PROYECTO

DISEO AVANZADO DE CONCRETO REFORZADO

Daniel Snchez Ballinas 1

1. CARACTERSTICAS GENERALES

La construccin se encuentra ubicada en la cuidad de

Villahermosa Tabasco, el cual consiste en una construccin de

tres niveles y ser destinada para uso de oficinas.

2. ESTRUCTURACIN La estructura de la construccin ser a base de marcos rgidos.

Los sistemas de pisos estarn formados: para el nivel 1 por losa

maciza; para el nivel 2 por losa aligerada y para el nivel 3 por

Losacero.

3. MATERIALES

a) Concreto

Toda la estructura (trabes, losas y columnas), se disearan para

una resistencia a la compresin del concreto de fc= 250 kg/cm2,

con un tamao mximo del agregado de 19 mm (3/4).

b) Acero de refuerzo

Para el diseo del acero de refuerzo por flexin, se considero un

valor del lmite de fluencia de fy= 4200 kg/cm2 (grado 42) para

todos los dimetros indicados, con excepcin del acero No 2

(alambrn) que ser de un fy= 2530 kg/cm2 (grado estructural).

Mientras que los prefabricados como la Malla electro soldada,

ser de un fy= 5000 kg/cm2 (grado 50).

1. DESARROLLO DEL PROYECTO

1.1. Proyecto arquitectnico


2 DANIEL SNCHEZ BALLINAS

TABLEROS EN LOSA 1

Acotacin en metros



TABLEROS EN LOSA 2

Acotacin en metros



TABLEROS EN LOSA 3

Acotacin en metros



=

3.1. Anlisis de carga

LOSA 1 (MACIZA) TABLEROS DEL II AL X

Losa (12 cm) 2400 kg/m3 x 0.12 m....288 kg/m2 Mortero inferior (1.5 cm) 1800 kg/m3 x 0.015 m....27 kg/m2 Mortero para nivelar (3 cm) 1800 kg/m3 x 0.03 m..54 kg/m2 Mortero para piso (2 cm) 1800 kg/m3 x 0.02 m..36 kg/m2 Piso.55 kg/m2 Reglamento ...40 kg/m2 Carga muerta .CM= 500 kg/m2 Carga viva mx. CV= 250 kg/m2 Carga viva inst. . CVi=180 kg/m2

CARGA EQUIVALENTE DEBIDA AL MURO DIVISORIO

EN EL TABLERO I

Tabla 1. Coeficientes para transformar cargas lineales en

equivalentes uniformes por m2.

Relacin de claros m= 1

2

0.5

0.8

1.0

Muro paralelo lado corto 1.3 1.5 1.6

Muro paralelo lado largo 1.8 1.7 1.6

MURO DE BLOCK MACIZO 10-20-40 cm

RECUBRIMIENTO CARGA (kg/m2)

CARGA (kg/m) ALTURA DE MURO (M)

2.00 2.60 MATERIAL MORTERO BLOCK MORTERO

234.00 468.00 608.4 ESPESOR 0.015 0.100 0.015

P. VOL 1800 1800 1800

W (kg/m2) 27.00 180.00 27.00



= 12

= 4

5 = 0.8

Carga equivalente uniforme = 1404 kg

20 m2 x 1.5 = 105.3 kg/m2

Datos:

a1 = 4 m

a2 = 5 m

Peso total del muro = 468 kg/m x 3 m = 1404 kg

Muro paralelo al lado corto

Coeficiente = 1.5

LOSA 1 (MACIZA) TABLERO I

Losa (12 cm) 2400 kg/m3 x 0.12 m....288 kg/m2 Mortero inferior (1.5 cm) 1800 kg/m3 x 0.015 m....27 kg/m2 Mortero para nivelar (3 cm) 1800 kg/m3 x 0.03 m..54 kg/m2 Mortero para piso (2 cm) 1800 kg/m3 x 0.02 m..36 kg/m2 Piso.55 kg/m2 Reglamento ...40 kg/m2 Carga equivalente uniforme .105.3 kg/m2 Carga muerta ....CM= 605.3 kg/m2 Carga viva mx. . CV= 250 kg/m2 Carga viva inst. . CVi=180 kg/m2

carga en volado =3122.32 kg

5.6 m2= 557.56 kg /m2

CARGA DEVIDA A LOS MUROS EN EL VOLADO.

