Diseño Estructural en Concreto Armado de Una Carcel Publica (1)

7/25/2019 Diseo Estructural en Concreto Armado de Una Carcel Publica (1)

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Criterios de DiseoSe pretende disear una edificacin de concreto armado, la cual deber poseeruna losa de techo Tipo Maciza y una losa Tipo Nervada de entrepiso, dichaedificacin deber estar sueta a una serie de criterios, normas y recomendacionest!cnicas hechas por el comit! venezolano de normas "C#$%N&N '()*+-. a trav!sde las distintas normas disponibles para el diseo pleno de edificaciones se/uras yresistentes0 1a cual tiene las si/uientes especificaciones0

1a estructura estudiada se divide en dos blo2ues de edificacin destinada al uso de%dificaciones de carceles de ambiente reas p3blicas, los cuales estran

conformada por un nivel ms planta baa, seran estructuras aporticadas deconcreto armado, y constara de una losa Nervada de entrepiso y una losa macizade techo sin acceso, los materiales a utilizar son45 f6c "resistencia especifica del concreto en compresin.para losa 7 8' 9/:cm;para vi/as *9/:cm; y para columnas * 9/:cm;5 fy "resistencia cedente especifica en armadura. 7


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4 m 5 m 7 m 6 m 6 m

Fc = 250 Kg/cm

Fy = 4200 Kg/cm

CV: 100 Kg/m2 = 0.85

Uso de la Edificacin: CARCEL

Luz mayor de losa = 5 m

Dimenciones de la losa. 30 m 10 m

Calculo de Carga Muerta Total

625 Kg/m26 Kg/m2

631 Kg/m2

Calculo para el Sentido de Armado de la Losa "Sa"

30 m Sa L/S > 2 Losa en 2 direccines

10 m Sa L/S < 2 Losa en 1 direcciones

30 m

10 m

LOSA MACIZA DE TECHO 1

Criterios de Diseo

Eje X = Eje Y =

TOTAL =

Peso propio de la losa =

L menor

3.00 m Losa en 1 direcciones

L mayor

Sa = =L mayor

L menor= Entonces

Esquema de Planta

5 m

4 m

6 m

7 m

7 m

Manto asfaltico de 5mm de espesor =

LT2

e=25cm

LT1

e=25cm


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Calculo para el Espesor de la Losa "e"

L 500 cm

20

L 500 cm24

L 500 cm

28

Calculo del peso propio de la losa

Pp = e x peso especifico del concreto

Pp = 0.25 x 2500

Pp = kg

Calculo para Carga Ultima "Cu"

1.4 1.7 x CV 1.4 x 631 + 1.7 x 100

C u = Kg/m ~ 1054 Kg/m

150 150

1054 Kg/m

0.5 4 5 0.5

. . . .

+-

-+

Calculo de Acero Minimo

x 100 x d x

x 100 x 22

4.4 cm2

677

206.75

851.87

677.000

2143.675

206.75

v

M

As min =

2820.6755848.481

=x CM +

1

21.23

1

1053.4

e = =

e =

e =

=

Cu =

2,663

0.002As min =

0.002

As min =

1493.844 3126.325

1973.20

2722

2170.844

20

25 Cm

625

= 21 cm24

= = 18 cm28

= 25 cm


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Momentos Positivos

kg-m x 100 cm/m

0.85 x 4200 g/cm2 22 cm x 0.81

kg-m x 100 cm/m0.85 X 4200 g/cm2 22 cm x 0.81

Momentos Negativo

kg-m x 100 cm/m

0.85 x 4200 g/cm2 22 cm x 0.81

Momentos Positivos Acero Asumido 1/2 A = 1.27 cm2

4.40 cm2

1.27 cm2

4.40 cm2

1.27 cm2

Momentos Negativos

4.40 cm2

1.27 cm2

CHEQUEO POR MOMENTO PARA EL MACIZADO

Calculo de separacion maxima

2 x d2 x 22 = 44 cm

Longitud de desarrollo

1 Ld= 12 = 23.8

2 Ld= d o r 0

3 Ld= L/16 0.31

=

= =As asumido

=N As

=

=Mact x 100

x Fy x d x J

As-

851.87

1973.20

x Fy x d x J

As+

As+

3.46 4 1/2

Numero de cacillas en funcion a los momentos actuantes en la losa

1/2N = 3.46As

=As asumido

=2663.38

=As asumido

N =As

cm10} 8.02

Smax=Smax=

1.34

=

4

=

=

Debido a que el acero minimo es mayor que todos los acero calculador se asumio el

valor de 4.4 cm para los aceros negativos y los positivos

cm2

cm2

As+

Nota= las areas de acero que sean menor al acero minimo se colocara el valor minimo de acero

calculado

4

As- 4.19

x barra

=

Mact x 100=

=

cm2

1/2

3.1

3.46


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1

4 m 5 m 7 m 6 m 6 m

Fc = 250 Kg/cm

Fy = 4200 Kg/cm

CV: 100 Kg/m2 = 0.85





625 Kg/m2

6 Kg/m2

631 Kg/m2


30 m Sa L/S < 2 Losa en 2 direccines

10 m Sa L/S > 2 Losa en 1 direcciones

30 m

10 m

2

m

4 m

5 m

Esquema de Planta

7 m

7 m

6

Manto asfaltico de 5mm de espesor =

TOTAL =

L mayor

LOSA MACIZA DE TECHO 2

Criterios de Diseo

Eje X = Eje Y =


L menor

L menor

Sa =L mayor

= = 3.00 m Entonces Losa en 1 direcciones

LT2

e=25cm

LT1

e=25cm


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L 500 cm

20

L 500 cm

24

L 500 cm

28

Calculo del peso propio de la losa

Pp = e x peso especifico del concreto

Pp = 0.25 x 2500

Pp = kg


1.4 1.7 x CV 1.4 x 631 + 1.7 x 100

C u = Kg/m ~ 1054 Kg/m

150 150

1054 Kg/m

0.5 5 4 0.5

. . . .

+-

-+


x 100 x d x

x 100 x 22

4.4 cm2

e = = = 25 cm20

21.23 25 Cm24

e = = = 18 cm

e = = = 21 cm

1

1053.4

2820.675 5848.481 2170.844

28

625

Cu =x CM +

=1

2143.675 2722.156 677.000

v

677 3126 1493.844

206.75 2,663 206.751

M

1973.20 851.87

As min = 0.002

As min = 0.002

As min =


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Momentos Positivos

kg-m x 100 cm/m

0.85 x 4200 g/cm2 22 cm x 0.81kg-m x 100 cm/m

0.85 X 4200 g/cm2 22 cm x 0.81

Momentos Negativo

kg-m x 100 cm/m

0.85 x 4200 g/cm2 22 cm x 0.81


4.40 cm2

1.27 cm2

4.40 cm2

1.27 cm2

Momentos Negativos

4.40 cm2

1.27 cm2



2 x d

2 x 22 = 44 cm


1 Ld= 12 = 23.8

2 Ld= d o r 0

3 Ld= L/16 0.31

As+ =Mact x 100

x Fy x d x J

= 1.34 cm2

As+ =1973.20

= 3.10 cm2

As- =Mact x 100

x Fy x d x J

As+ =851.87

As- =2663.38

= 4.19 cm2


Nota= las areas de acero que sean menor al acero minimo se colocara el valor minimo de acero

calculado

N =As

= = 3.46 4 1/2As asumido

1/2As asumido

Debido a que el acero minimo es mayor que todos los acero calculador se asumio el

