Calculo Final Zapatas

7/28/2019 Calculo Final Zapatas

1/175

EDIFICIO APORTICADO DE SIETE PISOS

Tanque de agua

3.0

3.0

3.0

3.0

3.0

3.0

3.0

EDCBA

4

3

2

1

6.5 7 6.5 7.5

5.0

5.0

5.5

PLANTA TIPICA.

ELEVACION.

VIGA 01 VIGA 04VIGA 03VIGA 02

VIGA 01 VIGA 04VIGA 03VIGA 02


2/175

Zona Uso Suelo local Cap. Nivel de Portico dedel Suelo diseo diseo

2 Biblioteca S1 3.5 7 2 5

USO S/C (Kg/m2300750400

L1= 7 m.

L2 = 7 m.

L3 = 6.5 m.

L4 = 7.5 m.

Nivel dealmacen

CONDICIONES DE DISEO

CARACTERISTICAS

Salas de lecturaSalas de almacenaje

Corredores y Escaleras

SOBRECARGA NORMA E-020

AMBIENTE

Considerando,

Prtico 2.

BIBLIOTECA

Suelo local: intermedio, S1 (S = 1.0 y TP = 0.4 s); Roca o suelos muy rgidos.

Ubicacin: zona 3 (Z = 0.4)

Uso: Hospital. (Sobrecarga, 750 Kg./m2 en todos los niveles y U = 1.3)


3/175


4/175

DATOS

L 5 m

0.25 h= 0.25 m

h (m) kg/m20.25

350

100100

D(total) 550L(total) SC 750D(total) 450

L(total) SC 500

L 7.5 m

0.63 mb= 0.3 mh= 0.6 m

0.32 m

L 5 m

0.42 mb= 0.25 mh= 0.45 m

0.21 m

b 0.25 m Asumidosh 0.5 m

3Carga (P)

7 m5 m6

*Peso especificodel concreto 2400 kg/m3

VIGA SECUNDARIA

PREDIMENSIONAMIENTO DE VIGAS Y COLUMNAS

*# Pisos tipicos

Distancia entre pisos

*L(Viga principal)*L(Viga secundaria)

TIPICO

COLUMNAS

Peso muerto por piso y cielo rasoPeso de tabaquera

Peso propio de losa

TECHO

LOSA ALIGERADA

VIGA PRINCIPAL

20Lh

12L

h

2h

b

12L

h

2

h b


5/175

25

W(D) 168168 KgW(L) 39656.25 Kg

P 207824.25 Kg

Interior 0.45Exterior 0.35

F'c= 210

Ac(inter.) 0.2199 cm2 b = 0.3 m Ac(exter.) 0.2828 cm2 h = 0.7 m

Area de columna

INTERIOR

Se tomara en cuenta toda la carga muerta y un % de la carga viva, (%) =

Factor paraTipo de columna

Kg/cm2

cFP

Ac


6/175


7/175

DATOS

Z 0.4 Tp 0.4 C 1.67U 1.3 hn 21 P 413.04 TnS 1 Ct 35 V 313.9 TnR 8 T 0.6 #PORTICOS 4

Viga princip. Viga secund. ColumnaWD = 550 b 0.3 0.25 0.3WL = 750 h 0.6 0.45 0.7 concreto= 2400 Element/piso 4 5 20

15.5

Fi (t) F i (t)En el portico 2* Acumulados

1 413040 3 1239120 11.177 2.79 2.792 413040 6 2478240 22.354 5.59 8.383 413040 9 3717360 33.531 8.38 16.764 413040 12 4956480 44.708 11.18 27.945 413040 15 6195600 55.884 13.97 41.916 413040 18 7434720 67.061 16.77 58.687 418040 21 8778840 79.185 19.8 78.48

34800360

27.5

OK

Vista en PlantaFi (Kg.)

fuerza sismica repartida

Cargas de Sismo

Nivel P i (Kg.) h i (m.) P i hi

L(total)=

PR

ZUCSV

V hi Pi

hi Pi Fi

Ct hm

T T

TpC 5.2 125.0

R

C


8/175

DATOS

2.71 12.06-27.28 6.13-27.28 12.1

M (-) V (+)

DIST W M DIST W M DIST W M DIST W M DIST W M

0 -22.63 0 -6.66 0 -27.28 0 2.71 0 -18.313.27 12.06 2.63 10.24 3.90 9.81 1.87 6.65 4.64 6.136.50 -21.97 6.50 -26.24 6.50 -6.72 6.50 -17.69 6.50 2.216.50 -26.19 6.50 -10.17 6.50 -29.11 6.50 0.51 6.50 -18.819.99 13.5 9.44 10.88 10.55 10.88 8.78 6.4 11.21 6.3813.50 -26.48 13.50 -29.34 13.50 -10.39 13.50 -18.87 13.50 0.4413.50 -23.14 13.50 -7.54 13.50 -27.16 13.50 1.96 13.50 -18.0416.75 11.16 16.13 9.31 17.37 9.31 15.38 5.98 18.10 5.9920.00 -23.25 20.00 -27.27 20.00 -7.60 20.00 -18.18 20.00 1.8820.00 -29.26 20.00 -12.98 20.00 -30.91 20.00 -1.14 20.00 -19.4123.74 16.22 23.24 12.58 24.24 13.02 22.65 6.8 24.85 7.3127.50 -29.73 27.50 -31.76 27.50 -12.84 27.50 -19.92 27.50 -0.63

0.9D + 1.43E

CUADRO DE MOMENTOS FLECTORES PARA CADA COMBINACION DE CARGA, SEG N METODO ACI

2.27

2.274.88

6.50 4.88

1.4D + 1.7L 0.75(1.4D + 1.7L+ 1.87E) 0.75(1.4D + 1.7L+1.87E)

6.50

6.50

6.50

4.88

4.88 4.88

4.88

VIGA 01

VIGA 02

VIGA 03

VIGA 04

CONVENCION

2.274.88

MOMENTOS (Tn-m)

2.27

2.27

2.274.88

2.27

2.27

0.9D + 1.43E

Mi

W

Vi

X

iii

i M wV W

wV

V Mx

2

2

W V

X imax


9/175


10/175

-22.630

12.060

-21.973

-6.660

10.240

-26.240-27.280

9.810

-6.720

-18.310

6.130

2.210

-26.19

13.5

-26.48

-23.14

11.16

-10.17

10.88

-29.34

-7.54

9.31

-29.11

10.88

-10.39

-27.16

9.31

0.51

6.4

-18.87

1.96

5.98

-18.81

6.38

0.44

-18.04

5.99

-35.00

-30.00

-25.00

-20.00

-15.00

-10.00

-5.00

0.00

5.00

10.00

15.00

20.00

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

M O M E N T O S

( T o n m

)

DIAGRAMA DE MOMENTOS DEL 7 PISO ( PORTICO 2)

1.4D+1.7 L 0.75(1.4D+1.7L+1.87E) 0.75(1.4D+1.7L-1.87E)


11/175

DIST0

3.27

6.506.509.99

13.5013.5016.7520.0020.0023.7427.50

2.7112.06

2.21

0.5113.500.441.96

11.161.88

-1.1416.22-0.63

-29.11-29.34 -29.34

-27.16

1.96

-1.14

11.16

-29.11

-30.91

-27.16

-27.286.13

-26.24

6.38

-31.76

6.38-29.34-27.165.98

6.80

5.98

M (Mu)-27.286.13

-26.24

-29.1113.50

-27.2812.06

VIGA 04 16.22-0.63

MOMENTO MAXIMO (Tn-m)

2.210.51

VIGA 03-27.27

-26.24

2.7112.06

11.161.88

M (Mu)

13.500.44

VIGA 01

VIGA 02

-30.916.80

-31.76 -31.76

-27.27-30.9116.22

-27.27


12/175

DIST W V DIST W V DIST W V DIST W V DIST W0 -21.24 0 -12.84 0 -19.02 0 -4.23 0.0 -10

3.27 0 2.63 0 3.90 0 1.87 0 4.64 06.50 21.03 6.50 18.86 6.50 12.69 6.50 10.51 6.50 4.26.50 -22.72 6.50 -14.33 6.50 -19.75 6.50 -5.17 6.50 -109.99 0 9.44 0 10.55 0 8.78 0 11.21 0

13.50 22.80 13.50 19.81 13.50 14.40 13.50 10.71 13.50 5.113.50 -21.12 13.50 -12.82 13.50 -18.86 13.50 -4.27 13.50 -1016.75 0 16.13 0 17.37 0 15.38 0 18.10 020.00 21.15 20.00 18.89 20.00 12.84 20.00 10.47 20.00 4.320.00 -24.32 20.00 -15.79 20.00 -20.70 20.00 -6.00 20.00 -1123.74 0 23.24 0 24.24 0 22.65 0 24.85 027.50 24.45 27.50 20.79 27.50 15.88 27.50 11.10 27.50 6.0

x x.1 v v0 -21.24

4.64 1.87 0 06.5 21.03

6.5 -22.7211.21 8.78 0 0

13.5 22.80 -25 6.50 13.50 20.00 27.5013.5 -21.12 0 6.50 13.50 20.00 27.50

18.10 15.38 0 0 25 6.50 13.50 20.00 27.5020 21.15

20 -24.3224.85 22.65 0 0

27.5 24.45

VIGA 02 6.50 4.88 4.88

CUADRO DE FUERZAS CORTANTES PARA CADA COMBINACION DE CARGA, SEG N METODO ACI

1.4D + 1.7L 0.75(1.4D + 1.7L+ 1.87E) 0.75(1.4D + 1.7L+1.87E) 0.9D + 1.43E

VIGA 04

2.27

2.27 2.27

CORTANTES (Tn)

2.27 2.27

0.9D + 1.43E

2.27

VIGA 03 6.50 4.88 4.88

2.27

2.27VIGA 04 6.50 4.88 4.88

ENVOLVENTE

VIGA 01

VIGA 02

VIGA 01 6.50 4.88 4.88

VIGA 03


13/175

-21.240

0.000

21.030

-12.840

0.000

18.860

-19.020

0.000

12.690

-10.530

0.000

4.210

-22.72

0

22.80

-21.12

0

21.15

-24.32

-14.33

0

19.81

-12.82

0

18.89

-15.79

-19.75

0

14.40

-18.86

0

12.84

-20.70

-5.17

0

10.71

-4.27

0

10.47

-6.00

-10.69

0

5.19

-10.44

0

4.31

-11.01

-25.00

-20.00

-15.00

-10.00

-5.00

0.00

5.00

10.00

15.00

20.00

25.00

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 2

C O R T A N T E S ( T o n

)

DIAGRAMA DE FUERZAS CORTANTES - 7 PISO ( PORTICO 2)

1.4D+1.7 L 0.75(1.4D+1.7L+1.87E) 0.75(1.4D+1.7L-1.87E) 0.9D+1.43EENVOLV. ENVOLV. ENVOLV. ENVOLV.ENVOLV. ENVOLV. ENVOLV.


