Losa Maciza Aci 1 Al 6

LOSA MACIZA EN DOS DIRECCIONES CONCRETO II

= =

= = x

= = x

=

=

=

=

=

=

=

=

Ib = inercia de la seccin en L Inercia de la losa

Is = inercia de la losa Is =

=

=

=

=

=

=



lm = dimensin media de la franja

Ib 0.0036619m4

0.0012122m4

= 3.021

0.30 yc 0.29m

OK

B 0.9

H = 0.45 Im 4.31

CALCULO DE LOS TRAMO 5-C

0.90 b+2(a-h) 0.90 m

0.15 b+8h 1.50 m

2.- DETERMINACION DE ESPESOR DE LOSA POR DEFLEXIONES

Se escoje el pao mas critico : PAO 12

Inercio de la seccion en "T" :

H = 0.45

0.90

f 1.6

b+2(a-h) 0.90 m

1.50 m b+8h OK

B = 3.28

CALCULO DE LOS TRAMO C-5

=

=

4.60

40

SE ESCOJE h = 0.15 m

= 0.12 m

15.76

180= 0.09 m

Se escoje el pao com las lucez libres mas grandes : PAO 12

PAO 12A= 4.60

2100000 kg/cm2

recubrimiento

VIGAS YY

VIGAS XX

1.- PREDIMENSIONAMIENTO:

Es

0.25 0.45

f'c

Ec

fy

217371 kg/cm2

4200 kg/cm2

DIMENSIONAMIENTO DE LOSA MACIZA EN DOS DIRECCIONES 1 al 6 NIVEL

DATOS GENERALES :

2.50 cm

0.25 0.45

210 kg/cm2

0.0036619m4

0.30


0.0009422m4

= 3.887

0.15

yc

Ib

0.29m

B

Im

0.9

3.35


h Ln

40

h Perimetro

180

B = Bw + H hf Bw + 4 hf

= 3

12

=


= 3

12

=

Sandoval Paredes Alexander Ingenieria Civil


=

=

=

=

=

=



=

=

=

=

=

=



+ + +

donde:

- Ln = Luz libre del pao en la direcc.mas larga

- = Relac. de ln mayor a ln menor

- m = Promedio de los valores en todo el

perimetro del pao. Para losas sin vigas

tomar m=0

- SE ENCUENTRA EN EL CASO :

pero no menor que 125 mm Ln =

=

- h =

pero no menor que 90 mm

ENTONCES h = 0.15 m es CORRECTO

4.628m

m > 2.0

Para m > 2.0, h no debe ser menor que:

para 0.2 < m < 2.0, h no debe ser menor que:

4.600m

1.402

0.104m

6.711

4==

3.021

6.711

3.887 3.021 4.895

0.0007481m4

= 4.895


PAO 12

3.8

87

4.8

95


0.30 yc 0.29m

Ib 0.0036619m4

OK

B 0.9

H = 0.45 Im 2.66

0.90 b+2(a-h) 0.90 m

0.15 b+8h 1.50 m

0.0005456m4

= 6.711


CALCULO DE LOS TRAMO 6-C


0.30 yc 0.29m

Ib 0.0036619m4

B 0.9

H = 0.45 Im 1.94

0.15 b+8h 1.50 m OK

CALCULO DE LOS TRAMO D-5

0.90 b+2(a-h) 0.90 m


= 3

12

=


= 3

12

=

h =Ln 0.8 +

fy14000

36 + 5 (m 0.2)

h =Ln 0.8 +

fy14000

36 + 9

h =Ln 0.8 +

fy14000

36 + 9



= =

=

=

= =

= * = * CV

Wu.cm = =

= * + * CV

Wu =

= = Wu =

357.84inf 0.032 0.053

prom 0.031 0.052

863.8 340.0 2.83 216.98 140.86

163.88inf 0.006 0.010

prom 0.006 0.0112.83

863.8 340.0 4.25 98.57 65.31

0.65

A

sup 0.007 0.012

B

sup 0.030 0.049

Cargas Luz

(m)

