Calculo de Aceros

UNIVERSIDAD NACIONAL DE JANCARRERA PROFESIONAL DE INGENIERA CIVIL

TEMA: COLOCACION DE ACERO EN VIGUETAS

DOCENTE: ing. JUAN OLANO GUZMAN

ALUMNO: OLANO BUSTAMANTE SEGUNDO

Curso: ESTRUCTURAS DEL CONCRETO ARMADO CICLO: VII

JAN PER2015

METRADO DE VIGUETAS Y COLOCACION DE ACERO EN LA LOSA

METRADO DE VIGUETAS 1,2,3 Y ASOTEA

1. Calculo de vigueta tipo A 1,2,3 Y ASOTEA

Espesor de Losa:

h = 2.6/25

h = 0.104 = 10 cm 17 cm

METRADO DE CARGAS:

CARGA MUERTA (D)

Losa aligerada: 300kg/m2 x 0.4m = 120kg/mCielo raso: 100kg/m2 x0.40m = 40 kg/mTabiquera: 100kg/m2 x0.40m = 40 kg/m 200 kg/m

Carga viva (l)

Carga viva: 200 kg/m2 x 0.40m = 80 kg/m

CARGA ULTIMA ( Wu )

Carga total: 1.4CM + 1.7CVwu = 1.4 x (200 kg/m) + 1.7 x (80 kg/m)wu = 280kg/m + 136 kg/mwu = 416 kg/m

Diagrama de fuerza cortante y momento flector

540.8

1.3 m

1.3m

+--540.8

+351.52 kg/m

CLCULOS DE DISEOMu = 351.52 kg.mCalculamos el acerod = h r /2d = 17 2 - 1d = 14

d

17cm

10 cm

Primer tanteo:

Asumir a = 0.9 cm.

As = = = 0.74

a = = = 1.74

Segundo tanteo:

As1 = = = 0.71

a = = = 1.67

As2 = = = 0.71

Hallamos la cuanta = = = 0.005

Hallamos la cuanta mxima

= 0.75 x 0.85 x x

=0.75 x 0.85 x x = 0.016

Hallamos la cuanta mnima

= = = 0.008

Comparamos cuantas

0.008 < 0.005 < 0.016

As = 0.71 3/8

2.- Calculo de vigueta tipo A 1,2,3 Y ASOTEA

Espesor de Losa:

h = 2.20 /25

h = 0.088 = 9 cm 17 cm

METRADO DE CARGAS:

CARGA MUERTA (D)


Carga viva (l)


CARGA ULTIMA ( Wu )


Diagrama de fuerza cortante y momento flector 416K

457.6

1.1 m

1.1m

+--457.6

+251.68 kg/m

CLCULOS DE DISEOMu = 251.68 kg.mCalculamos el acerod = h r /2d = 17 2 - 1d = 14

d

17cm

10 cm

Primer tanteo:

Asumir a = 0.9 cm.

As = = = 0.52

a = = = 1.22

Segundo tanteo:

As1 = = = 0.50

a = = = 1.18

As2 = = = 0.50



= 0.75 x 0.85 x x

=0.75 x 0.85 x x = 0.016


= = = 0.008

Comparamos cuantas

0.008 < 0.004 < 0.016

As = 0.50

3/8

3.- Calculo de vigueta tipo C 1,2,3 Y ASOTEA SIN MUROS

Cabe sealar que en el primer piso las 3 viguetas son sin carga distribuida y en el segundo, tercero y azotea 2 viguetas.

Espesor de Losa:

h = 3.625 /25

h = 0.145 = 15 cm 20 cm

METRADO DE CARGAS:

CARGA MUERTA (D)

Losa aligerada: 300kg/m2 x 0.4m = 120kg/mCielo raso: 100kg/m2 x0.40m = 40 kg/mTabiquera: 100kg/m2 x0.40m = 40 kg/m 200 kg/mCarga viva (l)


CARGA ULTIMA ( Wu )



416Kg/m

3.625m

2.08m

MU = =607.39

MU = =227.77

MU = =199.98

MU = =74.99

MU = =390.46

MU = =128.56

CLCULOS DE DISEO EN ESTE CASO UTILIZAMOS EL MOMENTOMu = 227.77 kg.mCalculamos el acero

d = h r /2d = 20 2 - 1d = 17

d

20cm

10 cm

Primer tanteo:

Asumir a = 0.9 cm.

