.17 Cálculo de los momentos 286.12 286.12 Cálculo de las excentricidades

e1= 286.12 192.35

1.49

1.925

Ray

RBy

S' '

1.49

Cálculo de las reacciones

∑▒ 〖�� =� 〗

RBy

∑▒ 〖� � =� 〗

96.17

RAy = 96.17 Cálculo de los momentos

Mizq. = Mder. =

185.14 185.14 Cálculo de las excentricidades

e2= 185.14 192.35

0.96

X T'

* DISEÑO DE UNA ZAPATA AISLADA * Datos de la Zapata: CM: CV: ɣc: ɣs: F'c: S/Cpiso: σ(ult): fy: P

87.92 43.95 2.30 1.95 210.00 500.00 3.50 4200.00 131.87

* Datos de la Columna: F'c: t1 t2

280.00 60.00 40.00

GRAFICA

Tn Tn Tn/m3 Tn/m3 Kg/cm2 Kg/cm2 Kg/cm2 Kg/cm2 Tn

N.P.T + 0.30

N.T.N ± 0.00 0.15

hf: 2.00

Df:

Kg/cm2 cm cm

* Datos de la Terreno:

N.F.C-1.95 σ(ult):

NPT NTN NFC

0.15 0.00 -1.85

m m m

* Esfuezo neto del terreno:

* Dimenciones de la Zapata:

�_𝑛 = �_𝑎𝑑𝑚 − ɣ𝑝𝑟𝑜𝑚 ∗ ℎ𝑓 − 𝑆/𝐶

𝑇 =√(�_𝑍 )+ (𝑡_1−𝑡_2)/2

�_𝑎𝑑𝑚 = �_𝑢𝑙𝑡/𝐹_𝑠 σn =

7.2142

* Area de la Zapata: �_𝑍 = 𝑃/�_𝑛

3.50

Tn/m2

𝑆 =√(�_𝑍 ) − (𝑡_1−𝑡_2)/2

T= 4.3755



T=

4.40

m

S= 4.1755



S=

4.20

m

Az =

18.48

m2

* Nueva Area de la Zapata: * Debe Cumplir: �_𝑣1= �_𝑣2

�_𝑣1= (𝑇 − 𝑡_1)/2

1.85

�_𝑍 = 𝑃/�_𝑛 Az = 18.2800 m2

�_𝑣1= �_𝑣2

�_𝑣1= (𝑇 − 𝑡_1)/2 �_𝑣2= (𝑆 − 𝑡_1)/2

Lv1 =

1.9

m Cumple

Lv2 =

1.9

m

ok !!

* DISEÑO POR PUNZONAMIENTO: 0.60 +d

�_𝑛𝑢= 𝑃_𝑢/�_𝑧 𝑃_𝑢= 1.7 𝐶𝑚+1.4 𝐶𝑣

m

Pu = 197.81006 Tn

S = 4.20

0.40

n

0.40 +d Wnu = 10.7040 Tn/m2

0.60

T = 4.40 * CONDICION DE DISEÑO: �_𝑈/∅ ≤ �_𝐶

Ø = 0.85

* Escogemos el menor de los dos: Vc=0.27(2+4/β) √( 〖𝑓 _� 〗 ^′ ) bod

〖� _𝑈 = 𝑃 〗 _𝑈− �_𝑛𝑢 ∗𝑚 ∗𝑛 Vu = Vu = Vu = Vu =

197.81006 − 10.7040 197.81006 − 10.7040 197.81006 − 2.5690 195.2411 − 10.7040

x (0.60 + d ) ( 0.40 + d ) x (0.24 + 1.00 d + d² ) − 10.7040 d − 10.7040 d² d −10.7040 d² 1

2

0.27 x

4

0.60 0.40 =

* Usamos:

+



+

( 307.2172d 261.1346 d d



+ +

��=1.06√( 〖𝑓 _� 〗 ^′ ) 𝑏𝑜d =

1.06

ok !!

* bo = 2m + 2n

1.26 Vc = Vc = Vc =

x 2 (0.60 +d + 0.40 + d ) d 1.06 210 x 10 307.2172 ( 1.00 + 2 d ) d + 307.2172 d 614.4344 d² 2

* Reemplazando 1 y 2 195.2411 − 10.7040 d −10.7040 d² ≤ 195.2411 − 10.7040 d −10.7040 d² ≤

^

614.4344 d² ) * 0.85 522.2692 d²

532.9732



+

271.8386

d



d= d=

ℎ_𝑧 = d + ∅/2 +r

195.2411 ≥ 0 0.4018 -0.9118

ℎ_𝑧 = d + ∅/2 +r

hz = 0.4018

+ (3/4")

hz = 0.48133 𝑑 = ℎ_𝑧 − ∅/2 −r d=

0.50

− (3/4")

d=

0.42

m

+

0.0254 2 ≈

0.07 hz =



0.0254 2

0.50

m

0.07

* VERIFICACION POR CORTANTE: �_𝑛 ≤ �_�

�_𝑛= �_𝑢𝑑/∅

�_�=0.53 √( 〖𝑓 _� 〗 ^′ ) ∗𝑆 ∗𝑑

Ø = 0.85

�_𝑢𝑑= �_𝑛𝑢 ∗𝑆 ∗(�_𝑣 −𝑑) Vud = 10.7040 * 4.20 Vud = 66.53611 Tn

Vc = Vc =

* ( 1.9



0.53 210 x 10 x 4.20 x 0.42 135.4828 Tn �_𝑛 ≤ �_�

0.42 )

78.277776

Vn = 66.53611 0.85 Vn = 78.277776 Tn



135.4828

Cumple

ok !!

* DISEÑO POR FLEXION: �_𝑢= �_𝑛𝑢 ∗ 𝑆∗ 〖� _𝑣 〗 ^2/2 Mu = 10.7040

* 4.20 *

Mu = 81.1471 Tn - m

Ø = 0.9 ( 1.9 )² 2

𝑎= (2𝑑 ± √(4 𝑑^2 −(8 �_𝑢)/(0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ ∅ ∗𝑆)))/2

a= a=

0.8103 0.0297

〖�𝑠〗 _𝑚𝑖𝑛=0.22 ∗√( 〖𝑓 _� 〗 ^′/10.197)/( 〖𝑓 _� 〗 ^′/10.197) ∗𝑆 ∗𝑑

a=

0.0297

m

〖�𝑠〗 _𝑚𝑖𝑛=0.22 ∗√( 〖𝑓 _� 〗 ^′/10.197)/( 〖𝑓 _� 〗 ^′/10.197) ∗𝑆 ∗𝑑

�_𝑠= �_𝑢/(∅ ∗ 〖𝑓 _� 〗 ^′∗(𝑑−𝑎/2)) 81.1471

As = 0.9

*

4.2 *

As =

0.42 − 0.0297 2

52.9854

0.22 *

As min =

210 10.197 4200 10.197

* 4.20

* 0.42

As min = 0.004276 m2 As min = 42.76 cm2

cm2

�_𝑠> 〖�𝑠〗 _𝑚𝑖𝑛

52.9854 > 42.76

*VARILLAS LONGITUDINALES Diametro(ø) =

0.75

〖𝑛 ^° 〗 _𝑣= �_𝑠/�_∅

n°v =

Cumple

Pulg.

52.9854 2.8502

n°v = 18.5899



n°v =

19

varillas

* Separación 𝑠= (𝑆 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)

s=

4.20 − 0.75 * 0.0254 − 2* 0.07 − 19

s=

0.2245

m

1

s=

22.4497



*VARILLAS TRANSVERSALES Diametro(ø) =

0.75

Pulg.

�_𝑠 (𝑇)= �_𝑠∗𝑇/𝑆 〖𝑛 ^° 〗 _𝑣= �_(𝑠(𝑇))/�_∅

As(T) =

n°v =

52.9854 *

55.5086 2.8502

4.40 4.20 n°v = 19.4751

* Separación 𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)



* 0.0254 − 2*

As(T) =



55.5086

n°v =

cm2

20

varillas

s=

22

cm

ok !!

𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)

s=

4.40 − 0.75 * 0.0254 − 2* 0.07 − 20

s=

0.2232

m

1

s=

22.3208

s=



22

cm

* VERIFICACION POR APLASTAMIENTO: *COLUMNA - ZAPATA 𝑃_𝑛 < 𝑃_𝑛𝑏

�_1= 𝑡_(1 )∗ 𝑡_2

Ø = 0.7

A1 = A1 =

𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_1 Pnb = Pnb =

0.85 * 280 571.2 Tn

0.60 0.24

*

𝑃_𝑛= 𝑃_𝑢/∅

0.40 m2

𝑃_𝑛 < 𝑃_𝑛𝑏

Pn = 197.81006 0.7 Pn = 282.5858 Tn

* 10 * 0.24

282.5858

<

Cumple

571.2

* ZAPATA - SUELO 𝑃_𝑛𝑏 > 𝑃_𝑛

𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_0

�_2=𝑇 ∗𝑋_1

√(�_2/�_1 ) ≤2 → �_0= √(�_2/�_1 ) ∗ �_1 Si:

𝑋_1=𝑇 ∗𝑡_2/𝑡_1

X1

√(�_2/�_1 ) >2 → �_0=2∗�_1

T Donde:

A2 = A2 =

4.4000 * 2.9333 12.9067 m2 A0 =

Pnb = Pnb =

0.85 * 210 856.8 Tn

* 10 * 0.48

2 * 0.24 𝑃_𝑛𝑏 > 𝑃_𝑛

856.8 * PARA ZONA SISMICA (DOWELLS) 𝑃_𝑛 ≤ 𝑃_𝑛𝑏

〖�𝑠〗 _𝑚𝑖𝑛=0.005 ∗ �_1

4.4000 0.24

>

282.5858

= 18.3333

A0 =

0.48

Cumple

ok !!

>

m2

2

X1 =

4.40

X1 =

2.9333

*

0.40 0.60 m

ok !!

〖�𝑠〗 _𝑚𝑖𝑛=0.005 ∗ �_1 As min = 0.005 * 2400 As min = 12 cm2 Diametro(ø) = 4

1

* 5.0671

Pulg. =

20.2683

cm2

Cumple

ok !!

* PLANOS DE PLANTA Y PERFIL:

20 ø3/4" @ 22

S = 4.20 19

ø3/4" @

T = 4.40

DOWELLS

4 ø 1"

VARILLAS TRANSVERSALES 20 ø3/4" @ 22 cm

VARILLAS LONGITUDINALES 19 ø3/4" @ 22 cm

22

d = 0.42

hz = 0.50

T = 4.40

* DISEÑO DE UNA ZAPATA AISLADA CON EXCENTRICIDADES * Datos de la Zapata N° 5: CM: CV: ɣc: ɣs: F'c: S/Cpiso: σ(ult): fy: P

45.58 17.69 2.30 1.95 210.00 500.00 3.50 4200.00 63.27

* Datos de la Columna: F'c: t1 t2

280.00 70.00 40.00

GRAFICA

Tn Tn Tn/m3 Tn/m3 Kg/cm2 Kg/cm2 Kg/cm2 Kg/cm2 Tn

N.P.T + 0.30

N.T.N ± 0.00 0.15

hf: 2.00

Df:

Kg/cm2 cm cm

* Datos de la Terreno:

N.F.C-1.95 σ(ult):

NPT NTN NFC

0.15 0.00 -1.85

m m m

* Esfuezo neto del terreno:

* Dimenciones de la Zapata:

�_𝑛 = �_𝑎𝑑𝑚 − ɣ𝑝𝑟𝑜𝑚 ∗ ℎ𝑓 − 𝑆/𝐶

𝑇 =√(�_𝑍 )+ (𝑡_1−𝑡_2)/2

�_𝑎𝑑𝑚 = �_𝑢𝑙𝑡/𝐹_𝑠 σn =

7.2142

* Area de la Zapata:

3.50

Tn/m2

𝑆 =√(�_𝑍 ) − (𝑡_1−𝑡_2)/2

T= 3.1116



T=

3.15

m

S= 2.8116



S=

2.85

m

Az =

8.9775

m2

* Nueva Area de la Zapata: * Debe Cumplir: �_𝑣1= (𝑇 − 𝑡_1)/2

1.85

�_𝑣1= �_𝑣2

�_𝑍 = 𝑃/�_𝑛 Az =

8.7709

m2

�_𝑣1= (𝑇 − 𝑡_1)/2

Lv1 =

1.225

m Cumple

�_𝑣2= (𝑆 − 𝑡_1)/2

Lv2 =

1.225

ok !!

m

* EFECTOS DE CARGA EXCENTRICA: e1 = 0.86 e2 = 0.72

e1

�_2= �/6

T 6

= 0.5250

e2

>

T 6

�_1= 𝑆/6

S 6

= 0.4750

e1

>

T 6

�_(1−2)= 𝑃/�_𝑍 (1 ± 〖 6� 〗 _1/𝑆 ± 〖 6� 〗 _2/𝑇)

e2

σ1 = T = 3.15

63.27 ( 1 8.9775

+ 6 *

0.86 2.85

+ 6 * 0.72 ) 3.15

σ1 = 29.4750 Tn/m2 �_1 < �_� 29.4750

P

7.2142 No Cumple

<

* POR TANTEO e

�_1= �/(𝑇 ∗𝑆)(1 + 〖 6� 〗 _1/� + 〖 6� 〗 _2/�) σ1 =

63.27 ( 1 T*S

+ 6 *

0.86 S

+ 6 * 0.72 ) T

T=

5.2

m

σ1 =

6.9669

Tn/m2

S=

5

m

σ2 =

-2.0997

Tn/m2

σ2

σ1

�_𝑣1= (𝑇 − 𝑡_1)/2

Lv1 =

2.25

m

* DISEÑO POR PUNZONAMIENTO: 0.70 +d

�_𝑛𝑢= 𝑃_𝑢/�_𝑧

m

𝑃_𝑢= 1.7 𝐶𝑚+1.4 𝐶𝑣

Pu = 93.892442 Tn

S = 5.00

0.40

n

0.40 +d Wnu = σ1

0.70

Wnu =

6.9669

Tn/m2

T = 5.20 * CONDICION DE DISEÑO: �_𝑈/∅ ≤ �_𝐶

Ø = 0.85

* Escogemos el menor de los dos: Vc=0.27(2+4/β) √( 〖𝑓 _� 〗 ^′ ) bod

〖� _𝑈 = 𝑃 〗 _𝑈− �_𝑛𝑢 ∗𝑚 ∗𝑛 Vu = Vu = Vu = Vu =

93.892442 − 93.892442 − 93.892442 − 91.9417 −

6.9669 x (0.70 + d ) ( 0.40 + d ) 6.9669 x (0.28 + 1.10 d + d² ) 1.9507 − 7.6636 d − 6.9669 d² 7.6636 d − 6.9669 d² 1

2

0.27 x

+

4 0.70 0.40

* bo = 2m + 2n

Vc = Vc = Vc =

x 2 (0.70 +d + 0.40 + d ) d 1.06 210 x 10 307.2172 ( 1.10 + 2 d ) d 337.9389 d 614.4344 d² 2 +

* Reemplazando 1 y 2



+

( 337.9389d 287.2481 d d

��=1.06√( 〖𝑓 _� 〗 ^′ ) 𝑏𝑜d = 1.06 ok !!

= 1.1571429 * Usamos:

91.9417 − 7.6636 d − 6.9669 d² ≤ 91.9417 − 7.6636 d − 6.9669 d² ≤

^



+ +

614.4344 d² ) * 0.85 522.2692 d²

529.2362 d²

+

294.9117 d



d= d=

ℎ_𝑧 = d + ∅/2 +r

91.9417 ≥ 0 0.2227 -0.7800

ℎ_𝑧 = d + ∅/2 +r

hz = 0.2227 + (3/4") 0.0254 + 0.07 2 hz = 0.30223 hz = ≈

0.35

m

𝑑 = ℎ_𝑧 − ∅/2 −r d= d=

0.35 − (3/4") 0.0254 − 0.07 2 0.27 m

* VERIFICACION POR CORTANTE: �_𝑛 ≤ �_�

�_𝑛= �_𝑢𝑑/∅

Ø = 0.85

σx =

3.5147

�_�=0.53 √( 〖𝑓 _� 〗 ^′ ) ∗𝑆 ∗𝑑

�_𝑢𝑑=((�_1+ �_𝑥)/2)∗� ∗(�_�−�)

�_𝑥=((�_1 − �_2)(�_𝑣+ 𝑡_1+𝑑))/𝑇+�_2

Vud = Vud =

5.2408 51.8840

* 5.00 Tn

* ( 2.25



0.27 )

Vc = Vc =

Vn = 51.88396 0.85 Vn = 61.0400 Tn

0.53 210 x 10 x 5.00 x 0.27 103.6858 Tn

�_𝑛 ≤ �_�

61.0400



103.6858

Cumple

ok !!

* DISEÑO POR FLEXION: �_𝑥=((�_1 − �_2)(�_𝑣+ 𝑡_1))/𝑇+�_2

σx =

3.0439

�_𝑢=(�_𝑥/2+�_1) ∗ 𝑆∗ 〖� _𝑣 〗 ^2/3 Mu =

8.4889

* 5.00 *

Mu =

71.6251

Tn - m

Ø = 0.9

( 2.25)² 3

𝑎= (2𝑑 ± √(4 𝑑^2 −(8 �_𝑢)/(0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ ∅ ∗𝑆)))/2

a= a=

0.5047 0.0353

a=

0.0353

m

〖�𝑠〗 _𝑚𝑖𝑛=0.22 ∗√( 〖𝑓 _� 〗 ^′/10.197)/( 〖𝑓 _� 〗 ^′/10.197) ∗𝑆 ∗𝑑

�_𝑠= �_𝑢/(∅ ∗ 〖𝑓 _� 〗 ^′∗(𝑑−𝑎/2)) 71.6251

As = 0.9

*

4.2 *

As =

As min = 0.27 − 0.0353 2

75.0936

0.22 *

210 10.197 4200 10.197

* 5.00

* 0.27

As min = 0.003272 m2 As min = 32.72 cm2

cm2

�_𝑠> 〖�𝑠〗 _𝑚𝑖𝑛

75.0936 > 32.72

*VARILLAS LONGITUDINALES Diametro(ø) =

0.75

〖𝑛 ^° 〗 _𝑣= �_𝑠/�_∅

n°v =

Cumple

Pulg.

75.0936 2.8502

n°v = 26.3465



n°v =

27

varillas

* Separación 𝑠= (𝑆 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)

s=

5.00 − 0.75 * 0.0254 − 2* 0.07 − 27 1

s= s=

0.1862 18.6190

m



*VARILLAS TRANSVERSALES Diametro(ø) =

0.75

Pulg.

�_𝑠 (𝑇)= �_𝑠∗𝑇/𝑆 〖𝑛 ^° 〗 _𝑣= �_(𝑠(𝑇))/�_∅ n°v =

As(T) =

75.0936 *

78.0973 2.8502

5.20 5.00 n°v = 27.4004

* Separación 𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)



* 0.0254 − 2*

As(T) =



78.0973

n°v =

cm2

28

varillas

s=

18

cm

ok !!

𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)

s=

5.20 − 0.75 * 0.0254 − 2* 0.07 − 28 1

s= s=

0.1867

m

18.6702

s=



18

cm

* VERIFICACION POR APLASTAMIENTO: *COLUMNA - ZAPATA

𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_1 Pnb = Pnb =

0.85 * 280 666.4 Tn

𝑃_𝑛= 𝑃_𝑢/∅

�_1= 𝑡_(1 )∗ 𝑡_2 A1 = 0.70 * 0.40 A1 = 0.28 m2

Ø = 0.7

𝑃_𝑛 < 𝑃_𝑛𝑏

𝑃_𝑛 < 𝑃_𝑛𝑏

134.1321 < 666.4

Pn = 93.892442 0.7 Pn = 134.1321 Tn

* 10 * 0.28

Cumple

* ZAPATA - SUELO 𝑃_𝑛𝑏 > 𝑃_𝑛

𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_0

�_2=𝑇 ∗𝑋_1

√(�_2/�_1 ) ≤2 → �_0= √(�_2/�_1 ) ∗ �_1 Si:

𝑋_1=𝑇 ∗𝑡_2/𝑡_1

X1

√(�_2/�_1 ) >2 → �_0=2∗�_1

X1 =

X1 =

T Donde:

A2 = A2 =

3.1500 5.6700

1.8000 * m2

A0 = Pnb = Pnb =

0.85 * 210 999.6 Tn

* 10 * 0.56

2 * 0.28 𝑃_𝑛𝑏 > 𝑃_𝑛

999.6 * PARA ZONA SISMICA (DOWELLS) 𝑃_𝑛 ≤ 𝑃_𝑛𝑏

> 134.1321

3.1500 0.28

= 11.2500

A0 =

0.56

Cumple

ok !!

>

m2

2

3.15 *

1.8000

0.40 0.70 m

ok !!

〖�𝑠〗 _𝑚𝑖𝑛=0.005 ∗ �_1 As min = 0.005 * 2800 As min = 14 cm2 Diametro(ø) = 4

1

Pulg.

* 5.0671

=

20.2683

cm2

Cumple

ok !!

* PLANOS DE PLANTA Y PERFIL:

28 ø 3/4" @ 18

S = 5.00 27 ø 3/4" @ 18

T = 5.20

DOWELLS

4

VARILLAS TRANSVERSALES 28 ø 3/4" @ 18

ø 1"

VARILLAS LONGITUDINALES 27 ø 3/4" @ 18

d = 0.27

hz = 0.35

T = 5.20

* DISEÑO DE UNA ZAPATA AISLADA CON EXCENTRICIDADES * Datos de la Zapata N° 6: CM: CV: ɣc: ɣs: F'c: S/Cpiso: σ(ult): fy: P

69.71 33.98 2.30 1.95 210.00 500.00 3.50 4200.00 103.69

GRAFICA

Tn Tn Tn/m3 Tn/m3 Kg/cm2 Kg/cm2 Kg/cm2 Kg/cm2 Tn

N.P.T + 0.30

N.T.N ± 0.00 0.15

* Datos de la Columna: hf: 2.00 F'c: t1 t2

280.00 60.00 40.00

Df:

Kg/cm2 cm cm

* Datos de la Terreno:

N.F.C-1.95 σ(ult):

NPT NTN NFC

0.15 0.00 -1.85

m m m

* Esfuezo neto del terreno:

* Dimenciones de la Zapata:

�_𝑛 = �_𝑎𝑑𝑚 − ɣ𝑝𝑟𝑜𝑚 ∗ ℎ𝑓 − 𝑆/𝐶

𝑇 =√(�_𝑍 )+ (𝑡_1−𝑡_2)/2

�_𝑎𝑑𝑚 = �_𝑢𝑙𝑡/𝐹_𝑠 σn =

7.2142

* Area de la Zapata:

3.50

Tn/m2

𝑆 =√(�_𝑍 ) − (𝑡_1−𝑡_2)/2

T= 3.8912



T=

3.90

m

S= 3.6912



S=

3.70

m

Az =

14.43

m2

* Nueva Area de la Zapata: * Debe Cumplir: �_𝑣1= (𝑇 − 𝑡_1)/2

1.85

�_𝑍 = 𝑃/�_𝑛 Az = 14.3729 m2

�_𝑣1= �_𝑣2

�_𝑣1= (𝑇 − 𝑡_1)/2 �_𝑣2= (𝑆 − 𝑡_1)/2

Lv1 =

1.65

m Cumple ok !!

Lv2 =

1.65

m

* EFECTOS DE CARGA EXCENTRICA: �_2= 𝑇/6

T 6

= 0.6500

e2

>

T 6

�_1= 𝑆/6

S 6

= 0.6167

e1

<

T 6

e1 = 0.00 e2 = 0.79

e1

�_(1−2)= 𝑃/�_𝑍 (1 ± 〖 6� 〗 _1/𝑆 ± 〖 6� 〗 _2/𝑇)

e2

σ1 = T = 3.90

103.69 ( 1 14.43

+ 6 *

0.00 3.70

+ 6 * 0.79 ) 3.90

σ1 = 15.9190 Tn/m2

15.9190

P

�_1 < �_𝑛 <

7.2142 No Cumple

* POR TANTEO �_1= 𝑃/(𝑇 ∗𝑆)(1 + 〖 6� 〗 _1/𝑆 + 〖 6� 〗 _2/𝑇)

e

σ1 =

σ2

103.69 ( 1 T*S

+ 6 *

0.00 S

+ 6 * 0.79 ) T

T=

5.4

m

σ1 =

6.9339

Tn/m2

S=

5.2

m

σ2 =

0.4513

Tn/m2

�_𝑣1= (𝑇 − 𝑡_1)/2

Lv1 =

2.4

m

σ1

* DISEÑO POR PUNZONAMIENTO: 0.60 +d

�_𝑛𝑢= 𝑃_𝑢/�_𝑧

m

𝑃_𝑢= 1.7 𝐶𝑚+1.4 𝐶𝑣

Pu = 155.35712 Tn

S = 5.20

0.40

n

0.40 +d Wnu = σ1

0.60

Wnu =

6.9339

Tn/m2

T = 5.40 * CONDICION DE DISEÑO: �_𝑈/∅ ≤ �_𝐶

Ø = 0.85

〖� _𝑈 = 𝑃 〗 _𝑈− �_𝑛𝑢 ∗𝑚 ∗𝑛 Vu = Vu = Vu = Vu =

155.35712 − 155.35712 − 155.35712 − 153.6930 −

6.9339 x (0.60 + d ) ( 0.40 + d ) 6.9339 x (0.24 + 1.00 d + d² ) 1.6641 − 6.9339 d − 6.9339 d² 6.9339 d − 6.9339 d² 1

* Escogemos el menor de los dos: Vc=0.27(2+4/β) √( 〖𝑓 _� 〗 ^′ ) bod 2

0.27 x

= * Usamos:

* Reemplazando 1 y 2

+

4 0.60 0.40

^

��=1.06√( 〖𝑓 _� 〗 ^′ ) 𝑏𝑜d = 1.06 ok !! * bo = 2m + 2n

1.26 Vc = Vc = Vc =

x 2 (0.60 +d + 0.40 + d ) d 1.06 210 x 10 307.2172 ( 1.00 + 2 d ) d 307.2172 d 614.4344 d² 2 +

153.6930 − 6.9339 d − 6.9339 d² ≤ 153.6930 − 6.9339 d − 6.9339 d² ≤ 529.2031 d²

+

( 307.2172d 261.1346 d

268.0685 d



+ +

614.4344 d² ) * 0.85 522.2692 d²

153.6930 ≥ 0

d= d=

0.3422 -0.8487

ℎ_𝑧 = d + ∅/2 +r

hz = 0.3422 + (3/4") 0.0254 + 0.07 2 hz = 0.42173 hz = ≈

0.45

m

𝑑 = ℎ_𝑧 − ∅/2 −r d= d=

0.45 − (3/4") 0.0254 − 0.07 2 0.37 m

* VERIFICACION POR CORTANTE: �_𝑛 ≤ �_�

�_𝑛= �_𝑢𝑑/∅

Ø = 0.85

�_𝑥=((�_1 − �_2)(�_𝑣+ 𝑡_1+𝑑))/𝑇+�_2

σx =

4.4969

�_�=0.53 √( 〖𝑓 _� 〗 ^′ ) ∗𝑆 ∗𝑑

�_𝑢𝑑=((�_1+ �_𝑥)/2)∗𝑆 ∗(�_�−𝑑) Vud = Vud =

5.7154 60.3321

* 5.20 Tn

* ( 2.4

Vn = 60.332109 0.85 Vn = 70.9790 Tn



0.37 )

Vc = Vc =

0.53 210 x 10 x 5.20 x 0.37 147.7715 Tn

�_𝑛 ≤ �_�

70.9790



147.7715

Cumple ok !!

* DISEÑO POR FLEXION: �_𝑥=((�_1 − �_2)(�_𝑣+ 𝑡_1))/𝑇+�_2

σx =

4.0528

�_𝑢=(�_𝑥/2+�_1) ∗ 𝑆∗ 〖� _𝑣 〗 ^2/3 Mu =

8.9603

* 5.20 *

Mu =

89.4597

Tn - m

Ø = 0.9

( 2.4 )² 3

𝑎= (2𝑑 ± √(4 𝑑^2 −(8 �_𝑢)/(0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ ∅ ∗𝑆)))/2

a= a=

0.7098 0.0302

a=

0.0302

m

〖�𝑠〗 _𝑚𝑖𝑛=0.22 ∗√( 〖𝑓 _� 〗 ^′/10.197)/( 〖𝑓 _� 〗 ^′/10.197) ∗𝑆 ∗𝑑

�_𝑠= �_𝑢/(∅ ∗ 〖𝑓 _� 〗 ^′∗(𝑑−𝑎/2)) 89.4597

As = 0.9

*

4.2 *

As =

As min = 0.37 − 0.0302 2

66.6827

0.22 *

210 10.197 4200 10.197

* 5.20

* 0.37

As min = 0.004664 m2 As min = 46.64 cm2

cm2

�_𝑠> 〖�𝑠〗 _𝑚𝑖𝑛

66.6827 > 46.64

*VARILLAS LONGITUDINALES Diametro(ø) =

0.75

〖𝑛 ^° 〗 _𝑣= �_𝑠/�_∅

n°v =

Cumple

Pulg.

66.6827 2.8502

n°v = 23.3956



n°v =

24

varillas

* Separación 𝑠= (𝑆 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)

s=

5.20 − 0.75 * 0.0254 − 2* 0.07 − 24 1

s= s=

0.2192 21.9172

m



*VARILLAS TRANSVERSALES Diametro(ø) =

0.75

Pulg.

�_𝑠 (𝑇)= �_𝑠∗𝑇/𝑆 〖𝑛 ^° 〗 _𝑣= �_(𝑠(𝑇))/�_∅ n°v =

As(T) =

66.6827 *

69.2474 2.8502

5.40 5.20 n°v = 24.2954

* Separación 𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)



* 0.0254 − 2*

As(T) =



69.2474

n°v =

cm2

25

varillas

s=

21

cm

ok !!

𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)

s=

5.40 − 0.75 * 0.0254 − 2* 0.07 − 25 1

s= s=

0.2184 21.8373

m



s=

21

cm

* VERIFICACION POR APLASTAMIENTO: *COLUMNA - ZAPATA

𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_1 Pnb = Pnb =

0.85 * 280 571.2 Tn

𝑃_𝑛= 𝑃_𝑢/∅

�_1= 𝑡_(1 )∗ 𝑡_2 A1 = 0.60 * 0.40 A1 = 0.24 m2

Ø = 0.7

𝑃_𝑛 < 𝑃_𝑛𝑏

𝑃_𝑛 < 𝑃_𝑛𝑏

221.9387 < 571.2

Pn = 155.35712 0.7 Pn = 221.9387 Tn

* 10 * 0.24

Cumple

* ZAPATA - SUELO 𝑃_𝑛𝑏 > 𝑃_𝑛

�_2=𝑇 ∗𝑋_1

√(�_2/�_1 ) ≤2 → �_0= √(�_2/�_1 ) ∗ �_1 Si:

𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_0

𝑋_1=𝑇 ∗𝑡_2/𝑡_1

X1

√(�_2/�_1 ) >2 → �_0=2∗�_1

X1 =

X1 =

T Donde:

A2 = A2 =

3.9000 * 2.6000 10.1400 m2 A0 =

Pnb = Pnb =

0.85 * 210 856.8 Tn

* 10 * 0.48

2 * 0.24 𝑃_𝑛𝑏 > 𝑃_𝑛

856.8 * PARA ZONA SISMICA (DOWELLS) 𝑃_𝑛 ≤ 𝑃_𝑛𝑏

〖�𝑠〗 _𝑚𝑖𝑛=0.005 ∗ �_1 As min = 0.005 * 2400 As min = 12 cm2

> 221.9387

3.9000 0.24

= 16.2500

A0 =

0.48

Cumple

ok !!

>

m2

2

3.90 *

2.6000

0.40 0.60 m

ok !!

Diametro(ø) = 4

1

Pulg.

* 5.0671

=

20.2683

cm2

Cumple

ok !!

* PLANOS DE PLANTA Y PERFIL:

25 ø 3/4" @ 21

S = 5.20 24 ø 3/4" @ 21

T = 5.40

DOWELLS

4

VARILLAS TRANSVERSALES 25 ø 3/4" @ 21

ø 1"

VARILLAS LONGITUDINALES 24 ø 3/4" @ 21

d = 0.37

hz = 0.45

T = 5.40

* DISEÑO DE UNA ZAPATA AISLADA CON EXCENTRICIDADES * Datos de la Zapata N° 8: CM: CV: ɣc: ɣs: F'c: S/Cpiso: σ(ult): fy: P

18.35 11.00 2.30 1.95 210.00 500.00 3.50 4200.00 29.35

GRAFICA

Tn Tn Tn/m3 Tn/m3 Kg/cm2 Kg/cm2 Kg/cm2 Kg/cm2 Tn

N.P.T + 0.30

N.T.N ± 0.00 0.15

* Datos de la Columna: hf: 2.00 F'c: t1 t2

280.00 40.00 40.00

Df:

Kg/cm2 cm cm

* Datos de la Terreno:

N.F.C-1.95 σ(ult):

NPT NTN NFC

0.15 0.00 -1.85

3.50

m m m

* Esfuezo neto del terreno:

* Dimenciones de la Zapata:

�_𝑛 = �_𝑎𝑑𝑚 − ɣ𝑝𝑟𝑜𝑚 ∗ ℎ𝑓 − 𝑆/𝐶

𝑇 =√(�_𝑍 )+ (𝑡_1−𝑡_2)/2

T= 2.0171



T=

2.05

m

1.85

�_𝑛 = �_𝑎𝑑𝑚 − ɣ𝑝𝑟𝑜𝑚 ∗ ℎ𝑓 − 𝑆/𝐶 �_𝑎𝑑𝑚 = �_𝑢𝑙𝑡/𝐹_𝑠 σn =

7.2142

Tn/m2

S= 2.0171

S=

2.05

m

Az =

4.2025

m2



* Debe Cumplir: �_𝑣1= �_𝑣2

�_𝑍 = 𝑃/�_𝑛 4.0685

𝑆 =√(�_𝑍 ) − (𝑡_1−𝑡_2)/2 * Nueva Area de la Zapata:

* Area de la Zapata:

Az =

𝑇 =√(�_𝑍 )+ (𝑡_1−𝑡_2)/2

m2

�_𝑣1= (𝑇 − 𝑡_1)/2

Lv1 =

0.825

m Cumple ok !!

�_𝑣2= (𝑆 − 𝑡_1)/2

Lv2 =

0.825

m

* EFECTOS DE CARGA EXCENTRICA: e1 = 0.39 e2 = 0.81 e2 e1

�_2= 𝑇/6

T 6

= 0.3417

e2

>

T 6

�_1= 𝑆/6

S 6

= 0.3417

e1

>

T 6

�_(1−2)= 𝑃/�_𝑍 (1 ± 〖 6� 〗 _1/𝑆 ± 〖 6� 〗 _2/𝑇) σ1 = T = 2.05

29.35 ( 1 4.2025

+ 6 *

0.39 2.05

σ1 = 31.5142 Tn/m2

31.5142

P

�_1 < �_𝑛 <

7.2142 No Cumple

* POR TANTEO e

�_1= 𝑃/(𝑇 ∗𝑆)(1 + 〖 6� 〗 _1/𝑆 + 〖 6� 〗 _2/𝑇)

+ 6 * 0.81 ) 2.05

σ1 =

29.35 ( 1 T*S

+ 6 *

0.39 S

+ 6 * 0.81 ) T

T=

3.7

m

σ1 =

6.7589

Tn/m2

S=

3.5

m

σ2 =

-2.2259

Tn/m2

σ2

�_𝑣1= (𝑇 − 𝑡_1)/2

Lv1 =

σ1

* DISEÑO POR PUNZONAMIENTO: 0.40 +d

�_𝑛𝑢= 𝑃_𝑢/�_𝑧

m

𝑃_𝑢= 1.7 𝐶𝑚+1.4 𝐶𝑣

Pu = 44.392191 Tn

S = 3.50

0.40

n

0.40 +d Wnu = σ1

0.40

Wnu =

6.7589

Tn/m2

T = 3.70 * CONDICION DE DISEÑO: �_𝑈/∅ ≤ �_𝐶

Ø = 0.85

〖� _𝑈 = 𝑃 〗 _𝑈− �_𝑛𝑢 ∗𝑚 ∗𝑛

* Escogemos el menor de los dos: Vc=0.27(2+4/β) √( 〖𝑓 _� 〗 ^′ ) bod

^

��=1.06√( 〖𝑓 _� 〗 ^′ ) 𝑏𝑜d

1.65

m

Vc=0.27(2+4/β) √( 〖𝑓 _� 〗 ^′ ) bod

〖� _𝑈 = 𝑃 〗 _𝑈− �_𝑛𝑢 ∗𝑚 ∗𝑛 Vu = Vu = Vu = Vu =

44.392191 − 44.392191 − 44.392191 − 43.3108 −

6.7589 x (0.40 + d ) ( 0.40 + d ) 6.7589 x (0.16 + 0.80 d + d² ) 1.0814 − 5.4071 d − 6.7589 d² 5.4071 d − 6.7589 d² 1

2

0.27 x

=

+

4 0.40 0.40

* bo = 2m + 2n

1.62 Vc = Vc = Vc =

* Usamos:

x 2 (0.40 +d + 0.40 + d ) d 1.06 210 x 10 ( + 2 d ) d 307.2172 0.80 245.7737 d + 614.4344 d² 2

* Reemplazando 1 y 2 43.3108 − 5.4071 d − 6.7589 d² ≤ 43.3108 − 5.4071 d − 6.7589 d² ≤ 529.0281 d²

+

( 245.7737d 208.9077 d

214.3148 d



d= d=

+ +

614.4344 d² ) * 0.85 522.2692 d²

43.3108 ≥ 0 0.1480 -0.5531

ℎ_𝑧 = d + ∅/2 +r

hz = 0.1480 + (3/4") 0.0254 + 0.07 2 hz = 0.22753 hz = ≈

𝑑 = ℎ_𝑧 − ∅/2 −r d= d=

0.25 − (3/4") 0.0254 − 0.07 2 0.17 m

* VERIFICACION POR CORTANTE: �_𝑛 ≤ �_�

�_𝑛= �_𝑢𝑑/∅

Ø = 0.85

0.25

��=1.06√( 〖𝑓 _� 〗 ^′ ) 𝑏𝑜d = 1.06 ok !!

m

σx =

3.1650

�_�=0.53 √( 〖𝑓 _� 〗 ^′ ) ∗𝑆 ∗𝑑

�_𝑢𝑑=((�_1+ �_𝑥)/2)∗𝑆 ∗(�_�−𝑑)

�_𝑥=((�_1 − �_2)(�_𝑣+ 𝑡_1+𝑑))/𝑇+�_2

Vud = Vud =

4.9619 25.7028

* 3.50 Tn

* ( 1.65



0.17 )

Vc = Vc =

Vn = 25.702847 0.85 Vn = 30.2386 Tn

0.53 210 x 10 x 3.50 x 0.17 45.6986 Tn

�_𝑛 ≤ �_�

30.2386



45.6986

Cumple ok !!