valor de 4.4 cm para los aceros negativos y los positivos

4 1/2As asumido

N =As

= = 3.46

N =As

= = 3.46

4

Smax=

cm

Smax=

x barra

} 8.02 10


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1

4 m 5 m 7 m 6 m 6 m

Fc = 250 Kg/cm

Fy = 4200 Kg/cm

CV: 300 Kg/m2 = 0.85





360 Kg/m2

17 Kg/m2

230 Kg/m2

40 Kg/m2

100

747 Kg/m2




30 m

10 m

4 m

5 m

7 m

7 m

6 m

Esquema de Planta

LOSA NERVADA DE ENTREPISO 1 EJE Y

Criterios de Diseo

Eje X = Eje Y =


Entonces Losa en 1 direccionesL menor

Sa =L mayor

= = 3.00 m

Granito artificial con espesor 5cm =

Revestimiento con cal y yeso e=1cm

frisado por ambas caras de arcillas 15 cm=

Revestimiento de porcelana en paredes

TOTAL =

L mayor

L menor

LE2

e=25cm

LE1

e=25cm


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L 500 cm

16

L 500 cm

18

L 500 cm

21


1.4 1.7 x CV 1.4 x 747 + 1.7 x 300

C u = Kg/m ~ 778 Kg/m

150 150

778 Kg/m

0.5 4 5 0.5

+

-

-

+


x 10 x d x

x 10 x 27

0.54 cm2

Numero de Cabillas para el Acero Minimo

Acero Asumido 3/8 A = 0.71 cm2

cm2

cm2

Cu =x CM +

=

2 2

e = = = 31 cm

As min = 0.002

172.25 1,956

2002 1588.225

1649.031 2127.2254303.744

1110.031 2301.775 539.000

v

539

1 1/2As asumido 1.27

As min = 0.002

As min =

N =

As min

=

0.54= 0.43

e = =18

e = =21

= 28 cm Cm

= 24 cm

27.61 30

16

777.9

172.25

M

619.63 1448.87


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Momentos Positivos

kg-m x 100 cm/m

0.85 x 4200 g/cm2 27 cm x 0.81kg-m x 100 cm/m

0.85 X 4200 g/cm2 27 cm x 0.81

Momentos Negativo

kg-m x 100 cm/m

0.85 x 4200 g/cm2 27 cm x 0.81

kg-m x 100 cm/m

0.85 x 4200 g/cm2 27 cm x 0.81

kg-m x 100 cm/m

0.85 x 4200 g/cm2 27 cm x 0.81


0.79 cm2

1.27 cm2

1.86 cm2

1.27 cm2

Momentos Negativos

0.22 cm2

1.27 cm2

2.51 cm2

1.27 cm2


Calculo del Momento Resistente o Requerido

x Fc x b x d22

0.17 x 250 kg/cm2 x 10 cm x 27

Kg/cm kg-m

MR > Mact

As+ =620

= 0.79 cm2

As+ =Mact x 100

x Fy x d x J

As+ =1449

= 1.86 cm2

As- =Mact x 100

x Fy x d x J

As- =1956

= 2.51 cm2

As- =172

= 0.22 cm2


N =As

= = 0.62 1 1/2As asumido

1/2As asumido

N =As

= = 1.46 2

N =As

= =

N =As

= = 0.17

1.97 2 1/2As asumido

1 1/2As asumido

3,098.25 1,956.13No se calcula el macizado por

Momento

Mr > Mact

Si esta condicion se cumpleNo se calcula el macizado por

Momento

Si esta condicion no se cumple

Se calcula el macizado por Momento

As- =172

= 0.22 cm2

Mr =

Mr =

Mr = 309,825.00 3,098.25


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CHEQUEO POR CORTE PARA EL MACIZADO

Vc = 0.53 x Rc x b` x d x

Vc = 0.53 x 15.81 x 50 x 27 x 0.85

Vc = kg/cm2 Vmax

50 x 27

Calculo del corte resistente

Vcu= 0.85 x 0.5 x Rc

Vcu= 0.85 x 0.5 x

Vcu=

>>


2 x d

2 x 27 = 54 cm


1 Ld= 12 = 23.8

2 Ld= d o r 0

3 Ld= L/16 0.31

Vu > Vcu

Si esta condicion se cumple

Se debe calcular el macizado por corte

Si esta condicion no se cuple

No se debe calcular el macizado por corte

9,616.09

Vu=Vmax

=2,301.78

= 1.71

cm

Smax=

x barra

} 8.02 10

Vu Vcu No se debe calcular el macizado por corte1.71 6.72

Smax=

kg/cm2b x d

2,301.78 No hay macizadopor or!e

".72

15.81


12/353

4 m 5 m 7 m 6 m 6 m

Fc = 250 Kg/cm

Fy = 4200 Kg/cm

CV: 300 Kg/m2 = 0.85





360 Kg/m2

17 Kg/m2

230 Kg/m2

40 Kg/m2

100

747 Kg/m2




30 m

10 m

7 m

6 m

4 m

5 m

Esquema de Planta

7 m

Revestimiento con cal y yeso e=1cm

frisado por ambas caras de arcillas 15 cm=

Revestimiento de porcelana en paredes

LOSA NERVADA DE ENTREPISO 1 EJE Y

Criterios de Diseo

Eje X = Eje Y =


= 3.00 m Entonces Losa en 1 direccionesL menor

Granito artificial con espesor 5cm =

TOTAL =

L mayor

L menor

Sa =L mayor

=

LE2

e=25cm

LE1

e=25cm


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L 500 cm

16

L 500 cm

18

L 500 cm

21


1.4 1.7 x CV 1.4 x 747 + 1.7 x 300

C u = Kg/m ~ 778 Kg/m

150 150

778 Kg/m

0.5 5 4 0.5

+

-

-

+


x 10 x d x

x 10 x 27

0.54 cm2

Numero de Cabillas para el Acero Minimo

Acero Asumido 3/8 A = 0.71 cm2

cm2

cm2

16e = = = 31 cm

Cu =x CM +

=

2 2

27.61 30

1110.031

Cm18

e = = = 24 cm

e = = = 28 cm

21

172.25

777.9

2127.225 4303.744 1649.031

1588.225 2001.969 539.000

M

1448.87 619.63

As min = 0.002

As min = 0.002

v

539 2302

172.25 1,956

1 1/2As asumido 1.27

As min =

N =

As min

=

0.54= 0.43


14/353

Calculo de Acero Minimo por Temperatura

x 10 x d x

x 10 x 5

0.1 cm2

Momentos Positivos

kg-m x 100 cm/m

0.85 x 4200 g/cm2 27 cm x 0.81

kg-m x 100 cm/m

0.85 X 4200 g/cm2 27 cm x 0.81

Momentos Negativo

kg-m x 100 cm/m

0.85 x 4200 g/cm2 27 cm x 0.81

kg-m x 100 cm/m

0.85 x 4200 g/cm2 27 cm x 0.81

kg-m x 100 cm/m

0.85 x 4200 g/cm2 27 cm x 0.81


1.86 cm2

1.27 cm2

0.79 cm2

1.27 cm2

Momentos Negativos

0.22 cm2

1.27 cm2

2.51 cm2

1.27 cm2


Calculo del Momento Resistente o Requerido

x Fc x b x d22

0.17 x 250 kg/cm2 x 10 cm x 27

Kg/cm kg-m

As+ =1449

= 1.86 cm2

As+ =Mact x 100

x Fy x d x J

As+ =620

= 0.79 cm2

As- =

Mact x 100

x Fy x d x J

As- =172

= 0.22 cm2

As- =172

= 0.22 cm2

As- =1956

= 2.51 cm2


N =As

= = 1.46 2 1/2As asumido

N =As

= = 0.62 1 As asumido

N =As

= = 0.17 1/2As asumido

1

N =As

= = 1.97

Mr =

Mr =

Mr = 309,825.00 3,098.25

Mr > Mact

Si esta condicion se cumpleNo se calcula el macizado por

Momento

Si esta condicion no se cumple

As min = 0.002

As min = 0.002

As min =

Se calcula el macizado por Momento

2 1/2As asumido

1/2


15/353

MR > Mact

CHEQUEO POR CORTE PARA EL MACIZADO

Vc = 0.53 x Rc x b` x d x

Vc = 0.53 x 15.81 x 50 x 27 x 0.85

Vc = kg/cm2 Vmax

50 x 27

Calculo del corte resistente

Vcu= 0.85 x 0.5 x Rc

Vcu= 0.85 x 0.5 x

Vcu=

>

>


2 x d

2 x 27 = 54 cm


1 Ld= 12 = 23.8

2 Ld= d o r 0

3 Ld= L/16 0.31

Si esta condicion se cumple

Se debe calcular el macizado por corte

Si esta condicion no se cuple

3,098.25 1,956.13No se calcula el macizado por

Momento

9,616.09 2,301.78 No hay macizado

por or!e

cm

Smax=

x barra

} 8.02 10

Vu VcuNo se debe calcular el macizado por corte

1.71 6.72

Smax=

kg/cm2b x d

15.81

".72

Vu > Vcu

No se debe calcular el macizado por corte

Vu=Vmax

=2,301.78

= 1.71


16/353

$i/as

decar/as

dela

losa

deTec

hodela

%difi

cacion'


17/353

VC-C

PREDIMENSIONADO. = 7 m

Seccin mnima de la viga (30 X 30) cm. Peso de la losa = m

Ader = 4.0

Aizq = 0.5

h = 10 % * Fc =

h = 0.7 m Rma =

= m

PESO PROPIO FY =

Pp = b X h X

Pp = m X m X Kg/m

Pp = Kg/m

Wu = Peso losa + Peso propio 1.00

= Kg/m + Kg/m= Kg/m

W'u = Wu X Ancho Tributario X (Carga que va a soportar la viga).

= X + X

= Kg/m

Mmax = X L NOTA:

= X

= X

= Kg/m

b calculado = 30 cm = m

Calculo de Rcu

= *

=Rcu 51

Rcu 300 0.17

4342.25 7.00

10

4342.25 49.00

10

21277.03

0.30

0.50 4.00 1.10

1 2

4342.25

W'u (El valor 10dependera del tipo de apoyo que

tenga la viga,pero en efecto del proyecto se

asumira constante).