14/175


15/175


16/175

DATOSFc (kg/cm 2 ) = 210Fy ( kg/cm2 ) = 4200

b 1 = 0.85b3 0.85

0.9 606

30d= 54d'= 6

r b = b 1b 3 fc ( 6000 ) r b = 0.02125fy 6000+fy r mx = 0.0106

Rub = r max fy ( 1 -r max fy ) Rub = 35.07131.7fc

Mub = Rub bd2 Mub (t-m) = 30.68

DISEO DE VIGAS

Una capa# capas traccion

# capas compresionUna capa

b = =

=

d' =


17/175

De la Envolvente Mu = t-m

Y como Mub = t-m

Por lo tanto Mu < Mub

Se tiene una viga simplemente reforzada

10.8 cm

cm2

cm

a = cm

cm2

cm

cm2

Entonces As(+)= 15 cm2 Ok 3 # 8 As = 15.3

3 # 8

Asumimos a = 0.20d

11.65

11.76

14.85

4.47

15

0.6

-27.28

30.68

a =

ELEMENTO O VIGA NUMERO 01 TRAMO L = 0 _m

11.76

0.3

cm2

2/ad Fy M

A uS

b Fc Fy As

a3 b

2/ad Fy M

A uS

b Fc Fy As

a3 b

d b Fy Fc

As 8.0min


18/175


Y como Mub = t-m



10.8 cm

cm2

cm

a = cm

cm2

cm

cm2

Entonces As(-)= 1.79 cm2 2 # 4 As = 2.58

2 # 4


2.71

30.68

Asumimos a = 0.20d a =

1.475

1.05

1.16

1.05

1.34

0.3

4.47

0.6

cm2

2/ad Fy M

A uS

b Fc Fy As

a3 b

2/ad Fy M

A uS

b Fc Fy As

a3 b

d b Fy Fc

As 8.0min


19/175


Y como Mub = t-m



10.8 cm

cm2

cm

a = 4.85 cm

cm2

cm

cm2

Entonces As= 6.19 cm2 Ok As = 8.26

0.6 2 # 4

0.3

5.15

30.68


ELEMENTO O VIGA NUMERO 01 TRAMO L = 3.27 _m

12.06

6.565

4.47

6.19

4.85

2 # 6 + 2 # 4

2 # 6 + 2 # 4 cm2

2/ad Fy M

A uS

b Fc Fy As

a3 b

2/ad Fy M

A uS

b Fc Fy As

a3 b

d b Fy Fc

As 8.0min


20/175


Y como Mub = t-m



10.8 cm

cm2

cm

a = cm

cm2

cm

cm2

Entonces As= 14.35 cm2 Ok 3 # 8 As = 15.3

3 # 8

30.68

4.47

11.25

14.284

11.2

-26.24

11.25

0.6

0.3


14.35


cm2

2/ad Fy M

A uS

b Fc Fy As

a3 b

2/ad Fy M

A uS

b Fc Fy As

a3 b

d b Fy Fc

As 8.0min


21/175


Y como Mub = t-m



10.8 cm

cm2

cm

a = cm

cm2

cm

cm2

Entonces As= 1.45 cm2 2 # 4 As = 2.58

2 # 4

30.68

a =


1.203

0.85

Asumimos a = 0.20d

2.21

0.94

0.85

1.09

4.47

0.6

0.3

cm2cm2

2/ad Fy M

A uS

b Fc Fy As

a3 b

2/ad Fy M

A uS

b Fc Fy As

a3 b

d b Fy Fc

As 8.0min


22/175


Y como Mub = t-m



10.8 cm

cm2

cm

a = cm

cm2

cm

cm2


2 # 7 + 2 # 8


12.67

2 # 70.6

0.3

2 # 7+ 2 # 8

4.47

12.43

12.67

30.68

15.846

-29.11


16.16

cm2

2/ad Fy M

A uS

b Fc Fy As

a3 b

2/ad Fy M

A uS

b Fc Fy As

a3 b

d b Fy Fc

As 8.0min


23/175


Y como Mub = t-m



10.8 cm

cm2

cm

a = cm

cm2

cm

cm2

Entonces As= 0.33 cm2 2 # 4 As = 2.58

0.278

0.25


0.51

0.22

30.68


0.2

0.2

4.47

0.62 # 4

0.3

cm2cm2

2/ad Fy M

A uS

b Fc Fy As

a3 b

2/ad Fy M

A uS

b Fc Fy As

a3 b

d b Fy Fc

As 8.0min


24/175


25/175


Y como Mub = t-m



10.8 cm

cm2

cm

a = cm

cm2

cm

cm2


2 # 7

2 # 7 2 # 8

12.78

2 # 7 2 # 8

4.47


-29.34


12.53

15.971

30.68

12.78

16.3

cm2cm2

2/ad Fy M

A uS

b Fc Fy As

a3 b

2/ad Fy M

A uS

b Fc Fy As

a3 b

d b Fy Fc

As 8.0min


26/175


Y como Mub = t-m



10.8 cm

cm2

cm

a = cm

cm2

cm

cm2

Entonces As= 0.29 cm2 2 # 4 As = 2.58

2 # 4

0.19

0.22

0.17

30.68



0.44

0.17

4.47

0.24

cm2cm2cm2cm2cm2cm2

2/ad Fy M

A uS

b Fc Fy As

a3 b

2/ad Fy M

A uS

b Fc Fy As

a3 b

d b Fy Fc

As 8.0min


27/175


Y como Mub = t-m



10.8 cm

cm2

cm

a = cm

cm2

cm

cm2


3 # 80.6

0.3

11.7


11.7

4.47

14.92

11.6

-27.16

30.68

14.784


3 # 8 cm2

2/ad Fy M

A uS

b Fc Fy As

a3 b

2/ad Fy M

A uS

b Fc Fy As

a3 b

d b Fy Fc

As 8.0min


28/175


Y como Mub = t-m



10.8 cm

cm2

cm

a = cm

cm2

cm

cm2

Entonces As= 1.29 cm2 2 # 4 As = 2.58

0.62 # 4

0.3

0.84

0.76

1.067

4.47

0.97

0.76


1.96

30.68


cm2cm2cm2

2/ad Fy M

A uS

b Fc Fy As

a3 b

2/ad Fy M

A uS

b Fc Fy As

a3 b

d b Fy Fc

As 8.0min


29/175


Y como Mub = t-m



10.8 cm

cm2

cm

a = 4.47 cm

cm2

cm

cm2


0.6

Asumimos a = 0.20d

0.3

30.68

6.075

4.47

2 # 6 + 2 # 4

4.47

2 # 4

a =

4.76

5.7


11.16

2 # 6 + 2 # 4

cm2cm2

2/ad Fy M

A uS

b Fc Fy As

a3 b

2/ad Fy M

A uS

b Fc Fy As

a3 b

d b Fy Fc

As 8.0min


30/175


Y como Mub = t-m



10.8 cm

cm2

cm

a = cm

cm2

cm

cm2


3 #8

0.3

11.7

-27.16

14.784

11.6

14.92

3 # 8

Asumimos a = 0.20d

4.47

a =

30.68


0.6

11.7

cm2cm2cm2

2/ad Fy M

A uS

b Fc Fy As

a3 b

2/ad Fy M

A uS

b Fc Fy As

a3 b

d b Fy Fc

As 8.0min


31/175


Y como Mub = t-m



10.8 cm

cm2

cm

a = cm

cm2

cm

cm2

Entonces As= 1.24 cm2 2 # 4 As = 2.58

2 # 4

0.3

1.023

0.73

0.93


1.88

30.68

4.47

0.73


0.8

0.6

cm2cm2cm2cm2cm2

2/ad Fy M

A uS

b Fc Fy As

a3 b

2/ad Fy M

A uS

b Fc Fy As

a3 b

d b Fy Fc

As 8.0min


32/175

De la Envolvente Mu =

Y como Mub =

Por lo tanto Mu > Mub

Se tiene una viga doblemente reforzada

> fy Fsb= 4200

fsb = fy ( a lo mas puede llegar hasta este valor)

