CONCRETO ARMADO ANALISIS 11

CONCRETO ARMADO VI SEMESTRE

I.S.T.P "JOSÉ CARLOS MARIATEGUI"

DISEÑOS DE : •

VS EN EL SEGUNDO NIVEL

•

COLUMNA DEL CUARTO PISO

•

VP EN ELQUINTO PISO

•

COLUMNA Y ZAPATA EN EL SEGUNDO PISO

•

LOSA EN EL PRIMER PISO

•

COLUMNA Y ZAPATA EN EL TERCER PISO

DATOS GENERALES UBICACIÓN :ANCASH USO : OFICINAS

1 er piso = 2 er piso =

4.00

Nº DE PISO : 5

3 er piso = 4 er piso =

3.60

5 er piso =

3.20

3.80 3.40

PLANO A DESARROLLAR Ancho Tributario 5.90

VS

VS

VS

VS

VS

SENTID O DEL ALIGERADO

7.50 VP

H

COL. EN EL 2º PISO

G

VS 5.50 VP

ZAPATA

VP

VP

VP

7.60 VP

VP EN EL 5º PISO

VS

E

VS

D

VP

6.50 VP

LOSA EN EL 1º PISO

VS

F

COLUMNA EN EL 3º PISO

5.20 VP

ZAPATA

VS

B

4.60

PLACA

4.70 VP

PLACA

C

4.50 VP

VS EN 2º PISO

COLUM 4º PISO

VS

A 7.30

1

DOCENTE : ING. JUAN LAJO RODRIGUEZ

4.50

2

5.60

3

5.30

4

5.60

5

6

ALUMNO :ROBERTO FLORES RAMIREZ



DISEÑO DE VS EN EL SEGUNDO NIVEL DATOS : 500 Kg/m2 salas de archivo 100 Kg/m2 2

210 Kg/m 4200 Kg/m2 20 cm

F'c = Fy = ESPESOR DE LOSA =

0.5

VIGA SECUNDARIA = RECUBRIMIENTO =

x

0.3

d

b

m

30

6 cm 300 Kg/m2 3 2400 Kg/m =

Pp de losa de 20cm = γ del concreto =

h

44

OFICINAS 50

S/C = PISO T =

2.4

ton/m3 28.30

4.60

PLACA

PLACA

4.70 VP

B 4.50 VP

VS EN 2º PISO

Ancho tributario

VS

C

VS

A 7.30

4.50

1

5.60

2

5.30

3

4

5.60

5

6

METRADO DE CARGAS Se realiza por ancho tributario

AT = AT =

CARGA MUERTA :

4.60 4.30

0.30

4.30 =

1.29 ton/m 0.36 ton/m

CM Pp losa

=

0.300

Pp viga

=

Pp piso T

=

0.30 x 0.10 x

ton/m2 0.50 x

x 2.4

4.30

= CM

CARGA VIVA :

CV

= =

0.43 ton/m 2.08 ton/m

Se realiza con el ancho tributario sin descontar la viga CV = S/C x AT 0.50 x

4.60 =

2.30 ton/m CV

CALCULO DEL WU

=

2.30 ton/m

RNC Wu= 1.5 (CM)+1.8(CV) Wu= 7.26 ton/m

PARA EL CALCULO DE " q " KU =

Ø

0.9

q

KU =

189

q 189

q

189

q

111.5 q2

-

111.5 q2

-

111.51 q2

-

q

=

q F'c ( 1-0.59 q )

KU =

-

+ KU = +

111.5 KU

1.695 q

+

1.695

1.695

-

210 ( 1-0.59 q ) 111.5 q2

111.5 2

-

KU 111.5

=

0

4

KU 111.5

0 =

0

2

para tomar el menor





DIAGRAMA A ANALIZAR

7.26 7.3

4.50 m

m

1/16

1/10 1/16

7.30

Mu =

5.90

24.18

4.500 25.27

41.63

9.19

43.51

ρ = (q x f`c )

0.01301

fy

AS= ρ x b x d

0.01374

17.18

18.13

6 Ø de 3/4

7 Ø de 3/4 4 Ø de 1''