Momentos Momentos

TotalesCm Cv Cum Cuv Mcm Mcv

caso2

B

sup 0.074

1203.8inf 0.077

4.25A

prom 0.076

0.666Coeficientes positivos

prom 0.015

Mto(-) kg-

m

0.7

A

sup 0.017

1203.8 4.25 325.13

2.83 733.18

PAO 2m=A/B

Coeficientes

negativosWu Luz (m)

463.21

217.81 25.81 243.61

0.035

0.062

0.067

0.063

0.011

0.009

0.010

0.005

0.004

0.005

0.034

0.036

B inf 0.014

prom

sup

inf

prom

Cm Cv

Coeficientes positivos

Cum Cuv

A4.25

caso 9

2.70

Luz

(m)

Momentos

Mcm Mcv

inf 863.8

863.8

340.0

340.0

4.25

2.70

73.42 389.79

Momentos

Totales

Cargas

A

B

0.635

1203.8 2.70 733.55

Mto(-) kg-

m

161.16

Luz (m)

1203.8 4.25

Coeficientes

negativosWu

0.083

0.085

0.084

sup

inf

prom

sup

inf

prom

0.008

0.006

0.007

A

B

0.6

sup

m=A/B

0.65

PAO 1

B

Cargas para el diceo:

863.80 kg/m2Wu.cm Wu.cv 340.00 kg/m2 1203.80 kg/m2

DETERMINACION DE LOS MOMENTOS (COEFICIENTES ACI)

Wu.cv

Wu.cv

1.7

340.00 kg/m2

100.00 kg/m2

157.00 kg/m2

617.00 kg/m2 CV 200.00 kg/m2

s/c 200.00 kg/m2

1.4 CM

863.80 kg/m2

1.4 CM 1.7

1203.80 kg/m2

Wu.cm

Wu

Peso propio

Acabados

Tabiqueria

CM

360.00 kg/m2

3.- METRADO DE CARGAS



2.83 163.94 99.51

187.762.83

inf 0.012 0.019

prom 0.012 0.019

863.8 340.0 3.3 115.73 72.03

0.85

A

sup 0.014 0.022

B

sup 0.022 0.034

263.45inf 0.024 0.037

Luz

(m)

Momentos Momentos


caso2

B

sup 0.055

1203.8inf 0.06

3.3A

prom 0.059


prom 0.024

B inf 0.031

prom 0.032

Mto(-) kg-

m

0.9

A

sup 0.037

1203.8 3.3 418.31

2.83 571.16

PAO 5m=A/B

Coeficientes

negativosWu Luz (m)

Cargas

0.037

863.8 340.0

2.70 180.33 101.40

171.312.70

inf 0.010 0.017

prom 0.011 0.018

863.8 340.0 3.3 104.33 66.98

0.80

A

sup 0.013 0.02

B

sup 0.028 0.039

281.72inf 0.029 0.042

Luz

(m)

Momentos Momentos


caso9

B

sup 0.072

1203.8inf 0.075

3.3A

prom 0.074


prom 0.029

B inf 0.017

prom 0.018

Mto(-) kg-

m

0.85

A

sup 0.021

1203.8 3.3 241.93

2.70 648.60

PAO 4m=A/B

Coeficientes

negativosWu Luz (m)

Cargas

0.041

863.8 340.0

441.89inf 0.031 0.046

prom 0.030 0.044

863.8 340.0 3.28 280.00 161.89

220.12inf 0.007 0.013

prom 0.008 0.0153.28

863.8 340.0 4.25 129.59 90.53

0.75

A

sup 0.010 0.017

B

sup 0.029 0.042

Cargas Luz

(m)

Momentos Momentos


caso9

B

sup 0.075

1203.8inf 0.078

4.25A

prom 0.077


B inf 0.014

prom 0.015

Mto(-) kg-

m

0.8

A

sup 0.017

1203.8 4.25 332.81

3.28 993.26

PAO 3m=A/B

Coeficientes

negativosWu Luz (m)