As = = = 0.39a = = = 0.92

Segundo tanteo:

As1 = = = 0.36

a = = = 0.85

As2 = = = 0.36


0.008 < 0.002 < 0.016

As = 0.28 1/4

CLCULOS DE DISEO EN ESTE CASO UTILIZAMOS EL MOMENTOMu = 390.46 kg.mPrimer tanteo:

Asumir a = 0.9 cm.

As = = = 0.68a = = = 1.6

Segundo tanteo:

As1 = = = 0.64

a = = = 1.5

As2 = = = 0.64


0.008 < 0.004 < 0.016

As = 0.64

3/8

CLCULOS DE DISEO EN ESTE CASO UTILIZAMOS EL MOMENTOMu = 607.39 kg.mCalculamos el acero Primer tanteo:

Asumir a = 0.9 cm.

As = = = 1.05a = = = 2.47

Segundo tanteo:

As1 = = = 1.02

a = = = 2.4

As2 = = = 1.02


Comparamos cuantas

0.008 < 0.006 < 0.016

As = 1.02

1/2


Primer tanteo:

Asumir a = 0.9 cm.

As = = = 0.35a = = = 0.82

Segundo tanteo:

As1 = = = 0.32

a = = = 2.4

As2 = = = 0.33


Comparamos cuantas

0.008 < 0.002 < 0.016

As = 0.33

1/4


Asumir a = 0.9 cm.

As = = = 0.22a = = = 0.52

Segundo tanteo:

As1 = = = 0.20

a = = = 0.47

As2 = = = 0.20


Comparamos cuantas

0.008 < 0.001 < 0.016

As = 0.20

1/4


Asumir a = 0.9 cm.

As = = = 0.13a = = = 0.31

Segundo tanteo:

As1 = = = 0.12

a = = = 0.28

As2 = = = 0.12


Comparamos cuantas

0.008 < 0.0007 < 0.016

As = 0.12

1/4

CALCULO DE VIGUETAS TIPO C CON CARGA DES MUROS

Cabe sealar que en el segundo, teser y azotea ay 1 vigueta del mismo tipo.

Espesor de Losa:

h = 3.625 /25

h = 0.145 = 15 cm 20 cm

METRADO DE CARGAS:

CARGA MUERTA (D)



CARGA ULTIMA ( Wu )

Carga total: 1.4CM + 1.7CVwu = 1.4 x (200 kg/m) + 1.7 x (80 kg/m)wu = 280kg/m + 136 kg/mwu = 416 kg/mMuro: 1800kg/m2 x 0.15m x 0.10 m x 2.68m = 72.36 Kg


571.42

512.9629.97


d = h r /2d = 20 2 - 1d = 17

d

20cm

10 cm

Primer tanteo:

Asumir a = 0.9 cm.

As = = = 0.052

a = = = 0.12

Segundo tanteo:

As1 = = = 0.046

a = = = 0.11

As2 = = = 0.047


0.008 < 0.0003 < 0.016

As = 0.047 1/4


Asumir a = 0.9 cm.

As = = = 0.94

a = = = 2.21

Segundo tanteo:

As1 = = = 0.90

a = = = 2.12

As2 = = = 0.90


0.008 < 0.005 < 0.016

As = 0.90 1/2


Asumir a = 0.9 cm.

As = = = 0.89

a = = = 2.09

Segundo tanteo:

As1 = = = 0.85

a = = = 2

As2 = = = 0.85


0.008 < 0.005 < 0.016

As = 0.85 1/2

4.- CALCULO DE VIGUETA TIPO D

En este tipo para todos los pisos las viguetas son del mismo tipo y sin carga concentrada de presencia de muros muros.