* DISEÑO POR FLEXION: �_𝑥=((�_1 − �_2)(�_𝑣+ 𝑡_1))/𝑇+�_2

σx =

2.7522

�_𝑢=(�_𝑥/2+�_1) ∗ 𝑆∗ 〖� _𝑣 〗 ^2/3 Mu =

8.1350

* 3.50 *

Mu =

25.8387

Tn - m

Ø = 0.9

( 1.65)² 3

𝑎= (2𝑑 ± √(4 𝑑^2 −(8 �_𝑢)/(0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ ∅ ∗𝑆)))/2

a= a=

0.3104 0.0296

a=

0.0296

m

〖�𝑠〗 _𝑚𝑖𝑛=0.22 ∗√( 〖𝑓 _� 〗 ^′/10.197)/( 〖𝑓 _� 〗 ^′/10.197) ∗𝑆 ∗𝑑

�_𝑠= �_𝑢/(∅ ∗ 〖𝑓 _� 〗 ^′∗(𝑑−𝑎/2)) 25.8387

As = 0.9

*

4.2 *

As =

As min = 0.17 − 0.0296 2

44.0456

0.22 *

210 10.197 4200 10.197

* 3.50

* 0.17

As min = 0.001442 m2 As min = 14.42 cm2

cm2

�_𝑠> 〖�𝑠〗 _𝑚𝑖𝑛

44.0456 > 14.42

*VARILLAS LONGITUDINALES Diametro(ø) =

0.75

〖𝑛 ^° 〗 _𝑣= �_𝑠/�_∅

n°v =

Cumple

Pulg.

44.0456 2.8502

n°v = 15.4533



n°v =

16

varillas

* Separación 𝑠= (𝑆 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)

s=

3.50 − 0.75 * 0.0254 − 2* 0.07 − 16 1

s= s=

0.2227 22.2730

m



*VARILLAS TRANSVERSALES Diametro(ø) =

0.75

Pulg.

�_𝑠 (𝑇)= �_𝑠∗𝑇/𝑆 〖𝑛 ^° 〗 _𝑣= �_(𝑠(𝑇))/�_∅ n°v =

As(T) =

44.0456 *

46.5625 2.8502

3.70 3.50 n°v = 16.3364

* Separación 𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)



* 0.0254 − 2*

As(T) =



46.5625

n°v =

cm2

17

varillas

s=

22

cm

ok !!

𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)

s=

3.70 − 0.75 * 0.0254 − 2* 0.07 − 17 1

s= s=

0.2213

m

22.1309

s=



22

cm

* VERIFICACION POR APLASTAMIENTO: *COLUMNA - ZAPATA

𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_1 Pnb = Pnb =

0.85 * 280 380.8 Tn

𝑃_𝑛= 𝑃_𝑢/∅

�_1= 𝑡_(1 )∗ 𝑡_2 A1 = 0.40 * 0.40 A1 = 0.16 m2

Ø = 0.7

𝑃_𝑛 < 𝑃_𝑛𝑏

𝑃_𝑛 < 𝑃_𝑛𝑏

Pn = 44.392191 0.7 Pn = 63.4174 Tn

* 10 * 0.16

63.4174

< 380.8

Cumple

* ZAPATA - SUELO 𝑃_𝑛𝑏 > 𝑃_𝑛

𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_0

�_2=𝑇 ∗𝑋_1

√(�_2/�_1 ) ≤2 → �_0= √(�_2/�_1 ) ∗ �_1 Si:

𝑋_1=𝑇 ∗𝑡_2/𝑡_1

X1

√(�_2/�_1 ) >2 → �_0=2∗�_1

X1 =

X1 =

T Donde:

A2 = A2 =

2.0500 4.2025

2.0500 * m2

A0 = Pnb = Pnb =

0.85 * 210 571.2 Tn

* 10 * 0.32

2 * 0.16 𝑃_𝑛𝑏 > 𝑃_𝑛

571.2 * PARA ZONA SISMICA (DOWELLS) 𝑃_𝑛 ≤ 𝑃_𝑛𝑏

> 63.4174

2.0500 0.16

= 12.8125

A0 =

0.32

Cumple

ok !!

>

m2

2

2.05 *

2.0500

0.40 0.40 m

ok !!

〖�𝑠〗 _𝑚𝑖𝑛=0.005 ∗ �_1 As min = 0.005 * 1600 As min = 8 cm2 Diametro(ø) = 4

1

Pulg.

* 5.0671

=

20.2683

cm2

Cumple

ok !!

* PLANOS DE PLANTA Y PERFIL:

17 ø 3/4" @ 22

S = 3.50 16 ø 3/4" @ 22

T = 3.70

DOWELLS

4

VARILLAS TRANSVERSALES 17 ø 3/4" @ 22

ø 1"

VARILLAS LONGITUDINALES 16 ø 3/4" @ 22

d = 0.17

hz = 0.25

T = 3.70

* DISEÑO DE UNA ZAPATA AISLADA CON EXCENTRICIDADES * Datos de la Zapata N° 9: CM: CV: ɣc: ɣs: F'c: S/Cpiso: σ(ult): fy: P

18.52 11.11 2.30 1.95 210.00 500.00 3.50 4200.00 29.62

GRAFICA

Tn Tn Tn/m3 Tn/m3 Kg/cm2 Kg/cm2 Kg/cm2 Kg/cm2 Tn

N.P.T + 0.30

N.T.N ± 0.00 0.15

* Datos de la Columna: hf: 2.00 F'c: t1 t2

280.00 40.00 40.00

Df:

Kg/cm2 cm cm

* Datos de la Terreno:

N.F.C-1.95 σ(ult):

NPT NTN NFC

0.15 0.00 -1.85

m m m

3.50

1.85

* Esfuezo neto del terreno:

* Dimenciones de la Zapata:

�_𝑛 = �_𝑎𝑑𝑚 − ɣ𝑝𝑟𝑜𝑚 ∗ ℎ𝑓 − 𝑆/𝐶

𝑇 =√(�_𝑍 )+ (𝑡_1−𝑡_2)/2

�_𝑎𝑑𝑚 = �_𝑢𝑙𝑡/𝐹_𝑠 σn =

7.2142

Tn/m2

T=

2.05

m

S= 2.0264



S=

2.05

m

Az =

4.2025

m2

* Debe Cumplir: �_𝑣1= �_𝑣2

�_𝑍 = 𝑃/�_𝑛 4.1064



* Nueva Area de la Zapata:

* Area de la Zapata:

Az =

𝑆 =√(�_𝑍 ) − (𝑡_1−𝑡_2)/2

T= 2.0264

m2

�_𝑣1= (𝑇 − 𝑡_1)/2

Lv1 =

0.825

m

Lv2 =

0.825

m

Cumple ok !!

�_𝑣2= (𝑆 − 𝑡_1)/2

* EFECTOS DE CARGA EXCENTRICA: e1 = 0.39 e2 = 0.83 e2 e1

�_2= 𝑇/6

T 6

= 0.3417

e2

>

T 6

�_1= 𝑆/6

S 6

= 0.3417

e1

>

T 6

�_(1−2)= 𝑃/�_𝑍 (1 ± 〖 6� 〗 _1/𝑆 ± 〖 6� 〗 _2/𝑇) σ1 = T = 2.05

29.62 ( 1 4.2025

+ 6 *

0.39 2.05

σ1 = 32.2203 Tn/m2

32.2203

�_1 < �_𝑛 <

7.2142 No Cumple

+ 6 * 0.83 ) 2.05

P

* POR TANTEO �_1= 𝑃/(𝑇 ∗𝑆)(1 + 〖 6� 〗 _1/𝑆 + 〖 6� 〗 _2/𝑇)

e

σ1 =

σ2

29.62 ( 1 T*S

+ 6 *

0.39 S

T=

3.7

m

σ1 =

6.8960

Tn/m2

S=

3.5

m

σ2 =

-2.3208

Tn/m2

�_𝑣1= (𝑇 − 𝑡_1)/2

σ1

* DISEÑO POR PUNZONAMIENTO: 0.40 +d

�_𝑛𝑢= 𝑃_𝑢/�_𝑧

m

𝑃_𝑢= 1.7 𝐶𝑚+1.4 𝐶𝑣

Pu = 44.805895 Tn

S = 3.50

0.40

n

0.40 +d Wnu = σ1

0.40

T = 3.70 * CONDICION DE DISEÑO:

+ 6 * 0.83 ) T

Wnu =

6.8960

Tn/m2

Lv1 =

1.65

m

�_𝑈/∅ ≤ �_𝐶

Ø = 0.85

* Escogemos el menor de los dos: Vc=0.27(2+4/β) √( 〖𝑓 _� 〗 ^′ ) bod

〖� _𝑈 = 𝑃 〗 _𝑈− �_𝑛𝑢 ∗𝑚 ∗𝑛 Vu = Vu = Vu = Vu =

44.805895 − 44.805895 − 44.805895 − 43.7025 −

6.8960 x (0.40 + d ) ( 0.40 + d ) 6.8960 x (0.16 + 0.80 d + d² ) 1.1034 − 5.5168 d − 6.8960 d² 5.5168 d − 6.8960 d² 1

2

0.27 x

=

+

4 0.40 0.40

* bo = 2m + 2n

Vc = Vc = Vc =

x 2 (0.40 +d + 0.40 + d ) d 1.06 210 x 10 307.2172 ( 0.80 + 2 d ) d 245.7737 d + 614.4344 d² 2

* Reemplazando 1 y 2

529.1652 d²

+

( 245.7737d 208.9077 d

214.4245 d



d= d=

+ +

614.4344 d² ) * 0.85 522.2692 d²

43.7025 ≥ 0 0.1490 -0.5542

ℎ_𝑧 = d + ∅/2 +r

hz = 0.1490 + (3/4") 0.0254 + 0.07 2 hz = 0.22853 hz = ≈

𝑑 = ℎ_𝑧 − ∅/2 −r d= d=

* VERIFICACION POR CORTANTE:

0.25 − (3/4") 0.0254 − 0.07 2 0.17 m

0.25

��=1.06√( 〖𝑓 _� 〗 ^′ ) 𝑏𝑜d = 1.06 ok !!

1.62

* Usamos:

43.7025 − 5.5168 d − 6.8960 d² ≤ 43.7025 − 5.5168 d − 6.8960 d² ≤

^

m

�_𝑛 ≤ �_�

�_𝑛= �_𝑢𝑑/∅

Ø = 0.85

σx =

3.2093

�_�=0.53 √( 〖𝑓 _� 〗 ^′ ) ∗𝑆 ∗𝑑

�_𝑢𝑑=((�_1+ �_𝑥)/2)∗𝑆 ∗(�_�−𝑑)

�_𝑥=((�_1 − �_2)(�_𝑣+ 𝑡_1+𝑑))/𝑇+�_2

Vud = Vud =

5.0527 26.1728

* 3.50 Tn

* ( 1.65



0.17 )

Vc = Vc =

Vn = 26.172784 0.85 Vn = 30.7915 Tn

0.53 210 x 10 x 3.50 x 0.17 45.6986 Tn

�_𝑛 ≤ �_�

30.7915



45.6986

Cumple ok !!

* DISEÑO POR FLEXION: �_𝑥=((�_1 − �_2)(�_𝑣+ 𝑡_1))/𝑇+�_2

σx =

2.7858

�_𝑢=(�_𝑥/2+�_1) ∗ 𝑆∗ 〖� _𝑣 〗 ^2/3 Mu =

8.2889

* 3.50 *

Mu =

26.3277

Tn - m

Ø = 0.9

( 1.65)² 3

𝑎= (2𝑑 ± √(4 𝑑^2 −(8 �_𝑢)/(0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ ∅ ∗𝑆)))/2

a= a=

0.3098 0.0302

a=

0.0302

m

〖�𝑠〗 _𝑚𝑖𝑛=0.22 ∗√( 〖𝑓 _� 〗 ^′/10.197)/( 〖𝑓 _� 〗 ^′/10.197) ∗𝑆 ∗𝑑

�_𝑠= �_𝑢/(∅ ∗ 〖𝑓 _� 〗 ^′∗(𝑑−𝑎/2)) 26.3277

As = 0.9

*

4.2 *

As =

As min = 0.17 − 0.0302 2

44.9691

0.22 *

210 10.197 4200 10.197

* 3.50

* 0.17

As min = 0.001442 m2 As min = 14.42 cm2

cm2

�_𝑠> 〖�𝑠〗 _𝑚𝑖𝑛

44.9691 > 14.42

*VARILLAS LONGITUDINALES Diametro(ø) =

0.75

〖𝑛 ^° 〗 _𝑣= �_𝑠/�_∅

n°v =

Cumple

Pulg.

44.9691 2.8502

n°v = 15.7774



n°v =

16

varillas

* Separación 𝑠= (𝑆 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)

s=

3.50 − 0.75 * 0.0254 − 2* 0.07 − 16 1

s= s=

0.2227 22.2730

m



*VARILLAS TRANSVERSALES Diametro(ø) =

0.75

Pulg.

�_𝑠 (𝑇)= �_𝑠∗𝑇/𝑆 〖𝑛 ^° 〗 _𝑣= �_(𝑠(𝑇))/�_∅ n°v =

As(T) =

44.9691 *

47.5388 2.8502

3.70 3.50 n°v = 16.6789

* Separación 𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)



* 0.0254 − 2*

As(T) =



47.5388

n°v =

cm2

17

varillas

s=

22

cm

ok !!

𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)

s=

3.70 − 0.75 * 0.0254 − 2* 0.07 − 17 1

s= s=

0.2213

m

22.1309

s=



22

cm

* VERIFICACION POR APLASTAMIENTO: *COLUMNA - ZAPATA

𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_1 Pnb = Pnb =

0.85 * 280 380.8 Tn

𝑃_𝑛= 𝑃_𝑢/∅

�_1= 𝑡_(1 )∗ 𝑡_2 A1 = 0.40 * 0.40 A1 = 0.16 m2

Ø = 0.7

𝑃_𝑛 < 𝑃_𝑛𝑏

𝑃_𝑛 < 𝑃_𝑛𝑏

Pn = 44.805895 0.7 Pn = 64.0084 Tn

* 10 * 0.16

64.0084

< 380.8

Cumple

* ZAPATA - SUELO 𝑃_𝑛𝑏 > 𝑃_𝑛

𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_0

�_2=𝑇 ∗𝑋_1

√(�_2/�_1 ) ≤2 → �_0= √(�_2/�_1 ) ∗ �_1 Si:

𝑋_1=𝑇 ∗𝑡_2/𝑡_1

X1

√(�_2/�_1 ) >2 → �_0=2∗�_1

X1 =

X1 =

T Donde:

A2 = A2 =

2.0500 4.2025

2.0500 * m2

A0 = Pnb = Pnb =

0.85 * 210 571.2 Tn

* 10 * 0.32

2 * 0.16 𝑃_𝑛𝑏 > 𝑃_𝑛

571.2 * PARA ZONA SISMICA (DOWELLS) 𝑃_𝑛 ≤ 𝑃_𝑛𝑏

> 64.0084

2.0500 0.16

= 12.8125

A0 =

0.32

Cumple

ok !!

>

m2

2

2.05 *

2.0500

0.40 0.40 m

ok !!

〖�𝑠〗 _𝑚𝑖𝑛=0.005 ∗ �_1 As min = 0.005 * 1600 As min = 8 cm2 Diametro(ø) = 4

1

Pulg.

* 5.0671

=

20.2683

cm2

Cumple

ok !!

* PLANOS DE PLANTA Y PERFIL:

17 ø 3/4" @ 22

S = 3.50 16 ø 3/4" @ 22

T = 3.70

DOWELLS

4

VARILLAS TRANSVERSALES 17 ø 3/4" @ 22

ø 1"

VARILLAS LONGITUDINALES 16 ø 3/4" @ 22

d = 0.17

hz = 0.25

T = 3.70

* DISEÑO DE UNA ZAPATA AISLADA CON EXCENTRICIDADES * Datos de la Zapata N° 11: CM: CV: ɣc: ɣs: F'c: S/Cpiso: σ(ult): fy: P

70.37 34.07 2.30 1.95 210.00 500.00 3.50 4200.00 104.44

* Datos de la Columna: F'c: t1 t2

280.00 60.00 40.00

GRAFICA

Tn Tn Tn/m3 Tn/m3 Kg/cm2 Kg/cm2 Kg/cm2 Kg/cm2 Tn

N.P.T + 0.30

0.15

hf: 2.00

Df:

Kg/cm2 cm cm

* Datos de la Terreno:

N.F.C-1.95 σ(ult):

NPT NTN NFC

0.15 0.00 -1.85

N.T.N ± 0.00

m m m

3.50

1.85

* Esfuezo neto del terreno:

* Dimenciones de la Zapata:

�_𝑛 = �_𝑎𝑑𝑚 − ɣ𝑝𝑟𝑜𝑚 ∗ ℎ𝑓 − 𝑆/𝐶

𝑇 =√(�_𝑍 )+ (𝑡_1−𝑡_2)/2

�_𝑎𝑑𝑚 = �_𝑢𝑙𝑡/𝐹_𝑠 σn =

7.2142

Tn/m2

𝑆 =√(�_𝑍 ) − (𝑡_1−𝑡_2)/2

T= 3.9049



T=

3.95

m

S= 3.7049



S=

3.75

m

* Nueva Area de la Zapata:

* Area de la Zapata:

Az = 14.8125 m2

* Debe Cumplir: �_𝑣1= �_𝑣2

�_𝑍 = 𝑃/�_𝑛 Az = 14.4772 m2

�_𝑣1= (𝑇 − 𝑡_1)/2

Lv1 =

1.675

m

Lv2 =

1.675

m

Cumple ok !!