2.70 184.10 105.27

161.302.70

inf 0.007 0.013

prom 0.010 0.017

863.8 340.0 3.4 96.33 64.97

0.75

A

sup 0.010 0.017

B

sup 0.029 0.042

289.37inf 0.031 0.046

Luz

(m)

Momentos Momentos


caso9

B

sup 0.075

1203.8inf 0.078

3.4A

prom 0.075


prom 0.029

B inf 0.014

prom 0.017

Mto(-) kg-

m

0.8

A

sup 0.017

1203.8 3.4 231.66

2.70 661.27

PAO 8m=A/B

Coeficientes

negativosWu Luz (m)

Cargas

0.042

863.8 340.0

2.83 102.04 83.05

223.212.83

inf 0.022 0.045

prom 0.021 0.043

863.8 340.0 2.6 124.09 99.12

0.90

A

sup 0.020 0.040

B

sup 0.016 0.033

185.08inf 0.014 0.029

Luz

(m)

Momentos Momentos


caso 2

B

sup 0.041

1203.8inf 0.037

2.6A

prom 0.038


prom 0.015

B inf 0.055

prom 0.053

Mto(-) kg-

m

0.95

A

sup 0.050

1203.8 2.6 432.33

2.83 371.17

PAO 7m=A/B

Coeficientes

negativosWu Luz (m)

Cargas

0.030

863.8 340.0

3.28 214.87 110.62

287.043.28

inf 0.017 0.025

prom 0.020 0.028

863.8 340.0 3.3 184.71 102.33

0.95

A

sup 0.020 0.028

B

sup 0.023 0.030

325.49inf 0.024 0.032

prom 0.023 0.030

Luz

(m)

Momentos Momentos


3.28 796.29inf 0.065

3.3A

prom 0.061

0.994Coeficientes positivos Cargas

863.8 340.0

B

caso9

B

sup 0.061

inf 0.029

prom 0.033

1203.8 3.3 426.25

WuPAO 6

m=A/BCoeficientes

negativosLuz (m)

Mto(-) kg-

m

A

sup 0.033

1.00

1203.8



2.70 335.25 167.05

182.952.70

inf 0.005 0.007

prom 0.007 0.009

863.8 340.0 4.53 121.26 61.69

0.55

A

sup 0.007 0.009

B

sup 0.053 0.067

502.30inf 0.056 0.072

Luz

(m)

Momentos Momentos


caso 4

B

sup 0.089

1203.8inf 0.092

4.53A

prom 0.089


prom 0.053

B inf 0.008

prom 0.011

Mto(-) kg-

m

0.6

A

sup 0.011

1203.8 4.53 265.84

2.70 783.13

PAO 11m=A/B

Coeficientes

negativosWu Luz (m)

Cargas

0.067

863.8 340.0

3.28 220.30 114.90

280.293.28

inf 0.017 0.025

prom 0.018 0.026

863.8 340.0 3.4 178.56 101.73

0.95

A

sup 0.020 0.028

B

sup 0.023 0.030

335.20inf 0.024 0.032

Luz

(m)

Momentos Momentos


caso 9

B

sup 0.061

1203.8inf 0.065

3.4A

prom 0.064


prom 0.024

B inf 0.029

prom 0.030

Mto(-) kg-

m

1.00

A

sup 0.033

1203.8 3.4 419.93

3.28 826.58

PAO 10m=A/B

Coeficientes

negativosWu Luz (m)

Cargas

0.031

863.8 340.0

2.83 170.92 104.60

188.212.83

inf 0.011 0.017

prom 0.012 0.018

863.8 340.0 3.4 116.30 71.90

0.80

A

sup 0.012 0.019

B

sup 0.024 0.037

275.51inf 0.026 0.041

Luz

(m)

Momentos Momentos


caso 2

B

sup 0.060

1203.8inf 0.065

3.4A

prom 0.062


prom 0.025

B inf 0.027

prom 0.030

Mto(-) kg-

m

0.85

A

sup 0.031

1203.8 3.4 411.75

2.83 595.48

PAO 9m=A/B

Coeficientes

negativosWu Luz (m)

Cargas

0.038

863.8 340.0



971.32M-

REP.