PRETIL DE BLOCK HUECO 10-20-40 cm

RECUBRIMIENTO CARGA (kg/m2)

CARGA (kg/m)

ALTURA DE MURO (M)

1.00

MATERIAL MORTERO BLOCK MORTERO

264.00 264.00 0 ESPESOR 0.015 0.015

P. VOL 1800 1800

W (kg/m2) 27.00 210.00 27.00

MATERIAL

PESO VOL

ESPESOR CARGA ALTURA kg/m

3 m kg/m

2 2

VIDRIO 2600 0.019 49.53 99.06 KG/M

Longitud total = 8.6 m

Peso total del muro = (264 kg/m + 99.06) x 8.6 m = 3122.32 kg

a1 = 0.80 m

a2 = 7 m



LOSA 1 (MACIZA) TABLERO V VOLADO Losa (12 cm) 2400 kg/m3 x 0.12 m....288 kg/m2 Mortero inferior (1.5 cm) 1800 kg/m3 x 0.015 m....27 kg/m2 Mortero para nivelar (3 cm) 1800 kg/m3 x 0.03 m..54 kg/m2 Mortero para piso (2 cm) 1800 kg/m3 x 0.02 m..36 kg/m2 Piso.55 kg/m2 Reglamento ...40 kg/m2 Carga en volado ... 557.56 kg/m2 Carga muerta ......CM= 1057.56 kg/m2 Carga viva mx. ... CV= 250 kg/m2 Carga viva inst. .... CVi=180 kg/m2

LOSA 2 (ALIGERADA) TABLEROS I AL III

Losa aligerada232.60 kg/m2 Mortero inferior (1.5 cm) 1800 kg/m3 x 0.015 m....27 kg/m2 Mortero para nivelar (3 cm) 1800 kg/m3 x 0.03 m..54 kg/m2 Mortero para piso (2 cm) 1800 kg/m3 x 0.02 m..36 kg/m2 Piso.55 kg/m2 Reglamento ...40 kg/m2 Carga muerta .CM= 444.6 kg/m2 Carga viva mx. CV= 250 kg/m2 Carga viva inst. . CVi=180 kg/m2

LOSA 2 (ALIGERADA) TABLEROS I AL III

Losa aligerada232.60 kg/m2 Mortero inferior (1.5 cm) 1800 kg/m3 x 0.015 m....27 kg/m2 Entortado (5 cm) 1800 kg/m3 x 0.05 m..90 kg/m2 Reglamento ...40 kg/m2 Carga muerta .CM= 389.6kg/m2 Carga viva mx. CV= 100 kg/m2 Carga viva inst. . CVi=70 kg/m2

LOSA 3 (LOSACERO) TABLEROS I AL VII

Lamina.. 8 kg/m2 Concreto 2400 kg/m3 x 0.095 m3/m2...228 kg/m2 Entortado (5 cm) 1800 kg/m3 x 0.05 m.....90 kg/m2 Plafn ..20 kg/m2 Carga muerta ...CM= 386 kg/m2 Carga viva mx. ... CV= 100 kg/m2 Carga viva inst. .. CVi=70 kg/m2