0.54

17.3 17.94

0.6

0.3

0.0109 BIEN

2 # 2

30.68

M1 = Mub =

0.01

30.68

2 # 7 + 2 # 8 As =

M2 = Mu M 1 = 0.23

0.13

4866.666667

r max 0.5r b + r =

0.0110741

0.0003

Ast = As1 + As2 =


-30.91

2 # 7 + 2 # 8

As1 = r max.b.d = 17.17

2 # 2 As =

r b = 0.02125

0.13

)6000

Fy)(60001(6000

"

d

d Fsb

b s F

Fy A A S S

2

d d Fy M

AS

2

2


33/175


Y como Mub = t-m



10.8 cm

cm2

cm

a = cm

cm2

cm

cm2

Entonces As= 0.75 cm2 2 # 4 As = 2.58

2 # 4

0.3

Asumimos a = 0.20d


-1.14

30.68

0.44

a =

0.621

0.49

0.56

0.44

4.47

0.6

cm2cm2cm2cm2cm2

2/ad Fy M

A uS

b Fc Fy As

a3 b

2/ad Fy M

A uS

b Fc Fy As

a3 b

d b Fy Fc

As 8.0min


34/175


Y como Mub = t-m



10.8 cm

cm2

cm

a = cm

cm2

cm

cm2

Entonces As= 8.47 cm2 Ok As = 8.52Entonces As= 9.04 cm2 Ok As = 11.1

( 2 capas )

0.6

2 # 40.3

16.22


30.68

6.64


6.92

6.64

4.47

2 # 4 + 3 # 6

8.47

3 # 6

3 # 6

2 # 4 + 3 # 6

8.829

cm2cm2cm2cm2cm2cm2

2/ad Fy M

A uS

b Fc Fy As

a3 b

2/ad Fy M

A uS

b Fc Fy As

a3 b

d b Fy Fc

As 8.0min


35/175

De la Envolvente Mu =

Y como Mub =

Por lo tanto Mu > Mub

Se tiene una viga doblemente reforzada

> fy Fsb= 4200

fsb = fy ( a lo mas puede llegar hasta este valor)

1.42

17.8 17.94

0.6

0.3

0.0115 BIEN

As1 = r max.b.d =


-31.76

0.0110741

r b = 0.021252 # 7 + 2 # 8

4866.666667

Ast = As1 + As2 =

M2 = Mu M 1 =

M1 = Mub = 30.68

30.68

2 # 3 As =

0.0009

0.6

0.6

2 # 3

2 # 7 + 2 # 8 As =

0.0110741

1.08

r max 0.5r b + r =

17.17

)6000

Fy)(60001(6000

"

d

d Fsb

b s F

Fy A A S S

2

d d Fy M

AS

2

2


36/175


Y como Mub = t-m



10.8 cm

cm2

cm

a = cm

cm2

cm

cm2

Entonces As= 0.41 cm2 2 # 4 As = 2.58

2 # 4

0.3


30.68

-0.63

0.6

4.47


0.31

0.24

0.343

0.24

0.27

cm2cm2cm2cm2cm2

2/ad Fy M

A uS

b Fc Fy As

a3 b

2/ad Fy M

A uS

b Fc Fy As

a3 b

d b Fy Fc

As 8.0min


37/175

cm2cm2cm2cm2cm2

2/ad Fy M

A uS

b Fc Fy As

a3 b

2/ad Fy M

A uS

b Fc Fy As

a3 b

d b Fy Fc

As 8.0min


38/175

Para varillas # 6:

Fy = 4200 ldF`c = 210 pulg cm m

a 1.3 5 5/8 1.587 0.9 0.90187509b 1 6 3/4 1.905 1.08 1.08259109l 1 8 1 2.54 1.81 1.44345478

. 4 1/2 1.27 0.72 0.721727397 7/8 2.222 1.58 1.262738793 3/8 0.953 0.54 0.54157969

AsRequerido (cm2)

Asproporcionado(cm2)

As req/ Asprop.

15.20 15.30 0.9917.30 17.94 0.9617.77 17.94 0.99

3.00 4.00 0.75

F= 0.99

# barra lbd ld lbd ld ldf pulg cm cm cm cm cm cm

5 5/8 1.587 36.8 36.43 26.66 26.39 36.436 3/4 1.905 44.17 43.73 32 31.68 43.738 1 2.54 58.89 58.3 42.67 42.24 58.34 1/2 1.27 29.45 29.16 21.34 21.13 29.167 7/8 2.222 51.52 51 37.33 36.96 51

CANTIDAD DE REFUERZO EN LA SECCION DE LA VIGA

COMPRESION

db

LONGITUD DE DESARROLLO

# barra

Para varillas # 6:

Para varillas # 7 y mayores:

TRACCION

c F

db Fy L d

63.6

l b a

c F

db Fy Ld 3.5

l b a

f ldb L d

c F

db Fy L d

08.0

Fydb L d 04.0

2d b

Mu Ru

bc F Fy As

a3 b


39/175

ANCLAJES

BARRAS Ref.Principal

pulg cm 12 db (cm)5 5/8 1.587 19.046 3/4 1.905 22.868 1 2.54 30.484 1/2 1.27 15.247 7/8 2.222 26.66

LONGITUD DE DESARROLLO TOTAL ( ldh)

f = 0.7

barra ldhpulg cm cm

5 5/8 1.587 24.386 3/4 1.905 29.268 1 2.54 39.024 1/2 1.27 19.517 7/8 2.222 34.13

EMPALMES DE REFUERZO ls (TRASLAPE)

barra d ld lspulg cm cm cm

5 5/8 1.587 36.43 47.366 3/4 1.905 43.73 56.858 1 2.54 58.3 75.794 1/2 1.27 29.16 37.917 7/8 2.222 51 66.3

d

d

Ls = 1.3ld (compresin)

f ldb L d

c F db

ldb318


40/175

FACTOR DE REDUCCION DE CORTE

= 0.85d = 54

Fc (kg/cm 2 ) = 210Fy ( kg/cm2 ) = 4200

L = 7.5 m 21.61bw = 30 cm

a) 24.32Vu = 24.32 tn

4.85 A la distancia d:

tg()= 5.014433Vud = 21.61 tn

La resistencia al corte aportada por el concreto

= 1 concreto de peso normalVc= 12.44 tn

Vc= 10.57 tn Requiere EstriboVc/2= 5.29 tn

b).- Comprobacin si se pueden disear estribos

Vs = 12.98 tn (1)

V2 = 49.3 tn (2) Se puede disear estribos

c).- Separacion Maxima

25.82 tn (3)(1) < (3)

si (1)(3)

Smax = 27 cm

Refuerzo minimo con separacion maxima

ELEMENTO O VIGA 04 - IZQUIERDA

REFUERZOS TRANSVERSALES

(1) < (2) Se pueden disear estribos:

0.54

d bc F Vc w53.0l

VcVud

Vs

d bc F V w1.22

d bc F w1.1

2max

d S

4max

d S


41/175

Av.min = 0.68 cm2

As = Av = 1.42 cm2

Ubicacin de la separacion maxima

Vu = 20.71 tna = 0.18 m q= 3.79 m

ao = 2.2 mm= 2.74 m

So = 19.91 cm

S1 = 24.8 cm

2 ramas de acero # 3

Fy

S b Av w

52.3min

VcVud Fy Av

So

VcS

d Fy AvVu

11 n

mSoS

sd Fy AvVs VnVu

Vud VuVud

d xa )(m

VcVu

VcVuq *

2/


42/175

1#3 , [email protected]+r @0.25

19.91 cm

24.3224.8 cm 20 cm

21.61

27 cm 25

10.57

5.29

0.18

ao= 2.2m= 2.74q= 3.79

x= 4.85

Tenemos la siguiente distribucin de estribos para la viga. 04-tramo izquierdo


a=

Vu

d=0.54

Vu =

Vud =

Vc=

Vc/2=

S =

S1=

cm

So=
mailto:1mailto:1


43/175


= 0.85d = 54

Fc (kg/cm 2 ) = 210Fy ( kg/cm2 ) = 4200

L = 7.5 m 21.73bw = 30 cm

a) 24.45Vu = 24.45 tn


tg()= 5.041237Vud = 21.73 tn





Vs = 13.12 tn (1)



25.82 tn (3)

(1) < (3)

si (1)(3)

Smax = 27 cm


ELEMENTO O VIGA 04 - DERECHA


0.54

d bc F Vc w53.0l

VcVud

Vs

d bc F V w1.22

d bc F w1.1

2max

d S

4max

d S


44/175

Av.min = 0.68 cm2

As = Av = 1.42 cm2Ubicacin de la separacion maxima

Vu = 20.71 tna = 0.2 m q= 3.8 m

ao = 2.21 mm= 2.75 m

So = 19.72 cm

S1 = 24.5 cm


Fy

S b Av w

52.3min

VcVud Fy Av

So

VcS

d Fy AvVu

11 n

mSoS

Vud VuVud

d xa )( mVcVuVcVu

q *2/


45/175

1#3 ,[email protected]+r @0.25

19.72 cm

24.4524.5 cm 20 cm

21.73

27 cm 25

10.575.29

0.2

ao= 2.21m= 2.75q= 3.8

x= 4.85


Tenemos la siguiente distribucin de estribos para la viga. 04 - tramo derecho

a=

Vu

d=0.54

Vu =

Vud =

Vc=

Vc/2=

S =

S1=

cm

So=
mailto:1mailto:1


46/175


= 0.85d = 54

Fc (kg/cm 2 ) = 210

Fy ( kg/cm2 ) =

4200

L = 6.5 m 18.64bw = 30 cm

a) 21.12Vu = 21.12 tn


tg()= 4.591304Vud = 18.64 tn





Vs = 9.49 tn (1)



25.82 tn (3)

(1) < (3)

si (1)(3)

Smax = 27 cm




0.54

d bc F Vc w53.0l

VcVud

Vs

d bc F V w1.22

d bc F w1.1

2max

d S

S b52.3

4max

d S


47/175

Av.min = 0.68 cm2

As = Av = 1.42 cm2


Vu = 20.71 tna = -0.45 m q= 3.45 m

ao = 1.76 mm= 2.3 m

So = 25.95 cm

S1 = 33.9 cm


Fy Avm n

VcVud Fy Av

So

VcS

d Fy AvVu

11 n

mSoS

sd Fy AvVs VnVu

Vud VuVud

d xa )( mVcVuVcVu

q *2/


48/175

1#3 @0.25

25.95 cm

21.12

18.64

27 cm 25

10.57

5.29

-0.45

ao= 1.76m= 2.3q= 3.45

x= 4.60

Como la distancia "a" es negativa la separacion de estribos sera la de laseparacin maxima es decir cada 25 cm