M+

M-

M+

M-

M-

M+

M-

M-

M-

M+

M-

M-

654.47

218.16

M-

M+

M-

M-

M+

M-

M-

M+

M-

M-

M+

M-

M-

M+

111.73

167.43

648.60

571.16

167.4329

502.30

783.13783.13

595.48

275.51

719.54

719.54

335.20

185.08

371.17

96.46

289.37

661.27

692.02

692.02

325.49

108.50

371.17

502.30

218.156

654.47

971.32

93.91

648.60

281.72

571.16

263.45

571.16

796.29

325.49

108.50

371.17

185.08

371.17

96.46

289.37

661.27

826.58

335.20

111.7337

9

10

11

12

4

5

6

7

8

182.949

60.983

325.131

733.18

357.84

733.18

993.26

441.89

147.30

ok

REP.

ok

8

231.659

161.298

231.659

265.844

4

M- 241.928

171.313

241.928

595.48

PAOMomento en

direccion A

1

M- 161.159

M+ 463.212

M- 161.159

M-

M+

M-

M-

M+

M-

595.48

275.51

M-

M-

M+

ok

81.20

243.61

733.55

733.18

357.84

872.80

872.80

441.89

147.30

93.91

281.72

3

REP.

2

M-

M+

M-

81.20

243.61

733.55

Momento en

direccion B

1

263.45

PAO VerfMomt.de

Diseo

M+

COMPENSACION DE LOS MOMENTOS NEGATIVOS

654.47inf 0.050 0.062

prom 0.047 0.059

863.8 340.0 3.28 439.87 214.59

7

9

3

6

10

12

M-

M+

M-

M-

307.493.28

inf 0.009 0.011

prom 0.010 0.013

863.8 340.0 4.8 205.65 101.84

0.65

A

sup 0.011 0.014

B

sup 0.046 0.057

Cargas Luz

(m)

Momentos Momentos


caso 4

B

sup 0.074

1203.8inf 0.077

4.8A

prom 0.075


B inf 0.014

prom 0.016

Mto(-) kg-

m

0.7

A

sup 0.017

1203.8 4.8 443.77

3.28 971.32

PAO 12m=A/B

Coeficientes

negativosWu Luz (m)

11

2

5

M+

M-

M-

M+

M-

M-

M+

M-

M-

M+

M-

M-

M+

M-

M-

M+

M-

M-

M+

M-

M-

M+

M-

163.884

325.131

418.308

187.764

418.308

432.333

223.214

432.333

411.748

188.205

411.748

332.806

220.121

332.806

426.254

287.041

419.934

419.934

280.293

419.934

443.769

654.468

60.983

325.131

163.884

365.858

365.858

187.764

418.308

432.333

223.214

M-

432.333

411.748

188.205

411.748

332.806

220.121

373.650

373.650

287.041

419.934

419.934

280.293

419.934

443.769

654.468

102.497

(Los momentos se encuentran en unidades de Kg-m)

102.497

REP.

OK

OK

REP.

OK

OK

REP.

OK

Verf.Momt.de

Diseo

161.159

463.212

196.462

196.462

171.313

241.928

231.659

161.298

231.659

265.844

182.949



419.93

111.734

DISTRIBUCION DE MOMENTOS

265.84

60.9831

783.13167.433

443.77

971.32

218.156

102.497

231.66

96.46 661.27

411.75

595.48

432.33

432.33

371.17 371.17

231.66 411.75

93.9078

418.31

418.31

571.16

307.4

9

654.47

182.9

5

502.30

161.3

0

289.37

188.2

1

275.51

280.2

9

335.20

595.48 826.58

419.93

22

3.2

1

185.08

17

1.3

1

281.72

18

7.7

6

263.45

28

7.0

4571.16 796.29

147.30

22

0.1

2

441.89

241.93

241.93

648.60

325.49

426.25

426.25

108.50

150.21 150.21

332.81

332.81

993.26

161.16

150.21

733.55

161.16

81.2041

243.61

46

3.2

1 733.18 733.18

325.13

325.13

16

3.8

8

357.84



= =

= =

= =

=

= " " @

= =

=

Distribucion

M+

M-

M-

M+

M-

M-

M+

M-

M-

DISEO POR FLEXION EN LA DIRECCION "B"

M-

Moment.