0.227

0.01014

0.141 0.164

0.01134

0.00707

0.00627

13.39 9.33

4 Ø de 3/4 2 Ø de 3/4

24.50 28.00

0.125

0.00707

5.83

37.13

0.203

11.25

20.30

14.23 16.26

21.95

0.141

0.00442

21.56

33.75

0.00852

0.01538

5.60 5.60

12.75

24.50

0.088

5.45

19.60

0.170

0.308

1/16 1/14

5.30

14.23

15.82

0.275

q = 0.260

1/10

5.45

28.98

47.58

5.60 m

1/16

5.60 16.83

27.63

KU = Mu/bd2

1/11 1/16

5.05

7.30

Promedio

5.30 m

m

1/11

1/14

Luces

5.6

0.00820

14.97

9.33

8.28 5 Ø de 3/4

2 Ø de 1''

10.83 5 Ø de 3/4

4 Ø de 3/4

3 Ø de 3/4

2 Ø de 1''

uniformizando 2 Ø de 3/4

3 Ø de 3/4

4 Ø de 3/4

1 Ø de 3/4

1 Ø de 3/4

4 Ø de 1''















4 Ø de 3/4



DISEÑO DE VP EN EL QUINTO NIVEL DATOS :

100

F'c =

210

Kg/m

2

Kg/m

2

4200

ESPESOR DE LOSA =

20

cm

VIGA PRINCIPAL =

0.7

x

RECUBRIMIENTO =

6 cm

0.35

300

Kg/m2

γ del concreto =

2400

Kg/m3

B

4.70

OFICINAS

h

d

b

m

35

Pp de losa de 20cm =

4.50

salas de archivo

64

PISO T =

Kg/m2 70

Kg/m

Fy =

A

2

500

S/C =

=

2.4

C

ton/m3

D

5.20

E

7.60

6.50

F

G

5.50

H

7.50

5

5.45

5.30

4

VP EN EL 5º PISO

5.60

PLACA

6 METRADO DE CARGAS Se realiza por ancho tributario

CARGA MUERTA :

AT =

5.45

AT =

5.10

x

5.10

0.35 CARGA VIVA :

CM

CV Se realiza con el ancho tributario sin descontar la viga

Pp losa

=

0.300

ton/m2

Pp viga

=

0.35

x

0.70

Pp piso T

=

0.10

x

5.10

x

2.4

CM


-

=

1.53

ton/m

=

0.588 ton/m

=

0.51

ton/m

=

2.63

ton/m

CV = S/C x AT

0.50

x

5.45

=

2.73

ton/m CV

=

2.73

ton/m




PARA EL CALCULO DE " q "

CALCULO DEL WU

RNC Wu= Wu=

1.5 (CM)+1.8(CV) 8.847

KU

=

Ø

q

KU

F'c ( 1-0.59 q ) q2

KU

ton/m

KU 111.51 q

=

0.9

q

=

189

q

2

-

111.51 q2

q

189

q

q

+

=

111.51 q2 +

KU

=

0

q

-

1.695

=

2

-

KU

4

=

111.51

KU +

111.51

0

111.51 1.695

189

111.51

1.695

( 1-0.59 q )

210 -

-

2

0

111.51

para tomar el menor DIAGRAMA A ANALIZAR

8.847 4.5

m

4.70

1/16

m

5.2

1/10

Promedio Mu =

11.20

18.72

KU = Mu/bd2

7.81

13.06 8.93

q=

0.0021

fy

AS= ρ x b x d

15.12

0.072

0.042

0.084

0.0036

4.75

0.0042 0.0023

8.08 5.45

4 Ø de 1/2

9.43 5.19

4 Ø de 5/8 2 Ø de 3/4


0.0066 0.0029 14.77 6.40

5 Ø de 5/8 2 Ø de 3/4

5 Ø de 3/4 1 Ø de 3/4 + 2 Ø de 5/8

0.0076

14.23

0.0062 0.0072

16.97

13.87

7.19 5 Ø de 3/4

2 Ø de 1''