10

VIGA DE CARGA EN LOSA DE TECHO. (Tipo maciza )

LDesf

1054

300

5848.481

Altura de Entre piso 3

Luz mas desf

4200

0.30 0.70 2500

525

1054.00 5251579.00

1.10

1579.00


18/353

CALCULO DE d

X b

h = 45 cm d = cm

X 5 cm

b =

cm 40 cm

Peso Propio Real de la Viga

Pp = b X h X Pp = m X m X Kg/m

Pp = Kg/m

Cu = + Peso propio

= +

= Kg Kg

kg/,2

0.5 0.5

0.00

# x= 2.1 x= 2.03 x= 2.753 x= 3.2552 x= $.23

%

30&3

%

#

Ass 2 3/4 2 3/4 2

Asi 5 3/4 5 3/4 5

%$&7.727 10&38.7"8

v

12&70.$7&8

17&5&.5202 12185.3$57 20087.35 231"5.5$ 17150.$5

M

773.25

1"0"3.$7&8 30518.17 2&213.&&7 $0223.807 $&317.0& 202$3.$$&

12558."5 17028."5 2013".$" 2"151.55 30&3.00

6185.981 6186.00

6186.00

5 $ " 7 7

0.30 0.45 2500

337.50

Rmax NOTA: El valor de Rmse asumira la

mas defavorable.5848.481 337.50

d = 1390.66 30 cm

d = 37.29

d = Mmax

Rcu

40

d = 21277.03

51 0.30 r =

3/4

3/4

110&8.$33 23001.218

132$5.8513 12$&&.23$$2 21"75.32"55 32277.118$3 773.2""72

1282$.""0


19/353

Valores maximos del esquema estructurales

Mr = X b X d

= X X 40

= X X

= Kg - m >

Condicion para el armado de la viga.

>

Calculo del Acero minimo

14 X b X d

fy

X 30 X 50

CALCULO DE AREAS DE ACERO

y

X X X 50 / 100

X X X

cm

4200

As =M act

0.85 0.874 4200 0.50

As =M act

1560.09

51.00 0.30 1600

24480.000 32277.118 Kg - m Doblemente Armada

Mr M act max SSA

Nota: Debido a que la seccion

dio doblemente armada se

subiran las dimensiones de la

viga o la resistencia del concretoMr M act max SDA

Vmax Mmax

26151.5503 32277.12

Rcu

51.00 0.30

En esta viga se trabaja con d de50cm

51.00 0.30

Rcu

2500

38250.000 32277.118 Kg - m Simplemente armada

51.00 0.30

Asmin =

Asmin =14

4200

Asmin = 5 cm

As =M act

j

As =M act

0.85 0.874


20/353

AREAS DE ACERO NEGATIVAS.

AREAS DE ACERO POSITIVAS.

= 13.89 cm

a cu o e numero e ca as para e acero con mayor area era co oca a en a par e n er or e a secc ono a: se ra a ara con = cm D cm

13.89 cm = 52.85 cm

a cu o e numero e ca a para e acero m n mo.

5.00 cm = 22.85 cm

2 de 3/4

5 de 3/4

Cabill =s ayor

=4.87 de 3/4

s asum o

Cabilla = s m n mo = 1.75 de 3/4 s asum o

As =10938.77

As = 7.01 cm1560.09

rea e acero mayor

2.85 1.91

As =12824.66

As = 8.22 cm1560.09

As =-497.73

As = 5.00 cm1560.09

As =12499.23

As = 8.01 cm1560.09

As =21675.33

As = 13.89 cm1560.09

As =773.25

As = 0.50 cm1560.09

As = 13245.85 As = 8.49 cm1560.09

Nota: se asumira el

acero minimo en las

areas menores del

minomo


21/353

Calculo de la longitud de desarrolloL cm16

44 cm

Ld = dr = 40 cm

Ld = 12 barra 12 x 1.91 cm = 23 cm

a cu o e a separac on en re ca as.

barra 3 cm = cm + 2.5 cm = cm cm

a cu o e os estr oson c on

s n > c e ca cu an es r oss n < c o se ca cu an es r os

> c

> e ca cu an estr os

Calculo de los estribosCalculo de la separacion de los estribos

= -

0.85 x 30 cm x 40 cm

= -= Kg/cm - Kg/cm

= Kg/cm2

Fc = 1.06 300 Kg/cm = Fc = 2.10 300 Kg/cm =

Comparacion 1.06 Fc

Vs 25.64 9.18

Vs 16.46

1.06

2.10 36.37 Kg/cm

Vs Si esto se cumple las separacion del los estribosse calcula (d/2) o 60cm16.46 18.36

1,06Rc vs 2,1Rc Si esto se cum le las se aracion del

Kg=

18.36 Kg/cm

x x 1,275.00

20.51 .

25.64 Kg/cm20.85 x b x dr

Vs As Vc

sV max

=26,151.55

c . 300

Vs As Vc

c 9.18

.

n ==

16

1.91 4.41 5

cm

26,151.55= 20.51

c .

Ld = =700

= 44


22/353

d 402 2

d 404 4

S = = x 40 cm = cm

Calculo del area y seleccin de los estribos

x S Kg x cmx d Kg/cm x 40 cm

e ecc n e ame ro e es r o.

Se usara estribos de dos ramas se 1/2"Estribos d A = 0.71 cm D = cm

2 x cm = 1.42 cm

Calculo de se aracion maxima en el area de confinamiento.40 cm

Se selecciona el romedio se redo =

cm = 22.9 cm

16.04 20 cm

S max = 24 xdiametro

de

x 1.91 cm

= 24 x 0.95

=

3/8Av .

S max =dr

= = 10 10 cm4 4 cm

S max =x ame ro

barra= 8 15.24 cm

Av 1/4" - 3/8" 3/8"

0.95

3/8" - 1/2"

estribos de3

Av = 0.71

# estribos =c .

= 2.19=

05Xd 0.50 20.00

As 3/8" 1/2" 5/8"Area 0.71 . .

A c = Vmax = 26,151.5520.00

Fy 4200

A c = 3.11 cmCon este valor se selecciona sugun su area el

diametro de los estribos

S = = = 20.00 cm

S = = = 10.00 cm

Nota: Cuando la dos condiciones de diseo no se cumplan se calculara la

separacion de los estribos segn lo establecido en las norma venezolana

referente a proyctos y construcciones de obras en concreto estructural, lo cual

establece en la tabla 11:4 que la separacion minima sera de 0,5d

los estribos se calcula (dr/4) o 30mc18.36 16.46 36.37


23/353

cm

2.5 2.5

2.5 cm

Gancho

10

DESARROLLO.

cm

m

2.5 cm

30 cm

@ cada cm110 cm 4.8 m ## cm

@ c/ 10 cm

7.0 m

@ cada cm

110 cm 3.8 m ## cm

@ c/ 10 cm

6.0 m

@ cada cm

110 cm 1.8 m ## cm

@ c/ 10 cm

4.0 m

cm

55 cm 50.0 cm

170

3/8'' 20.00

1.70

3/8''

3/8''

3/8'' 20.00

3/8''

3/8'' 20.00

25.0

Ganchos


24/353

@ cada cm

110 cm 2.8 m ## cm

@ c/ 10 cm

5.0 m

3/8'' 20.00

3/8''


25/353

VC-B



Ader = 5.0

Aizq = 4.0

h = 10 % * Fc =

h = 0.7 m Rma =

= m

PESO PROPIO FY =

Pp = b X h X

Pp = m X m X Kg/m

Pp = Kg/m


= Kg/m + Kg/m= Kg/m


= X + X

= Kg/m

Mmax = X L NOTA:

= X

= X

= Kg/m


Calculo de Rcu

= *=

CALCULO DE d

X b

h = 60 cm d = cm

X 5 cm

b =


LDesf

1054

Luz mas desf 300

5848.481


4200

0.30 0.70 2500

525

(El valor 10dependera del tipo de apoyo que


asumira constante).

10

1054.00 5251579.00

1.10

1579.00 4.00 5.00 1.10

7816.05 7.00

10

7816.05 49.00

10

2 2

7816.05

W'u

38298.65

0.30

Rcu 300 0.17Rcu 51

r =

d = 2503.18 30 cm

d = Mmax

Rcu

55

d = 38298.65

51 0.30


26/353

cm 55 cm


Pp = b X h X

Pp = m X m X Kg/m

Pp = Kg/m

Cu = + Peso propio

= +

= Kg Kg

kg/,2

0.5 0.5

0.00

# x= 2.1 x= 2.03 x= 2.753 x= 3.2552 x= $.23

%

3150

%

#

Ass 2 3/4 2 3/4 2

Asi 5 3/4 5 3/4 5


d = 50.03

0.30 0.60

5 $ " 7 7

2500

450.00



1"35".&12 31075."5 2&7$7."51 $0&58.577" 50217.&7 20"13.237

6298.481 6299.00

6299.00

v

18287.588 12$07.&3" 20$5$.2& 23588.71 17$"3.7$

13207.$12 12788.0" 1733&.72 2050$.2& 2""2&.2" 31$&.50

11138.588 11301.173 23$21.3&1

787.375 13$87.81$5 12727.558$7 22071.2"871 328"".72 787.382

Vmax Mmax

26629.2625 32866.72

M

13058.&2& %50".81&

3/4

3/4


27/353

Mr = X b X d

= X X 55

= X X

= Kg - m >


>

c e ca cu an estr oss n < c o se ca cu an es r os

As =13058.93

As = 7.61 cm1716.10

As =11138.59

As = 6.49 cm1716.10

As = -506.82 As = 5.50 cm1716.10

rea e acero mayor

2.85 1.91

Cabill =s ayor

=4.51 de 3/4

de 3/4 s asum o

2 de 3/4

s asum o

Cabilla =s m n mo

=1.93

5 de 3/4

Ld = =700

= 44 cm16

1.91 4.41 5


29/353

a cu o e es uerzo cor an e e concre o.= c

= g cm

= ga cu o e es uerzo c uan e. =

V actuante ma

n oncess n > c



= -

0.85 x 30 cm x 55 cm

= -= Kg/cm - Kg/cm

= Kg/cm2

Fc = 1.06 300 Kg/cm =

Fc = 2.10

300 Kg/cm =

Comparacion 1.06 Fc

d 552 2

d 554 4

S = = x 55 cm = cm



c . 300

c .

c 9.18

.

n ==

26,629.26= 18.99

=

18.36 Kg/cm

x x 1,402.50

18.99 .