TRABES SECUNDARIAS LOSA 1

SECCION PESO VOL BASE PERALTE CARGA

kg/m3 m m kg/m

20X35 2400 0.2 0.35 168

25X55 2400 0.25 0.55 330



kg/m3 m m kg/m

20X35 2400 0.2 0.35 168

25X45 2400 0.25 0.45 270

25X55 2400 0.25 0.55 330



kg/m3 m m kg/m

IR 14X34 50.6

COLUMNAS


kg/m3 m m kg/m

50X50 2400 0.5 0.5 600

50X50 2400 0.5 0.5 600

DIA 45 2400 0.45 381.70

TRABES PRINCIPALES


kg/m3 m m kg/m

3 nivel 25x50 2400 0.25 0.5 300

2 nivel 35x70 2400 0.35 0.7 588

1 nivel 40x70 2400 0.4 0.7 672

TINACO 27 KG

AGUA 1100 KG

PESO TOTAL 1127 KG

TANQUE 210 KG

GAS 1000 KG

PESO TOTAL 1210 KG

SISTEMA VIDRIO VENTANA 363.06 KG/M



4. BAJA DE CARGA



5. CALCULO DE LA FUERZA SSMICA.

NIVEL 3

ELEMENTOS QUE

INTEGRAN EL NIVEL 3

NUMERO DE VECES

CARGA BASE LARGO ALTURA PESO KG

LOSA 456.00 13 7 41496.00

TRABE SECUNDARIA

50.6 7 3 1062.60

TRABE SECUNDARIA

50.6 4 2 404.80

TRABE PRINCIPAL 300 13 2 7800.00

TRABE PRINCIPAL 300 7 3 6300.00

MURO 234.00 10 1.5 3510.00

VENTANA 49.53 34 1.5 2526.03

COLUMNA 600 1.5 4 3600.00

COL CIRCULAR 381.70 1.5 2 1145.11

PESO DEL NIVEL 3 67844.54 KG

PESO DEL NIVEL 3 67.84 TON



NIVEL 2

ELEMENTOS QUE

INTEGRAN EL NIVEL 2

NUMERO DE VECES


LOSA 624.60 13 7 56838.98 LOSA 459.60 13 5.5 32861.70 TRABE

SECUNDARIA 168 4 672.00 TRABE

SECUNDARIA 270 5.5 1485.00 TRABE

SECUNDARIA 330 12.5 4125.00 TRABE PRICIPAL 588 13 3 22932.00 TRABE PRICIPAL 588 12.5 3 22050.00 MURO 234.00 10 3.25 7605.00 VIDRIO 49.53 0.8 7 277.37 PRETIL 264.00 34 1 8976.00 VENTANA 49.53 34 1.75 2947.04 COLUMNA 600 3.25 6 11700.00 COL CIRCULAR 381.70 3.25 3 3721.61 TINACO 1127.00 TANQUE DE GAS 1210.00





NIVEL 1

ELEMENTOS QUE INTEGRAN EL NIVEL 1

NUMERO DE

VECES


LOSA 680 12.5 13 110500 TRABE SECUNDARIA 168 4 2 1344 TRABE SECUNDARIA 330 12.5 3 12375 TRABE PRICIPAL 672 13 3 26208 TRABE PRICIPAL 672 12.5 3 25200 MURO 234.00 13 3.25 42.25 PRETIL 264.00 46.6 12302.4 COLUMNA 600 3.25 6 11700 COL CIRCULAR 381.70 3.25 3 3721.6092 VOLADO 680 0.8 7 3808





NIVEL 0

ELEMENTOS QUE

INTEGRAN EL NIVEL 0

NUMERO DE VECES


MURO 234.00 10 1.75 17.50 PRETIL 264.00 45 11880.00 COLUMNA 600 1.75 6 6300.00 COL

CIRCULAR 381.70 1.75 3 2003.94





DISEO ESTRUCTURAL

DISEO DE TRABES SECUNDARIAS

Trabe secundaria en losa 1 de 4 m en eje 2 entre A y B

Datos:

fc = 250 kg/cm2

fy = 4200 kg/cm2

f*c = 0.8 fc = 0.8( 250 kg/cm2) = 200 kg/cm2

fc = 0.85 f*c = 0.85( 200 kg/cm2) =170 kg/cm2

h = 35 cm

b= 20 cm

d= 30 cm

=0.7

=

0.7 250 /2

4200 /2= 0.0026

=

6000 16000 +

= 170

4200

6000 0.85

6000 + 4200 = 0.0202

Diseo a flexin

Diagrama de momentos



Mu = 1.4 (3.26 ton-m) =4.56 ton-m

= 1 1 2

2= 1 1

2(4.56)(100)(1000)