OBSERVACIN:



a=

Vu

d=0.54

Vu =

Vud =

Vc=

Vc/2=

S = cm

So=
mailto:1mailto:1


49/175


= 0.85d = 54

Fc (kg/cm 2 ) = 210Fy ( kg/cm2 ) = 4200

L = 6.5 m 18.68bw = 30 cm

a) 21.15Vu = 21.15 tn


tg()= 4.577922Vud = 18.68 tn





Vs = 9.54 tn (1)



25.82 tn (3)

(1) < (3)

si (1)(3)

Smax = 27 cm




0.54

d bc F Vc w53.0l

VcVud

Vs

d bc F V w1.22

d bc F w1.1

2max

d S

S b Av w

52.3min

4max

d S


50/175

Av.min = 0.68 cm2

As = Av = 1.42 cm2


Vu = 20.71 tna = -0.44 m q= 3.46 m

ao = 1.77 mm= 2.31 m

So = 25.87 cm

S1 = 33.8 cm


y

VcVud Fy Av

So

VcS

d Fy AvVu

11 n

mSoS

Vud VuVud

d xa )( mVcVuVcVu

q *2/


51/175

1#3 @0.25

25.87 cm

21.15

18.68

27 cm 25

10.57

5.29

-0.44

ao= 1.77m= 2.31q= 3.46

x= 4.62



OBSERVACIN:



a=

Vu

d=0.54

Vu =

Vud =

Vc=

Vc/2=

S = cm

So=
mailto:1mailto:1


52/175

= 0.85d = 54

Fc (kg/cm 2 ) = 210Fy ( kg/cm2 ) = 4200

L = 7 m 20.12bw = 30 cm

a) 22.72Vu = 22.72 tn


tg()= 4.813559Vud = 20.12 tn





Vs = 11.23 tn (1)



25.82 tn (3)

(1) < (3)

si (1)(3)

Smax = 27 cm




0.54

d bc F Vc w53.0l

VcVud

Vs

d bc F V w1.22

d bc F w1.1

2maxd

S

S b Av w

52.3min

4max d S


53/175

Av.min = 0.68 cm2

As = Av = 1.42 cm2


Vu = 20.71 tna = -0.12 m q= 3.62 m

ao = 1.98 mm= 2.52 m

So = 22.53 cm

S1 = 28.7 cm


y

VcVud Fy Av

So

VcS

d Fy AvVu

11 n

mSoS

sd Fy AvVs VnVu

Vud VuVud

d xa )( mVcVuVcVu

q *2/


54/175

1#3 @0.25

22.53 cm

22.72

20.12

27 cm 25

10.57

5.29

-0.12

ao= 1.98m= 2.52q= 3.62

x= 4.72



OBSERVACIN:



a=

Vu

d=0.54

Vu =

Vud =

Vc=

Vc/2=

S = cm

So=
mailto:1mailto:1


55/175

= 0.85d = 54

Fc (kg/cm 2 ) = 210Fy ( kg/cm2 ) = 4200

L = 7 m 20.19bw = 30 cm

a) 22.80Vu = 22.80 tn


tg()= 4.830508Vud = 20.19 tn





Vs = 11.31 tn (1)



25.82 tn (3)

(1) < (3)

si (1)(3)

Smax = 27 cm




0.54

d bc F Vc w53.0l

VcVud

Vs

d bc F V w1.22

d bc F w1.1

2maxd

S

S b Av w

52.3min

4max d S


56/175

Av.min = 0.68 cm2

As = Av = 1.42 cm2


Vu = 20.71 tna = -0.11 m q= 3.62 m

ao = 1.99 mm= 2.53 m

So = 22.38 cm

S1 = 28.5 cm


y

VcVud Fy Av

So

VcS

d Fy AvVu

11 n

mSoS

Vud VuVud

d xa )( mVcVuVcVu

q *2/


57/175

1#3 @0.25

22.38 cm

22.80

20.19

27 cm 25

10.57

5.29

-0.11

ao= 1.99m= 2.53q= 3.62

x= 4.72



OBSERVACIN:



a=

Vu

d=0.54

Vu =

Vud =

Vc=

Vc/2=

S = cm

So=
mailto:1mailto:1


58/175

= 0.85d = 54

Fc (kg/cm 2 ) = 210Fy ( kg/cm2 ) = 4200

L = 7 m 18.77bw = 30 cm

a) 21.24Vu = 21.24 tn


tg()= 4.577586Vud = 18.77 tn





Vs = 9.64 tn (1)



25.82 tn (3)

(1) < (3)

si (1)(3)

Smax = 27 cm




0.54

d bc F Vc w53.0l

VcVud

Vs

d bc F V w1.22

d bc F w1.1

2maxd

S

S b Av w

52.3min

4max d S


59/175

Av.min = 0.68 cm2

As = Av = 1.42 cm2


Vu = 20.71 tna = -0.42 m q= 3.48 m

ao = 1.79 mm= 2.33 m

So = 25.66 cm

S1 = 33.4 cm


y

VcVud Fy Av

So

VcS

d Fy AvVu

11 n

mSoS

sd Fy AvVs VnVu

Vud VuVud

d xa )( mVcVuVcVu

q *2/


60/175

1#3 @0.25

25.66 cm

21.24

18.77

27 cm 25

10.57

5.29

-0.42

ao= 1.79m= 2.33q= 3.48

x= 4.64



OBSERVACIN:



a=

Vu

d=0.54

Vu =

Vud =

Vc=

Vc/2=

S = cm

So=
mailto:1mailto:1


61/175

= 0.85d = 54

Fc (kg/cm 2 ) = 210Fy ( kg/cm2 ) = 4200

L = 7 m 18.58bw = 30 cm

a) 21.03Vu = 21.03 tn


tg()= 4.542117Vud = 18.58 tn





Vs = 9.42 tn (1)



25.82 tn (3)

(1) < (3)

si (1)(3)

Smax = 27 cm




0.54

d bc F Vc w53.0l

VcVud

Vs

d bc F V w1.22

d bc F w1.1

2maxd

S

S b Av w

52.3min

4max d S


62/175

Av.min = 0.68 cm2

As = Av = 1.42 cm2


Vu = 20.71 tna = -0.47 m q= 3.46 m

ao = 1.76 mm= 2.3 m

So = 26.17 cm

S1 = 34.2 cm


y

VcVud Fy Av

So

VcS

d Fy AvVu

11 n

mSoS

Vud VuVud

d xa )( mVcVuVcVu

q *2/


63/175

1#3 @0.25

26.17 cm

21.03

18.58

27 cm 25

10.57

5.29

-0.47

ao= 1.76m= 2.3q= 3.46

x= 4.63



OBSERVACIN:

a=

Vu

d=0.54

Vu =

Vud =

Vc=

Vc/2=

S = cm

So=
mailto:1mailto:1


64/175

1.128194691.354260171.805680230.902840111.579614750.67748553


65/175

DATOS

L 5 m

0.25 h= 0.25 m

h (m) kg/m20.25

350

100D(total) 450L(total) SC 500

WD = 450 kg/m2

Wl = 500 kg/m2

1 2 3 4

Wu = 592 kg/m

1/16 apoyo monolitico1/24 apoyo simple

1/10 1/11 1/11 1/11 1/11 1/111/16 1/16

1/14 apoyo monolitico en E1/11 apoyo simple en E

PREDIMENSIONAMIENTO DE LOSA

LOSA ALIGERADA

Peso propio de losa

Peso muerto por piso y cielo raso

TECHO

Por Vigueta

Calculo de Momentos

COHEFICIENTES DEL ACI

A1 A2 A3

E

20Lh

2 LuWuCoef Mu

5.27.14.1 L D

Wu


66/175

L(A1) = 5.5 m L(A2) = 5 m 5 m

M(-)

Mu = 746.17 kg-m

M(+)

Mu = 1628 kg-m

M(-)

Mu = 1631.7 kg-m

M(+)Mu = 925 kg-m

M(-)

Mu = 1345.45 kg-m

M(+)

Mu = 1345.45 kg-m

M(-)