�_𝑣2= (𝑆 − 𝑡_1)/2

* EFECTOS DE CARGA EXCENTRICA: e1 = 0.00 e2 = 0.84

e1

�_2= 𝑇/6

T 6

= 0.6583

e2

>

T 6

�_1= 𝑆/6

S 6

= 0.6250

e1

<

T 6

�_(1−2)= 𝑃/�_𝑍 (1 ± 〖 6� 〗 _1/𝑆 ± 〖 6� 〗 _2/𝑇)

e2

σ1 = T = 3.95

104.44 ( 1 14.8125

+ 6 *

0.00 3.75

σ1 = 16.0474 Tn/m2

16.0474

�_1 < �_𝑛 <

7.2142 No Cumple

+ 6 * 0.84 ) 3.95

P

* POR TANTEO �_1= 𝑃/(𝑇 ∗𝑆)(1 + 〖 6� 〗 _1/𝑆 + 〖 6� 〗 _2/𝑇)

e

σ1 =

σ2

104.44 ( 1 T*S

+ 6 *

0.00 S

T=

5.5

m

σ1 =

6.8661

Tn/m2

S=

5.3

m

σ2 =

0.2997

Tn/m2

�_𝑣1= (𝑇 − 𝑡_1)/2

σ1

* DISEÑO POR PUNZONAMIENTO: 0.60 +d

�_𝑛𝑢= 𝑃_𝑢/�_𝑧

m

𝑃_𝑢= 1.7 𝐶𝑚+1.4 𝐶𝑣

Pu = 156.43861 Tn

S = 5.30

0.40

n

0.40 +d Wnu = σ1

0.60

T = 5.50 * CONDICION DE DISEÑO: �_𝑈/∅ ≤ �_𝐶

+ 6 * 0.84 ) T

Wnu =

6.8661

Tn/m2

Lv1 =

2.45

m

�_𝑈/∅ ≤ �_𝐶

Ø = 0.85

* Escogemos el menor de los dos: Vc=0.27(2+4/β) √( 〖𝑓 _� 〗 ^′ ) bod

〖� _𝑈 = 𝑃 〗 _𝑈− �_𝑛𝑢 ∗𝑚 ∗𝑛 Vu = Vu = Vu = Vu =

156.43861 − 156.43861 − 156.43861 − 154.7907 −

6.8661 x (0.60 + d ) ( 0.40 + d ) 6.8661 x (0.24 + 1.00 d + d² ) 1.6479 − 6.8661 d − 6.8661 d² 6.8661 d − 6.8661 d² 1

2

0.27 x

=

+

4 0.60 0.40

* bo = 2m + 2n

Vc = Vc = Vc =

x 2 (0.60 +d + 0.40 + d ) d 1.06 210 x 10 ( + 2 d ) d 307.2172 1.00 307.2172 d + 614.4344 d² 2

* Reemplazando 1 y 2

529.1353 d²

+

( 307.2172d 261.1346 d

268.0007 d



d= d=

+ +

614.4344 d² ) * 0.85 522.2692 d²

154.7907 ≥ 0 0.3440 -0.8505

ℎ_𝑧 = d + ∅/2 +r

hz = 0.3440 + (3/4") 0.0254 + 0.07 2 hz = 0.42353 hz = ≈

𝑑 = ℎ_𝑧 − ∅/2 −r d= d=

* VERIFICACION POR CORTANTE:

0.45 − (3/4") 0.0254 − 0.07 2 0.37 m

0.45

��=1.06√( 〖𝑓 _� 〗 ^′ ) 𝑏𝑜d = 1.06 ok !!

1.26

* Usamos:

154.7907 − 6.8661 d − 6.8661 d² ≤ 154.7907 − 6.8661 d − 6.8661 d² ≤

^

m

�_𝑛 ≤ �_�

�_𝑛= �_𝑢𝑑/∅

Ø = 0.85

σx =

4.3828

�_�=0.53 √( 〖𝑓 _� 〗 ^′ ) ∗𝑆 ∗𝑑

�_𝑢𝑑=((�_1+ �_𝑥)/2)∗𝑆 ∗(�_�−𝑑)

�_𝑥=((�_1 − �_2)(�_𝑣+ 𝑡_1+𝑑))/𝑇+�_2

Vud = Vud =

5.6244 62.0038

* 5.30 Tn

* ( 2.45



0.37 )

Vc = Vc =

Vn = 62.003772 0.85 Vn = 72.9456 Tn

0.53 210 x 10 x 5.30 x 0.37 150.6132 Tn

�_𝑛 ≤ �_�

72.9456



150.6132

Cumple ok !!

* DISEÑO POR FLEXION: �_𝑥=((�_1 − �_2)(�_𝑣+ 𝑡_1))/𝑇+�_2

σx =

3.9410

�_𝑢=(�_𝑥/2+�_1) ∗ 𝑆∗ 〖� _𝑣 〗 ^2/3 Mu =

8.8366

* 5.30 *

Mu =

93.7071

Tn - m

Ø = 0.9

( 2.45)² 3

𝑎= (2𝑑 ± √(4 𝑑^2 −(8 �_𝑢)/(0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ ∅ ∗𝑆)))/2

a= a=

0.7090 0.0310

a=

0.0310

m

〖�𝑠〗 _𝑚𝑖𝑛=0.22 ∗√( 〖𝑓 _� 〗 ^′/10.197)/( 〖𝑓 _� 〗 ^′/10.197) ∗𝑆 ∗𝑑

�_𝑠= �_𝑢/(∅ ∗ 〖𝑓 _� 〗 ^′∗(𝑑−𝑎/2)) 93.7071

As = 0.9

*

4.2 *

As =

As min = 0.37 − 0.0310 2

69.9348

0.22 *

210 10.197 4200 10.197

* 5.30

* 0.37

As min = 0.004753 m2 As min = 47.53 cm2

cm2

�_𝑠> 〖�𝑠〗 _𝑚𝑖𝑛

69.9348 > 47.53

*VARILLAS LONGITUDINALES Diametro(ø) =

0.75

〖𝑛 ^° 〗 _𝑣= �_𝑠/�_∅

n°v =

Cumple

Pulg.

69.9348 2.8502

n°v = 24.5366



n°v =

25

varillas

* Separación 𝑠= (𝑆 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)

s=

5.30 − 0.75 * 0.0254 − 2* 0.07 − 25 1

s= s=

0.2142 21.4206

m



*VARILLAS TRANSVERSALES Diametro(ø) =

0.75

Pulg.

�_𝑠 (𝑇)= �_𝑠∗𝑇/𝑆 〖𝑛 ^° 〗 _𝑣= �_(𝑠(𝑇))/�_∅ n°v =

As(T) =

69.9348 *

72.5739 2.8502

5.50 5.30 n°v = 25.4625

* Separación 𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)



* 0.0254 − 2*

As(T) =



72.5739

n°v =

cm2

26

varillas

s=

21

cm

ok !!

𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)

s=

5.50 − 0.75 * 0.0254 − 2* 0.07 − 26 1

s= s=

0.2136 21.3638

m



s=

21

cm

* VERIFICACION POR APLASTAMIENTO: *COLUMNA - ZAPATA

𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_1 Pnb = Pnb =

0.85 * 280 571.2 Tn

𝑃_𝑛= 𝑃_𝑢/∅

�_1= 𝑡_(1 )∗ 𝑡_2 A1 = 0.60 * 0.40 A1 = 0.24 m2

Ø = 0.7

𝑃_𝑛 < 𝑃_𝑛𝑏

𝑃_𝑛 < 𝑃_𝑛𝑏

223.4837 < 571.2

Pn = 156.43861 0.7 Pn = 223.4837 Tn

* 10 * 0.24

Cumple

* ZAPATA - SUELO 𝑃_𝑛𝑏 > 𝑃_𝑛

�_2=𝑇 ∗𝑋_1

√(�_2/�_1 ) ≤2 → �_0= √(�_2/�_1 ) ∗ �_1 Si:

𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_0

𝑋_1=𝑇 ∗𝑡_2/𝑡_1

X1

√(�_2/�_1 ) >2 → �_0=2∗�_1

X1 =

X1 =

T Donde:

A2 = A2 =

3.9500 * 2.6333 10.4017 m2 A0 =

Pnb = Pnb =

0.85 * 210 856.8 Tn

* 10 * 0.48

2 * 0.24 𝑃_𝑛𝑏 > 𝑃_𝑛

856.8 * PARA ZONA SISMICA (DOWELLS) 𝑃_𝑛 ≤ 𝑃_𝑛𝑏

〖�𝑠〗 _𝑚𝑖𝑛=0.005 ∗ �_1 As min = 0.005 * 2400 As min = 12 cm2

> 223.4837

3.9500 0.24

= 16.4583

A0 =

0.48

Cumple

ok !!

>

m2

2

3.95 *

2.6333

0.40 0.60 m

ok !!

Diametro(ø) = 4

1

Pulg.

* 5.0671

=

20.2683

cm2

Cumple

ok !!

* PLANOS DE PLANTA Y PERFIL:

26 ø 3/4" @ 21

S = 5.30 25 ø 3/4" @ 21

T = 5.50

DOWELLS

4

VARILLAS TRANSVERSALES 26 ø 3/4" @ 21

ø 1"

VARILLAS LONGITUDINALES 25 ø 3/4" @ 21

d = 0.37

hz = 0.45

T = 5.50

* DISEÑO DE UNA ZAPATA AISLADA CON EXCENTRICIDADES * Datos de la Zapata N° 12: CM: CV: ɣc: ɣs: F'c: S/Cpiso: σ(ult): fy: P

47.77 19.84 2.30 1.95 210.00 500.00 3.50 4200.00 67.61

* Datos de la Columna: F'c: t1 t2

280.00 70.00 40.00

GRAFICA

Tn Tn Tn/m3 Tn/m3 Kg/cm2 Kg/cm2 Kg/cm2 Kg/cm2 Tn

N.P.T + 0.30

N.T.N ± 0.00 0.15

hf: 2.00

Df:

Kg/cm2 cm cm

* Datos de la Terreno:

N.F.C-1.95 σ(ult):

NPT NTN NFC

0.15 0.00 -1.85

3.50

m m m

* Esfuezo neto del terreno:

* Dimenciones de la Zapata:

�_𝑛 = �_𝑎𝑑𝑚 − ɣ𝑝𝑟𝑜𝑚 ∗ ℎ𝑓 − 𝑆/𝐶

𝑇 =√(�_𝑍 )+ (𝑡_1−𝑡_2)/2

T= 3.2113



T=

3.25

m

1.85

𝑇 =√(�_𝑍 )+ (𝑡_1−𝑡_2)/2

�_𝑛 = �_𝑎𝑑𝑚 − ɣ𝑝𝑟𝑜𝑚 ∗ ℎ𝑓 − 𝑆/𝐶

𝑆 =√(�_𝑍 ) − (𝑡_1−𝑡_2)/2

�_𝑎𝑑𝑚 = �_𝑢𝑙𝑡/𝐹_𝑠 σn =

7.2142

Tn/m2

2.95

m

Az =

9.5875

m2

* Debe Cumplir: �_𝑣1= �_𝑣2

�_𝑍 = 𝑃/�_𝑛 9.3718

S=



* Nueva Area de la Zapata:

* Area de la Zapata:

Az =

S= 2.9113

m2

�_𝑣1= (𝑇 − 𝑡_1)/2

Lv1 =

1.275

m Cumple

�_𝑣2= (𝑆 − 𝑡_1)/2

Lv2 =

1.275

ok !!

m

* EFECTOS DE CARGA EXCENTRICA: e1 = 0.88 e2 = 0.75

e1 e2

�_2= 𝑇/6

T 6

= 0.5417

e2

>

T 6

�_1= 𝑆/6

S 6

= 0.4917

e1

>

T 6

�_(1−2)= 𝑃/�_𝑍 (1 ± 〖 6� 〗 _1/𝑆 ± 〖 6� 〗 _2/𝑇) σ1 =

T = 3.25

67.61 ( 1 9.5875

+ 6 *

0.88 2.95

σ1 = 29.4375 Tn/m2

29.4375

P

�_1 < �_𝑛 <

7.2142 No Cumple

* POR TANTEO e

�_1= 𝑃/(𝑇 ∗𝑆)(1 + 〖 6� 〗 _1/𝑆 + 〖 6� 〗 _2/𝑇)

+ 6 * 0.75 ) 3.25

σ1 =

67.61 ( 1 T*S

+ 6 *

0.88 S

+ 6 * 0.75 ) T

T=

5.5

m

σ1 =

6.6985

Tn/m2

S=

5.2

m

σ2 =

-1.9705

Tn/m2

σ2

�_𝑣1= (𝑇 − 𝑡_1)/2

Lv1 =

σ1

* DISEÑO POR PUNZONAMIENTO: 0.70 +d

�_𝑛𝑢= 𝑃_𝑢/�_𝑧

m

𝑃_𝑢= 1.7 𝐶𝑚+1.4 𝐶𝑣

Pu = 100.60583 Tn

S = 5.20

0.40

n

0.40 +d Wnu = σ1

0.70

Wnu =

6.6985

Tn/m2

T = 5.50 * CONDICION DE DISEÑO: �_𝑈/∅ ≤ �_𝐶

Ø = 0.85

〖� _𝑈 = 𝑃 〗 _𝑈− �_𝑛𝑢 ∗𝑚 ∗𝑛

* Escogemos el menor de los dos: Vc=0.27(2+4/β) √( 〖𝑓 _� 〗 ^′ ) bod

^

��=1.06√( 〖𝑓 _� 〗 ^′ ) 𝑏𝑜d

2.4

m

Vc=0.27(2+4/β) √( 〖𝑓 _� 〗 ^′ ) bod

〖� _𝑈 = 𝑃 〗 _𝑈− �_𝑛𝑢 ∗𝑚 ∗𝑛 Vu = Vu = Vu = Vu =

100.60583 − 100.60583 − 100.60583 − 98.7303 −

6.6985 x (0.70 + d ) ( 0.40 + d ) 6.6985 x (0.28 + 1.10 d + d² ) 1.8756 − 7.3683 d − 6.6985 d² 7.3683 d − 6.6985 d² 1

2

0.27 x

+

4 0.70 0.40

* bo = 2m + 2n

= 1.1571429 Vc = Vc = Vc =

* Usamos:

x 2 (0.70 +d + 0.40 + d ) d 1.06 210 x 10 ( + 2 d ) d 307.2172 1.10 337.9389 d + 614.4344 d² 2

* Reemplazando 1 y 2 98.7303 − 7.3683 d − 6.6985 d² ≤ 98.7303 − 7.3683 d − 6.6985 d² ≤ 528.9677 d²

+

( 337.9389d 287.2481 d

294.6164 d



d= d=

+ +

614.4344 d² ) * 0.85 522.2692 d²

98.7303 ≥ 0 0.2355 -0.7925

ℎ_𝑧 = d + ∅/2 +r

hz = 0.2355 + (3/4") 0.0254 + 0.07 2 hz = 0.31503 hz = ≈

𝑑 = ℎ_𝑧 − ∅/2 −r d= d=

0.35 − (3/4") 0.0254 − 0.07 2 0.27 m

* VERIFICACION POR CORTANTE: �_𝑛 ≤ �_�

�_𝑛= �_𝑢𝑑/∅

Ø = 0.85

��=1.06√( 〖𝑓 _� 〗 ^′ ) 𝑏𝑜d = 1.06 ok !!

0.35

m

σx =

3.3412

�_�=0.53 √( 〖𝑓 _� 〗 ^′ ) ∗𝑆 ∗𝑑

�_𝑢𝑑=((�_1+ �_𝑥)/2)∗𝑆 ∗(�_�−𝑑)

�_𝑥=((�_1 − �_2)(�_𝑣+ 𝑡_1+𝑑))/𝑇+�_2

Vud = Vud =

5.0198 55.5997

* 5.20 Tn

* ( 2.4



0.27 )

Vc = Vc =

Vn = 55.599663 0.85 Vn = 65.4114 Tn

0.53 210 x 10 x 5.20 x 0.27 107.8332 Tn

�_𝑛 ≤ �_�

65.4114



107.8332

Cumple

ok !!

* DISEÑO POR FLEXION: �_𝑥=((�_1 − �_2)(�_𝑣+ 𝑡_1))/𝑇+�_2

σx =

2.9156

�_𝑢=(�_𝑥/2+�_1) ∗ 𝑆∗ 〖� _𝑣 〗 ^2/3 Mu =

8.1563

* 5.20 *

Mu =

81.4323

Tn - m

Ø = 0.9

( 2.4 )² 3

𝑎= (2𝑑 ± √(4 𝑑^2 −(8 �_𝑢)/(0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ ∅ ∗𝑆)))/2

a= a=

0.5011 0.0389

a=

0.0389

m

〖�𝑠〗 _𝑚𝑖𝑛=0.22 ∗√( 〖𝑓 _� 〗 ^′/10.197)/( 〖𝑓 _� 〗 ^′/10.197) ∗𝑆 ∗𝑑

�_𝑠= �_𝑢/(∅ ∗ 〖𝑓 _� 〗 ^′∗(𝑑−𝑎/2)) 81.4323

As = 0.9

*

4.2 *

As =

As min = 0.27 − 0.0389 2

85.9837

0.22 *

210 10.197 4200 10.197

* 5.20

* 0.27

As min = 0.003403 m2 As min = 34.03 cm2

cm2

�_𝑠> 〖�𝑠〗 _𝑚𝑖𝑛

85.9837 > 34.03

*VARILLAS LONGITUDINALES Diametro(ø) =

0.75

〖𝑛 ^° 〗 _𝑣= �_𝑠/�_∅

n°v =

Cumple

Pulg.

85.9837 2.8502

n°v = 30.1673



n°v =

31

varillas

* Separación 𝑠= (𝑆 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)

s=

5.20 − 0.75 * 0.0254 − 2* 0.07 − 31 1

s= s=

0.1680 16.8032

m



*VARILLAS TRANSVERSALES Diametro(ø) =

0.75

Pulg.

�_𝑠 (𝑇)= �_𝑠∗𝑇/𝑆 〖𝑛 ^° 〗 _𝑣= �_(𝑠(𝑇))/�_∅ n°v =

As(T) =

85.9837 *

90.9443 2.8502

5.50 5.20 n°v = 31.9077

* Separación 𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)



* 0.0254 − 2*

As(T) =



90.9443

n°v =

cm2

32

varillas

s=

16

cm

ok !!

𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)

s=

5.50 − 0.75 * 0.0254 − 2* 0.07 − 32 1

s= s=

0.1723

m

17.2289

s=



17

cm

* VERIFICACION POR APLASTAMIENTO: *COLUMNA - ZAPATA

𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_1 Pnb = Pnb =

0.85 * 280 666.4 Tn

𝑃_𝑛= 𝑃_𝑢/∅

�_1= 𝑡_(1 )∗ 𝑡_2 A1 = 0.70 * 0.40 A1 = 0.28 m2

Ø = 0.7

𝑃_𝑛 < 𝑃_𝑛𝑏

𝑃_𝑛 < 𝑃_𝑛𝑏

143.7226 < 666.4

Pn = 100.60583 0.7 Pn = 143.7226 Tn

* 10 * 0.28

Cumple

* ZAPATA - SUELO 𝑃_𝑛𝑏 > 𝑃_𝑛

𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_0

�_2=𝑇 ∗𝑋_1

√(�_2/�_1 ) ≤2 → �_0= √(�_2/�_1 ) ∗ �_1 Si:

𝑋_1=𝑇 ∗𝑡_2/𝑡_1

X1

√(�_2/�_1 ) >2 → �_0=2∗�_1

X1 =

X1 =

T Donde:

A2 = A2 =

3.2500 6.0357

1.8571 * m2

A0 = Pnb = Pnb =

0.85 * 210 999.6 Tn

* 10 * 0.56

2 * 0.28 𝑃_𝑛𝑏 > 𝑃_𝑛

999.6 * PARA ZONA SISMICA (DOWELLS) 𝑃_𝑛 ≤ 𝑃_𝑛𝑏

> 143.7226

3.2500 0.28

= 11.6071

A0 =

0.56

Cumple

ok !!

>

m2

2

3.25 *

1.8571

0.40 0.70 m

ok !!

〖�𝑠〗 _𝑚𝑖𝑛=0.005 ∗ �_1 As min = 0.005 * 2800 As min = 14 cm2 Diametro(ø) = 4

1

Pulg.

* 5.0671

=

20.2683

cm2

Cumple

ok !!