Kg-mPAO

81.20

Datos para Diseo :

f'c 210 kg/cm2

fy 4200 kg/cm2

rec 2.50 cm

b 100.00 cm

3/8

h 15.00 cm

db 12.02 cm

Area de acero Minimo

Asmin

M-

M+

M-

M-

M+

M-

M-

M+

M-

M-

M+

M-

M-

M+

243.61

733.55

733.18

357.84

872.80

872.80

441.89

147.30

93.91

M+

M-

M-

M-

M+

M-

281.72

648.60

571.16

263.45

692.02

692.02

325.49

108.50

371.17

185.08

371.17

96.46

289.37

661.27

595.48

275.51

719.54

719.54

335.20

111.73

167.43

502.30

783.13

971.32

654.47

M-

M+

M-

218.16

1

2

3

4

5

6

7

8

9

10

11

12

12.02

12.02

12.02

12.02

12.02

12.02

12.02

12.02

12.02

12.02

12.02

12.02

12.02

12.02

12.02

12.02M-

M-

M+

0.0018*b*d

Asmin 2.16 cm2

S 0.33

ASUMIENDO 3/8 0.3

Asmin 2.38 cm2

12.02

12.02

12.02

12.02

12.02

12.02

12.02

12.02

12.02

12.02

12.02

12.02

12.02

12.02

d (cm)

a (cm)

As

(cm2)

As

requerida

0.04

0.13

0.18

0.54

2.38

2.38

0.39

12.02

12.02

12.02

12.02

12.02

12.02

0.39

0.19

0.46

0.46

0.23

0.08

0.05

0.15

0.34

0.30

0.14

0.36

0.36

0.17

0.06

0.19

0.10

0.19

0.05

0.15

0.35

0.31

0.14

0.38

0.38

0.17

0.06

0.09

0.26

0.41

0.51

0.34

0.11

1.64

1.64

0.79

1.96

1.96

0.98

0.33

0.21

0.62

1.45

1.27

0.58

1.55

1.55

0.72

0.24

0.82

0.41

0.82

0.21

0.64

1.48

1.33

0.61

1.61

2.38

2.38

2.38

2.38

2.38

2.38

2.38

1.61

0.74

0.25

0.37

1.12

1.75

2.18

1.46

0.48

2.38

2.38

2.38

2.38

2.38

2.38

2.38

2.38

2.38

2.38

2.38

2.38

2.38

2.38

2.38

2.38

3/8" @ 0.30

3/8" @ 0.30

3/8" @ 0.30

3/8" @ 0.30

3/8" @ 0.30

3/8" @ 0.30

3/8" @ 0.30

3/8" @ 0.30

3/8" @ 0.30

3/8" @ 0.30

3/8" @ 0.30

3/8" @ 0.30

3/8" @ 0.30

3/8" @ 0.30

2.38

2.38

2.38

2.38

2.38

2.38

2.38

2.38

2.38

2.38

2.38

3/8" @ 0.30

3/8" @ 0.30

3/8" @ 0.30

3/8" @ 0.30

3/8" @ 0.30

3/8" @ 0.30

3/8" @ 0.30

DIRECCION B

db

3/8" @ 0.30

3/8" @ 0.30

3/8" @ 0.30

3/8" @ 0.30

3/8" @ 0.30

3/8" @ 0.30

3/8" @ 0.30

3/8" @ 0.30

3/8" @ 0.30

3/8" @ 0.30

3/8" @ 0.30

3/8" @ 0.30

3/8" @ 0.30

3/8" @ 0.30

3/8" @ 0.30



= =

= =

= =

=

= " " @

= =

=

DISEO POR FLEXION EN LA DIRECCION "A"