0.9 20 302 (170)= 0.1822

=

=

0.1822(170)

4200= 0.0074

bien

As = b d = 0.0074( 20 cm)(30 cm) = 4.44 cm2

# =

=

4.44

1.98 = 2.24 3 5 8

As min = min b d = 0.0026( 20 cm)(30 cm) = 1.56 cm2

# =

=

1.56

1.27 = 1.23 2 1 2

Diseo por cortante

Diagrama de cortante

Vd = V d W = 3.26 ton 0.30m(1.63 ton/m) = 2.77 ton Vu= 1.4(2770 kg) =3878 kg

2.5 = 2.5 0.8 200 20 30 = 16,970.56

1.5 = 1.5 0.8 200 20 30 = 10,182.34

Vu < 1.5

1 =

2=

30

2= 15



2 =

0.3 =

2 0.71 (4200)

0.3 200 (20)= 70.28

=

=

2 1.27 2

20 30 = 0.0042 < 0.015

= 0.2 + 20

= 0.8 0.2 + 200.0042 200 20 30 = 1932.38

3 =

=

0.8 20.71 4200 (30)

3878 1932.38= 73.56

Rige S = 15 cm

ARMADO DE LA TRABE



Diseo de trabe secundaria en losa 1

Datos:

fc = 250 kg/cm2

fy = 4200 kg/cm2

fc = 0.85 f*c = 0.85( 200 kg/cm2) =170 kg/cm2

h = 55 cm

b= 25 cm

d= 50 cm

=0.7

=

0.7 250 /2

4200 /2= 0.0026

=

6000 16000 +

= 170

4200

6000 0.85

6000 + 4200 = 0.0202



Diseo a flexin


Mu (+) = 1.4(2.64 ton-m)= 3.70 ton-m

= 1 1 2

2= 1 1

2(3.70)(100)(1000)

0.9 25 502 (170)= 0.0394

=

=

0.0394(170)

4200= 0.0016

As = b d = 0.0026( 25 cm)(50 cm) = 3.25 cm2

# =

=

3.25

1.98 = 1.64 2 5 8

Mu (+) = 1.4(10.35 ton-m)= 14.49 ton-m

= 1 1 2

2= 1 1

2(14.49)(100)(1000)

0.9 25 502 (170)= 0.1652

=

=

0.1652 170

4200= 0.0067

bien

As = b d = 0.0067( 25 cm)(50 cm) = 8.38 cm2

As = 8.38 cm2 2(1.98 cm2) = 4.42 cm2

# =

=

4.42

1.98 = 2.25 3 5 8

Mu (-) = 1.4(12.05 ton-m)= 16.87 ton-m

= 1 1 2

2= 1 1

2(16.87)(100)(1000)

0.9 25 502 (170)= 0.1955

=

=

0.1955 170

4200= 0.0079

bien



As = b d = 0.0079( 25 cm)(50 cm) = 9.88 cm2

# =

=

9.88

1.98 = 4.99 5 5 8

Diseo por cortante


Vd = V d W = 10.75 ton 0.50m(2.58 ton/m) = 9.46 ton Vu= 1.4(9.46 ton) = 13.24 ton

2.5 = 2.5 0.8 200 25 50 = 35,355.34

1.5 = 1.5 0.8 200 25 50 = 21,213.20

Vu < 1.5

1 =

2=

50

2= 25

2 =

0.3 =

2 0.71 (4200)

0.3 200 (25)= 56.23

=

=

5 1.98 2

25 50 = 0.0079 < 0.015

= 0.2 + 20

= 0.8 0.2 + 200.0079 200 25 50 = 5068.54

3 =

=

0.8 20.71 4200 (50)