Espesor de Losa:

h = 4.30 /25

h = 0.172 = 18 cm 20 cm

METRADO DE CARGAS:

CARGA MUERTA (D)


Carga viva (l)


CARGA ULTIMA ( Wu )



1/24MU = =607.39

1/141/101/111/101/111/141/24

= = 6.87

= = 16.51

= = 699.28

= = 549.42

= = 769.184

= = 569.33

= = 447.33

= = 260.94

CLCULOS DE DISEO CON EL MOMENTOSMu = 769.18 kg.mCalculamos el acero

d = h r /2d = 20 2 - 1d = 17

d

20cm

Primer tanteo:

Asumir a = 0.9 cm.

As = = = 1.33a = = = 3.13

Segundo tanteo:

As1 = = = 1.23

a = = = 2.89

As2 = = = 1.22


Comparamos cuantas

0.008 < 0.007 < 0.016

As = 1.22

1/2

CLCULOS DE DISEO CON EL MOMENTOSMu = 6.87 kg.mCalculamos el acero Primer tanteo:

Asumir a = 0.9 cm.

As = = = 0.012a = = = 0.028

Segundo tanteo:

As1 = = = 0.011

a = = = 0.026

As2 = = = 0.011


Comparamos cuantas

0.008 < 0.00006 < 0.016

As = 0.011

1/4


Asumir a = 0.9 cm.

As = = = 0.029a = = = 0.068

Segundo tanteo:

As1 = = = 0.026

a = = = 0.061

As2 = = = 0.026


Comparamos cuantas

0.008 < 0.0002 < 0.016

As = 0.026

1/4


Asumir a = 0.9 cm.

As = = = 1.21a = = = 2.85

Segundo tanteo:

As1 = = = 1.14

a = = = 2.68

As2 = = = 1.13


Comparamos cuantas

0.008 < 0.007 < 0.016

As = 1.13

1/2


Asumir a = 0.9 cm.

As = = = 0.95a = = = 2.24

Segundo tanteo:

As1 = = = 0.92

a = = = 2.16

As2 = = = 0.91


Comparamos cuantas

0.008 < 0.005 < 0.016

As = 0.91

1/2


Asumir a = 0.9 cm.

As = = = 0.98a = = = 2.31

Segundo tanteo:

As1 = = = 0.95

a = = = 2.24

As2 = = = 0.95


Comparamos cuantas

0.008 < 0.006 < 0.016

As = 0.95

1/2


Asumir a = 0.9 cm.

As = = = 0.77a = = = 1.81

Segundo tanteo:

As1 = = = 0.74

a = = = 1.74

As2 = = = 0.73


Comparamos cuantas

0.008 < 0.004 < 0.016

As = 0.73

3/8


Asumir a = 0.9 cm.

As = = = 0.45a = = = 1.06

Segundo tanteo:

As1 = = = 0.42

a = = = 0.99

As2 = = = 0.42


Comparamos cuantas

0.008 < 0.002 < 0.016

As = 0.42

3/8

5.- CALCULO DE VIGUETA TIPO E

Sin presencia de muros tenemos 6 en el primer piso 2 en el segundo y tercero piso y azotea

Espesor de Losa:

h = 4.40 /25

h = 0.176 = 18 cm 20 cm

METRADO DE CARGAS:

CARGA MUERTA (D)


Carga viva (l)


CARGA ULTIMA ( Wu )


Diagrama momento flector

1/101/111/111/101/141/111/111/111/141/161/161/161/111/241/24

= = 6.87

= = 11.79

= = 16.51

= = 699.28

= = 480.74

= = 531.82

= = 365.63

= = 732.16

= = 503.36

= = 548.16

= = 391.54

= = 228.40

CLCULOS DE DISEO EN ESTE CASO UTILIZAMOS EL MOMENTO MAXIMO.Mu = 732.16 kg.mCalculamos el acero

d = h r /2d = 20 2 - 1d = 17

d

20cm

Primer tanteo:

Asumir a = 0.9 cm.