0.124 0.143

0.0032

10.21 7 Ø de 3/4

5 Ø de 3/4

0.151

0.0064

18.29

21.70 24.79

0.064

0.0046

14.28

26.07

0.127

0.0082

31.10 35.55

11.67

0.091

0.0064

37.38

22.22

0.163

7.50 7.50

16.73

16.30

0.127

6.50

31.85

27.88

0.132 0.057

1/16

5.50

23.36

22.28

m

1/14

6.00

39.97

22.98

7.50

1/10

6.50

31.94

10.43

0.046

0.0024

32.94

m

1/16

7.05 7.60

14.95

8.52

0.049 ρ = (q x f`c )

21.68

5.50

1/16

6.40 5.20

12.21

m

1/10

1/16

4.95 4.700

12.80

6.50

1/11

1/16

4.60 4.50

m

1/11

1/16

4.50

7.60

1/10

1/14

Luces

m

16.05 6 Ø de 3/4

3 Ø de 3/4

5 Ø de 3/4 6 Ø de 3/4



Ancho tributario


ton/m





para tomar el menor

5 Ø de 3/4





ANALISIS DE DISEÑO DE COLUMNAS - ESQUINERA

3.65

COLUMNA ESQUINERA :

3.65

B

del 4º PISO

h

I

4.00

50

II

3.80

40

III

3.60

x

70

VS = 30

x

C4 = 40

x

Kg/m2

IV

3.40

f'c = 210

Kg/m2

V

3.20

γ c = 2.4

2.25

fy = 4200

VP

Nº

VP = 35

4.50

DATOS

2.25

Nº PISOS

Ton/m3

losa = 20 cm PISO T =

Kg/m2

100

s/c =

300

s/c =

500

Kg/m2

Pp de losa de 20cm

# de veces =

5 pisos

# de pisos =

1 pisos

A

salas de archivo

kg/cm2

-

VS

1

OFICINAS

2

7.30

4 pisos

METRADOS A

vp

=

(AT

y

-

b

col A vs ) x = (ATx b vp -

AREA VP

= ( 2.25

-

0.40 ) X

0.35

=

AREA VS

= ( 3.65

-

0.40 ) X

0.3

=

0.40

X

0.40

AREA COL. =

b

col = col)xb A vp

L

X

A

0.65 m2 0.98 m2 0.160 m2 1.78 m2

AREA TOTAL =

3.65

X

2.25

=

AREA LOSA. =

8.21

-

1.78

=

AT =

8.21

A LOSA = 6.430

CALCULO DE CARGAS

a) CARGAS VIVAS CV

cv =

cv =

S/C x ( AreaT - Area COL ) X # piso

cv =

0.5

8.21

-

=

0.10

X(

8.21

-

0.16 ) X

=

6.430

x

0.300

x

1

=

0.65

x

0.70

x

2.40

x

1

=

0.98

x

0.50

x

2.40

x

=

0.40

x

0.40

x

3.20

x

X(

0.16 ) X

1

4.026 ton

b) CARGAS MUERTAS CM

PPpt = S/C x (AreaT - AreaCol) x # de piso PP loza = A losa x S/C x # PP vp = Area vp x hvp x γ c' x # de piso PP vs = Area vs x hvs x γc' # de piso 5º piso PP col = b x t x h piso x γc'

PP pt

=

0.805 ton

PP L

=

1.929 ton

PP vs

=

1.088 ton

1

PP vp

=

1.17 ton

2.40

PP col

=

1.229 ton

CM

=

6.221 ton

1

CARGAS ULTIMA PU =

1.5 CM + 1.8 CV

PU =(

1.5

PU =

16.579


x

6.221 ) + ( 1.8

X

4.026 )

ton




PARA UNA COLUMNA CON ESTRIBOS

REFUERZO LONGITUDINAL

PU = Ø x 0.80 x ( 0.85 x f'c ( Ag - As ) + As x fy )

-0.016 -0.016

16.579 =

0.70

x (

0.85

X

16.58

=

0.56

x ( 0.179 x (

0.16

- As ) +

16.58

=

0.56

x ( 0.029

-

0.179 As +

16.58

=

0.56

x ( 0.029

+

4.022 As )

+

x

16.58

=

0.016

+

16.58

=

2.252 As

+

16.58

= As

7.354

= As

0.80

0.210 x ( 0.16

- As ) + As

x

4.200

4.200 As )

4.200 As )

2.252 As

2.252

As =

7.35

cm2

ADOPTAMOS =

4 Ø 5/8"

REFUERZO TRANSVERSAL

* POR CONFINAMIENTO ( NORMA 2.4.6 )

LONGITUD =

t=

0.40

m

h/6 =

0.53

m

@

0.10

si h =

3.20

m

Ø

3/8"

m

* ZONAS NO CONFINADAS ( R.C.N.)