Vs As Vc

0.85 x b x dr

Vs As Vc

sV max

=26,629.26 Kg

1,06Rc vs 2,1Rc Si esto se cumple las separacion dellos estribos se calcula (dr/4) o 30mc18.36 9.81 36.37

2.10 36.37


S = = = 13.75 cm

4200

S = = = 27.50 cm

05Xd 0.50 27.50

A c = Vmax = 26,629.26 27.50Fy

Kg/cm





Vs 18.99 9.18

Vs 9.81

1.06

18.99 Kg/cm2


30/353



2 x cm = 1.42 cm

Calculo de se aracion maxima en el area de confinamiento.

55 cm


cm2.5 2.5

2.5 cm

Gancho

10

DESARROLLO.

cm

m

2.5 cm

30 cm

@ cada cm

120 cm 4.6 m ## cm

@ c/ 13.8 cm7.0 m

60 cm 55.0 cm

1.80

3/8'' 27.50

3/8''

3/8" - 1/2"As 3/8" 1/2" 5/8"Area 0.71 . .



Av = 0.71

# estribos =c

=

Av 1/4" - 3/8" 3/8"

.= 2.23

3 estribos de

15 cm4 4

Av .

S max = dr = = 14 cm


de

S max =x ame ro

barra=

= 24 x 0.95 cm =

25.0

15.24 cm8 x 1.91 cm =

cm

180

22.9 cm

17.29 20 cm

3/8

0.95


31/353

@ cada cm

120 cm 3.6 m ## cm

@ c/ 13.8 cm

6.0 m

@ cada cm

120 cm 1.6 m ## cm

@ c/ 13.8 cm

4.0 m

@ cada cm

120 cm 2.6 m ## cm

@ c/ 13.8 cm

5.0 m

3/8''

3/8'' 27.50

3/8''

3/8'' 27.50

3/8''

3/8'' 27.50

Ganchos


32/353

VC-C



Ader = 0.5

Aizq = 5.0

h = 10 % * Fc =

h = 0.7 m Rma =

= m

PESO PROPIO FY =

Pp = b X h X

Pp = m X m X Kg/m

Pp = Kg/m


= Kg/m + Kg/m= Kg/m


= X + X

= Kg/m

Mmax = X L NOTA:

= X

= X

= Kg/m


Calculo de Rcu

= *=

CALCULO DE d

X b

h = 50 cm d = cm

X 5 cm

b =


LDesf

1054

Luz mas desf 300

5848.481


4200

0.30 0.70 2500

525



asumira constante).

10

1054.00 5251579.00

1.10

1579.00 5.00 0.50 1.10

5210.70 7.00

10

5210.70 49.00

10

2 1

5210.7

W'u

25532.43

0.30

Rcu 300 0.17Rcu 51

r =

d = 1668.79 30 cm

d = Mmax

Rcu

45

d = 25532.43

51 0.30


33/353

cm 45 cm


Pp = b X h X

Pp = m X m X Kg/m

Pp = Kg/m

Cu = + Peso propio

= +

= Kg Kg

kg/,2

0.5 0.5

0.00

# x= 2.1 x= 2.03 x= 2.753 x= 3.2552 x= $.23

%

3112

%

#

Ass 2 3/4 2 3/4 2

Asi 5 3/4 5 3/4 5


d = 40.85

0.30 0.50

5 $ " 7 7

2500

375.00



1"1"2.15" 30705."5 2&3&3.$5" $0$70.8&8 $&"20.0$ 203"7.803

6223.481 6224.00

6224.00

v

180"&.8$$ 122"0.1&& 20210.7$ 23307.85 17255.80

13050.15" 12"35.80 17133.2" 202"0.1" 2"312.20 3112.00

11005.&"5 111""."13 231$2.51&

778 13327.21&5 1257".01532 21808.$73"7 32$75.38& 778.00&

Vmax Mmax

26312.197 32475.39

M

12&03.$$1 %500.78$

3/4

3/4


34/353

Mr = X b X d

= X X 45

= X X

= Kg - m >


>


14 X b X d

fy

X 30 X 50


y

X X X 50 / 100

X X X

cm


Rcu

51.00 0.30

Doblemente Armada




viga o la resistencia del concreto

Mr M act max SSA

Mr M act max SDA

51.00 0.30 2025

30982.500 32475.389 Kg - m

Kg - m Simplemente armada

Asmin =

Asmin =14

4200

En esta viga se trabaja con d de

50cm el cual esta permitido en el

rango de trabajo de 40cm a 70cmRcu

51.00 0.30

51.00 0.30 2500

Asmin = 5 cm

As =M act

38250.000 32475.389

As =M act

0.85 0.874 4200

As =M act

0.85 0.874 4200 0.50

As =M act

1560.09

As =778.00

As = 0.50 cm

Nota: se asumira el

acero minimo en lasareas menores del

1560.09


35/353


= 13.98 cm

a cu o e numero e ca as para e acero con mayor area era co oca a en a parte n er or e a secc ono a: se ra a ara con = cm D cm

13.98 cm = 5

2.85 cm


5.00 cm = 22.85 cm


45 cm

Ld = dr = 45 cm

Ld = 12 barra 12 x 1.91 cm = 23 cm

As =12576.02

As = 8.06 cm1560.09

minomoAs =

13327.22As = 8.54 cm

1560.09

As =12903.44

As = 8.27 cm1560.09

As =21808.47

As = 13.98 cm1560.09

As =11005.97

As = 7.05 cm1560.09

As =-500.78

As = 5.00 cm1560.09

rea e acero mayor

2.85 1.91

Cabill =

s ayor

=

4.90 de 3/4

de 3/4 s asum o

2 de 3/4

s asum o

Cabilla =s m n mo

=1.75

5 de 3/4

Ld = =700

= 44 cm16


36/353



a cu o e os es r os

on c ons n > c e ca cu an estr oss n < c o se ca cu an es r os

> c

> e ca cu an es r os


= -

0.85 x 30 cm x 45 cm

= -= Kg/cm - Kg/cm

= Kg/cm2

Fc = 1.06 300 Kg/cm =Fc = 2.10 300 Kg/cm =

Comparacion 1.06 Fc

c . 300

1.91 4.41 5

c .

c 9.18

.

n ==

26,312.20= 20.64

=

18.36 Kg/cm

x x 1,275.00

20.64 .

Vs As Vc

0.85 x b x dr

Vs As Vc

s V max = 26,312.20 Kg


2.10 36.37


Kg/cm





Vs 22.93 9.18

Vs 13.75

1.06

22.93 Kg/cm2


37/353

d 452 2

d 454 4

S = = x 45 cm = cm





2 x cm = 1.42 cm



cm

2.5 2.5

2.5 cm

Gancho

10

DESARROLLO.

cm

m

2.5 cm

30 cm

55 cm 50.0 cm

1.70

S = = = 11.25 cm

4200

S = = = 22.50 cm

05Xd 0.50 22.50

3/8" - 1/2"

A c =Vmax

=26,312.20 22.50

Fy

As 3/8" 1/2" 5/8"

Area 0.71 . .



Av = 0.71

# estribos =c

=

Av 1/4" - 3/8" 3/8"

.= 2.21

3 estribos de

15 cm

4 4

Av .