As = = = 1.27

a = = = 2.99

Segundo tanteo:

As1 = = = 1.25

a = = = 2.94

As2 = = = 1.25


Comparamos cuantas

0.008 < 0.007 < 0.016

As = 1.25

1/2


Asumir a = 0.9 cm.

As = = = 0.012a = = = 0.028

Segundo tanteo:

As1 = = = 0.011

a = = = 0.026

As2 = = = 0.011


Comparamos cuantas

0.008 < 0.00006 < 0.016

As = 0.011

1/4


Asumir a = 0.9 cm.

As = = = 0.020a = = = 0.047

Segundo tanteo:

As1 = = = 0.018

a = = = 0.042

As2 = = = 0.018


Comparamos cuantas

0.008 < 0.0001 < 0.016

As = 0.018

1/4


Asumir a = 0.9 cm.

As = = = 0.029a = = = 0.068

Segundo tanteo:

As1 = = = 0.026

a = = = 0.061

As2 = = = 0.026


Comparamos cuantas

0.008 < 0.0002 < 0.016

As = 0.026

1/4


Asumir a = 0.9 cm.

As = = = 1.21a = = = 2.85

Segundo tanteo:

As1 = = = 1.14

a = = = 2.68

As2 = = = 1.13


Comparamos cuantas

0.008 < 0.007 < 0.016

As = 1.13

1/2 CLCULOS DE DISEO CON EL MOMENTOSMu = 480.74 kg.mCalculamos el acero Primer tanteo:

Asumir a = 0.9 cm.

As = = = 0.83a = = = 1.95

Segundo tanteo:

As1 = = = 0.79

a = = = 1.86

As2 = = = 0.79


Comparamos cuantas

0.008 < 0.005 < 0.016

As = 0.79

3/8


Asumir a = 0.9 cm.

As = = = 0.92a = = = 2.16

Segundo tanteo:

As1 = = = 0.88

a = = = 2.07

As2 = = = 0.88


Comparamos cuantas

0.008 < 0.005 < 0.016

As = 0.88

1/2


Asumir a = 0.9 cm.

As = = = 0.63a = = = 1.48

Segundo tanteo:

As1 = = = 0.59

a = = = 1.39

As2 = = = 0.59


Comparamos cuantas

0.008 < 0.003 < 0.016

As = 0.59

3/8


Asumir a = 0.9 cm.

As = = = 0.87a = = = 2.05

Segundo tanteo:

As1 = = = 0.83

a = = = 1.95

As2 = = = 0.83


Comparamos cuantas

0.008 < 0.005 < 0.016

As = 0.83

1/2


Asumir a = 0.9 cm.

As = = = 0.95a = = = 2.24

Segundo tanteo:

As1 = = = 0.91

a = = = 2.14

As2 = = = 0.91


Comparamos cuantas

0.008 < 0.005 < 0.016

As = 0.91

1/2


Asumir a = 0.9 cm.

As = = = 0.68a = = = 1.6

Segundo tanteo:

As1 = = = 0.64

a = = = 1.51

As2 = = = 0.64


Comparamos cuantas

0.008 < 0.004 < 0.016

As = 0.64

3/8


Asumir a = 0.9 cm.

As = = = 0.39a = = = 0.92

Segundo tanteo:

As1 = = = 0.37

a = = = 0.87

As2 = = = 1.37


Comparamos cuantas

0.008 < 0.002 < 0.016

As = 0.37

3/8

6.- CALCULO DE VIGUETA TIPO F

La vigueta es tpicas y no presentan muros para los 4 pisos

Espesor de Losa:

h = 4.40 /25

h = 0.176 = 18 cm 20 cm

METRADO DE CARGAS:

CARGA MUERTA (D)


Carga viva (l)


CARGA ULTIMA ( Wu )



1/241/141/241/111/101/161/111/101/14

= = 86.20

= = 147.77

= = 206.87

= = 699.28

= = 503.36

= = 805.38

= = 498.32

= = 391.54

= = 228.40


d = h r /2d = 20 2 - 1d = 17

d

20cm

Primer tanteo:

Asumir a = 0.9 cm.