Mu = 616.67 kg-m

Intermedio

Extremo final

Vigueta A3

Intermedio

Extremo final

L(A3) =

Extremo Inicial

Intermedio

Vigueta A1

Extremo final

Vigueta A2


67/175


b 1 = 0.85b3 0.85

0.9 253

10d= 22d'= 0



Mub

= Rub

bd2 Mub

(t-m) = 1.7

DISEO DE VIGAS

# capas traccion

Una capa

# capas compresion

b = =

=

d' =


68/175


Y como Mub = t-mPor lo tanto Mu < Mub


4.4 cm

cm2

cm

a = cm

cm2

cm

cm2

Entonces As(+)= 0.95 cm2 Ok 1 # 4 As = 1.29

1 # 4

10

25

0.95

2.24

0.61

ELEMENTO O VIGUETA A1 TRAMO L = 0 _m

1.002

2.36

2.24

-0.75

1.7


2/ad Fy M

A uS

b Fc Fy As

a3 b

2/ad Fy M

A uS

b Fc Fy As

a3 b

d b Fy Fc

As 8.0min


69/175


70/175

De la Envolvente Mu = t-mY como Mub = t-mPor lo tanto Mu < Mub


4.4 cm

cm2

cm

a = cm

cm2

cm

cm2

Entonces As(+)= 2.227 cm2 Ok As = 2.29 cm2

2.227

25

10

ELEMENTO O VIGUETA A1 TRAMO L = 5.5 _m

-1.631.7


2.18

5.13

5.24

1 # 4 + 1 # 5

1 # 4 + 1 # 5

5.24

0.61

2/ad Fy M

A uS

b Fc Fy As

a3 b

2/ad Fy M

A uS

b Fc Fy Asa

3 b

d b Fy Fc

As 8.0min


71/175

De la Envolvente Mu = t-m b = 40 cm



4.25 cm c = 5 cm

cm2

cm Seccion Rectangular

4.4 cm

cm2

cm

a = cm

cm2

cm

cm2

Entonces As(-)= 1.51 cm2 As = 2.0 cm21 # 3 + 1 # 4

0.66

251 # 3 + 1 # 4

2.43 40

0.66

1.129

1.236

0.73

1.231

0.72


ELEMENTO O VIGUETA A2 TRAMO L = 2.5 _m SECCION T

0.93

1.7

a =

2/ad Fy M

A uS

b Fc Fy As

a3 b

2/ad Fy M

A uS

b Fc

Fy Asa

3 b

d b Fy Fc

As 8.0min

ca 1 b

2/ad Fy M

A uS

b Fc Fy As

a3 b


72/175




4.4 cm

cm2

cm

a = cm

cm2

cm

cm2


10

1 # 3 + 1 # 425

4.21

0.61

1 # 3 + 1 # 4

4.21

1.789

1.798

4.23

ELEMENTO O VIGUETA A2 TRAMO L = 5.0 _m

-1.345


1.7

2/ad Fy M

A uS

b Fc Fy As

a3 b

2/ad Fy M

A uS

b Fc Fy As

a3 b

d b Fy Fc

As 8.0min


73/175

De la Envolvente Mu = t-m b = 40 cm



4.25 cm c = 5 cm

cm2

cm Seccion Rectangular

4.4 cm

cm2

cm

a = cm

cm2

cm

cm2

0.97

251 # 3 + 1 # 5

2.43 40

1.06

0.97

1.654


1.798

1.791

1.05

ELEMENTO O VIGUETA A3 TRAMO L = 2.5 _m SECCION T

1.345

1.7

a =

2/ad Fy M

A uS

b Fc Fy As

a3 b

2/ad Fy M

A uS

b Fc Fy Asa

3 b

d b Fy Fc

As 8.0min

ca 1 b

2/ad Fy M

A uS

b Fc Fy As

a3 b


74/175

Entonces As(-)= 2.21 cm2 As = 2.71 cm2




4.4 cm

cm2

cm

a = cm

cm2

cm

cm2


10

1 # 425

1.82

0.61

1 # 4

1.82

0.774

0.824

1.94

1 # 3 + 1 # 5

ELEMENTO O VIGUETA A3 TRAMO L = 5.0 _m-0.617

1.7


2/ad Fy M

A uS

b Fc Fy As

a3 b

2/ad Fy M

A uS

b Fc Fy As

a3 b

d b Fy Fc

As 8.0min


75/175

Coef = 0.575

= 1 concreto de peso normalVc= 1858.66 kg

Vc= 1579.861 kgVu = 1872.2 kg

1872.2 > 1579.9

b = 25 cmVc= 4646.66 kg

Vc= 3949.661 kg

1872.2 < 3949.7 ok

Coef = 0.5

= 1 concreto de peso normalVc= 1858.66 kg

Vc= 1579.861 kgVu = 1480 kg

1480 < 1579.9 ok

Debe de cumplir Vu < oVc

ANALISIS DE FUERZA CORTANTE PARA EL EXTREMO CRTICO

En caso de losas nervadas, la resistencia admisible del concreto podr incrementarse en un 10%.


Tendremos que aumentar la base

ANALISIS DE FUERZA CORTANTE PARA PUNTOS NO CRITICOS

En caso de losas nervadas, la resistencia admisible del concreto podr incrementarse en un 10%.


d bc F Vc w53.0l

LuWuCoef Vu

d bc F Vc w53.0l

LuWuCoef Vu


76/175


77/175

2#8+2#7Momentos negativos en las caras de las columnas

2#4kg-m kg-mkg-m kg-m

kg-m kg-mkg-m kg-m

Momentos positivos en el centro del claro

kgkg

kg

kg

n= 9

En la seccion no fisurada

E:N 30 cm

30 cm

cm

Momentos de inercia de las ecciones fisuradas

En la seccion fisurada, en el centro del claro (region positiva)

82 cm2

6c 2#8 As = cm2

54EN 2#43#6 As = cm2

100 cm2

CONTROL DE DEFLECCIONES

MD = 8767.2ML = 6243.1

b

Extremo final Extremo inicial

cmh

3060

Fy =F`c =

4200210

k/cm2k/cm2

cm-kg

MD+L =10015.815010.2

MD+.20L =

MD+.20L =

7083.3

MD+L = 10517.0

MD =

k/cm2

4292.2

m-kg

cm

30

Ig =Yt =Ec =

Mcr =

cm4

6224.9

cm

Calculos previos

Mcr =

MD = 8771.4ML =

Fr= 28.9828 k/cm2

54000030

217371

5216.90521690

5981.8MD+.20L = 9967.8

MD+L = 14753.2

ML =

10.20

11.130

Fc F r 2

Fc Ec 15000c

Ig Fr Mcr

s An )1(

Asn )(


78/175

Calculo de la profundidad del EN

M.EN =030 c (c/2) + (c-6) 82 - 100 = 0

15 c^2 + 182 c - = 0

c = cm

Calculo del momento de inercia de la seccion fisurada Icr

cm4

En la seccion fisurada, en los apoyos (region negativa)

161 cm2

2#8+2#7 As = cm2

54

c 6 2#4 As = cm2

21 cm2

Calculo de la profundidad del EN

M.EN =030 c (c/2) + (c-6) 21 - 161 = 0

15 c^2 + 182 c - = 0

c = cm

Calculo del momento de inercia de la seccion fisurada Icr

cm4

Calculo de las relaciones: Mcr / Ma

Regin Positiva

Carga Muerta: Mcr / MD :

Carga Viva : Mcr / ML :

Carga Muerta + 0.2L: Mcr / MD +0.2L :

Carga Total Mcr / M D+L :

Icr = 269867

EN

15

Icr = 192308

17.94

(54-c)

5884.2

0.737

8842.68

19

2.630

(54-c)

0.496

0.838

1.215

s An )1(

Asn )(


79/175

Regin Negativa

Carga Muerta: Mcr / MD :

Carga Viva : Mcr / ML :

Carga Muerta + 0.2L: Mcr / MD +0.2L :

Carga Total Mcr / M D+L :

Momentos de inercia equivalentes o efectivas

Regin Positiva

Para D

cm4 < cm4

Para D + 0.2L

cm4 < cm4

Para D +L

cm4 < cm4

Regin Negativa

Para D

cm4 < cm4

Para D + 0.2L

cm4 < cm4

Para D +L

cm4 < cm4

Momentos de inercia equivalentes promedios

Para D

cm4

Para D + 0.2L

cm4

Para D +Lcm4

Ie = 234734.3074 540000

Ig

Ig

0.595

540000

0.836

0.521

0.348

Ie = 396917.7465 540000

Ig

Ie = 331494.2154 540000

Ig

Ig

Ie = 308069.1225 540000

Ie = 326768.8636

248689.3786

Ie = 281251.2113

Ie =

540000

Ie = 375873.0816

Ig

Ie = 324466.6875

Icr Mx Mcr

Ig Mx Mcr

Ie

33

1

))(2(15.0)(7.0)( Ie Ie pr Ie


80/175


81/175

Deflexin total

cm

Comparacion:

Con los varores permisibles del Reglamento

cm BIEN

cm BIEN

cm MAL

cm BIEN

1.91667

1.4375

2.875

< 2.085

> 2.085

> 0.455

> 0.455

T = 2.085

3.83333

L D LT 2.0 l l a a

l n L l

240,480,360,180


82/175


83/175


84/175


85/175


86/175


87/175


88/175


89/175

PORTICO 2 SEPTIMO NIVEL


90/175

Elemento Nudo Carga V N M2 m nText Text Text Ton Ton Ton-m140 80 DEAD 5.01 -8.20 -6.35 6.35 8.2140 85 DEAD -5.01 -8.20 8.67 8.67140 80 L 3.77 -5.74 -5.14 5.14 5.74140 85 L -3.77 -5.74 6.17 6.17140 80 Sx -1.74 2.20 -2.14 2.14 2.2140 85 Sx 1.74 2.20 -7.35 7.35141 81 DEAD 0.95 -16.99 -1.27 1.27 16.99141 86 DEAD -0.95 -16.99 1.57 1.57141 81 L 0.73 -11.74 -1.02 1.02 11.74141 86 L -0.73 -11.74 1.19 1.19141 81 Sx -5.62 -0.27 3.15 3.15 0.27141 86 Sx 5.62 -0.27 -13.72 13.72142 82 DEAD -0.75 -17.00 0.93 0.93 17142 87 DEAD 0.75 -17.00 -1.31 1.31142 82 L -0.55 -11.84 0.76 0.76 11.84142 87 L 0.55 -11.84 -0.89 0.89

142 82 Sx -5.66 0.23 3.24 3.24 0.23142 87 Sx 5.66 0.23 -13.75 13.75143 83 DEAD 1.35 17.66 -1.68 1.68 17.66143 88 DEAD -1.35 -17.66 2.36 2.36143 83 L 1.02 -12.21 -1.46 1.46 12.21143 88 L -1.02 -12.21 1.59 1.59143 83 Sx -5.43 -0.40 2.87 2.87 0.4143 88 Sx 5.43 -0.40 -13.40 13.4144 84 DEAD -6.55 -9.45 8.24 8.24 9.45144 89 DEAD 6.55 -9.45 -11.41 11.41144 84 L -4.98 -6.60 6.83 6.83 6.6144 89 L 4.98 -6.60 -8.09 8.09144 84 Sx -1.35 -1.75 -2.69 2.69 1.75144 89 Sx 1.35 -1.75 -6.74 6.74