Ø

3/8"

16 Ø L = 16

x

0.953

=

15.25 cm

48 Ø e = 48

x

0.953

=

45.74 cm

0.953

b

Para diseño tomamos el menor

= 40 cm

0.40

0.40

resto

1

@

0.05

2

@

0.10

2

@

0.15

@

0.20

4 Ø 5/8"


Ø 3/8"




ANALISIS DE DISEÑO DE COLUMNA PERIMETRAL

2.80

COLUMNA ESQUINERA :

2.80

E

del 3º PISO

h

I

4.00

VS = 30 x 50 C4 = 40 x 40 fy = 4200 Kg/m2 f'c = 210 Kg/m2

II III IV

3.80 3.60 3.40

V

3.20

γ c = 2.4

3.80

Nº 70

D 5.2

Ton/m3


Kg/m2

100

s/c =

300

s/c =

500

6.40

x

2.60

VP = 35

7.6

DATOS

VP

Nº PISOS

Kg/m2

C

Pp de losa de 20cm

kg/cm2

# de veces =

5 pisos

# de pisos =

2 pisos

salas de archivo -

VS

5

OFICINAS

6

5.60

3 pisos

METRADOS A vp = (AT y - b col ) x b vp

A vs = (ATx - b col)xb vp

AREA VP

= ( 6.40

-

0.40 ) X

0.35

=

AREA VS

= ( 2.80

-

0.40 ) X

0.3

=

X

0.40

AREA COL. =

0.40

A col = L X A

2.10 m2 0.72 m2 0.160 m2 2.98 m2

AREA TOTAL =

6.40

X

2.80

=

AT =

17.92

AREA LOSA. = 17.92

-

2.98

=

A LOSA =

14.940

CALCULO DE CARGAS

a) CARGAS VIVAS CV

cv =

cv =

0.5

X ( 17.92

cv =

17.8

ton

-

0.16

X(

)X

2



PPpt = S/C x (AreaT - AreaCol) x # de piso

=

17.92

-

0.16

PP loza = A losa x S/C x #

= 14.940 x

0.300

x

2

=

2.10

x

0.70

x

2.40

x

2

PP vp = Area vp x hvp x γ c' x # de piso PP vs = Area vs x hvs x γc' # de piso PP col = b x t x h piso x γc'

0.10

)X

2

PP pt

=

3.552 ton

PP L

=

8.964 ton

PP vs

=

7.056 ton

=

0.72

x

0.50

x

2.40

x

2

PP vp

=

1.728 ton

4º piso =

0.40

x

0.40

x

3.40

x

2.40

PP col

=

1.306 ton

5º piso =

0.40

x

0.40

x

3.20

x

2.40

PP col

=

1.229 ton

=

23.83 ton

CM

CARGAS ULTIMA PU =

1.5 CM + 1.8 CV

PU =(

1.5

PU =

67.720


x

23.83 ) + ( 1.8

X

17.76 )

ton






PU = Ø x 0.80 x ( 0.85 x f'c ( Ag - As ) + As x fy ) 67.720 =

0.70

x (

0.85

X

67.72

=

0.56

x ( 0.179 x (

0.16

- As ) +

67.72

=

0.56

x ( 0.029

-

0.179 As +

67.72

=

0.56

x ( 0.029

+

4.022 As )

+

x

67.72

=

0.016

-0.016

+

67.72

=

2.252 As

-0.016

+

67.72

= As

30.06

= As

0.80

0.210 x (

0.16

4.200 As

-

As ) + As

x

4.200

)

4.200 As )

2.252 As

2.252

As =

30.06 cm2

ADOPTAMOS =

6 Ø DE 1"



LONGITUD =

t=

0.40

m

h/6 =

0.53

m

@

0.10

si h =

3.20

m

Ø

3/8"

m


Ø

3/8"