* PLANOS DE PLANTA Y PERFIL:

32 ø 3/4" @ 17

S = 5.20 31 ø 3/4" @ 16

T = 5.50

DOWELLS

4

VARILLAS TRANSVERSALES 32 ø 3/4" @ 17

ø 1"

VARILLAS LONGITUDINALES 31 ø 3/4" @ 16

d = 0.27

hz = 0.35

T = 5.50

* DISEÑO DE UNA ZAPATA AISLADA CON EXCENTRICIDADES * Datos de la Zapata N° 13: CM: CV: ɣc: ɣs: F'c: S/Cpiso: σ(ult): fy: P

63.11 24.54 2.30 1.95 210.00 500.00 3.50 4200.00 87.65

GRAFICA

Tn Tn Tn/m3 Tn/m3 Kg/cm2 Kg/cm2 Kg/cm2 Kg/cm2 Tn

N.P.T + 0.30

N.T.N ± 0.00 0.15

* Datos de la Columna: hf: 2.00 F'c: t1 t2

280.00 70.00 40.00

Df:

Kg/cm2 cm cm

* Datos de la Terreno:

N.F.C-1.95 σ(ult):

NPT NTN NFC

0.15 0.00 -1.85

m m m

3.50

1.85

* Esfuezo neto del terreno:

* Dimenciones de la Zapata:

�_𝑛 = �_𝑎𝑑𝑚 − ɣ𝑝𝑟𝑜𝑚 ∗ ℎ𝑓 − 𝑆/𝐶

𝑇 =√(�_𝑍 )+ (𝑡_1−𝑡_2)/2

𝑆 =√(�_𝑍 ) − (𝑡_1−𝑡_2)/2

�_𝑎𝑑𝑚 = �_𝑢𝑙𝑡/𝐹_𝑠 σn =

7.2142

Tn/m2

T= 3.6357



T=

3.65

m

S= 3.3357



S=

3.35

m

* Nueva Area de la Zapata:

* Area de la Zapata:

Az = 12.2275 m2

* Debe Cumplir:

�_𝑍 = 𝑃/�_𝑛

�_𝑣1= �_𝑣2

Az = 12.1502 m2

�_𝑣1= (𝑇 − 𝑡_1)/2

Lv1 =

1.475

m

Lv2 =

1.475

m

Cumple

�_𝑣2= (𝑆 − 𝑡_1)/2

ok !!

* EFECTOS DE CARGA EXCENTRICA: e1 = 0.77 e2 = 0.00

e1 e2

�_2= 𝑇/6

T 6

= 0.6083

e2

<

T 6

�_1= 𝑆/6

S 6

= 0.5583

e1

>

T 6

�_(1−2)= 𝑃/�_𝑍 (1 ± 〖 6� 〗 _1/𝑆 ± 〖 6� 〗 _2/𝑇) σ1 =

T = 3.65

87.65 ( 1 12.2275

+ 6 *

0.77 3.35

σ1 = 17.0548 Tn/m2

17.0548

�_1 < �_𝑛 <

7.2142 No Cumple

+ 6 * 0.00 ) 3.65

P

* POR TANTEO �_1= 𝑃/(𝑇 ∗𝑆)(1 + 〖 6� 〗 _1/𝑆 + 〖 6� 〗 _2/𝑇)

e

σ1 =

σ2

87.65 ( 1 T*S

+ 6 *

0.77 S

T=

5

m

σ1 =

7.1675

Tn/m2

S=

4.8

m

σ2 =

0.1370

Tn/m2

�_𝑣1= (𝑇 − 𝑡_1)/2

σ1

* DISEÑO POR PUNZONAMIENTO: 0.70 +d

�_𝑛𝑢= 𝑃_𝑢/�_𝑧

m

𝑃_𝑢= 1.7 𝐶𝑚+1.4 𝐶𝑣

Pu = 130.07753 Tn

S = 4.80

0.40

n

0.40 +d Wnu = σ1

0.70

T = 5.00 * CONDICION DE DISEÑO:

+ 6 * 0.00 ) T

Wnu =

7.1675

Tn/m2

Lv1 =

2.15

m

�_𝑈/∅ ≤ �_𝐶

Ø = 0.85

* Escogemos el menor de los dos: Vc=0.27(2+4/β) √( 〖𝑓 _� 〗 ^′ ) bod

〖� _𝑈 = 𝑃 〗 _𝑈− �_𝑛𝑢 ∗𝑚 ∗𝑛 Vu = Vu = Vu = Vu =

130.07753 − 130.07753 − 130.07753 − 128.0706 −

7.1675 x (0.70 + d ) ( 0.40 + d ) 7.1675 x (0.28 + 1.10 d + d² ) 2.0069 − 7.8843 d − 7.1675 d² 7.8843 d − 7.1675 d² 1

2

0.27 x

+

4 0.70 0.40

* bo = 2m + 2n

Vc = Vc = Vc =

x 2 (0.70 +d + 0.40 + d ) d 1.06 210 x 10 307.2172 ( 1.10 + 2 d ) d 337.9389 d + 614.4344 d² 2

* Reemplazando 1 y 2

529.4367 d²

+

( 337.9389d 287.2481 d

295.1323 d



d= d=

+ +

614.4344 d² ) * 0.85 522.2692 d²

128.0706 ≥ 0 0.2866 -0.8440

ℎ_𝑧 = d + ∅/2 +r

hz = 0.2866 + (3/4") 0.0254 + 0.07 2 hz = 0.36613 hz = ≈

𝑑 = ℎ_𝑧 − ∅/2 −r d= d=

* VERIFICACION POR CORTANTE:

0.40 − (3/4") 0.0254 − 0.07 2 0.32 m

��=1.06√( 〖𝑓 _� 〗 ^′ ) 𝑏𝑜d = 1.06 ok !!

= 1.1571429 * Usamos:

128.0706 − 7.8843 d − 7.1675 d² ≤ 128.0706 − 7.8843 d − 7.1675 d² ≤

^

0.40

m

�_𝑛 ≤ �_�

�_𝑛= �_𝑢𝑑/∅

Ø = 0.85

σx =

4.5943

�_�=0.53 √( 〖𝑓 _� 〗 ^′ ) ∗𝑆 ∗𝑑

�_𝑢𝑑=((�_1+ �_𝑥)/2)∗𝑆 ∗(�_�−𝑑)

�_𝑥=((�_1 − �_2)(�_𝑣+ 𝑡_1+𝑑))/𝑇+�_2

Vud = Vud =

5.8809 51.6580

* 4.80 Tn

* ( 2.15



0.32 )

Vc = Vc =

Vn = 51.658002 0.85 Vn = 60.7741 Tn

0.53 210 x 10 x 4.80 x 0.32 117.9714 Tn

�_𝑛 ≤ �_�

60.7741



117.9714

Cumple

ok !!

* DISEÑO POR FLEXION: �_𝑥=((�_1 − �_2)(�_𝑣+ 𝑡_1))/𝑇+�_2

σx =

4.1444

�_𝑢=(�_𝑥/2+�_1) ∗ 𝑆∗ 〖� _𝑣 〗 ^2/3 Mu =

9.2397

* 4.80 *

Mu =

68.3368

Tn - m

Ø = 0.9

( 2.15)² 3

𝑎= (2𝑑 ± √(4 𝑑^2 −(8 �_𝑢)/(0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ ∅ ∗𝑆)))/2

a= a=

0.6110 0.0290

a=

0.0290

m

〖�𝑠〗 _𝑚𝑖𝑛=0.22 ∗√( 〖𝑓 _� 〗 ^′/10.197)/( 〖𝑓 _� 〗 ^′/10.197) ∗𝑆 ∗𝑑

�_𝑠= �_𝑢/(∅ ∗ 〖𝑓 _� 〗 ^′∗(𝑑−𝑎/2)) 68.3368

As = 0.9

*

4.2 *

As =

As min = 0.32 − 0.0290 2

59.1777

0.22 *

210 10.197 4200 10.197

* 4.80

* 0.32

As min = 0.003723 m2 As min = 37.23 cm2

cm2

�_𝑠> 〖�𝑠〗 _𝑚𝑖𝑛

59.1777 > 37.23

*VARILLAS LONGITUDINALES Diametro(ø) =

0.75

〖𝑛 ^° 〗 _𝑣= �_𝑠/�_∅

n°v =

Cumple

Pulg.

59.1777 2.8502

n°v = 20.7624



n°v =

21

varillas

* Separación 𝑠= (𝑆 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)

s=

4.80 − 0.75 * 0.0254 − 2* 0.07 − 21 1

s= s=

0.2320 23.2048

m



*VARILLAS TRANSVERSALES Diametro(ø) =

0.75

Pulg.

�_𝑠 (𝑇)= �_𝑠∗𝑇/𝑆 〖𝑛 ^° 〗 _𝑣= �_(𝑠(𝑇))/�_∅ n°v =

As(T) =

59.1777 *

61.6434 2.8502

5.00 4.80 n°v = 21.6275

* Separación 𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)



* 0.0254 − 2*

As(T) =



61.6434

n°v =

cm2

22

varillas

s=

23

cm

ok !!

𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)

s=

5.00 − 0.75 * 0.0254 − 2* 0.07 − 22 1

s= s=

0.2305

m

23.0521

s=



23

cm

* VERIFICACION POR APLASTAMIENTO: *COLUMNA - ZAPATA

𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_1 Pnb = Pnb =

0.85 * 280 666.4 Tn

𝑃_𝑛= 𝑃_𝑢/∅

�_1= 𝑡_(1 )∗ 𝑡_2 A1 = 0.70 * 0.40 A1 = 0.28 m2

Ø = 0.7

𝑃_𝑛 < 𝑃_𝑛𝑏

𝑃_𝑛 < 𝑃_𝑛𝑏

185.8250 < 666.4

Pn = 130.07753 0.7 Pn = 185.8250 Tn

* 10 * 0.28

Cumple

* ZAPATA - SUELO 𝑃_𝑛𝑏 > 𝑃_𝑛

𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_0

�_2=𝑇 ∗𝑋_1

√(�_2/�_1 ) ≤2 → �_0= √(�_2/�_1 ) ∗ �_1 Si:

𝑋_1=𝑇 ∗𝑡_2/𝑡_1

X1

√(�_2/�_1 ) >2 → �_0=2∗�_1

X1 =

X1 =

T Donde:

A2 = A2 =

3.6500 7.6129

2.0857 * m2

A0 = Pnb = Pnb =

0.85 * 210 999.6 Tn

* 10 * 0.56

2 * 0.28 𝑃_𝑛𝑏 > 𝑃_𝑛

999.6 * PARA ZONA SISMICA (DOWELLS) 𝑃_𝑛 ≤ 𝑃_𝑛𝑏

> 185.8250

3.6500 0.28

= 13.0357

A0 =

0.56

Cumple

ok !!

>

m2

2

3.65 *

2.0857

0.40 0.70 m

ok !!

〖�𝑠〗 _𝑚𝑖𝑛=0.005 ∗ �_1 As min = 0.005 * 2800 As min = 14 cm2 Diametro(ø) = 4

1

Pulg.

* 5.0671

=

20.2683

cm2

Cumple

ok !!

* PLANOS DE PLANTA Y PERFIL:

22 ø 3/4" @ 23

S = 4.80 21 ø 3/4" @ 23

T = 5.00

DOWELLS

4

VARILLAS TRANSVERSALES 22 ø 3/4" @ 23

ø 1"

VARILLAS LONGITUDINALES 21 ø 3/4" @ 23

d = 0.32

hz = 0.40

T = 5.00

* DISEÑO DE UNA ZAPATA AISLADA CON EXCENTRICIDADES * Datos de la Zapata N° 16: CM: CV: ɣc: ɣs: F'c: S/Cpiso: σ(ult): fy: P

24.37 15.98 2.30 1.95 210.00 500.00 3.50 4200.00 40.35

* Datos de la Columna: F'c: t1 t2

280.00 40.00 40.00

GRAFICA

Tn Tn Tn/m3 Tn/m3 Kg/cm2 Kg/cm2 Kg/cm2 Kg/cm2 Tn

N.P.T + 0.30

0.15

hf: 2.00

Df:

Kg/cm2 cm cm

* Datos de la Terreno:

N.F.C-1.95 σ(ult):

NPT NTN NFC

0.15 0.00 -1.85

N.T.N ± 0.00

m m m

3.50

1.85

* Esfuezo neto del terreno:

* Dimenciones de la Zapata:

�_𝑛 = �_𝑎𝑑𝑚 − ɣ𝑝𝑟𝑜𝑚 ∗ ℎ𝑓 − 𝑆/𝐶

𝑇 =√(�_𝑍 )+ (𝑡_1−𝑡_2)/2

�_𝑎𝑑𝑚 = �_𝑢𝑙𝑡/𝐹_𝑠 σn =

7.2142

Tn/m2

T=

2.40

m

S= 2.3649



S=

2.40

m

Az =

5.76

m2

* Debe Cumplir: �_𝑣1= �_𝑣2

�_𝑍 = 𝑃/�_𝑛 5.5928



* Nueva Area de la Zapata:

* Area de la Zapata:

Az =

𝑆 =√(�_𝑍 ) − (𝑡_1−𝑡_2)/2

T= 2.3649

m2

�_𝑣1= (𝑇 − 𝑡_1)/2

Lv1 =

1

m

Lv2 =

1

m

Cumple ok !!

�_𝑣2= (𝑆 − 𝑡_1)/2

* EFECTOS DE CARGA EXCENTRICA: e1 = 0.41 e2 = 0.02 e2 e1

�_2= 𝑇/6

T 6

= 0.4000

e2

<

T 6

�_1= 𝑆/6

S 6

= 0.4000

e1

>

T 6

�_(1−2)= 𝑃/�_𝑍 (1 ± 〖 6� 〗 _1/𝑆 ± 〖 6� 〗 _2/𝑇) σ1 = T = 2.40

40.35 ( 1 5.76

+ 6 *

0.41 2.40

σ1 = 14.5348 Tn/m2

14.5348

�_1 < �_𝑛 <

7.2142 No Cumple

+ 6 * 0.02 ) 2.40

P

* POR TANTEO �_1= 𝑃/(𝑇 ∗𝑆)(1 + 〖 6� 〗 _1/𝑆 + 〖 6� 〗 _2/𝑇)

e

σ1 =

σ2

40.35 ( 1 T*S

+ 6 *

0.41 S

T=

3.5

m

σ1 =

6.4953

Tn/m2

S=

3.2

m

σ2 =

0.7095

Tn/m2

�_𝑣1= (𝑇 − 𝑡_1)/2

σ1

* DISEÑO POR PUNZONAMIENTO: 0.40 +d

�_𝑛𝑢= 𝑃_𝑢/�_𝑧

m

𝑃_𝑢= 1.7 𝐶𝑚+1.4 𝐶𝑣

Pu = 61.280535 Tn

S = 3.20

0.40

n

0.40 +d Wnu = σ1

0.40

T = 3.50 * CONDICION DE DISEÑO: �_𝑈/∅ ≤ �_𝐶

+ 6 * 0.02 ) T

Wnu =

6.4953

Tn/m2

Lv1 =

1.55

m

�_𝑈/∅ ≤ �_𝐶

Ø = 0.85

* Escogemos el menor de los dos: Vc=0.27(2+4/β) √( 〖𝑓 _� 〗 ^′ ) bod

〖� _𝑈 = 𝑃 〗 _𝑈− �_𝑛𝑢 ∗𝑚 ∗𝑛 Vu = Vu = Vu = Vu =

61.280535 − 61.280535 − 61.280535 − 60.2413 −

6.4953 x (0.40 + d ) ( 0.40 + d ) 6.4953 x (0.16 + 0.80 d + d² ) 1.0392 − 5.1962 d − 6.4953 d² 5.1962 d − 6.4953 d² 1

2

0.27 x

=

+

4 0.40 0.40

* bo = 2m + 2n

Vc = Vc = Vc =

x 2 (0.40 +d + 0.40 + d ) d 1.06 210 x 10 ( + 2 d ) d 307.2172 0.80 245.7737 d + 614.4344 d² 2

* Reemplazando 1 y 2

528.7645 d²

+

( 245.7737d 208.9077 d

214.1039 d



d= d=

+ +

614.4344 d² ) * 0.85 522.2692 d²

60.2413 ≥ 0 0.1911 -0.5961

ℎ_𝑧 = d + ∅/2 +r

hz = 0.1911 + (3/4") 0.0254 + 0.07 2 hz = 0.27063 hz = ≈

𝑑 = ℎ_𝑧 − ∅/2 −r d= d=

* VERIFICACION POR CORTANTE:

0.30 − (3/4") 0.0254 − 0.07 2 0.22 m

0.30

��=1.06√( 〖𝑓 _� 〗 ^′ ) 𝑏𝑜d = 1.06 ok !!

1.62

* Usamos:

60.2413 − 5.1962 d − 6.4953 d² ≤ 60.2413 − 5.1962 d − 6.4953 d² ≤

^

m

�_𝑛 ≤ �_�

�_𝑛= �_𝑢𝑑/∅

Ø = 0.85

σx =

4.2967

�_�=0.53 √( 〖𝑓 _� 〗 ^′ ) ∗𝑆 ∗𝑑

�_𝑢𝑑=((�_1+ �_𝑥)/2)∗𝑆 ∗(�_�−𝑑)

�_𝑥=((�_1 − �_2)(�_𝑣+ 𝑡_1+𝑑))/𝑇+�_2

Vud = Vud =

5.3960 22.9654

* 3.20 Tn

* ( 1.55



0.22 )

Vc = Vc =

Vn = 22.965404 0.85 Vn = 27.0181 Tn

0.53 210 x 10 x 3.20 x 0.22 54.0702 Tn

�_𝑛 ≤ �_�

27.0181



54.0702

Cumple ok !!

* DISEÑO POR FLEXION: �_𝑥=((�_1 − �_2)(�_𝑣+ 𝑡_1))/𝑇+�_2

σx =

3.9330

�_𝑢=(�_𝑥/2+�_1) ∗ 𝑆∗ 〖� _𝑣 〗 ^2/3 Mu =

8.4618

* 3.20 *

Mu =

21.6848

Tn - m

Ø = 0.9

( 1.55)² 3

𝑎= (2𝑑 ± √(4 𝑑^2 −(8 �_𝑢)/(0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ ∅ ∗𝑆)))/2

a= a=

0.4199 0.0201

a=

0.0201

m

〖�𝑠〗 _𝑚𝑖𝑛=0.22 ∗√( 〖𝑓 _� 〗 ^′/10.197)/( 〖𝑓 _� 〗 ^′/10.197) ∗𝑆 ∗𝑑

�_𝑠= �_𝑢/(∅ ∗ 〖𝑓 _� 〗 ^′∗(𝑑−𝑎/2)) 21.6848

As = 0.9

*

4.2 *

As =

As min = 0.22 − 0.0201 2

27.3237

0.22 *

210 10.197 4200 10.197

* 3.20

* 0.22

As min = 0.001706 m2 As min = 17.06 cm2

cm2

�_𝑠> 〖�𝑠〗 _𝑚𝑖𝑛

27.3237 > 17.06

*VARILLAS LONGITUDINALES Diametro(ø) =

0.75

〖𝑛 ^° 〗 _𝑣= �_𝑠/�_∅

n°v =

Cumple

Pulg.

27.3237 2.8502

n°v =

9.5865



n°v =

10

varillas

* Separación 𝑠= (𝑆 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)

s=

3.20 − 0.75 * 0.0254 − 2* 0.07 − 10 1

s= s=

0.3379 33.7883

m



*VARILLAS TRANSVERSALES Diametro(ø) =

0.75

Pulg.