13240 5068.54= 29.19

Rige S = 25 cm



ARMADO DE LA TRABE



DISEO DE TRABE ACERO (METODO ASD)

Datos :

IR 14 x 34

Sx = 796 cm3

tw = 0.72 cm

d = 35.5 cm

Acero A36

fy = 2530 kg/cm2

Diseo a flexin

Diagrama de momento



La trabe al tener conectores de cortante, estos hacen que la trabe

se encuentre con soporte lateral completo. Y al ser compacta el

perfil el esfuerzo admisible de la trabe es:

= 0.66 = 0.66 2530

2 = 1669.8

2

Modulo de seccin requerido

=

=

6.89 100 (1000)

1669.8= 412.62 3 < Sx =796 cm3 Bien

Diseo por cortante


Esfuerzo Cortante admisible Fv= 0.4 fy = 0.4(2530 kg/cm2) = 1012 kg/cm2

Esfuerzo actuante

=

=

3.99 1000

0.72 35.5 = 156.10

2 < Fv = 1012 kg/cm 2

Bien



DISEO DE TRABES

Trabe primer nivel

DISEO A FLEXION

CM + CVMAX

DIAGRAMA DE MOMENTOS



CM + CVINT + SISMO

DIAGRAMA DE MOMENTO

Datos:

fc = 250 kg/cm2

fy = 4200 kg/cm2

f*c = 0.8 fc = 0.8( 250 kg/cm2) = 200 kg/cm2

fc = 0.85 f*c = 0.85( 200 kg/cm2) =170 kg/cm2

h = 70 cm

b= 40 cm

d= 65 cm



=0.7

=

0.7 250 /2

4200 /2= 0.0026

= 0.75

6000 16000 +

= 170

4200

6000 0.85

6000 + 4200 = 0.0152

Mu(+) = 1.4 (18.28 ton-m) = 25.59 ton-m

= 1 1 2

2= 1 1

2(25.59)(100)(1000)

0.9 40 652 (170)= . 1044

=

=

0.1044 170

4200= 0.0042

bien

As = b d = 0.0042( 40 cm)(65 cm) = 10.99 cm2

# =

=

10.99

2.85 = 3.86 4 3/4

Mu(+) = 1.1 (25.2 ton-m) = 35.28 ton-m

= 1 1 2

2= 1 1

2(35.28)(100)(1000)

0.9 40 652 (170)= 0.0060

=

=

0.1473(170)

4200= 0.0060

bien

As = b d = 0.0060( 40 cm)(65 cm) = 15.50 cm2

As = 15.50 cm2 -4(2.85cm2) = 4.10 cm2

# =

=

4.10

2.85 = 1.43 2 3/4

Mu(-) = 1.1 (24.68 ton-m) = 34.55 ton-m

= 1 1 2

2= 1 1

2(34.55)(100)(1000)

0.9 40 652 (170)

= . 1440

=

=

0.1440 170

4200= 0.0058

bien

As = b d = 0.0058( 40 cm)(65 cm) = 15.15 cm2

# =

=

15.15

2.85 = 5.32 6 3/4



Mu(-) = 1.1 (31.86 ton-m) = 44.60 ton-m

= 1 1 2

2= 1 1

2(44.60)(100)(1000)

0.9 40 652 (170)= . 1907

=

=

0.1907 170

4200= 0.0077

bien

As = b d = 0.0077( 40 cm)(65 cm) = 20.07 cm2 As= 20.07 cm2 6(2.85 cm2)= 2.97 cm2

# =

=

2.97

1.98 = 1.5 2 5/8

DISEO POR CORTANTE

CM + CVMAX




CM + CVINT + SISMO



2.5 = 2.5 0.8 200 40 65 = 73,539.11

1.5 = 1.5 0.8 200 40 65 = 44,123.46

Vu < 1.5

1 =

2=

65

2= 32.5

2 =

0.3 =

2 0.71 (4200)