16 Ø L = 16

x

0.953

=

15.25 cm

48 Ø e = 48

x

0.953

=

45.74 cm

0.953

b


= 40 cm

0.40

0.40

resto

1

@

0.05

2

@

0.10

2

@

0.15

@

0.20

6 Ø DE 1"


Ø 3/8"


ANALISIS DE DISEÑO DE COLUMNA CENTRICA

5.05

H

del 2º PISO

50

II

3.80

40

III

3.60

fy = 4200

Kg/m2

IV

3.40

f'c =

210

Kg/m2

V

3.20

γc =

2.4

Ton/m3

VS = 30

x x

C4 =

40

2.25

2.80

G

5.5

4.00

70

3.75

h

I

x

2.75

Nº

VP = 35

6.50

DATOS

VP

Nº PISOS

7.5

COLUMNA ESQUINERA :


Kg/m2

100

s/c =

300

s/c =

500

Kg/m

2

F

Pp de losa de 20cm

kg/cm2

VS

2

OFICINAS

3

4.5

5.6

4

salas de archivo

# de veces = 5 pisos

-

2 pisos

# de pisos = 3 pisos

METRADOS A

vp

=

(AT

y

-

b

colA )vsx= b(ATx vp

AREA VP

= (

6.50

AREA VS

= (

AREA COL. =

-

-

0.40

)X

0.35

=

5.05

-

0.40

)X

0.3

=

0.40

X

0.40

b

col)xb

2.14

m2

1.40

m2

A col = vp

L

X

A

0.160 m2 3.69

m2

2

AREA TOTAL =

6.50

X

5.05

=

AT =

32.83

m

AREA LOSA. =

32.83

-

3.69

=

A LOSA =

29.135

m2

CALCULO DE CARGAS

a) CARGAS VIVAS CV

cv =

cv =

0.5

X ( 32.83

cv =

49.0

ton

-

0.16

)X

3



PPpt = S/C x (AreaT - AreaCol) x # de piso

=

0.10

PP loza = A losa x S/C x #

=

29.135

PP vp = Area vp x hvp x γ c' x # de piso

=

PP vs = Area vs x hvs x γc' # de piso PP col = b x t x h piso x γc'

1.5

PU =

171.776

x

26.222 ton

3

PP vs

=

10.76 ton

x

3

PP vp

=

5.022 ton

x

3.60

x

2.40

PP col

=

1.3824 ton

x

3.40

x

2.40

PP col

=

1.3056 ton

x

3.20

x

2.40

PP col

=

1.2288 ton

CM

=

55.72 ton

x

3

2.14

x

0.70

x

2.40

x

=

1.40

x

0.50

x

2.40

3º piso =

0.40

x

0.40

4º piso =

0.40

x

0.40

5º piso =

0.40

x

0.40

55.72 ) + ( ton

9.7995 ton

=

0.16

0.300

1.5 CM + 1.8 CV

PU =(

=

PP L

-

x

CARGAS ULTIMA PU =

PP pt

X ( 32.83

1.8

X

48.998 )

)X

3



PU = Ø x 0.80 x ( 0.85 x f'c ( Ag - As ) + As x fy ) ###### =

0.70

x

0.80

x (

0.85

X

171.78

=

0.56

x(

0.179 x (

0.16

- As ) +

171.78

=

0.56

x ( 0.0286

171.78

=

0.56

x ( 0.0286

171.78

=

0.016

+ As

-0.016

+

171.78

=

2.252

-0.016

+

171.78

=

As

76.269

=

As

2.252

-

0.179

As

+

4.022

As )

0.210 x (

+

0.16

- As ) + As

x 4.200

4.200 As )

4.200 As )

As

2.252

As =

76.27 cm2

ADOPTAMOS =

4 Ø 1 1/4" + 8 Ø 1''



t=

0.40

m

h/6 =

0.53

m

si h =

3.20

LONGITUD =

m

@

0.10

Ø

3/8"

m


Ø

16 Ø L =

16

x

0.953

=

15.248 cm

3/8"

48 Ø e =

48

x

0.953

=

45.744 cm

0.953

b

=


40 cm

0.40

0.40

resto

4 Ø 1 1/4" + 8 Ø 1'' Ø 3/8"

1

@

0.05

2

@

0.10

2

@

0.15

@

0.20

CONCRETO ARMADO ANALISIS 11

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