�_𝑠 (𝑇)= �_𝑠∗𝑇/𝑆 〖𝑛 ^° 〗 _𝑣= �_(𝑠(𝑇))/�_∅ n°v =

As(T) =

27.3237 *

29.8852 2.8502

3.50 3.20 n°v = 10.4852

* Separación 𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)



* 0.0254 − 2*

As(T) =



29.8852

n°v =

cm2

11

varillas

s=

33

cm

ok !!

𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)

s=

3.50 − 0.75 * 0.0254 − 2* 0.07 − 11 1

s= s=

0.3341

m

33.4095

s=



33

cm

* VERIFICACION POR APLASTAMIENTO: *COLUMNA - ZAPATA

𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_1 Pnb = Pnb =

0.85 * 280 380.8 Tn

𝑃_𝑛= 𝑃_𝑢/∅

�_1= 𝑡_(1 )∗ 𝑡_2 A1 = 0.40 * 0.40 A1 = 0.16 m2

Ø = 0.7

𝑃_𝑛 < 𝑃_𝑛𝑏

𝑃_𝑛 < 𝑃_𝑛𝑏

Pn = 61.280535 0.7 Pn = 87.5436 Tn

* 10 * 0.16

87.5436

< 380.8

Cumple

* ZAPATA - SUELO 𝑃_𝑛𝑏 > 𝑃_𝑛

𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_0

�_2=𝑇 ∗𝑋_1

√(�_2/�_1 ) ≤2 → �_0= √(�_2/�_1 ) ∗ �_1 Si:

𝑋_1=𝑇 ∗𝑡_2/𝑡_1

X1

√(�_2/�_1 ) >2 → �_0=2∗�_1

X1 =

X1 =

T Donde:

A2 = A2 =

2.4000 5.7600

2.4000 * m2

A0 = Pnb = Pnb =

0.85 * 210 571.2 Tn

* 10 * 0.32

2 * 0.16 𝑃_𝑛𝑏 > 𝑃_𝑛

571.2 * PARA ZONA SISMICA (DOWELLS) 𝑃_𝑛 ≤ 𝑃_𝑛𝑏

> 87.5436

2.4000 0.16

= 15.0000

A0 =

0.32

Cumple

ok !!

>

m2

2

2.40 *

2.4000

0.40 0.40 m

ok !!

〖�𝑠〗 _𝑚𝑖𝑛=0.005 ∗ �_1 As min = 0.005 * 1600 As min = 8 cm2 Diametro(ø) = 4

1

Pulg.

* 5.0671

=

20.2683

cm2

Cumple

ok !!

* PLANOS DE PLANTA Y PERFIL:

11 ø 3/4" @ 33

S = 3.20 10 ø 3/4" @ 33

T = 3.50

DOWELLS

4

VARILLAS TRANSVERSALES 11 ø 3/4" @ 33

ø 1"

VARILLAS LONGITUDINALES 10 ø 3/4" @ 33

d = 0.22

hz = 0.30

T = 3.50

* DISEÑO DE UNA ZAPATA AISLADA CON EXCENTRICIDADES * Datos de la Zapata N° 17: CM: CV: ɣc: ɣs: F'c: S/Cpiso: σ(ult): fy: P

18.44 11.06 2.30 1.95 210.00 500.00 3.50 4200.00 29.51

* Datos de la Columna: F'c: t1 t2

280.00 40.00 40.00

GRAFICA

Tn Tn Tn/m3 Tn/m3 Kg/cm2 Kg/cm2 Kg/cm2 Kg/cm2 Tn

N.P.T + 0.30

0.15

hf: 2.00

Df:

Kg/cm2 cm cm

* Datos de la Terreno:

N.F.C-1.95 σ(ult):

NPT NTN NFC

0.15 0.00 -1.85

N.T.N ± 0.00

m m m

3.50

1.85

* Esfuezo neto del terreno:

* Dimenciones de la Zapata:

�_𝑛 = �_𝑎𝑑𝑚 − ɣ𝑝𝑟𝑜𝑚 ∗ ℎ𝑓 − 𝑆/𝐶

𝑇 =√(�_𝑍 )+ (𝑡_1−𝑡_2)/2

�_𝑎𝑑𝑚 = �_𝑢𝑙𝑡/𝐹_𝑠 σn =

7.2142

Tn/m2

T=

2.05

m

S= 2.0224



S=

2.05

m

Az =

4.2025

m2

* Debe Cumplir: �_𝑣1= �_𝑣2

�_𝑍 = 𝑃/�_𝑛 4.0902



* Nueva Area de la Zapata:

* Area de la Zapata:

Az =

𝑆 =√(�_𝑍 ) − (𝑡_1−𝑡_2)/2

T= 2.0224

m2

�_𝑣1= (𝑇 − 𝑡_1)/2

Lv1 =

0.825

m

Lv2 =

0.825

m

Cumple ok !!

�_𝑣2= (𝑆 − 𝑡_1)/2

* EFECTOS DE CARGA EXCENTRICA: e1 = 0.40 e2 = 0.80 e2 e1

�_2= 𝑇/6

T 6

= 0.3417

e2

>

T 6

�_1= 𝑆/6

S 6

= 0.3417

e1

>

T 6

�_(1−2)= 𝑃/�_𝑍 (1 ± 〖 6� 〗 _1/𝑆 ± 〖 6� 〗 _2/𝑇) σ1 = T = 2.05

29.51 ( 1 4.2025

+ 6 *

0.40 2.05

σ1 = 31.6818 Tn/m2

31.6818

�_1 < �_𝑛 <

7.2142 No Cumple

+ 6 * 0.80 ) 2.05

P

* POR TANTEO �_1= 𝑃/(𝑇 ∗𝑆)(1 + 〖 6� 〗 _1/𝑆 + 〖 6� 〗 _2/𝑇)

e

σ1 =

σ2

29.51 ( 1 T*S

+ 6 *

0.40 S

T=

3.8

m

σ1 =

6.5424

Tn/m2

S=

3.5

m

σ2 =

-2.1052

Tn/m2

�_𝑣1= (𝑇 − 𝑡_1)/2

σ1

* DISEÑO POR PUNZONAMIENTO: 0.40 +d

�_𝑛𝑢= 𝑃_𝑢/�_𝑧

m

𝑃_𝑢= 1.7 𝐶𝑚+1.4 𝐶𝑣

Pu = 44.629623 Tn

S = 3.50

0.40

n

0.40 +d Wnu = σ1

0.40

T = 3.80 * CONDICION DE DISEÑO: �_𝑈/∅ ≤ �_𝐶

+ 6 * 0.80 ) T

Wnu =

6.5424

Tn/m2

Lv1 =

1.7

m

�_𝑈/∅ ≤ �_𝐶

Ø = 0.85

* Escogemos el menor de los dos: Vc=0.27(2+4/β) √( 〖𝑓 _� 〗 ^′ ) bod

〖� _𝑈 = 𝑃 〗 _𝑈− �_𝑛𝑢 ∗𝑚 ∗𝑛 Vu = Vu = Vu = Vu =

44.629623 − 44.629623 − 44.629623 − 43.5828 −

6.5424 x (0.40 + d ) ( 0.40 + d ) 6.5424 x (0.16 + 0.80 d + d² ) 1.0468 − 5.2339 d − 6.5424 d² 5.2339 d − 6.5424 d² 1

2

0.27 x

=

+

4 0.40 0.40

* bo = 2m + 2n

Vc = Vc = Vc =

x 2 (0.40 +d + 0.40 + d ) d 1.06 210 x 10 ( + 2 d ) d 307.2172 0.80 245.7737 d + 614.4344 d² 2

* Reemplazando 1 y 2

528.8116 d²

+

( 245.7737d 208.9077 d

214.1416 d



d= d=

+ +

614.4344 d² ) * 0.85 522.2692 d²

43.5828 ≥ 0 0.1488 -0.5538

ℎ_𝑧 = d + ∅/2 +r

hz = 0.1488 + (3/4") 0.0254 + 0.07 2 hz = 0.22833 hz = ≈

𝑑 = ℎ_𝑧 − ∅/2 −r d= d=

* VERIFICACION POR CORTANTE:

0.25 − (3/4") 0.0254 − 0.07 2 0.17 m

0.25

��=1.06√( 〖𝑓 _� 〗 ^′ ) 𝑏𝑜d = 1.06 ok !!

1.62

* Usamos:

43.5828 − 5.2339 d − 6.5424 d² ≤ 43.5828 − 5.2339 d − 6.5424 d² ≤

^

m

�_𝑛 ≤ �_�

�_𝑛= �_𝑢𝑑/∅

Ø = 0.85

σx =

3.0606

�_�=0.53 √( 〖𝑓 _� 〗 ^′ ) ∗𝑆 ∗𝑑

�_𝑢𝑑=((�_1+ �_𝑥)/2)∗𝑆 ∗(�_�−𝑑)

�_𝑥=((�_1 − �_2)(�_𝑣+ 𝑡_1+𝑑))/𝑇+�_2

Vud = Vud =

4.8015 25.7119

* 3.50 Tn

* ( 1.7



0.17 )

Vc = Vc =

Vn = 25.711875 0.85 Vn = 30.2493 Tn

0.53 210 x 10 x 3.50 x 0.17 45.6986 Tn

�_𝑛 ≤ �_�

30.2493



45.6986

Cumple ok !!

* DISEÑO POR FLEXION: �_𝑥=((�_1 − �_2)(�_𝑣+ 𝑡_1))/𝑇+�_2

σx =

2.6737

�_𝑢=(�_𝑥/2+�_1) ∗ 𝑆∗ 〖� _𝑣 〗 ^2/3 Mu =

7.8792

* 3.50 *

Mu =

26.5661

Tn - m

Ø = 0.9

( 1.7 )² 3

𝑎= (2𝑑 ± √(4 𝑑^2 −(8 �_𝑢)/(0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ ∅ ∗𝑆)))/2

a= a=

0.3095 0.0305

a=

0.0305

m

〖�𝑠〗 _𝑚𝑖𝑛=0.22 ∗√( 〖𝑓 _� 〗 ^′/10.197)/( 〖𝑓 _� 〗 ^′/10.197) ∗𝑆 ∗𝑑

�_𝑠= �_𝑢/(∅ ∗ 〖𝑓 _� 〗 ^′∗(𝑑−𝑎/2)) 26.5661

As = 0.9

*

4.2 *

As =

As min = 0.17 − 0.0305 2

45.4207

0.22 *

210 10.197 4200 10.197

* 3.50

* 0.17

As min = 0.001442 m2 As min = 14.42 cm2

cm2

�_𝑠> 〖�𝑠〗 _𝑚𝑖𝑛

45.4207 > 14.42

*VARILLAS LONGITUDINALES Diametro(ø) =

0.75

〖𝑛 ^° 〗 _𝑣= �_𝑠/�_∅

n°v =

Cumple

Pulg.

45.4207 2.8502

n°v = 15.9358



n°v =

16

varillas

* Separación 𝑠= (𝑆 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)

s=

3.50 − 0.75 * 0.0254 − 2* 0.07 − 16 1

s= s=

0.2227 22.2730

m



*VARILLAS TRANSVERSALES Diametro(ø) =

0.75

Pulg.

�_𝑠 (𝑇)= �_𝑠∗𝑇/𝑆 〖𝑛 ^° 〗 _𝑣= �_(𝑠(𝑇))/�_∅ n°v =

As(T) =

45.4207 *

49.3139 2.8502

3.80 3.50 n°v = 17.3017

* Separación 𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)



* 0.0254 − 2*

As(T) =



49.3139

n°v =

cm2

18

varillas

s=

22

cm

ok !!

𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)

s=

3.80 − 0.75 * 0.0254 − 2* 0.07 − 18 1

s= s=

0.2142

m

21.4174

s=



21

cm

* VERIFICACION POR APLASTAMIENTO: *COLUMNA - ZAPATA

𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_1 Pnb = Pnb =

0.85 * 280 380.8 Tn

𝑃_𝑛= 𝑃_𝑢/∅

�_1= 𝑡_(1 )∗ 𝑡_2 A1 = 0.40 * 0.40 A1 = 0.16 m2

Ø = 0.7

𝑃_𝑛 < 𝑃_𝑛𝑏

𝑃_𝑛 < 𝑃_𝑛𝑏

Pn = 44.629623 0.7 Pn = 63.7566 Tn

* 10 * 0.16

63.7566

< 380.8

Cumple

* ZAPATA - SUELO 𝑃_𝑛𝑏 > 𝑃_𝑛

𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_0

�_2=𝑇 ∗𝑋_1

√(�_2/�_1 ) ≤2 → �_0= √(�_2/�_1 ) ∗ �_1 Si:

𝑋_1=𝑇 ∗𝑡_2/𝑡_1

X1

√(�_2/�_1 ) >2 → �_0=2∗�_1

X1 =

X1 =

T Donde:

A2 = A2 =

2.0500 4.2025

2.0500 * m2

A0 = Pnb = Pnb =

0.85 * 210 571.2 Tn

* 10 * 0.32

2 * 0.16 𝑃_𝑛𝑏 > 𝑃_𝑛

571.2 * PARA ZONA SISMICA (DOWELLS) 𝑃_𝑛 ≤ 𝑃_𝑛𝑏

> 63.7566

2.0500 0.16

= 12.8125

A0 =

0.32

Cumple

ok !!

>

m2

2

2.05 *

2.0500

0.40 0.40 m

ok !!

〖�𝑠〗 _𝑚𝑖𝑛=0.005 ∗ �_1 As min = 0.005 * 1600 As min = 8 cm2 Diametro(ø) = 4

1

Pulg.

* 5.0671

=

20.2683

cm2

Cumple

ok !!

* PLANOS DE PLANTA Y PERFIL:

18 ø 3/4" @ 21

S = 3.50 16 ø 3/4" @ 22

T = 3.80

DOWELLS

4

VARILLAS TRANSVERSALES 18 ø 3/4" @ 21

ø 1"

VARILLAS LONGITUDINALES 16 ø 3/4" @ 22

d = 0.17

hz = 0.25

T = 3.80

* DISEÑO DE UNA ZAPATA AISLADA CON EXCENTRICIDADES * Datos de la Zapata N° 19: CM: CV: ɣc: ɣs: F'c: S/Cpiso: σ(ult): fy: P

65.06 34.90 2.30 1.95 210.00 500.00 3.50 4200.00 99.96

* Datos de la Columna: F'c: t1 t2

280.00 60.00 40.00

GRAFICA

Tn Tn Tn/m3 Tn/m3 Kg/cm2 Kg/cm2 Kg/cm2 Kg/cm2 Tn

N.P.T + 0.30

0.15

hf: 2.00

Df:

Kg/cm2 cm cm

* Datos de la Terreno:

N.F.C-1.95 σ(ult):

NPT NTN NFC

0.15 0.00 -1.85

N.T.N ± 0.00

m m m

3.50

1.85

* Esfuezo neto del terreno:

* Dimenciones de la Zapata:

�_𝑛 = �_𝑎𝑑𝑚 − ɣ𝑝𝑟𝑜𝑚 ∗ ℎ𝑓 − 𝑆/𝐶

𝑇 =√(�_𝑍 )+ (𝑡_1−𝑡_2)/2

�_𝑎𝑑𝑚 = �_𝑢𝑙𝑡/𝐹_𝑠 σn =

7.2142

Tn/m2

𝑆 =√(�_𝑍 ) − (𝑡_1−𝑡_2)/2

T= 3.8223



T=

3.85

m

S= 3.6223



S=

3.65

m

* Nueva Area de la Zapata:

* Area de la Zapata:

Az = 14.0525 m2

* Debe Cumplir: �_𝑣1= �_𝑣2

�_𝑍 = 𝑃/�_𝑛 Az = 13.8558 m2

�_𝑣1= (𝑇 − 𝑡_1)/2

Lv1 =

1.625

m

Lv2 =

1.625

m

Cumple ok !!

�_𝑣2= (𝑆 − 𝑡_1)/2

* EFECTOS DE CARGA EXCENTRICA: e1 = 0.01 e2 = 0.77 e2 e1

�_2= 𝑇/6

T 6

= 0.6417

e2

>

T 6

�_1= 𝑆/6

S 6

= 0.6083

e1

<

T 6

�_(1−2)= 𝑃/�_𝑍 (1 ± 〖 6� 〗 _1/𝑆 ± 〖 6� 〗 _2/𝑇) σ1 = T = 3.85

99.96 ( 1 14.0525

+ 6 *

0.01 3.65

σ1 = 15.7659 Tn/m2

15.7659

�_1 < �_𝑛 <

7.2142 No Cumple

+ 6 * 0.77 ) 3.85

P

* POR TANTEO �_1= 𝑃/(𝑇 ∗𝑆)(1 + 〖 6� 〗 _1/𝑆 + 〖 6� 〗 _2/𝑇)

e

σ1 =

σ2

99.96 ( 1 T*S

+ 6 *

0.01 S

T=

5.4

m

σ1 =

6.9140

Tn/m2

S=

5

m

σ2 =

0.4903

Tn/m2

�_𝑣1= (𝑇 − 𝑡_1)/2

σ1

* DISEÑO POR PUNZONAMIENTO: 0.60 +d

�_𝑛𝑢= 𝑃_𝑢/�_𝑧

m

𝑃_𝑢= 1.7 𝐶𝑚+1.4 𝐶𝑣

Pu = 150.41074 Tn

S = 5.00

0.40

n

0.40 +d Wnu = σ1

0.60

T = 5.40 * CONDICION DE DISEÑO: �_𝑈/∅ ≤ �_𝐶

+ 6 * 0.77 ) T

Wnu =

6.9140

Tn/m2

Lv1 =

2.4

m

�_𝑈/∅ ≤ �_𝐶

Ø = 0.85

* Escogemos el menor de los dos: Vc=0.27(2+4/β) √( 〖𝑓 _� 〗 ^′ ) bod

〖� _𝑈 = 𝑃 〗 _𝑈− �_𝑛𝑢 ∗𝑚 ∗𝑛 Vu = Vu = Vu = Vu =

150.41074 − 150.41074 − 150.41074 − 148.7514 −

6.9140 x (0.60 + d ) ( 0.40 + d ) 6.9140 x (0.24 + 1.00 d + d² ) 1.6594 − 6.9140 d − 6.9140 d² 6.9140 d − 6.9140 d² 1

2

0.27 x

=

+

4 0.60 0.40

* bo = 2m + 2n

Vc = Vc = Vc =

x 2 (0.60 +d + 0.40 + d ) d 1.06 210 x 10 ( + 2 d ) d 307.2172 1.00 307.2172 d + 614.4344 d² 2

* Reemplazando 1 y 2

529.1832 d²

+

( 307.2172d 261.1346 d

268.0486 d



d= d=

+ +

614.4344 d² ) * 0.85 522.2692 d²

148.7514 ≥ 0 0.3343 -0.8408

ℎ_𝑧 = d + ∅/2 +r

hz = 0.3343 + (3/4") 0.0254 + 0.07 2 hz = 0.41383 hz = ≈

𝑑 = ℎ_𝑧 − ∅/2 −r d= d=

* VERIFICACION POR CORTANTE:

0.45 − (3/4") 0.0254 − 0.07 2 0.37 m

0.45

��=1.06√( 〖𝑓 _� 〗 ^′ ) 𝑏𝑜d = 1.06 ok !!