S max =dr

= = 11 cm


de

S max =x ame ro

barra=

= 24 x 0.95 cm =

25.0

15.24 cm8 x 1.91 cm =

cm

170

22.9 cm

16.45 20 cm

3/8

0.95


38/353

@ cada cm

110 cm 4.8 m cm

@ c/ 11.3 cm

7.0 m

@ cada cm

110 cm 3.8 m cm

@ c/ 11.3 cm6.0 m

@ cada cm

110 cm 1.8 m cm

@ c/ 11.3 cm

4.0 m

@ cada cm

110 cm 2.8 m cm

@ c/ 11.3 cm

5.0 m

3/8''

110

110

110

110

3/8'' 22.50

3/8''

3/8'' 22.50

3/8''

3/8'' 22.50

3/8'' 22.50

3/8''


39/353

$i/as

demar

resde

lalosa

deTec

hodela

%difi

cacion'


40/353

VA-1



Ader = 0.5

Aizq = 5.0

Fc =

Rma =

= m

PESO PROPIO FY =

Pp = b X h X

Pp = m X m X Kg/m

Pp = Kg/m


= Kg/m + Kg/m= Kg/m


= X + X

= Kg/m

Mmax = X L NOTA:

= X

= X

= Kg/m


Calculo de Rcu

= *=

CALCULO DE d

X b

h = 35 cm d = cm

X 5 cm

b =

VIGA DE AMARRE EN LOSA DE TECHO. (Tipo maciza )

LDesf

1054

300

8402.879


4200

0.30 0.30 2500

225



asumira constante).

10

1054.00 2251279.00

1.40

1279.00 5.00 0.50 1.40

5371.80 5.00

10

5371.80 25.00

10

2 1

5371.8

W'u

13429.50

0.30

d = Mmax

Rcu

30

d = 13429.50

Rcu 300 0.17Rcu 51

51 0.30 r =

d = 877.75 30 cm


41/353

cm 30 cm


Pp = b X h X

Pp = m X m X Kg/m

Pp = Kg/m

Cu = + Peso propio

= +

= Kg Kg

Kg/m

4 5 0.5

+

-

-+

Ass 2 7/8 2 7/8

Asi 5 7/8 9.4


Mr = X b X d

= X X 30

= X X

= Kg - m >

2500

262.50



d = 29.63

0.30 0.35

1083.25

4333 22613 17440.3

4333.000

8665.379 8666.00

21773.3

Vmax Mmax

25889.675 22206.63

Rcu

51.00 0.30

1083.3 22,206.63

M

7296.07

Doblemente Armada

51.00 0.30 900

13770.000 22206.625 Kg - m

16466.08

0.5

8666.00

16384.156

12051.156

48502.519

25889.675

v

7/810.54


42/353


>


14 X b X d

fy

X 30 X 40


y

X X X 40 / 100

X X X

cm






Mr M act max SSA

Mr M act max SDA


Asmin =

Asmin =14

4200


Rcu

51.00 0.30

51.00 0.30 1600

Asmin = 4 cm

As = M act

24480.000 22206.625

As =M act

0.85 0.874 4200

As =M act

0.85 0.874 4200 0.40

As =M act

1248.07

As =1083.25

As = 0.87 cm

As =1083.25

As = 4.00 cm1248.07

Nota: se asumira el

acero minimo en las

areas menores del

minomo

1248.07

As =22206.63

As = 17.79 cm1248.07


43/353


= 17.79 cm


17.79 cm = 53.88 cm


4.00 cm = 23.88 cm


31 cmLd = dr = 30 cm

Ld = 12 barra 12 x 2.22 cm = 27 cm

a cu o e a separac on entre ca as.


a cu o e os es r oson c on

s n > c e ca cu an estr oss n < c o se ca cu an estr os

As =7296.07

As = 5.85 cm1248.07

As = 16466.08 As = 13.19 cm1248.07

rea e acero mayor

3.88 2.22

Cabill =s ayor

=4.59 de 7/8

de 7/8 s asum o

2 de 7/8

s asum o

Cabilla =s m n mo

=1.03

5 de 7/8

Ld = =500

= 31 cm16

2.22 4.72 5


44/353


45/353

e ecc n e ametro e estr o.


2 x cm = 1.42 cm



cm

2.5 2.5

2.5 cm

Gancho

10

DESARROLLO.

cm

m

2.5 cm

30 cm

@ cada cm

90 cm 2.2 m 90 cm

@ c/ 7.5 cm

4.0 m

45 cm 40.0 cm

1.50

3/8'' 15.00

3/8''



3/8" - 1/2"

0.95

As 3/8" 1/2" 5/8"

Area 0.71 . .

Av = 0.71

# estribos =c

=

Av 1/4" - 3/8" 3/8"

S max =dr

= = 8 cm

.=

x 2.22 cm = 17.78

3/8Av .2.17

3 estribos de

cm

10 cm

cm

150

22.9 cm

16.05 20 cm

= 24 x 0.95 cm =

25.0

diametro

deS max = 24 x

4 4

S max =x ame ro

barra= 8


46/353

@ cada cm

90 cm 3.2 m 90 cm

@ c/ 7.5 cm

5.0 m

3/8'' 15.00

3/8''


47/353

VA-2



Ader = 5.0

Aizq = 4.0

Fc =

Rma =

= m

PESO PROPIO FY =

Pp = b X h X

Pp = m X m X Kg/m

Pp = Kg/m


= Kg/m + Kg/m= Kg/m


= X + X

= Kg/m

Mmax = X L NOTA:

= X

= X

= Kg/m


Calculo de Rcu= *=

CALCULO DE d

X b

h = 45 cm d = cm

X 5 cm

b =


LDesf

1054

300

8402.879


4200

0.30 0.30 2500

225



asumira constante).

10

1054.00 2251279.00

1.40

1279.00 4.00 5.00 1.40

8057.70 5.00

10

8057.70 25.00

10

2 2

8057.7

W'u

20144.25

0.30

d = Mmax

Rcu

40

d = 20144.25

Rcu 300 0.17

Rcu 51

51 0.30 r =

d = 1316.62 30 cm


48/353

cm 40 cm


Pp = b X h X

Pp = m X m X Kg/m

Pp = Kg/m

Cu = + Peso propio

= +

= Kg Kg

Kg/m

4 5 0.5

+

-

-+

Ass 2 7/8 2 7/8

Asi 5 7/8 9.4


Mr = X b X d

= X X 40

= X X

= Kg - m >


> c e ca cu an estr oss n < c o se ca cu an es r os

> c


Cabill =s ayor

=4.63 de 7/8

de 7/8 s asum o

2 de 7/8

s asum o

Cabilla =s m n mo

=1.03

5 de 7/8

Ld = =500

= 31 cm

c . 300

16

2.22 4.72 5

c .

x x 1,020.00

25.60 .

c 9.18

.

n ==

26,113.74= 25.60


51/353


= -

0.85 x 30 cm x 40 cm

= -= Kg/cm - Kg/cm

= Kg/cm2

Fc = 1.06 300 Kg/cm =Fc = 2.10 300 Kg/cm =

Comparacion

1.06 Fc

d 402 2

d 404 4

S = = x 40 cm = cm





2 x cm = 1.42 cm

Vs As Vc

Vs 25.60 9.18

Vs 16.42

1.06

25.60 Kg/cm20.85 x b x dr

Vs As Vc

sV max

=26,113.74 Kg

=

18.36 Kg/cm


2.10 36.37


S = = = 10.00 cm

4200

S = = = 20.00 cm

05Xd 0.50 20.00

3/8" - 1/2"

A c =Vmax

=26,113.74 20.00

Fy

As 3/8" 1/2" 5/8"Area 0.71 . .

A c = 3.11 cm Con este valor se selecciona sugun su area eldiametro de los estribos

Av = 0.71

Av 1/4" - 3/8" 3/8"

0.95

Kg/cm




establece en la tabla 11:4 ue la se aracion minima sera de 0,5d


52/353



cm

2.5 2.5

2.5 cm

Gancho

10

DESARROLLO.

cm

m

2.5 cm30 cm

@ cada cm

90 cm 2.2 m 90 cm

@ c/ 10 cm

4.0 m

@ cada cm

90 cm 3.2 m 90 cm

@ c/ 10 cm

5.0 m

3/8'' 20.00

3/8''

45 cm 40.0 cm

1.50

3/8'' 20.00

3/8''

# estribos =c

=Av .

S max =dr

= = 10 cm

=

4 4


de

S max =x ame ro

barra=

= 24 x 0.95 cm =

25.0

17.78 cm8 x 2.22 cm =

cm

150

22.9 cm

16.88 20 cm

3/8.

2.19

3 estribos de

10 cm


53/353

VA-3



Ader = 4.0

Aizq = 6.0

Fc =

Rma =

= m

PESO PROPIO FY =

Pp = b X h X

Pp = m X m X Kg/m

Pp = Kg/m


= Kg/m + Kg/m= Kg/m


= X + X

= Kg/m

Mmax = X L NOTA:

= X

= X

= Kg/m


Calculo de Rcu

= *=

CALCULO DE d

X b

h = 45 cm d = cm

X 5 cm

b =


LDesf

1054

300

8402.879


4200

0.30 0.30 2500

225



asumira constante).