Nivel Nudo U (m)1 55 0.01092 60 0.03163 65 0.0544 70 0.07475 75 0.0926 80 0.10517 85 0.1137

Resumen para los elementos del septimo nivel

Desplazamienos por niveles


91/175


92/175

Estabilidad

7 Entrepiso

Pu = 134.1244 tn.

tn

Q1= 0.028 < 0.05 Arriostrado

Momentos de Inercia

Columna:

b = 0.3 m

h = 0.7 m 0.006 m4Viga:

b = 0.3 mh = 0.6 m 0.0038 m4

Rigideces

Columna 140: 7.41

3.705

Columna 141: 3.705

1.853

110.068 Sismo fuerzasVu _ 87.175.0

LcVu

PuQ 11

1270.0

3hb Ic

1270.0

3hb Iv

vig L EI

col L EI

K

K

piso

col

/

/80

vig L EI col L EI

K

K

piso

col

/

/85

vig L EI

col L EI

K

K

piso

col

/

/81

vig L EI

col L EI

K

K

piso

col

/

/86


93/175

Longitudes Efectivas

Segn los Monogramas:

Columna 140: Con desplazamiento K = 2.21 K x Lu = 5.3 mSin desplazamiento K = 0.93 K x Lu = 2.23 m

Columna 141: Con desplazamiento K = 1.78 K x Lu = 4.27 mSin desplazamiento K = 0.88 K x Lu = 2.11 m

Radio de Giro

0.169

DISEO DE LA COLUMNA 140

Sin desplazamineto U = 1.4D + 1.7LM1= 17.63 t-m.M2 = 22.63 t-m.

Si:

13.2

Y el valor limite es: 43.3 < 40

Como : 13.2 < 43.3

Pu = 21.236 tn.M2 = 22.63 t-m.

Verificacin de la exentricidad minima

3.6 cm

10.66 cm ok

Con desplazamineto

Como

No Considerar Esbeltez disear como Columna Corta

1.4D + 1.7L =

Ac Ic

r

r Lu K

2

11234

M

M

he 03.05.1min

Pu

M e 2

E L DU 87.17.14.175.0


94/175

31.36 > 22 Considerar Esbeltez

Con cargas gravitacionales

M2ns= 16.97 m-tn.

Con cargas de sismo

M2s= 10.308 m-tn.

El valor de s, se determina:

1.03 < 1.5

Para esto de determinaran:

Pu =Pu = 19.01 tn.Pu = 33.19 tn.Pu = 33.27 tn.Pu = 34.67 tn.Pu = 20.79 tn.

140.93 tn.

Pc =

5219.054 m2-t

1833.757 tn.

2825.126 tn.

EI = 0.4 Ec Ig =

Columna 140

Columna 141

Columna 142

Columna 143Columna 144

Por ser de la misma dimension todas las columnas

Columna 140Columna 141Columna 142

r Lu K

Q s 11

Pc

Pu s

75.01

1

E L D P P P Pu 87.17.14.175.0

22

Lu K

EI Pc

22

Lu K

EI Pc


95/175

2825.126 tn.

2825.126 tn.

1833.757 tn.

12142.89 tn.

1.02

1.02

Entonces la carga y momento de diseo seran:

Pu = 19.01 tn.

Mc= 27.48 tn-m.

Columna 144

Comparando de toma el menor valor de s =

Columna 143

22

Lu K

EI Pc

22

Lu K EI Pc

22

Lu K

EI Pc

Pc

Pu s

75.01

1

Ns s s M M Mc 22


96/175

Diseo segn tablas

0.3

P = 21.24 tn.M = 22.63 tn-m.

0.83

Para 1=0.75

10.11

Pg1 = 0.025

1.52

Para 1=0.90

10.11

Pg2 = 0.02

1.52

Interpolando Para 1=0.83 Pg = 0.023

48 cm2

pulg cm0.3 10#8 8 1 2.54

4 1/2 1.273 3/8 0.9532 1/4 0.625

Espaciamiento maximo vertical de los estribos; Smax es:

16 db (longitudinal) = 40.64 cm48 db (estribo) = 45.744 cm

Menor dimension de seccion transversal de la columna = 30 cm

Smax = 30 cm

#3

0.7

# barra db

0.7

As=51 cm2.

70

1270

hh

o

Ag

Pu

h Pu Mu

he

Ag Pu

h Pu Mu

he

hb Pg As


97/175


98/175


99/175


100/175


101/175


102/175


103/175


104/175


105/175


106/175


107/175


108/175


109/175


110/175


111/175


112/175


113/175


114/175

ANALIZAREMOS LA ZAPATA DE LA COLUMNA Datos 40

Dimension de Columna : b = 0.3 mh = 0.65 m

Sobrecarga (S/C) = 0 Kg/m2Peso Volumetrico del Suelo = 1.6 t/m3 s)Profundidad de Cimentacion = 1 mResistencia Admisible del Suelo = 3 Kg/cm2 (qa)Resistencia Admisible Conctreto = 210 Kg/cm2Resistencia Admisible Acero = 4200 Kg/cm2

Cargas en Servicio

PD = 138.894 Tn.PL = 46.312 Tn.PE = 3.381 Tn.

Calculo de la Presion Efectiva o Neta del Suelo Asumiendo un peralte de zapata de h = 0.7 m, por que la longitud de desarrollo de labarra # 8 en compresion es 58.3 cm, donde :d = 60 cmrecubrimiento = 10 cm

Presion Efectiva sin considerar carga de Sismo.

qa = 3 Kg/cm2s/c = 0 Kg/cm2

s = 0.0016 Kg/cm3hs = 30 cmc = 0.0024 Kg/cm3

hc = 70 cm

2.784 Kg/cm2

Presion Efectiva considerando carga de Sismo.

3.684 Kg/cm2

Dimensionamiento en planta

Area minima de la zapata en planta

Sin Sismo

66525 cm2

DISE O DE ZAPATA AISLADA INTERIOR 2xo

cc s sae hhc sqq /

cc s sae hhc sqq /3.1

e

L D

q

P P Az


115/175

Con Sismo

51191 cm2

Tomamos la mayor area Az = 66525

Buscar que m = nS 30

65

T

275 cm 2.85 m

ok

240 cm 2.5 m

m = 110 cmn = 110 cm

Dimension Final en Planta

110110

250 3065

285

Dimensionamiento en altura

Corte por Punzonamiento

Asumiendo d = 60 cm

285 AZAP = 71250 cm2

30

250 30 bo = 430 cm65

Ao = 11250 cm2

nm

d/2=

e

E L D

q

P P P Az

2

hb AZAP T

2hb AZAP S


116/175

Presion Factorizada o ultima del suelo, considerando la carga ultima. El mayor de las combinaciones

273183 Kg.

234889 Kg.

273183 Kg.

3.83 Kg/cm2

La fuerza Cortante ultima actuante en el perimetro de falla es:

Pu

Vuo = 230095 Kg.Vuo Vuo

qu

Resistencia Nominal del concreto al cortante, se elige el menor valor de los siguenyes valores:Donde :

ss = 40 Correspondiente a la columna interior 40

3020

2.17

c = 2.17

387971

765319

411265

Tomamos el menor Vco = 387971

Cortante resistente del concreto de diseo

Col Esquina

Pu(mayor) =

Col InternaCol Externa

L D Pu 7.14.1

E L D Pu )(25.1

AZAP Pu

qu

0Pu AoqVuo u

columnademenor Dimensioncolumnademayor Dimension

c _ _ _ _ _ _

b

d boc f Vco

c b

4227.0

d boc f bo

d Vco s 227.0

a

d boc f Vco 1.1


117/175

= 0.85

270700 < 387971

Corte por flexion:60

285

60

B = 250 30

65

n = 50

50

Vu 47875 Kg

qu

Corte resistente de diseo del concreto

115206 Kg.

56324 < 115206

Verificacion de las dimensiones en planta de la zapataNo es necesario modificar las dimensiones de la zapata en planta, por que el peralte asumidopara hallar el qe coincide con el necesario para evitar las fallas por corte perimetral y flexion.

No es necesario modificar el peralte asumido

Se verificara el peralte que setisface el corte perimetral para d =


d =

VcoVuo

BnqVu u

Bd c f Vc 53.0

VcVu


118/175

285

Seccion crtica

B = 250 3065

m =

Momento Ultimo Actuante

cm-Kg

Refuerzo Para un metro de ancho con:

d = 60 cm

b = 100 cm

Mu(1 metro) = 23.172 tn-m/m.

110

5792875

CALCULO DEL REFURZO POR FLEXIN

2

2m Bq Mu u


119/175

Resistencia al Aplastamiento

En la superficie de apoyo:

Pu = 273183 Kg. A1 = 30 x 65 = 1950 cm2 A2 = 250 x 285 = 71250 cm2

6.04 raiz = 2

Fuerza reisitente al aplastamiento

487305 = 0.7

273183 < 487305

2.85

#5@ 0.125

2.5 0.30.65

#5@ 0.125

N.F.P0.05

#3@ 0.3Especificacion en Planta

1

0.050.7 0.25

0.1

ZAPATA EN PLANTA

Dimension en Planta

ELEVACIN TIPICA DE ZAPATA

No falla por aplastamiento

1

2

A

A

11

285.0 A

A A

c f Pn

Pn Pu
mailto:#3@mailto:#3@


120/175

ANALIZAREMOS LA ZAPATA DE LA COLUMNA 1 Datos 40

Dimension de Columna : b = 0.3 mh = 0.65 m

Sobrecarga (S/C) = 0 Kg/m2Peso Volumetrico del Suelo = 1.6 t/m3 s)Profundidad de Cimentacion = 1 mResistencia Admisible del Suelo = 3 Kg/cm2 (qa)Resistencia Admisible Conctreto = 210 Kg/cm2Resistencia Admisible Acero = 4200 Kg/cm2

Cargas en Servicio positivas

PD = 64.514 Tn.PL = 21.744 Tn.PE = 13.172 Tn.