1.26

* Usamos:

148.7514 − 6.9140 d − 6.9140 d² ≤ 148.7514 − 6.9140 d − 6.9140 d² ≤

^

m

�_𝑛 ≤ �_�

�_𝑛= �_𝑢𝑑/∅

Ø = 0.85

σx =

4.4992

�_�=0.53 √( 〖𝑓 _� 〗 ^′ ) ∗𝑆 ∗𝑑

�_𝑢𝑑=((�_1+ �_𝑥)/2)∗𝑆 ∗(�_�−𝑑)

�_𝑥=((�_1 − �_2)(�_𝑣+ 𝑡_1+𝑑))/𝑇+�_2

Vud = Vud =

5.7066 57.9216

* 5.00 Tn

* ( 2.4



0.37 )

Vc = Vc =

Vn = 57.921611 0.85 Vn = 68.1431 Tn

0.53 210 x 10 x 5.00 x 0.37 142.0879 Tn

�_𝑛 ≤ �_�

68.1431



142.0879

Cumple ok !!

* DISEÑO POR FLEXION: �_𝑥=((�_1 − �_2)(�_𝑣+ 𝑡_1))/𝑇+�_2

σx =

4.0590

�_𝑢=(�_𝑥/2+�_1) ∗ 𝑆∗ 〖� _𝑣 〗 ^2/3 Mu =

8.9435

* 5.00 *

Mu =

85.8574

Tn - m

Ø = 0.9

( 2.4 )² 3

𝑎= (2𝑑 ± √(4 𝑑^2 −(8 �_𝑢)/(0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ ∅ ∗𝑆)))/2

a= a=

0.7099 0.0301

a=

0.0301

m

〖�𝑠〗 _𝑚𝑖𝑛=0.22 ∗√( 〖𝑓 _� 〗 ^′/10.197)/( 〖𝑓 _� 〗 ^′/10.197) ∗𝑆 ∗𝑑

�_𝑠= �_𝑢/(∅ ∗ 〖𝑓 _� 〗 ^′∗(𝑑−𝑎/2)) 85.8574

As = 0.9

*

4.2 *

As =

As min = 0.37 − 0.0301 2

63.9922

0.22 *

210 10.197 4200 10.197

* 5.00

* 0.37

As min = 0.004484 m2 As min = 44.84 cm2

cm2

�_𝑠> 〖�𝑠〗 _𝑚𝑖𝑛

63.9922 > 44.84

*VARILLAS LONGITUDINALES Diametro(ø) =

0.75

〖𝑛 ^° 〗 _𝑣= �_𝑠/�_∅

n°v =

Cumple

Pulg.

63.9922 2.8502

n°v = 22.4516



n°v =

23

varillas

* Separación 𝑠= (𝑆 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)

s=

5.00 − 0.75 * 0.0254 − 2* 0.07 − 23 1

s= s=

0.2200 22.0043

m



*VARILLAS TRANSVERSALES Diametro(ø) =

0.75

Pulg.

�_𝑠 (𝑇)= �_𝑠∗𝑇/𝑆 〖𝑛 ^° 〗 _𝑣= �_(𝑠(𝑇))/�_∅ n°v =

As(T) =

63.9922 *

69.1116 2.8502

5.40 5.00 n°v = 24.2477

* Separación 𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)



* 0.0254 − 2*

As(T) =



69.1116

n°v =

cm2

25

varillas

s=

22

cm

ok !!

𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)

s=

5.40 − 0.75 * 0.0254 − 2* 0.07 − 25 1

s= s=

0.2184

m

21.8373

s=



21

cm

* VERIFICACION POR APLASTAMIENTO: *COLUMNA - ZAPATA

𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_1 Pnb = Pnb =

0.85 * 280 571.2 Tn

𝑃_𝑛= 𝑃_𝑢/∅

�_1= 𝑡_(1 )∗ 𝑡_2 A1 = 0.60 * 0.40 A1 = 0.24 m2

Ø = 0.7

𝑃_𝑛 < 𝑃_𝑛𝑏

𝑃_𝑛 < 𝑃_𝑛𝑏

214.8725 < 571.2

Pn = 150.41074 0.7 Pn = 214.8725 Tn

* 10 * 0.24

Cumple

* ZAPATA - SUELO 𝑃_𝑛𝑏 > 𝑃_𝑛

𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_0

�_2=𝑇 ∗𝑋_1

√(�_2/�_1 ) ≤2 → �_0= √(�_2/�_1 ) ∗ �_1 Si:

𝑋_1=𝑇 ∗𝑡_2/𝑡_1

X1

√(�_2/�_1 ) >2 → �_0=2∗�_1

X1 =

X1 =

T Donde:

A2 = A2 =

3.8500 9.8817

2.5667 * m2

A0 = Pnb = Pnb =

0.85 * 210 856.8 Tn

* 10 * 0.48

2 * 0.24 𝑃_𝑛𝑏 > 𝑃_𝑛

856.8 * PARA ZONA SISMICA (DOWELLS) 𝑃_𝑛 ≤ 𝑃_𝑛𝑏

> 214.8725

3.8500 0.24

= 16.0417

A0 =

0.48

Cumple

ok !!

>

m2

2

3.85 *

2.5667

0.40 0.60 m

ok !!

〖�𝑠〗 _𝑚𝑖𝑛=0.005 ∗ �_1 As min = 0.005 * 2400 As min = 12 cm2 Diametro(ø) = 4

1

Pulg.

* 5.0671

=

20.2683

cm2

Cumple

ok !!

* PLANOS DE PLANTA Y PERFIL:

25 ø 3/4" @ 21

S = 5.00 23 ø 3/4" @ 22

T = 5.40

DOWELLS

4

VARILLAS TRANSVERSALES 25 ø 3/4" @ 21

ø 1"

VARILLAS LONGITUDINALES 23 ø 3/4" @ 22

d = 0.37

hz = 0.45

T = 5.40

* DISEÑO DE UNA ZAPATA AISLADA CON EXCENTRICIDADES * Datos de la Zapata N° 20: CM: CV: ɣc: ɣs: F'c: S/Cpiso: σ(ult): fy: P

47.65 19.97 2.30 1.95 210.00 500.00 3.50 4200.00 67.61

* Datos de la Columna: F'c: t1 t2

280.00 70.00 40.00

GRAFICA

Tn Tn Tn/m3 Tn/m3 Kg/cm2 Kg/cm2 Kg/cm2 Kg/cm2 Tn

N.P.T + 0.30

0.15

hf: 2.00

Df:

Kg/cm2 cm cm

* Datos de la Terreno:

N.F.C-1.95 σ(ult):

NPT NTN NFC

0.15 0.00 -1.85

N.T.N ± 0.00

m m m

3.50

1.85

* Esfuezo neto del terreno:

* Dimenciones de la Zapata:

�_𝑛 = �_𝑎𝑑𝑚 − ɣ𝑝𝑟𝑜𝑚 ∗ ℎ𝑓 − 𝑆/𝐶

𝑇 =√(�_𝑍 )+ (𝑡_1−𝑡_2)/2

𝑆 =√(�_𝑍 ) − (𝑡_1−𝑡_2)/2

�_𝑎𝑑𝑚 = �_𝑢𝑙𝑡/𝐹_𝑠 σn =

7.2142

Tn/m2

T=

3.25

m

S= 2.9114



S=

2.95

m

Az =

9.5875

m2

* Debe Cumplir: �_𝑣1= �_𝑣2

�_𝑍 = 𝑃/�_𝑛 9.3721



* Nueva Area de la Zapata:

* Area de la Zapata:

Az =

T= 3.2114

m2

�_𝑣1= (𝑇 − 𝑡_1)/2

Lv1 =

1.275

m

Lv2 =

1.275

m

Cumple

�_𝑣2= (𝑆 − 𝑡_1)/2

ok !!

* EFECTOS DE CARGA EXCENTRICA: e1 = 0.88 e2 = 0.78

e1 e2

�_2= 𝑇/6

T 6

= 0.5417

e2

>

T 6

�_1= 𝑆/6

S 6

= 0.4917

e1

>

T 6

�_(1−2)= 𝑃/�_𝑍 (1 ± 〖 6� 〗 _1/𝑆 ± 〖 6� 〗 _2/𝑇) σ1 =

T = 3.25

67.61 ( 1 9.5875

+ 6 *

0.88 2.95

σ1 = 29.8293 Tn/m2

29.8293

�_1 < �_𝑛 <

7.2142 No Cumple

+ 6 * 0.78 ) 3.25

P

* POR TANTEO �_1= 𝑃/(𝑇 ∗𝑆)(1 + 〖 6� 〗 _1/𝑆 + 〖 6� 〗 _2/𝑇)

e

σ1 =

σ1

67.61 ( 1 T*S

+ 6 *

0.88 S

T=

5.5

m

σ1 =

6.7761

Tn/m2

S=

5.2

m

σ2 =

-2.0480

Tn/m2

�_𝑣1= (𝑇 − 𝑡_1)/2

σ2

* DISEÑO POR PUNZONAMIENTO: 0.70 +d

�_𝑛𝑢= 𝑃_𝑢/�_𝑧

m

𝑃_𝑢= 1.7 𝐶𝑚+1.4 𝐶𝑣

Pu = 100.64719 Tn

S = 5.20

0.40

n

0.40 +d Wnu = σ1

0.70

T = 5.50 * CONDICION DE DISEÑO: �_𝑈/∅ ≤ �_𝐶

+ 6 * 0.78 ) T

Wnu =

6.7761

Tn/m2

Lv1 =

2.4

m

�_𝑈/∅ ≤ �_𝐶

Ø = 0.85

* Escogemos el menor de los dos: Vc=0.27(2+4/β) √( 〖𝑓 _� 〗 ^′ ) bod

〖� _𝑈 = 𝑃 〗 _𝑈− �_𝑛𝑢 ∗𝑚 ∗𝑛 Vu = Vu = Vu = Vu =

100.64719 − 100.64719 − 100.64719 − 98.7499 −

6.7761 x (0.70 + d ) ( 0.40 + d ) 6.7761 x (0.28 + 1.10 d + d² ) 1.8973 − 7.4537 d − 6.7761 d² 7.4537 d − 6.7761 d² 1

2

0.27 x

+

4 0.70 0.40

* bo = 2m + 2n

Vc = Vc = Vc =

x 2 (0.70 +d + 0.40 + d ) d 1.06 210 x 10 ( + 2 d ) d 307.2172 1.10 337.9389 d + 614.4344 d² 2

* Reemplazando 1 y 2

529.0453 d²

+

( 337.9389d 287.2481 d

294.7018 d



d= d=

+ +

614.4344 d² ) * 0.85 522.2692 d²

98.7499 ≥ 0 0.2355 -0.7926

ℎ_𝑧 = d + ∅/2 +r

hz = 0.2355 + (3/4") 0.0254 + 0.07 2 hz = 0.31503 hz = ≈

𝑑 = ℎ_𝑧 − ∅/2 −r d= d=

* VERIFICACION POR CORTANTE:

0.35 − (3/4") 0.0254 − 0.07 2 0.27 m

��=1.06√( 〖𝑓 _� 〗 ^′ ) 𝑏𝑜d = 1.06 ok !!

= 1.1571429 * Usamos:

98.7499 − 7.4537 d − 6.7761 d² ≤ 98.7499 − 7.4537 d − 6.7761 d² ≤

^

0.35

m

�_𝑛 ≤ �_�

�_𝑛= �_𝑢𝑑/∅

Ø = 0.85

σx =

3.3588

�_�=0.53 √( 〖𝑓 _� 〗 ^′ ) ∗𝑆 ∗𝑑

�_𝑢𝑑=((�_1+ �_𝑥)/2)∗𝑆 ∗(�_�−𝑑)

�_𝑥=((�_1 − �_2)(�_𝑣+ 𝑡_1+𝑑))/𝑇+�_2

Vud = Vud =

5.0674 56.1269

* 5.20 Tn

* ( 2.4



0.27 )

Vc = Vc =

Vn = 56.126914 0.85 Vn = 66.0317 Tn

0.53 210 x 10 x 5.20 x 0.27 107.8332 Tn

�_𝑛 ≤ �_�

66.0317



107.8332

Cumple

ok !!

* DISEÑO POR FLEXION: �_𝑥=((�_1 − �_2)(�_𝑣+ 𝑡_1))/𝑇+�_2

σx =

2.9256

�_𝑢=(�_𝑥/2+�_1) ∗ 𝑆∗ 〖� _𝑣 〗 ^2/3 Mu =

8.2389

* 5.20 *

Mu =

82.2571

Tn - m

Ø = 0.9

( 2.4 )² 3

𝑎= (2𝑑 ± √(4 𝑑^2 −(8 �_𝑢)/(0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ ∅ ∗𝑆)))/2

a= a=

0.5007 0.0393

a=

0.0393

m

〖�𝑠〗 _𝑚𝑖𝑛=0.22 ∗√( 〖𝑓 _� 〗 ^′/10.197)/( 〖𝑓 _� 〗 ^′/10.197) ∗𝑆 ∗𝑑

�_𝑠= �_𝑢/(∅ ∗ 〖𝑓 _� 〗 ^′∗(𝑑−𝑎/2)) 82.2571

As = 0.9

*

4.2 *

As =

As min = 0.27 − 0.0393 2

86.9288

0.22 *

210 10.197 4200 10.197

* 5.20

* 0.27

As min = 0.003403 m2 As min = 34.03 cm2

cm2

�_𝑠> 〖�𝑠〗 _𝑚𝑖𝑛

86.9288 > 34.03

*VARILLAS LONGITUDINALES Diametro(ø) =

0.75

〖𝑛 ^° 〗 _𝑣= �_𝑠/�_∅

n°v =

Cumple

Pulg.

86.9288 2.8502

n°v = 30.4989



n°v =

31

varillas

* Separación 𝑠= (𝑆 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)

s=

5.20 − 0.75 * 0.0254 − 2* 0.07 − 31 1

s= s=

0.1680 16.8032

m



*VARILLAS TRANSVERSALES Diametro(ø) =

0.75

Pulg.

�_𝑠 (𝑇)= �_𝑠∗𝑇/𝑆 〖𝑛 ^° 〗 _𝑣= �_(𝑠(𝑇))/�_∅ n°v =

As(T) =

86.9288 *

91.9439 2.8502

5.50 5.20 n°v = 32.2584

* Separación 𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)



* 0.0254 − 2*

As(T) =



91.9439

n°v =

cm2

33

varillas

s=

16

cm

ok !!

𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)

s=

5.50 − 0.75 * 0.0254 − 2* 0.07 − 33 1

s= s=

0.1669

m

16.6905

s=



16

cm

* VERIFICACION POR APLASTAMIENTO: *COLUMNA - ZAPATA

𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_1 Pnb = Pnb =

0.85 * 280 666.4 Tn

𝑃_𝑛= 𝑃_𝑢/∅

�_1= 𝑡_(1 )∗ 𝑡_2 A1 = 0.70 * 0.40 A1 = 0.28 m2

Ø = 0.7

𝑃_𝑛 < 𝑃_𝑛𝑏

𝑃_𝑛 < 𝑃_𝑛𝑏

143.7817 < 666.4

Pn = 100.64719 0.7 Pn = 143.7817 Tn

* 10 * 0.28

Cumple

* ZAPATA - SUELO 𝑃_𝑛𝑏 > 𝑃_𝑛

𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_0

�_2=𝑇 ∗𝑋_1

√(�_2/�_1 ) ≤2 → �_0= √(�_2/�_1 ) ∗ �_1 Si:

𝑋_1=𝑇 ∗𝑡_2/𝑡_1

X1

√(�_2/�_1 ) >2 → �_0=2∗�_1

X1 =

X1 =

T Donde:

A2 = A2 =

3.2500 6.0357

1.8571 * m2

A0 = Pnb = Pnb =

0.85 * 210 999.6 Tn

* 10 * 0.56

2 * 0.28 𝑃_𝑛𝑏 > 𝑃_𝑛

999.6 * PARA ZONA SISMICA (DOWELLS) 𝑃_𝑛 ≤ 𝑃_𝑛𝑏

> 143.7817

3.2500 0.28

= 11.6071

A0 =

0.56

Cumple

ok !!

>

m2

2

3.25 *

1.8571

0.40 0.70 m

ok !!

〖�𝑠〗 _𝑚𝑖𝑛=0.005 ∗ �_1 As min = 0.005 * 2800 As min = 14 cm2 Diametro(ø) = 4

1

Pulg.

* 5.0671

=

20.2683

cm2

Cumple

ok !!

* PLANOS DE PLANTA Y PERFIL:

33 ø 3/4" @ 16

S = 5.20 31 ø 3/4" @ 16

T = 5.50

DOWELLS

4

VARILLAS TRANSVERSALES 33 ø 3/4" @ 16

ø 1"

VARILLAS LONGITUDINALES 31 ø 3/4" @ 16

d = 0.27

hz = 0.35

T = 5.50

* DISEÑO DE UNA ZAPATA AISLADA CON EXCENTRICIDADES * Datos de la Zapata N° 21: CM: CV: ɣc: ɣs: F'c: S/Cpiso: σ(ult): fy: P

38.60 15.15 2.30 1.95 210.00 500.00 3.50 4200.00 53.75

* Datos de la Columna: F'c: t1 t2

280.00 70.00 40.00

GRAFICA

Tn Tn Tn/m3 Tn/m3 Kg/cm2 Kg/cm2 Kg/cm2 Kg/cm2 Tn

N.P.T + 0.30

0.15

hf: 2.00

Df:

Kg/cm2 cm cm

* Datos de la Terreno:

N.F.C-1.95 σ(ult):

NPT NTN NFC

0.15 0.00 -1.85

N.T.N ± 0.00

m m m

3.50

1.85

* Esfuezo neto del terreno:

* Dimenciones de la Zapata:

�_𝑛 = �_𝑎𝑑𝑚 − ɣ𝑝𝑟𝑜𝑚 ∗ ℎ𝑓 − 𝑆/𝐶

𝑇 =√(�_𝑍 )+ (𝑡_1−𝑡_2)/2

𝑆 =√(�_𝑍 ) − (𝑡_1−𝑡_2)/2

�_𝑎𝑑𝑚 = �_𝑢𝑙𝑡/𝐹_𝑠 σn =

7.2142

Tn/m2

T=

2.90

m

S= 2.5795



S=

2.60

m

Az =

7.54

m2

* Debe Cumplir: �_𝑣1= �_𝑣2

�_𝑍 = 𝑃/�_𝑛 7.4501



* Nueva Area de la Zapata:

* Area de la Zapata:

Az =

T= 2.8795

m2

�_𝑣1= (𝑇 − 𝑡_1)/2

Lv1 =

1.1

m

Lv2 =

1.1

m

Cumple

�_𝑣2= (𝑆 − 𝑡_1)/2

ok !!