10

1054.00 2251279.00

1.40

1279.00 6.00 4.00 1.40

8953.00 5.00

10

8953.00 25.00

10

2 2

8953

W'u

22382.50

0.30

d = Mmax

Rcu

40

d = 22382.50

Rcu 300 0.17Rcu 51

51 0.30 r =

d = 1462.91 30 cm


54/353

cm 40 cm


Pp = b X h X

Pp = m X m X Kg/m

Pp = Kg/m

Cu = + Peso propio

= +

= Kg Kg

Kg/m

4 5 0.5

+

-

-+

Ass 2 7/8 2 7/8

Asi 5 7/8 9.4


Mr = X b X d

= X X 40

= X X

= Kg - m >


> c e ca cu an es r oss n < c o se ca cu an es r os

> c> e ca cu an es r os

Cabill =s ayor

=4.63 de 7/8

de 7/8 s asum o

2 de 7/8

s asum o

Cabilla =s m n mo

=1.03

5 de 7/8

Ld = =500

= 31 cm

c . 300

16

2.22 4.72 5

c .

x x 1,020.00

25.60 .

c 9.18

.

n ==

26,113.74= 25.60


57/353


= -

0.85 x 30 cm x 40 cm

= -= Kg/cm - Kg/cm

= Kg/cm2

Fc = 1.06 300 Kg/cm =Fc = 2.10 300 Kg/cm =

Comparacion

1.06 Fc

d 402 2

d 404 4

S = = x 40 cm = cm





2 x cm = 1.42 cm

Vs As Vc

Vs 25.60 9.18

Vs 16.42

1.06

25.60 Kg/cm20.85 x b x dr

Vs As Vc

sV max

=26,113.74 Kg

=

18.36 Kg/cm


2.10 36.37


S = = = 10.00 cm

4200

S = = = 20.00 cm

05Xd 0.50 20.00

3/8" - 1/2"

A c =Vmax

=26,113.74 20.00

Fy

As 3/8" 1/2" 5/8"Area 0.71 . .


Av = 0.71

Av 1/4" - 3/8" 3/8"

0.95

Kg/cm






58/353



cm

2.5 2.5

2.5 cm

Gancho

10

DESARROLLO.

cm

m

2.5 cm30 cm

@ cada cm

90 cm 2.2 m 90 cm

@ c/ 10 cm

4.0 m

@ cada cm

90 cm 3.2 m 90 cm

@ c/ 10 cm

5.0 m

3/8'' 20.00

3/8''

45 cm 40.0 cm

1.50

3/8'' 20.00

3/8''

# estribos =c

=Av .

S max =dr

= = 10 cm

=

4 4


de

S max =x ame ro

barra=

= 24 x 0.95 cm =

25.0

17.78 cm8 x 2.22 cm =

cm

150

22.9 cm

16.88 20 cm

3/8.

2.19

3 estribos de

10 cm


59/353

VA-4



Ader = 6.0

Aizq = 7.0

Fc =

Rma =

= m

PESO PROPIO FY =

Pp = b X h X

Pp = m X m X Kg/m

Pp = Kg/m


= Kg/m + Kg/m= Kg/m


= X + X

= Kg/m

Mmax = X L NOTA:

= X

= X

= Kg/m


Calculo de Rcu

= *=

CALCULO DE d

X b

h = 50 cm d = cm

X 5 cm

b =


LDesf

1054

300

8402.879


4200

0.30 0.30 2500

225



asumira constante).

10

1054.00 2251279.00

1.40

1279.00 7.00 6.00 1.40

11638.90 5.00

10

11638.90 25.00

10

2 2

11638.9

W'u

29097.25

0.30

d = Mmax

Rcu

45

d = 29097.25

Rcu 300 0.17Rcu 51

51 0.30 r =

d = 1901.78 30 cm


60/353

cm 45 cm


Pp = b X h X

Pp = m X m X Kg/m

Pp = Kg/m

Cu = + Peso propio

= +

= Kg Kg

Kg/m

4 5 0.5

+

-

-+

Ass 2 7/8 2 7/8

Asi 5 7/8 9.4


Mr = X b X d

= X X 45

= X X

= Kg - m >



a cu o e es uerzo cor an e e concre o.

= c= g cm

= g

a cu o e es uerzo c uan e. =

V actuante ma

n oncess n > c


Cabill =s ayor

=4.13 de 7/8

de 7/8 s asum o

2 de 7/8

s asum o

Cabilla =s m n mo

=1.16

5 de 7/8

Ld = =500

= 31 cm

c . 300

16

2.22 4.72 5

c .

x x 1,147.50

22.85 .

c 9.18

.

n ==

26,224.28= 22.85


63/353


= -

0.85 x 30 cm x 45 cm

= -= Kg/cm - Kg/cm

= Kg/cm2

Fc = 1.06 300 Kg/cm =Fc = 2.10 300 Kg/cm =

Comparacion

1.06 Fc

d 452 2

d 454 4

S = = x 45 cm = cm





2 x cm = 1.42 cm

Vs As Vc

Vs 22.85 9.18

Vs 13.67

1.06

22.85 Kg/cm20.85 x b x dr

Vs As Vc

sV max

=26,224.28 Kg

=

18.36 Kg/cm


2.10 36.37


S = = = 11.25 cm

4200

S = = = 22.50 cm

05Xd 0.50 22.50

3/8" - 1/2"

A c =Vmax

=26,224.28 22.50

Fy

As 3/8" 1/2" 5/8"Area 0.71 . .



Av = 0.71

# estribos =

c

=

Av 1/4" - 3/8" 3/8"

Av . = 3/8

.

2.20 3 estribos de

0.95

Kg/cm






64/353



cm

2.5 2.5

2.5 cm

Gancho10

DESARROLLO.

cm

m

2.5 cm

30 cm

@ cada cm

100 cm 2 m ## cm

@ c/ 11.3 cm

4.0 m

@ cada cm

100 cm 3 m ## cm

@ c/ 11.3 cm

5.0 m

3/8'' 22.50

3/8''

50 cm 45.0 cm

1.60

3/8'' 22.50

3/8''

S max =dr

= = 11 cm4 4


de

S max =x ame ro

barra=

= 24 x 0.95 cm =

25.0

17.78 cm8 x 2.22 cm =

cm

160

22.9 cm

17.30 20 cm

15 cm


65/353

VA-5



Ader = 7.0

Aizq = 7.0

Fc =

Rma =

= m

PESO PROPIO FY =

Pp = b X h X

Pp = m X m X Kg/m

Pp = Kg/m


= Kg/m + Kg/m= Kg/m


= X + X

= Kg/m

Mmax = X L NOTA:

= X

= X

= Kg/m


Calculo de Rcu

= *=

CALCULO DE d

X b

h = 55 cm d = cm

X 5 cm

b =


LDesf

1054

300

8402.879


4200

0.30 0.30 2500

225



asumira constante).

10

1054.00 2251279.00

1.40

1279.00 7.00 7.00 1.40

12534.20 5.00

10

12534.20 25.00

10

2 2

12534.2

W'u

31335.50

0.30

d = Mmax

Rcu

50

d = 31335.50

Rcu 300 0.17Rcu 51

51 0.30 r =

d = 2048.07 30 cm


66/353

cm 50 cm


Pp = b X h X

Pp = m X m X Kg/m

Pp = Kg/m

Cu = + Peso propio

= +

= Kg Kg

Kg/m

4 5 0.5

+

-

-+

Ass 2 7/8 2 7/8

Asi 4 7/8 9.4


Mr = X b X d

= X X 50

= X X

= Kg - m >



> c> e ca cu an es r os

Cabill =s ayor

=3.73 de 7/8

de 7/8 s asum o

2 de 7/8

s asum o

Cabilla =s m n mo

=1.29

4 de 7/8

Ld = =500

= 31 cm

c . 300

16

2.22 4.72 5

c .

x x 1,275.00

20.66 .

c 9.18

.

n ==

26,337.80= 20.66


69/353


= -

0.85 x 30 cm x 50 cm

= -= Kg/cm - Kg/cm

= Kg/cm2

Fc = 1.06 300 Kg/cm =Fc = 2.10 300 Kg/cm =

Comparacion

1.06 Fc

d 502 2

d 504 4

S = = x 50 cm = cm





2 x cm = 1.42 cm

Vs As Vc

Vs 20.66 9.18

Vs 11.48

1.06

20.66 Kg/cm20.85 x b x dr

Vs As Vc

sV max

=26,337.80 Kg

=

18.36 Kg/cm


2.10 36.37


S = = = 12.50 cm

4200

S = = = 25.00 cm

05Xd 0.50 25.00

3/8" - 1/2"

A c =Vmax

=26,337.80 25.00

Fy

As 3/8" 1/2" 5/8"Area 0.71 . .


Av = 0.71

Av 1/4" - 3/8" 3/8"

0.95

Kg/cm






70/353



cm

2.5 2.5

2.5 cm

Gancho

10

DESARROLLO.

cm

m

2.5 cm

30 cm

@ cada cm

110 cm 1.8 m ## cm

@ c/ 12.5 cm

4.0 m

@ cada cm

110 cm 2.8 m ## cm

@ c/ 12.5 cm

5.0 m

3/8'' 25.00

3/8''

55 cm 50.0 cm

1.70

3/8'' 25.00

3/8''

# estribos =c

=Av .