Calculo de la Presion Efectiva o Neta del Suelo

Asumiendo un peralte de zapata de h = 0.7 m, por que la longitud de desarrollo de labarra # 8 en compresion es 58.3 cm, donde :d = 60 cmrecubrimiento = 10 cm

Presion Efectiva sin considerar carga de Sismo.

qa = 3 Kg/cm2s/c = 0 Kg/cm2

s = 0.0016 Kg/cm3hs = 30 cmc = 0.0024 Kg/cm3

hc = 70 cm

2.784 Kg/cm2

Presion Efectiva considerando carga de Sismo.

3.684 Kg/cm2

Dimensionamiento en planta Area minima de la zapata en planta

Sin Sismo

30984 cm2

DISE O DE ZAPATA AISLADA EXTERIOR

cc s sae hhc sqq /

cc s sae hhc sqq /3.1

e

L D

q

P P Az


121/175

Con Sismo

26990 cm2

Tomamos la mayor area Az = 30984

B65 B = ( 2 - 2.5 ) A

A 30B = 2A

Az = 2AxA = 30984 A = 124.5 cm 1.25 m

okB = 249 cm 2.5 m

Dimension Final en Planta

25065

125 30

110

qu = Pu/B

Para el calculo de las cargas desconocidas primero analizaremos la viga de conexin

Pu=Peu+Pvu+Riu

B

e

E L D

q

P P P Az


122/175

Dimensionamiento de viga

0.3 Edificio Pequeob = 0.4 0.5 Edificio Mediano

0.5 0.8 Edificio Altos

2.85

0.3 0.32.5 2.5

0.65 0.65

L= 6.5

Como la separacin entre las zapatas aisladas es minima disearemos ZapatasCombinadas

l

he0.3 0.3

b0.65 0.65

L

R = Pe + PiPe Pi

qe

4.15

DISEO DE ZAPATA COMBINADA

1.25

DISE O DE VIGA DE CONEXI N

87 L

a L

h


123/175

Dimensionamiento de la zapata en planta (Cargas en servicio)