As = = = 1.39

a = = = 3.27

Segundo tanteo:

As1 = = = 1.39

a = = = 3.27

As2 = = = 1.39


Hallamos la cuanta mxima0.008 < 0.008 < 0.016

As = 1.39

1/2


Asumir a = 0.9 cm.

As = = = 0.15a = = = 0.35

Segundo tanteo:

As1 = = =0.14

a = = = 0.33

As2 = = = 0.14


Comparamos cuantas

0.008 < 0.0008 < 0.016

As = 0.14

1/4


Asumir a = 0.9 cm.

As = = = 0.26a = = = 0.61

Segundo tanteo:

As1 = = = 0.23

a = = = 0.54

As2 = = = 0.23


Comparamos cuantas

0.008 < 0.001 < 0.016

As = 0.23

1/4


Asumir a = 0.9 cm.

As = = = 0.36a = = = 0.85

Segundo tanteo:

As1 = = = 0.33

a = = = 0.78

As2 = = = 0.33


Comparamos cuantas

0.008 < 0.002 < 0.016

As = 0.33

1/4


Asumir a = 0.9 cm.

As = = = 1.21a = = = 2.85

Segundo tanteo:

As1 = = = 1.14

a = = = 2.68

As2 = = = 1.13


Comparamos cuantas

0.008 < 0.007 < 0.016

As = 1.13

1/2


Asumir a = 0.9 cm.

As = = = 0.87a = = = 2.05

Segundo tanteo:

As1 = = = 0.83

a = = = 1.95

As2 = = = 0.83


Comparamos cuantas

0.008 < 0.005 < 0.016

As = 0.83

1/2


Asumir a = 0.9 cm.

As = = = 0.86a = = = 2.02

Segundo tanteo:

As1 = = = 0.82

a = = = 1.93

As2 = = = 0.82


Comparamos cuantas

0.008 < 0.005 < 0.016

As = 0.82

1/2


Asumir a = 0.9 cm.

As = = = 0.68a = = = 1.6

Segundo tanteo:

As1 = = = 0.64

a = = = 1.51

As2 = = = 0.64


Comparamos cuantas

0.008 < 0.004 < 0.016

As = 0.64

3/8


Asumir a = 0.9 cm.

As = = = 0.39a = = = 0.92

Segundo tanteo:

As1 = = = 0.37

a = = = 0.87

As2 = = = 1.37


Comparamos cuantas

0.008 < 0.002 < 0.016

As = 0.37

3/8

7.- CALCULO DE VIGUETA TIPO G

Viguetas sin carga concentrada primer piso 1,segundo piso, tercer piso y azotea 6.

Espesor de Losa:

h = 4.40 /25

h = 0.176 = 18 cm 25 cm

METRADO DE CARGAS:

CARGA MUERTA (D)


Carga viva (l)


CARGA ULTIMA ( Wu )



1/101/141/141/241/111/161/111/101/24

= = 206.87

= = 732.16

= = 503.36

= = 805.38

= = 82.84

= = 65.09

= = 37.97


d = h r /2d = 20 2 - 1d = 17

d

20cm

Primer tanteo:

Asumir a = 0.9 cm.

As = = = 1.39

a = = = 3.27

Segundo tanteo:

As1 = = = 1.39

a = = = 3.27

As2 = = = 1.39


Comparamos cuantas

0.008 < 0.008 < 0.016

As = 1.39

1/2


Asumir a = 0.9 cm.