S max =dr

= = 13 cm

=

4 4


de

S max =x ame ro

barra=

= 24 x 0.95 cm =

25.0

17.78 cm8 x 2.22 cm =

cm

170

22.9 cm

17.72 20 cm

3/8.

2.21

3 estribos de

15 cm


71/353

VA-6



Ader = 7.0

Aizq = 0.5

Fc =

Rma =

= m

PESO PROPIO FY =

Pp = b X h X

Pp = m X m X Kg/m

Pp = Kg/m


= Kg/m + Kg/m= Kg/m


= X + X

= Kg/m

Mmax = X L NOTA:

= X

= X

= Kg/m


Calculo de Rcu

= *=

CALCULO DE d

X b

h = 40 cm d = cm

X 5 cm

b =


LDesf

1054

300

8402.879


4200

0.30 0.30 2500

225



asumira constante).

10

1054.00 2251279.00

1.40

1279.00 0.50 7.00 1.40

7162.40 5.00

10

7162.40 25.00

10

1 2

7162.4

W'u

17906.00

0.30

d = Mmax

Rcu

35

d = 17906.00

Rcu 300 0.17Rcu 51

51 0.30 r =

d = 1170.33 30 cm


72/353

cm 35 cm


Pp = b X h X

Pp = m X m X Kg/m

Pp = Kg/m

Cu = + Peso propio

= +

= Kg Kg

Kg/m

4 5 0.5

+

-

-+

Ass 2 7/8 2 7/8

Asi 5 7/8 9.4


Mr = X b X d

= X X 35

= X X

= Kg - m >

2500

300.00



d = 34.21

0.30 0.40

8702.879 8703.00

8703.00

0.5

16454.109 48709.603 21866.3

1087.88

M

7327.22 16536.38

12102.609 26000.212 4351.500

v

4351.5 22709 17514.8

Vmax Mmax

26000.212 22301.44

Rcu

51.00 0.30

1087.9 22,301.44

Doblemente Armada

51.00 0.30 1225

18742.500 22301.438 Kg - m

7/810.54


73/353


>


14 X b X d

fy

X 30 X 40


y

X X X 40 / 100

X X X

cm






Mr M act max SSA

Mr M act max SDA


Asmin =

Asmin =14

4200


Rcu

51.00 0.30

51.00 0.30 1600

Asmin = 4 cm

As = M act

24480.000 22301.438

As =M act

0.85 0.874 4200

As =M act

0.85 0.874 4200 0.40

As =M act

1248.07

As =1087.88

As = 0.87 cm

As =1087.88

As = 4.00 cm1248.07

Nota: se asumira el

acero minimo en las

areas menores del

minomo

1248.07

As =22301.44

As = 17.87 cm1248.07


74/353


= 17.87 cm

a cu o e numero e ca as para e acero con mayor area era co oca a en a par e n er or e a secc onota: se tra a ara con = cm D cm

17.87 cm = 53.88 cm


4.00 cm = 23.88 cm


35 cm

Ld = dr = 35 cm

Ld = 12 barra 12 x 2.22 cm = 27 cm




s n > c e ca cu an es r oss n < c o se ca cu an es r os

> c



= -

0.85 x 30 cm x 35 cm

= -= Kg/cm - Kg/cm

= Kg/cm2

Fc = 1.06 300 Kg/cm =

Fc = 2.10

300 Kg/cm =

Comparacion 1.06 Fc

d 352 2

d 354 4

S = = x 35 cm = cm



c . 300

c .

x x 1,020.00

25.49 .

Vs As Vc

c 9.18

.

n ==

26,000.21= 25.49

Vs 29.13 9.18

Vs 19.95

1.06

29.13 Kg/cm20.85 x b x dr

Vs As Vc

sV max

=26,000.21 Kg

=

18.36 Kg/cm


2.10 36.37


S = = = 8.75 cm

4200

S = = = 17.50 cm

05Xd 0.50 17.50

A c = Vmax = 26,000.21 17.50Fy

Kg/cm






76/353



2 x cm = 1.42 cm

Calculo de se aracion maxima en el area de confinamiento.

35 cm


cm2.5 2.5

2.5 cm

Gancho

10

DESARROLLO.

cm

m

2.5 cm

30 cm

@ cada cm

90 cm 2.2 m 90 cm

@ c/ 8.75 cm4.0 m

45 cm 40.0 cm

1.50

3/8'' 17.50

3/8''

3/8" - 1/2"As 3/8" 1/2" 5/8"Area 0.71 . .



Av = 0.71

# estribos =c

=

Av 1/4" - 3/8" 3/8"

Av .

S max = dr = = 9 cm

=

4 4


de

S max =x ame ro

barra=

= 24 x 0.95 cm =

25.0

17.78 cm8 x 2.22 cm =

cm

150

22.9 cm

16.47 20 cm

3/8.

2.18

3 estribos de

10 cm

0.95


77/353

@ cada cm

90 cm 3.2 m 90 cm

@ c/ 8.75 cm

5.0 m

3/8'' 17.50

3/8''


78/353

$i/asde

Car/as

dela

losa

de%

ntrep

isodela%

difica

cio


79/353

VC-A



Ader = 4.0

Aizq = 0.5

h = 10 % * Fc =

h = 0.7 m Rma =

= m

PESO PROPIO FY =

Pp = b X h X

Pp = m X m X Kg/m

Pp = Kg/m


= Kg/m + Kg/m= Kg/m


= X + X

= Kg/m

Mmax = X L NOTA:

= X

= X

= Kg/m


Calculo de Rcu

= *=

CALCULO DE d

X b

h = 40 cm d = cm

X 5 cm

b =

VIGA DE CARGA EN LOSA DE ENTREPISO. (Tipo NERVADA )

LDesf

778

Luz mas desf 300

4303.744


4200

0.30 0.70 2500

525



asumira constante).

10

778.00 5251303.00

1.10

1303.00 0.50 4.00 1.10

3583.25 7.00

10

3583.25 49.00

10

1 2

3583.25

W'u

17557.93

0.30

d = Mmax

Rcu

35

d = 17557.93

Rcu 300 0.17Rcu 51

51 0.30 r =

d = 1147.58 30 cm


80/353

cm 35 cm


Pp = b X h X

Pp = m X m X Kg/m

Pp = Kg/m

Cu = + Peso propio

= +

= Kg Kg

kg/,2

0.5 0.5

0.00

# x= 2.1 x= 2.03 x= 2.753 x= 3.2552 x= $.23

%

2302

%

#

Ass 2 3/4 2 3/4 2

Asi 5 3/4 5 3/4 5


&"53.$25 &3$".&2 12"73.77 1$&8".7& 1&$"3.58 2302.00

17118.&08

2500

300.00



d = 33.88

0.30 0.40

4603.744 4604.00

4604.00

5 $ " 7 7

11&55.$25 22713.$& 217$2.8$" 2&&37.02 3"70$.80 150"".$1$

575.5 1"132.108$5 2$022."13"& 575.5205$&858.37$85 &302."&883&

v

133"".575 &0"&.081 1$&50.2$ 172$1.22 127"$.$2

Vmax Mmax

19463.5847 24022.61

M

81$1.2&8 82"0.12&%370.$$1&5$$.8&7

3/4

3/4


81/353

Mr = X b X d

= X X 35

= X X

= Kg - m >


>


14 X b X d

fy

X 30 X 40


y

X X X 40 / 100

X X X

cm


Rcu

51.00 0.30

Doblemente Armada





Mr M act max SSA

Mr M act max SDA

51.00 0.30 1225

18742.500 24022.614 Kg - m


Asmin =

Asmin =14

4200

En esta viga se trabaja con d de

40cm

Rcu

51.00 0.30

51.00 0.30 1600

Asmin = 4 cm

As =M act

24480.000 24022.614

As =M act

0.85 0.874 4200

As =M act

0.85 0.874 4200 0.40

As =M act

1248.07

As =575.50

As = 0.46 cm

Nota: se asumira el

acero minimo en lasareas menores del

1248.07


82/353


= 12.93 cm


12.93 cm = 5

2.85 cm


4.00 cm = 22.85 cm


44 cmLd = dr = 35 cm

Ld = 12 barra 12 x 1.91 cm = 23 cm

As =9302.70

As = 7.45 cm1248.07

minomoAs =

9858.37As = 7.90 cm

1248.07

As =9544.90

As = 7.65 cm1248.07

As =16132.11

As = 12.93 cm1248.07

As =8141.30

As = 6.52 cm1248.07

As =-370.44

As = 4.00 cm1248.07

rea e acero mayor

2.85 1.91

Cabill =

s ayor

=

4.54 de 3/4

de 3/4 s asum o

2 de 3/4

s asum o

Cabilla =s m n mo

=1.40

5 de 3/4

Ld = =700

= 44 cm16


83/353

a cu o e a separac on entre ca as.



s n > c e ca cu an es r oss n < c o se ca cu an estr os

> c



= -

0.85 x 30 cm x 35 cm

= -= Kg/cm - Kg/cm

= Kg/cm2

Fc = 1.06 300 Kg/cm = Fc = 2.10 300 Kg/cm =

Comparacion 1.06 Fc

1.91 4.41 5

c .