Pe = 99.43Pi = 188.59qe = 2.784q*e = 3.684L = 6.5

he = 0.65

103455 cm2

78181 cm2

AZAP = 103455 cm2

9.2 m l = 9.2 m

1.1 m b = 1.1 m

l = 9.2

he0.3 0.3 1.1

b0.65 0.65

L = 6.5 2.05

Dimensionamiento en altura

P = D + L + E

Sin Sismo

Con Sismo

qe

Pi Pe AZAP

eq

Pi Pe AZAP

*

he

Pi Pe Pi L

l 2

l

AZAP b


124/175

COLUMNA INTERIOR


Asumiendo d = 70 cm

920 cm AZAP = 101200 cm2

35

110 30 bo = 470 cm65

Ao = 13500 cm2


273183 Kg.

234889 Kg.

273183 Kg.

2.7 Kg/cm2


Pu


qu



30

20

2.17

c = 2.17


Col Esquina

Pu(mayor) =

d/2=

L D Pu 7.14.1

E L D Pu )(25.1

AZAP Pu

qu

0Pu AoqVuo u


c _ _ _ _ _ _

b


125/175

494738

1E+06

524443



= 0.85

278509 < 494738

COLUMNA EXTERIOR


Asumiendo d = 70 cm

AZAP = 101200 cm2

3565 bo = 400 cm

30920 Ao = 10000 cm2

110 cm


127285 Kg.

120994 Kg.

127285 Kg.


Pu(mayor) =

d/2=

d boc f Vco

c b

4227.0

d boc f bo

d Vco

s 227.0a

d boc f Vco 1.1

VcoVuo

L D Pu 7.14.1

E L D Pu )(25.1


126/175

1.26 Kg/cm2


Pu


qu



30

20

2.17

c = 2.17

421054

794272

446334



= 0.85

134923 < 421054


Col Esquina


AZAP

Puqu

0Pu AoqVuo u


c _ _ _ _ _ _

b

d boc f Vco

c b

4227.0

d boc f bo

d Vco s 227.0

a

d boc f Vco 1.1

VcoVuo


127/175

Diseo en le sentido longitudinal

Cargas Distribuidas

Peu = 127.28 tn Piu = 273.18 tn

43.53 tn/m 0.65 he = hi

Xo 2.05

Analizando un corte a la distancia Xo

Cortantes

2.92 m

Momentos

-144.73 t-m

DIAGRAMA DE FUERZAS CORTANTES155.65 tn

2.92

-89.237 tn-98.99 tn

DIAGRAMA DE MOMENTOS FLECTORES

-144.73 tn-m

91.467 t-m

a

Piu Peuuqe

0uq Xo Peu A

22max

2 Xouq

h Xo Peu M A

e

uq Peu Xo

A


128/175

Diseo en la direccion transversal 1.6

0.65 d/2 d/2 0.65 d/2

Pe Pi

0.7

1 1.35

2.925 2.925

Area Contribuyente = 3.575 X 0.55 Area Contribuyente = 1.9663 m2

28.46 t/m2

Cortante V = 55.96 Tn Vd = -15.262

Momento M = 15.389 tn-m

Area Contribuyente = 5.625 X 0.55 Area Contribuyente = 3.0938 m2

28.46 t/m2

Cortante V = 88.049 Tn Vd = -24.013

Momento M = 24.213 tn-m

Analizando tramo de columna exterior

Analizando tramo de columna interior

l b

P qu

total

l b P qu total

C AreaqV u . 2d V M


129/175


130/175


131/175


132/175


133/175


134/175


135/175


136/175


137/175


138/175

El dieo de Acero para la parrilla de la zapata de hara por flexin


139/175


140/175


141/175


142/175


143/175


144/175


145/175


146/175


147/175


148/175


149/175

Fc (kg/cm 2 ) = 210Fy ( kg/cm2 ) = 4200

b 1 = 0.85b3 0.85

0.9 7010

100d= 60 cm




DISEO DE PARRILLA DE ZAPATA INTERIOR

cm

b = =

=


150/175


Y como Mub = t-m



12 cm

cm2

cm

a = cm

cm2

cm

cm2

Entonces As(-)= 14.1333333 cm2/m As = 35.33 cm2

Barra #5 (As)= 2 Barra #4 (Diam)= 0.0159 m

18

Espaciamiento = 13 cm

Por lo Tanto La Distribucin sera: #5@ 0.125

cm2

10.6

2.49

16.56

11.352

2.67

4.36

DISEO DE PARRILLA DE ZAPATA

23.17

126.26


2/ad Fy M

A uS

b Fc Fy As

a3 b

2/ad Fy M

A uS

b Fc Fy Asa

3 b

d b Fy Fc

As 8.0min

A As

n

nrecubr B .2
mailto:#5@mailto:#5@


151/175

Fc (kg/cm 2 ) = 210

Fy ( kg/cm2 ) =

4200b 1 = 0.85b3 0.85

0.9 709

292.5d= 61d'=

r b = b 1b 3 fc ( 6000 ) r b = 0.02125

fy 6000+fy r mx = 0.0106



# capas compresion

DISEO DE VIGA DE CONEXIN

# capas traccion

Dos capas

b = =

=

d' =


152/175

0 m




12.2 cm

cm2

cm

a = cm

cm2

cm

cm2

Entonces As(+)= 0 cm2 5 # 8 As = 25.5

Refuerzo en la cara inferior

cm2 As(-) / 2 0 cm2

Entonces As(-)= 49.25 cm2 As = 15.88

5 # 8

2 # 8+2 # 6

49.25

2.925

DISE O DE VIGA DE CONEXI N TRAMO L =

0.7

49.25

0

0

0

0

18.64

0.00

381.71


2 # 8+2 # 6

cm2

cm2

2/ad Fy M

A uS

b Fc Fy As

a3 b

2/ad Fy M

A uS

b Fc Fy As

a3 b

d b Fy Fc

As 8.0min

d b Fy Fc

As 8.0min


153/175

DATOS 40Fc (kg/cm 2 ) = 210

Fy ( kg/cm2 ) =

4200b 1 = 0.85b3 0.85

0.9 010

0d= -10 cm

r b = b 1b 3 fc ( 6000 ) r b = 0.02125

fy 6000+fy r mx = 0.0106


Mub = Rub bd2 Mub (t-m) = 0

cm

DISEO DE PARRILLA DE ZAPATA EXTERIOR

b = =

=


154/175


155/175

DATOS 40Fc (kg/cm 2 ) = 210Fy ( kg/cm2 ) = 4200

b 1 = 0.85b3 0.85

0.9 706

110d= 64




Una capa

# capas compresion

DISE O DE PLATEA PARA ZAPATAS COMBINADAS

# capas traccion

b = =

=


156/175

2.92 m




12.8 cm

cm2

cm

a = cm

cm2

cm

cm2

Entonces As(+)= 62.58 cm2 25 # 8 As = 127.5

25 # 80.7

19.43

1.1

13.39

14.22

5.64

DISEO DE PLATEA PARA ZAPATAS COMBINADAS TRAMO L =

62.58


66.473

-144.73

158.02

cm2

2/ad Fy M

A uS

b Fc Fy As

a3 b

2/ad Fy M

A uS

b Fc Fy As

a3 b

d b Fy Fc

As 8.0min


157/175




12.8 cm

cm2

cm

a = cm

cm2

cm

cm2

Entonces As(-)= 39.46 cm2 24 # 8 As = 122.4

0.724 # 8

8.44

19.43

8.99

5.37

39.46

DISEO DE PLATEA PARA ZAPATAS COMBINADAS TRAMO DERECHO

158.02


42.01

91.47

1.1

cm2

2/ad Fy M

A uS

b Fc Fy As

a3 b

2/ad Fy M

A uS

b Fc Fy As

a3 b

d b Fy Fc

As 8.0min


158/175


b 1 = 0.85b3 0.85

0.9 7010

135d= 60




DISE O DE VIGA TRANSVERSAL DE ZAPATA INTERIOR

b = =

=


159/175


160/175

DATOSFc (kg/cm 2 ) = 210

Fy ( kg/cm2 ) =

4200b 1 = 0.85b3 0.85

0.9 7010

100d= 60

r b = b 1b 3 fc ( 6000 ) r b = 0.02125

fy 6000+fy r mx = 0.0106



DISEO DE VIGA TRANSVERSAL DE ZAPATA EXTERIOR

b =

==


161/175




12 cm

cm2

cm

a = cm

cm2

cm

cm2

Entonces As(+)= 9.6 cm2 7 # 8 As = 35.7

7 # 80.7

4 # 8

Entonces As(-)= 16.56 cm2 4 # 8 As = 20.4

16.56

7.539

1.77

7.2

1

1.69

6.84

126.26


DISEO DE VIGA TRANSVERSAL DE ZAPATA EXTERIOR

15.39

cm2

cm2

2/ad Fy M

A uS

b Fc

Fy Asa

3 b

2/ad Fy M

A uS

b Fc Fy As

a3 b

d b Fy Fc

As 8.0min


162/175


163/175

Para varillas # 6:

Fy = 4200 ldF`c = 210 pulg cm m

a 1.3 5 5/8 1.587 0.9 0.90187509b 1 6 3/4 1.905 1.08 1.08259109l 1 8 1 2.54 1.81 1.44345478

. 4 1/2 1.27 0.72 0.721727397 7/8 2.222 1.58 1.262738793 3/8 0.953 0.54 0.54157969

AsRequerido (cm2)

Asproporcionado(cm2)

As req/ Asprop.

15.20 15.30 0.9917.30 17.94 0.9617.77 17.94 0.99

3.00 4.00 0.75

F= 0.99

# barra lbd ld lbd ld ldf pulg cm cm cm cm cm cm

5 5/8 1.587 36.8 36.43 26.66 26.39 36.436 3/4 1.905 44.17 43.73 32 31.68 43.738 1 2.54 58.89 58.3 42.67 42.24 58.34 1/2 1.27 29.45 29.16 21.34 21.13 29.167 7/8 2.222 51.52 51 37.33 36.96 51

CANTIDAD DE REFUERZO EN LA SECCION DE LA VIGA

LONGITUD DE DESARROLLO

TRACCION

# barra db

Para varillas # 6:

Para varillas # 7 y mayores:

COMPRESION

c F

db Fy L d

63.6

l b a

c F

db Fy Ld 3.5

l b a

f ldb L d

c F

db Fy L d

08.0

Fydb L d 04.0

2d b

Mu Ru

bc F Fy As

a3 b


164/175

ANCLAJES

BARRAS Ref.Principal

pulg cm 12 db (cm)5 5/8 1.587 19.046 3/4 1.905 22.868 1 2.54 30.484 1/2 1.27 15.247 7/8 2.222 26.66

LONGITUD DE DESARROLLO TOTAL ( ldh)

f = 0.7

barra ldhpulg cm cm

5 5/8 1.587 24.386 3/4 1.905 29.268 1 2.54 39.024 1/2 1.27 19.517 7/8 2.222 34.13

EMPALMES DE REFUERZO ls (TRASLAPE)

barra d ld lspulg cm cm cm

5 5/8 1.587 36.43 47.366 3/4 1.905 43.73 56.858 1 2.54 58.3 75.794 1/2 1.27 29.16 37.917 7/8 2.222 51 66.3

d

d

Ls = 1.3ld (compresin)

f ldb L d

c F db

ldb318


165/175


= 0.85d = 61

Fc (kg/cm 2 ) = 210Fy ( kg/cm2 ) = 4200

L = 0 m #DIV/0!bw = 292.5 cm

a) 0.00Vu = 0.00 tn


tg()= #DIV/0!Vud = #DIV/0! tn


= 1 concreto de peso normal

Vc= 137.04 tn

Vc= 116.48 tn #DIV/0!

Vc/2= 58.24 tn


Vs = #DIV/0! tn (1)

V2 = 542.98 tn (2) #DIV/0!



0.84

d bc F Vc w53.0l

VcVud

Vs

d bc F V w1.22


166/175


284.4 tn (3)

(1) #DIV/0! (3)

si (1)(3)

Smax = #DIV/0! cm Smax = 40 cm


Av.min = #DIV/0! cm2

As = Av = #DIV/0! cm2 # 3

Distribucin: # 3 @ 0.4

2 ramas de acero

d bc F w1.1

2max

d S

Fy

S b Av w

52.3min

4max

d S


167/175


= 0.85d = 70

Fc (kg/cm 2 ) = 210Fy ( kg/cm2 ) = 4200

L = 9.2 m 125.22bw = 110 cm

a) 155.65Vu = 155.65 tn


tg()= 43.4781Vud = 125.22 tn





Vs = 88.18 tn (1)



122.7 tn (3)

(1) < (3)

si (1)(3)

Smax = 35 cm


PLATEA PARA ZAPATAS COMBINADAS


0.70

d bc F Vc w53.0l

VcVud Vs

d bc F V w1.22

d bc F w1.1

2max

d S

4max

d S


168/175


Av.min = 3.23 cm2 As = Av = 10.32 cm2 # 4


Vu = 123.95 tna = 0.03 m q= 3 m

ao = 1.72 mm= 2.42 m

So = 24.47 cm

S1 = 34.4 cm

8 ramas de acero

Fy

S b Av w

52.3min

VcVud Fy Av

So

VcS

d Fy AvVu

11 n

mSoS

Vud VuVud d xa )( mVcVu

VcVuq *2/


169/175

24.47 cm

155.65

125.22

35 cm 30

50.27

25.14

0.03

ao= 1.72m= 2.42q= 3

x= 3.58


Distribucin: # 4 @ 0.3


OBSERVACI N:

a=

Vu

d=0.54

Vu =

Vud =

Vc=

Vc/2=

S = cm

So=


170/175

1.128194691.354260171.805680230.902840111.579614750.67748553


171/175

MURO DE CONTENCION

s/c= 0.02 kg/cm21.- GEOMETRIA 0.20

H= 5.65

1.30

0.20

0.30

B= 1.5

2.- PARAMETROS DE DISEO

(grados) = 30

suelo(Kg/m3) = 1800

qa(Kg/cm2)= 0.07

= 0.5

(grados) = 0

3.- EMPUJE EFECTIVO

Ka= 0.33333


172/175

Ea= 1064.08 kg/m

4.- ANALISIS DE DESLIZAMIENTO y VOLTEO

w5 Ea= 1064.08 kg/m

w4w6

w1 w2 w3

Carga Area c peso(kg) Brazo(m) Mr w1 0.39 2400 936 0.35 327.6w2 0 2400 0 0.55 0w3 0 2400 0 1.55 0w4 0 2400 0 0.83 0w5 1.13 2400 2712 0.9 2440.8w6 1.04 1800 1872 1.55 2901.6

N= 5520 Mr= 5670

Seguridad al Deslizamiento:

*N > F.S.*Eah2760 > 1596.13 ok

Seguridad por Volteo:MEa= 2128.17 kg-m

Mr= 5670 kg-m

Mr/Mea= 2.66 > F.S.=2 ok


173/175

Verificacion de las presiones aplicadas a la fundacion:

h= 1.5 h/6= 0.2500

e=h/2-(Mr-Mea)/N e= 0.11

como:e < h/6

0.11 < 0.25Calculo de las presiones normales en la base de la estructura de contencin

qmax=N/A(1+6*e/B) qmax= 5299.20 kg/m

qmin=N/A(1-6*e/B) qmin= 2060.80 kg/m

Calculo de Zapatas:

zapata anterior zapata posterior

w5

0.9*Pagua= 1100 w6w4 1.4*Ev= 10948

h=1.50

w1 w2 w3

1.4*qmin

1.7*qmx 5645.28 3229.674

Zapata Anterior:

18863.5 kg-m


174/175

f'c = 210 kg/cm2rec = 7.5 fy = 4200 kg/cm3d = 22.5 b = 100 cm

ku = Mu / [ bd^2 ] = 37.26a = 1

As = 22.68 cm2 / m

a = 5.34 As min = 14/fy bd = 7.500 cm2 / m As min = 4/3 As cal 30.244 cm2 / m

Se colocar5/8" @ 25.00 As= 8.20 cm2 / m

Zapata Posterior:

-2762.4


ku = Mu / [ bd^2 ] = 5.46a = 0.73

As = 3.30 cm2 / ma = 0.78

As min = 14/fy bd = 7.500 cm2 / m As min = 4/3 As cal 4.402 cm2 / m

Se colocar1/2" @ 20.00 As= 6.35 cm2 / m

Diseo de Pantalla: 0.2

As=0.0018*b*d

0.26

0.3314.5

2773.11

0.4


175/175


ku = Mu / [ bd^2 ] = 8.10a = 0.7

As = 4.04 cm2 / m

a = 0.95 As min = 14/fy bd = 6.167 cm2 / m As min = 4/3 As cal 5.389 cm2 / m

Se colocar1/2" @ 25.00 As= 2.84 cm2 / m

Acero de temperatura:

Tercio inferior interno: As= 3.3507

Se colocar3/8" @ 20.00 As= 3.55 cm2 / m

Tercio inferior externo: As= 6.7014

Documents

Calculo Final Zapatas