As = = = 0.36a = = = 0.85

Segundo tanteo:

As1 = = = 0.33

a = = = 0.78

As2 = = = 0.33


Comparamos cuantas

0.008 < 0.002 < 0.016

As = 0.33

1/4

CLCULOS DE DISEO CON EL MOMENTO.Mu = 732.16 kg.mCalculamos el acero

Primer tanteo:

Asumir a = 0.9 cm.

As = = = 1.27

a = = = 2.99

Segundo tanteo:

As1 = = = 1.25

a = = = 2.94

As2 = = = 1.25


Comparamos cuantas

0.008 < 0.007 < 0.016

As = 1.25

1/2


Asumir a = 0.9 cm.

As = = = 0.87a = = = 2.05

Segundo tanteo:

As1 = = = 0.83

a = = = 1.95

As2 = = = 0.83


Comparamos cuantas

0.008 < 0.005 < 0.016

As = 0.83

1/2


Asumir a = 0.9 cm.

As = = = 0.14a = = = 0.33

Segundo tanteo:

As1 = = = 0.13

a = = = 0.31

As2 = = = 0.13


Comparamos cuantas

0.008 < 0.005 < 0.016

As = 0.13

1/4


Asumir a = 0.9 cm.

As = = = 0.11a = = = 0.26

Segundo tanteo:

As1 = = = 0.10

a = = = 0.24

As2 = = = 0.10


Comparamos cuantas

0.008 < 0.0006 < 0.016

As = 0.10

1/4


Asumir a = 0.9 cm.

As = = = 0.066a = = = 0.16

Segundo tanteo:

As1 = = = 0.059

a = = = 0.14

As2 = = = 0.059


Comparamos cuantas

0.008 < 0.0003 < 0.016

As = 0.059

1/4

CON CARGA DISTRIBUIDA PARA EL PRIMER PISO 5 VIGUETAS DEL MISMO TIPO

Espesor de Losa:

h = 4.40/25

h = 0.176 = 17 cm 20 cm

METRADO DE CARGAS:

CARGA MUERTA (D)



CARGA ULTIMA ( Wu )

Carga total: 1.4CM + 1.7CVwu = 1.4 x (200 kg/m) + 1.7 x (80 kg/m)wu = 280kg/m + 136 kg/mwu = 416 kg/mMuro: 1800kg/m2 x 0.15m x 0.10 m x 3.35m = 90.45 KgDiagrama de fuerza cortante y momento flector

571.42

575.92581.79

437.7387.84

DISEO EN ESTE CASO UTILIZAMOS EL MOMENTO ULTIMOMu = 581.79 kg.mCalculamos el acero

d = h r /2d = 20 2 - 1d = 17

d

20cm

10 cm

Primer tanteo:

Asumir a = 0.9 cm.

As = = = 1.01

a = = = 2.38

Segundo tanteo:

As1 = = = 0.97

a = = = 2.28

As2 = = = 0.97


0.008 < 0.0005 < 0.016

As = 0.047 1/2

8.- CALCULO DE VIGUETA TIPO H

Todos los pisos el mismo tipo

Espesor de Losa:

h = 1.5 /25

h = 0.06 = 6 cm 17 cm

METRADO DE CARGAS:

CARGA MUERTA (D)


Carga viva (l)


CARGA ULTIMA ( Wu )



312

0.75 m

0.75m

+--312

+117 kg/m

CLCULOS DE DISEO EN ESTE CASO UTILIZAMOS EL MOMENTO MAXIMO.Mu = 117 kg.mCalculamos el acero

d = h r /2d = 20 2 - 1d = 14

d

17cm

Primer tanteo:

Asumir a = 0.9 cm.

As = = = 0.25

a = = = 0.59

Segundo tanteo:

As1 = = = 0.23

a = = = 0.54

As2 = = = 0.23



= 0.75 x 0.85 x x

=0.75 x 0.85 x x = 0.016


= = = 0.008

Comparamos cuantas

0.008 < 0.005 < 0.016

As = 0.23 1/4

Calculo de Aceros

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