Datos para Diseo : Area de acero Minimo

f'c 210 kg/cm2 Asmin 0.0018*b*d db

fy 4200 kg/cm2 Asmin 1.99 cm2

rec 2.50 cm S 0.36

b 100.00 cm

3/8 ASUMIENDO 3/8 0.3

h 15.00 cm Asmin 2.38 cm2

db 11.07 cm

DIRECCION A

PAOMoment.

Kg-md

(cm)

a (cm)

As

(cm2)

As

requeridaDistribucion

1

M- 161.16 11.07 0.09 0.39 2.38 3/8" @ 0.30

M+ 463.21 12.02 0.24 1.03 2.38 3/8" @ 0.30

M- 196.46 12.02 0.10 0.43 2.38 3/8" @ 0.30

4

M- 196.46 12.02 0.10 0.43 2.38 3/8" @ 0.30

M+ 171.31 12.02 0.09 0.38 2.38 3/8" @ 0.30

M- 241.93 12.02 0.13 0.54 2.38 3/8" @ 0.30

8

M- 231.66 12.02 0.12 0.51 2.38 3/8" @ 0.30

M+ 161.30 12.02 0.08 0.36 2.38 3/8" @ 0.30

M- 231.66 12.02 0.12 0.51 2.38 3/8" @ 0.30

11

M- 265.84 12.02 0.14 0.59 2.38 3/8" @ 0.30

M+ 182.95 12.02 0.10 0.40 2.38 3/8" @ 0.30

M- 60.98 12.02 0.03 0.13 2.38 3/8" @ 0.30

2

M- 325.13 12.02 0.17 0.72 2.38 3/8" @ 0.30

M+ 163.88 12.02 0.09 0.36 2.38 3/8" @ 0.30

M- 365.86 12.02 0.19 0.81 2.38 3/8" @ 0.30

5

M- 365.86 12.02 0.19 0.81 2.38 3/8" @ 0.30

M+ 187.76 12.02 0.10 0.41 2.38 3/8" @ 0.30

M- 418.31 12.02 0.22 0.93 2.38 3/8" @ 0.30

7

M- 432.33 12.02 0.23 0.96 2.38 3/8" @ 0.30

M+ 223.21 12.02 0.12 0.49 2.38 3/8" @ 0.30

M- 432.33 12.02 0.23 0.96 2.38 3/8" @ 0.30

9

M- 411.75 12.02 0.22 0.91 2.38 3/8" @ 0.30

M+ 188.21 12.02 0.10 0.42 2.38 3/8" @ 0.30

M- 411.75 12.02 0.22 0.91 2.38 3/8" @ 0.30

3

M- 332.81 12.02 0.17 0.74 2.38 3/8" @ 0.30

M+ 220.12 12.02 0.11 0.49 2.38 3/8" @ 0.30

M- 373.65 12.02 0.20 0.83 2.38 3/8" @ 0.30

6

M- 373.65 12.02 0.20 0.83 2.38 3/8" @ 0.30

M+ 287.04 12.02 0.15 0.64 2.38 3/8" @ 0.30

M- 419.93 12.02 0.22 0.93 2.38 3/8" @ 0.30

10

M- 419.93 12.02 0.22 0.93 2.38 3/8" @ 0.30

M+ 280.29 12.02 0.15 0.62 2.38 3/8" @ 0.30

M- 419.93 12.02 0.22 0.93 2.38 3/8" @ 0.30

12

M- 443.77 12.02 0.23 0.99 2.38 3/8" @ 0.30

M+ 654.47 12.02 0.34 1.46 2.38 3/8" @ 0.30

M- 102.50 12.02 0.05 0.23 2.38 3/8" @ 0.30


Losa Maciza Aci 1 Al 6

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