19.08 .

Vs As Vc

c . 300

c 9.18

.n =

=19,463.58

= 19.08x x 1,020.00

Kg/cm2

0.85 x b x dr


2.10 36.37


Vs As Vc

sV max

=19,463.58 Kg

= 21.81

18.36 Kg/cmKg/cm





Vs 21.81 9.18

Vs 12.63

1.06


84/353

d 402 2

d 404 4

S = = x 40 cm = cm





2 x cm = 1.42 cm



cm

2.5 2.52.5 cm

Gancho

10

DESARROLLO.

cm

m

2.5 cm

30 cm

= = = 10.00 cm

4200

S = = = 20.00 cm

05Xd 0.50

A c =Vmax

=19,463.58

=c

=

Av 1/4" - 3/8" 3/8"

.

Area 0.71 .

Av .

Av = 0.71

# estribos

10 cm

1.50

45 cm 40.0 cm

S max =x ame ro

barra= 8 x 1.91 cm =

= 24 x

10 cm

4 4

25.0

cm

150

22.9 cm

16.04 20 cm

0.95 cm =

15.24 cm

= 1.63

2 estribos de

20.00

3/8" - 1/2"

3/8

0.95

20.00

Fy

As 3/8" 1/2" 5/8"

.



S

=


de

S max =dr

=


85/353

@ cada cm

90 cm 5.2 m 90 cm

@ c/ 10 cm

7.0 m

@ cada cm

90 cm 4.2 m 90 cm

@ c/ 10 cm

6.0 m

@ cada cm

90 cm 2.2 m 90 cm

@ c/ 10 cm

4.0 m

@ cada cm

90 cm 3.2 m 90 cm

@ c/ 10 cm

5.0 m

3/8'' 20.00

3/8''

3/8'' 20.00

3/8''

3/8'' 20.00

3/8''

3/8''

20.00 3/8''


86/353

VC-B



Ader = 5.0

Aizq = 4.0

h = 10 % * Fc =

h = 0.7 m Rma =

= m

PESO PROPIO FY =

Pp = b X h X

Pp = m X m X Kg/m

Pp = Kg/m


= Kg/m + Kg/m= Kg/m


= X + X

= Kg/m

Mmax = X L NOTA:

= X

= X

= Kg/m


Calculo de Rcu

= *=

CALCULO DE d

X b

h = 55 cm d = cm

X 5 cm

b =

VIGA DE CARGA EN LOSA DE ENTREPISO. (Tipo NERVADA)

LDesf

778

Luz mas desf 300

4303.744


4200

0.30 0.70 2500

525



asumira constante).

10

778.00 5251303.00

1.10

1303.00 4.00 5.00 1.10

6449.85 7.00

10

6449.85 49.00

10

2 2

6449.85

W'u

31604.27

0.30

Rcu 300 0.17Rcu 51

r =

d = 2065.64 30 cm

d = Mmax

Rcu

50

d = 31604.27

51 0.30


87/353

cm 50 cm


Pp = b X h X

Pp = m X m X Kg/m

Pp = Kg/m

Cu = + Peso propio

= +

= Kg Kg

kg/,2

0.5 0.5

0.00

# x= 2.1 x= 2.03 x= 2.753 x= 3.2552 x= $.23

%

235&

%

#

Ass 2 3/4 2 3/4 2

Asi 4 3/4 4 3/4 4


83$1.123 8$"2.872 1753&.07&

d = 45.45

0.30 0.55

5 $ " 7 7

2500

412.50



122$8.858 23270.&7 2227".$&&7 30"71.7& 37"05."8 15$3".2

4716.244 4717.00

4717.00

v

13"&$."$2 &2&1."71 15317.17 17""$.38 13077.70

&8&0.358 &57".33 12&8$.83 1535$."2 1&&$1.30 2358.50

58&."25 10100.33$7 &531.0182&1 1"528.0$5"1 2$"12.215 58&."3&

Vmax Mmax

19941.2965 24612.21

M

&77&.1"7 %37&.52&

3/4

3/4


88/353

Mr = X b X d

= X X 50

= X X

= Kg - m >


>

c e ca cu an es r os

s n < c o se ca cu an estr os

As =9779.17

As = 6.27 cm1560.09

As =8341.12

As = 5.35 cm1560.09

As = -379.53 As = 5.00 cm1560.09

rea e acero mayor

2.85 1.91

Cabill =s ayor

=3.72 de 3/4

de 3/4 s asum o

2 de 3/4

s asum o

Cabilla =s m n mo

=1.75

4 de 3/4

Ld = =700

= 44 cm

16

1.91 4.41 5


90/353

a cu o e es uerzo cortante e concreto.= c

= g cm

= g

a cu o e es uerzo ctuante. =

V actuante ma

ntoncess n > c



= -

0.85 x 30 cm x 50 cm

= -= Kg/cm - Kg/cm

= Kg/cm2

Fc = 1.06 300 Kg/cm =Fc = 2.10 300 Kg/cm =

Comparacion 1.06 Fc

d 502 2

d 504 4

S = = x 50 cm = cm


x S Kg x cm

x d Kg/cm x 50 cm

c . 300

c .

c 9.18

.

n ==

19,941.30= 15.64

18.36 Kg/cm

x x 1,275.00

15.64 .

Vs As Vc

Kg/cm20.85 x b x dr

Vs As Vc

s V max = 19,941.30 Kg = 15.64


2.10 36.37


S = = = 12.50 cm

4200

S = = = 25.00 cm

05Xd 0.50

Kg/cm





Vs 15.64 9.18

Vs 6.46

1.06

25.00

A c =

Vmax

=

19,941.30 25.00

Fy


91/353



2 x cm = 1.42 cm



2.5 2.52.5 cm cm

10

2.5 cm DESARROLLO.

30 cm cm

m

@ cada cm

110 cm 4.8 m cm

@ c/ 12.5 cm

7.0 m

110

3/8'' 25.00

3/8''

5/8"

Area 0.71 . .



Av .

Av = 0.71

# estribos =c

=

Av 1/4" - 3/8" 3/8"

.

= 13 cm

1.70

55 cm 50.0 cm

S max =x ame ro

barra= 8 x 1.91 cm =

= 24 x

15 cm4 4


de

S max =dr

=

cm

170

22.9 cm

16.87 20 cm

25.0

3/8

0.95 cm =

15.24 cm

= 1.67

2 estribos de

0.95

3/8" - 1/2"

As 3/8" 1/2"


92/353

@ cada cm

110 cm 3.8 m cm

@ c/ 12.5 cm

6.0 m

@ cada cm

110 cm 1.8 m cm

@ c/ 12.5 cm4.0 m

@ cada cm

110 cm 2.8 m cm

@ c/ 12.5 cm

5.0 m

3/8''

3/8'' 25.00

3/8''

110

110

110

3/8'' 25.00

3/8''

3/8'' 25.00


93/353

VC-C



Ader = 0.5

Aizq = 5.0

h = 10 % * Fc =

h = 0.7 m Rma =

= m

PESO PROPIO FY =

Pp = b X h X

Pp = m X m X Kg/m

Pp = Kg/m


= Kg/m + Kg/m= Kg/m


= X + X

= Kg/m

Mmax = X L NOTA:

= X

= X

= Kg/m


Calculo de Rcu

= *=

CALCULO DE d

X b

h = 45 cm d = cm

X 5 cm

b =

VIGA DE CARGA EN LOSA DE ENTREPISO. (Tipo NERVADA )

LDesf

778

Luz mas desf 300

4303.744


4200

0.30 0.70 2500

525



asumira constante).

10

778.00 5251303.00

1.10

1303.00 5.00 0.50 1.10

4299.90 7.00

10

4299.90 49.00

10

2 1

4299.9

W'u

21069.51

0.30

d = Mmax

Rcu

40

d = 21069.51

Rcu 300 0.17Rcu 51

51 0.30 r =

d = 1377.09 30 cm


94/353

cm 40 cm


Pp = b X h X

Pp = m X m X Kg/m

Pp = Kg/m

Cu = + Peso propio

= +

= Kg Kg

kg/,2

0.5 0.5

0.00

# x= 2.1 x= 2.03 x= 2.753 x= 3.2552 x= $.23

%

2321

%

#

Ass 2 3/4 2 3/4 2

Asi 5 3/4 5 3/4 5


&733.1017 &$2$.07

2500

337.50



d = 37.11

0.30 0.45

4641.244 4642.00

4642.00

5 $ " 7 7

12778.37 15110.$8 1&"2$.23 2321.00

1205$.1017 22&00.&" 21&22.30$7 3018$.111 37007.75 151&0.7"8

8328.315

580.25 1"2"5.250&2 2$220.87732 580.25508

v

13$7".8&83 &1$3.&338 15073."

Diseño Estructural en Concreto Armado de Una Carcel Publica (1)

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Transcript of Diseño Estructural en Concreto Armado de Una Carcel Publica (1)