* EFECTOS DE CARGA EXCENTRICA: e1 = 0.82 e2 = 0.18

e1 e2

�_2= 𝑇/6

T 6

= 0.4833

e2

<

T 6

�_1= 𝑆/6

S 6

= 0.4333

e1

>

T 6

�_(1−2)= 𝑃/�_𝑍 (1 ± 〖 6� 〗 _1/𝑆 ± 〖 6� 〗 _2/𝑇) σ1 =

T = 2.90

53.75 ( 1 7.54

+ 6 *

0.82 2.60

σ1 = 23.2714 Tn/m2

23.2714

�_1 < �_𝑛 <

7.2142 No Cumple

+ 6 * 0.18 ) 2.90

P

* POR TANTEO �_1= 𝑃/(𝑇 ∗𝑆)(1 + 〖 6� 〗 _1/𝑆 + 〖 6� 〗 _2/𝑇)

e

σ1 =

σ1

53.75 ( 1 T*S

+ 6 *

0.82 S

T=

4.5

m

σ1 =

6.8574

Tn/m2

S=

4.2

m

σ2 =

-1.1700

Tn/m2

�_𝑣1= (𝑇 − 𝑡_1)/2

σ2

* DISEÑO POR PUNZONAMIENTO: 0.70 +d

�_𝑛𝑢= 𝑃_𝑢/�_𝑧

m

𝑃_𝑢= 1.7 𝐶𝑚+1.4 𝐶𝑣

Pu = 79.78838 Tn

S = 4.20

0.40

n

0.40 +d Wnu = σ1

0.70

T = 4.50 * CONDICION DE DISEÑO: �_𝑈/∅ ≤ �_𝐶

+ 6 * 0.18 ) T

Wnu =

6.8574

Tn/m2

Lv1 =

1.9

m

�_𝑈/∅ ≤ �_𝐶

Ø = 0.85

〖� _𝑈 = 𝑃 〗 _𝑈− �_𝑛𝑢 ∗𝑚 ∗𝑛 Vu = Vu = Vu = Vu =

79.78838 79.78838 79.78838 77.8683

x x − − 7.5431 d

− 6.8574 − 6.8574 − 1.9201

* Escogemos el menor de los dos: Vc=0.27(2+4/β) √( 〖𝑓 _� 〗 ^′ ) bod

(0.70 + d ) ( 0.40 + d ) (0.28 + 1.10 d + d² ) 7.5431 d − 6.8574 d² 1 − 6.8574 d²

2

0.27 x

+

4 0.70 0.40

* bo = 2m + 2n

Vc = Vc = Vc =

x 2 (0.70 +d + 0.40 + d ) d 1.06 210 x 10 ( + 2 d ) d 307.2172 1.10 337.9389 d + 614.4344 d² 2

* Reemplazando 1 y 2

529.1266 d²

+

( 337.9389d 287.2481 d

294.7912 d



d= d=

+ +

614.4344 d² ) * 0.85 522.2692 d²

77.8683 ≥ 0 0.1955 -0.7527

ℎ_𝑧 = d + ∅/2 +r

hz = 0.1955 + (3/4") 0.0254 + 0.07 2 hz = 0.27503 hz = ≈

𝑑 = ℎ_𝑧 − ∅/2 −r d= d=

* VERIFICACION POR CORTANTE:

0.30 − (3/4") 0.0254 − 0.07 2 0.22 m

��=1.06√( 〖𝑓 _� 〗 ^′ ) 𝑏𝑜d = 1.06 ok !!

= 1.1571429 * Usamos:

77.8683 − 7.5431 d − 6.8574 d² ≤ 77.8683 − 7.5431 d − 6.8574 d² ≤

^

0.30

m

�_𝑛 ≤ �_�

�_𝑛= �_𝑢𝑑/∅

Ø = 0.85

σx =

3.8605

�_�=0.53 √( 〖𝑓 _� 〗 ^′ ) ∗𝑆 ∗𝑑

�_𝑢𝑑=((�_1+ �_𝑥)/2)∗𝑆 ∗(�_�−𝑑)

�_𝑥=((�_1 − �_2)(�_𝑣+ 𝑡_1+𝑑))/𝑇+�_2

Vud = Vud =

5.3590 37.8128

* 4.20 Tn

* ( 1.9



0.22 )

Vc = Vc =

Vn = 37.812829 0.85 Vn = 44.4857 Tn

0.53 210 x 10 x 4.20 x 0.22 70.9672 Tn

�_𝑛 ≤ �_�

44.4857



70.9672

Cumple

ok !!

* DISEÑO POR FLEXION: �_𝑥=((�_1 − �_2)(�_𝑣+ 𝑡_1))/𝑇+�_2

σx =

3.4681

�_𝑢=(�_𝑥/2+�_1) ∗ 𝑆∗ 〖� _𝑣 〗 ^2/3 Mu =

8.5914

* 4.20 *

Mu =

43.4211

Tn - m

Ø = 0.9

( 1.9 )² 3

𝑎= (2𝑑 ± √(4 𝑑^2 −(8 �_𝑢)/(0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ ∅ ∗𝑆)))/2

a= a=

0.4085 0.0315

a=

0.0315

m

〖�𝑠〗 _𝑚𝑖𝑛=0.22 ∗√( 〖𝑓 _� 〗 ^′/10.197)/( 〖𝑓 _� 〗 ^′/10.197) ∗𝑆 ∗𝑑

�_𝑠= �_𝑢/(∅ ∗ 〖𝑓 _� 〗 ^′∗(𝑑−𝑎/2)) 43.4211

As = 0.9

*

4.2 *

As =

As min = 0.22 − 0.0315 2

56.2413

0.22 *

210 10.197 4200 10.197

* 4.20

* 0.22

As min = 0.002240 m2 As min = 22.40 cm2

cm2

�_𝑠> 〖�𝑠〗 _𝑚𝑖𝑛

56.2413 > 22.40

*VARILLAS LONGITUDINALES Diametro(ø) =

0.75

〖𝑛 ^° 〗 _𝑣= �_𝑠/�_∅

n°v =

Cumple

Pulg.

56.2413 2.8502

n°v = 19.7322



n°v =

20

varillas

* Separación 𝑠= (𝑆 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)

s=

4.20 − 0.75 * 0.0254 − 2* 0.07 − 20 1

s= s=

0.2127 21.2682

m



*VARILLAS TRANSVERSALES Diametro(ø) =

0.75

Pulg.

�_𝑠 (𝑇)= �_𝑠∗𝑇/𝑆 〖𝑛 ^° 〗 _𝑣= �_(𝑠(𝑇))/�_∅ n°v =

As(T) =

56.2413 *

60.2586 2.8502

4.50 4.20 n°v = 21.1417

* Separación 𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)



* 0.0254 − 2*

As(T) =



60.2586

n°v =

cm2

22

varillas

s=

21

cm

ok !!

𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)

s=

4.50 − 0.75 * 0.0254 − 2* 0.07 − 22 1

s= s=

0.2067

m

20.6712

s=



20

cm

* VERIFICACION POR APLASTAMIENTO: *COLUMNA - ZAPATA

𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_1 Pnb = Pnb =

0.85 * 280 666.4 Tn

𝑃_𝑛= 𝑃_𝑢/∅

�_1= 𝑡_(1 )∗ 𝑡_2 A1 = 0.70 * 0.40 A1 = 0.28 m2

Ø = 0.7

𝑃_𝑛 < 𝑃_𝑛𝑏

𝑃_𝑛 < 𝑃_𝑛𝑏

113.9834 < 666.4

Pn = 79.78838 0.7 Pn = 113.9834 Tn

* 10 * 0.28

Cumple

* ZAPATA - SUELO 𝑃_𝑛𝑏 > 𝑃_𝑛

𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_0

�_2=𝑇 ∗𝑋_1

√(�_2/�_1 ) ≤2 → �_0= √(�_2/�_1 ) ∗ �_1 Si:

𝑋_1=𝑇 ∗𝑡_2/𝑡_1

X1

√(�_2/�_1 ) >2 → �_0=2∗�_1

X1 =

X1 =

T Donde:

A2 = A2 =

2.9000 4.8057

1.6571 * m2

A0 = Pnb = Pnb =

0.85 * 210 999.6 Tn

* 10 * 0.56

2 * 0.28 𝑃_𝑛𝑏 > 𝑃_𝑛

999.6 * PARA ZONA SISMICA (DOWELLS) 𝑃_𝑛 ≤ 𝑃_𝑛𝑏

> 113.9834

2.9000 0.28

= 10.3571

A0 =

0.56

Cumple

ok !!

>

m2

2

2.90 *

1.6571

0.40 0.70 m

ok !!

〖�𝑠〗 _𝑚𝑖𝑛=0.005 ∗ �_1 As min = 0.005 * 2800 As min = 14 cm2 Diametro(ø) = 4

1

Pulg.

* 5.0671

=

20.2683

cm2

Cumple

ok !!

* PLANOS DE PLANTA Y PERFIL:

22 ø 3/4" @ 20

S = 4.20 20 ø 3/4" @ 21

T = 4.50

DOWELLS

4

VARILLAS TRANSVERSALES 22 ø 3/4" @ 20

ø 1"

VARILLAS LONGITUDINALES 20 ø 3/4" @ 21

d = 0.22

hz = 0.30

T = 4.50

* DISEÑO DE UNA ZAPATA AISLADA CON EXCENTRICIDADES * Datos de la Zapata N° 22: CM: CV: ɣc: ɣs: F'c: S/Cpiso: σ(ult): fy: P

58.03 26.00 2.30 1.95 210.00 500.00 3.50 4200.00 84.03

GRAFICA

Tn Tn Tn/m3 Tn/m3 Kg/cm2 Kg/cm2 Kg/cm2 Kg/cm2 Tn

N.P.T + 0.30

N.T.N ± 0.00 0.15

* Datos de la Columna: hf: 2.00 F'c: t1 t2

280.00 60.00 40.00

Df:

Kg/cm2 cm cm

* Datos de la Terreno:

N.F.C-1.95 σ(ult):

NPT NTN NFC

0.15 0.00 -1.85

m m m

3.50

1.85

* Esfuezo neto del terreno:

* Dimenciones de la Zapata:

�_𝑛 = �_𝑎𝑑𝑚 − ɣ𝑝𝑟𝑜𝑚 ∗ ℎ𝑓 − 𝑆/𝐶

𝑇 =√(�_𝑍 )+ (𝑡_1−𝑡_2)/2

�_𝑎𝑑𝑚 = �_𝑢𝑙𝑡/𝐹_𝑠 σn =

7.2142

Tn/m2

𝑆 =√(�_𝑍 ) − (𝑡_1−𝑡_2)/2

T= 3.5129



T=

3.55

m

S= 3.3129



S=

3.35

m

* Nueva Area de la Zapata:

* Area de la Zapata:

Az = 11.8925 m2

* Debe Cumplir: �_𝑣1= �_𝑣2

�_𝑍 = 𝑃/�_𝑛 Az = 11.6478 m2

�_𝑣1= (𝑇 − 𝑡_1)/2

Lv1 =

1.475

m

Lv2 =

1.475

m

Cumple ok !!

�_𝑣2= (𝑆 − 𝑡_1)/2

* EFECTOS DE CARGA EXCENTRICA: e1 = 0.00 e2 = 0.27 e2 e1

�_2= 𝑇/6

T 6

= 0.5917

e2

<

T 6

�_1= 𝑆/6

S 6

= 0.5583

e1

<

T 6

�_(1−2)= 𝑃/�_𝑍 (1 ± 〖 6� 〗 _1/𝑆 ± 〖 6� 〗 _2/𝑇) σ1 = T = 3.55

84.03 ( 1 11.8925

+ 6 *

0.00 3.35

σ1 = 10.2901 Tn/m2

10.2901

�_1 < �_𝑛 <

7.2142 No Cumple

+ 6 * 0.27 ) 3.55

P

* POR TANTEO �_1= 𝑃/(𝑇 ∗𝑆)(1 + 〖 6� 〗 _1/𝑆 + 〖 6� 〗 _2/𝑇)

e

σ1 =

σ2

84.03 ( 1 T*S

+ 6 *

0.00 S

T=

4.4

m

σ1 =

6.5322

Tn/m2

S=

4

m

σ2 =

3.0165

Tn/m2

�_𝑣1= (𝑇 − 𝑡_1)/2

σ1

* DISEÑO POR PUNZONAMIENTO: 0.60 +d

�_𝑛𝑢= 𝑃_𝑢/�_𝑧

m

𝑃_𝑢= 1.7 𝐶𝑚+1.4 𝐶𝑣

Pu = 125.44149 Tn

S = 4.00

0.40

n

0.40 +d Wnu = σ1

0.60

T = 4.40 * CONDICION DE DISEÑO:

+ 6 * 0.27 ) T

Wnu =

6.5322

Tn/m2

Lv1 =

1.9

m

�_𝑈/∅ ≤ �_𝐶

Ø = 0.85

* Escogemos el menor de los dos: Vc=0.27(2+4/β) √( 〖𝑓 _� 〗 ^′ ) bod

〖� _𝑈 = 𝑃 〗 _𝑈− �_𝑛𝑢 ∗𝑚 ∗𝑛 Vu = Vu = Vu = Vu =

125.44149 − 125.44149 − 125.44149 − 123.8738 −

6.5322 x (0.60 + d ) ( 0.40 + d ) 6.5322 x (0.24 + 1.00 d + d² ) 1.5677 − 6.5322 d − 6.5322 d² 6.5322 d − 6.5322 d² 1

2

0.27 x

=

+

4 0.60 0.40

* bo = 2m + 2n

Vc = Vc = Vc =

x 2 (0.60 +d + 0.40 + d ) d 1.06 210 x 10 307.2172 ( 1.00 + 2 d ) d 307.2172 d + 614.4344 d² 2

* Reemplazando 1 y 2

528.8014 d²

+

( 307.2172d 261.1346 d

267.6668 d



d= d=

+ +

614.4344 d² ) * 0.85 522.2692 d²

123.8738 ≥ 0 0.2931 -0.7993

ℎ_𝑧 = d + ∅/2 +r

hz = 0.2931 + (3/4") 0.0254 + 0.07 2 hz = 0.37263 hz = ≈

𝑑 = ℎ_𝑧 − ∅/2 −r d= d=

* VERIFICACION POR CORTANTE:

0.40 − (3/4") 0.0254 − 0.07 2 0.32 m

0.40

��=1.06√( 〖𝑓 _� 〗 ^′ ) 𝑏𝑜d = 1.06 ok !!

1.26

* Usamos:

123.8738 − 6.5322 d − 6.5322 d² ≤ 123.8738 − 6.5322 d − 6.5322 d² ≤

^

m

�_𝑛 ≤ �_�

�_𝑛= �_𝑢𝑑/∅

Ø = 0.85

σx =

5.2698

�_�=0.53 √( 〖𝑓 _� 〗 ^′ ) ∗𝑆 ∗𝑑

�_𝑢𝑑=((�_1+ �_𝑥)/2)∗𝑆 ∗(�_�−𝑑)

�_𝑥=((�_1 − �_2)(�_𝑣+ 𝑡_1+𝑑))/𝑇+�_2

Vud = Vud =

5.9010 37.2943

* 4.00 Tn

* ( 1.9



Vc = Vc =

0.32 )

Vn = 37.294289 0.85 Vn = 43.8756 Tn

0.53 210 x 10 x 4.00 x 0.32 98.3095 Tn

�_𝑛 ≤ �_�

43.8756



98.3095

Cumple ok !!

* DISEÑO POR FLEXION: �_𝑥=((�_1 − �_2)(�_𝑣+ 𝑡_1))/𝑇+�_2

σx =

5.0141

�_𝑠= �_𝑢/(∅ ∗ 〖𝑓 _� 〗 ^′∗(𝑑−𝑎/2))

�_𝑢=(�_𝑥/2+�_1) ∗ 𝑆∗ 〖� _𝑣 〗 ^2/3 Mu =

9.0393

* 4.00 *

Mu =

43.5090

Tn - m

Ø = 0.9

( 1.9 )² 3

As min = 0.9

*

4.2 *

As =

0.32 − 0.0219 2

37.2447

cm2

a= a=

0.6181 0.0219

a=

0.0219

m

〖�𝑠〗 _𝑚𝑖𝑛=0.22 ∗√( 〖𝑓 _� 〗 ^′/10.197)/( 〖𝑓 _� 〗 ^′/10.197) ∗𝑆 ∗𝑑

43.5090

As =

𝑎= (2𝑑 ± √(4 𝑑^2 −(8 �_𝑢)/(0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ ∅ ∗𝑆)))/2

0.22 *

210 10.197 4200 10.197

* 4.00

As min = 0.003103 m2 As min = 31.03 cm2

* 0.32

�_𝑠> 〖�𝑠〗 _𝑚𝑖𝑛

37.2447 > 31.03

Cumple

ok !!

*VARILLAS LONGITUDINALES Diametro(ø) =

0.75

〖𝑛 ^° 〗 _𝑣= �_𝑠/�_∅

n°v =

Pulg.

37.2447 2.8502

n°v = 13.0673



n°v =

14

varillas

* Separación 𝑠= (𝑆 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)

s=

4.00 − 0.75 * 0.0254 − 2* 0.07 − 14 1

s= s=

0.2955

m

29.5458



s=

29

cm

s=

30

cm

*VARILLAS TRANSVERSALES Diametro(ø) =

0.75

Pulg.

�_𝑠 (𝑇)= �_𝑠∗𝑇/𝑆

As(T) =

〖𝑛 ^° 〗 _𝑣= �_(𝑠(𝑇))/�_∅ n°v =

40.9692 2.8502

37.2447 *

4.40 4.00 n°v = 14.3740

As(T) =



40.9692

n°v =

cm2

15

varillas

* Separación 𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)

s=

4.40 − 0.75 * 0.0254 − 2* 0.07 − 15 1

s= s=

0.3029 30.2925

m



* VERIFICACION POR APLASTAMIENTO: *COLUMNA - ZAPATA Ø = 0.7

𝑃_𝑛 < 𝑃_𝑛𝑏

𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_1 *

* 10 *

�_1= 𝑡_(1 )∗ 𝑡_2 A1 = 0.60 * 0.40 A1 = 0.24 m2

𝑃_𝑛= 𝑃_𝑢/∅

Pn = 125.44149 0.7

𝑃_𝑛 < 𝑃_𝑛𝑏

179.2021 < 571.2

Cumple

ok !!

Pnb = Pnb =

0.85 * 280 571.2 Tn

* 10 * 0.24

Pn = 179.2021 Tn

* ZAPATA - SUELO 𝑃_𝑛𝑏 > 𝑃_𝑛

�_2=𝑇 ∗𝑋_1

√(�_2/�_1 ) ≤2 → �_0= √(�_2/�_1 ) ∗ �_1 Si:

𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_0

𝑋_1=𝑇 ∗𝑡_2/𝑡_1

X1

√(�_2/�_1 ) >2 → �_0=2∗�_1

X1 =

X1 =

T Donde:

A2 = A2 =

3.5500 8.4017

2.3667 * m2

A0 = Pnb = Pnb =

0.85 * 210 856.8 Tn

3.5500 0.24

2 * 0.24

* 10 * 0.48

𝑃_𝑛𝑏 > 𝑃_𝑛

856.8 * PARA ZONA SISMICA (DOWELLS)

> 179.2021

A0 =

0.48

Cumple

ok !!

𝑃_𝑛 ≤ 𝑃_𝑛𝑏

〖�𝑠〗 _𝑚𝑖𝑛=0.005 ∗ �_1 As min = 0.005 * 2400 As min = 12 cm2 Diametro(ø) = 4

1

* 5.0671

Pulg. =

20.2683

cm2

* PLANOS DE PLANTA Y PERFIL:

15 ø 3/4" @ 30

Cumple

= 14.7917

ok !!

>

m2

2

3.55 *

2.3667

0.40 0.60 m

S = 4.00 14 ø 3/4" @ 29

T = 4.40

DOWELLS

4

VARILLAS TRANSVERSALES 15 ø 3/4" @ 30

ø 1"

VARILLAS LONGITUDINALES 14 ø 3/4" @ 29

d = 0.32

hz = 0.40

T = 4.40

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