0.3 200 (40)= 35.14

=

=

7 2.85 2

40 65 = 0.0077 < 0.015

= 0.2 + 20

= 0.8 0.2 + 200.0077 200 40 65 = 10,413.14

3 =

=

0.8 20.71 4200 (65)

22370 10413.14= 25.93

Rige S = 25 cm




2.5 = 2.5 0.8 200 40 65 = 73,539.11

1.5 = 1.5 0.8 200 40 65 = 44,123.46

Vu < 1.5

1 =

2=

65

2= 32.5

2 =

0.3 =

2 0.71 (4200)

0.3 200 (40)= 35.14

=

=

7 2.85 2

40 65 = 0.0077 < 0.015

= 0.2 + 20

= 0.8 0.2 + 200.0077 200 40 65 = 10,413.14

3 =

=

0.8 20.71 4200 (65)

20.06 10413.14= 32.14

Rige S = 30 cm

ARMADO DE LA TRABE



Trabe 2 nivel

DISEO A FLEXION

CM + CVMAX




CM + CVINT + SISMO


Datos:

fc = 250 kg/cm2

fy = 4200 kg/cm2

f*c = 0.8 fc = 0.8( 250 kg/cm2) = 200 kg/cm2

fc = 0.85 f*c = 0.85( 200 kg/cm2) =170 kg/cm2

h = 70 cm

b= 35 cm

d= 65 cm

=0.7

=

0.7 250 /2

4200 /2= 0.0026

= 0.75

6000 16000 +

= 170

4200

6000 0.85

6000 + 4200

= 0.0152



Mu(+) = 1.4 (16.07 ton-m) = 22.50 ton-m

= 1 1 2

2= 1 1

2(22.50)(100)(1000)

0.9 30 652 (170)= . 1049

=

=

0.1049 170

4200= 0.0042

bien

As = b d = 0.0042( 35 cm)(65 cm) = 10.99 cm2

# =

=

10.99

2.85 = 3.86 4 3/4

Mu(+) = 1.1 (18.31 ton-m) = 25.63 ton-m

= 1 1 2

2= 1 1

2(25.63)(100)(1000)

0.9 30 652 (170)= . 1206

=

=

0.1206 170

4200= 0.0049

As = b d = 0.0049( 35 cm)(65 cm) = 11.10 cm2

# =

=

11.10

2.85 = 3.90 4 3/4

Mu(-) = 1.1 (21.68 ton-m) = 30.35 ton-m

= 1 1 2

2= 1 1

2(30.35)(100)(1000)

0.9 30 652 (170)

= . 1446

=

=

0.1446 170

4200= 0.0059

bien

As = b d = 0.0059( 35 cm)(65 cm) = 13.32 cm2

# =

=

13.32

2.85 = 4.67 5 3/4

Mu(-) = 1.1 (22.46 ton-m) = 31.44 ton-m

= 1 1 2

2= 1 1

2(31.44)(100)(1000)

0.9 30 652 (170)

= . 1503

=

=

0.1503 170

4200= 0.0061

As = b d = 0.0061( 35 cm)(65 cm) = 13.84 cm2

# =

=

13.84

2.85 = 4.86 5 3/



DISEO POR CORTANTE

CM + CVMAX


CM + CVINT + SISMO




Vd = V d W = 11.73 0.65m(1.28 ton/m) = 10.90 ton Vu= 1.4(10.90 ton) = 15.26 ton

2.5 = 2.5 0.8 200 35 65 = 64,346.72

1.5 = 1.5 0.8 200 35 65 = 38,608.03

Vu < 1.5

1 =

2=

65

2= 32.5

2 =

0.3 =

2 0.71 (4200)

0.3 200 (35)= 40.16

=

=

5 2.85 2

40 65 = 0.0063 < 0.015

= 0.2 + 20

= 0.8 0.2 + 200.0063 200 35 65 = 8390.81

3 =

=

0.8 20.71 4200 (65)

15260 8390.81= 45.15

Rige S = 30 cm


2.5 = 2.5 0.8 200 35 65 = 64,346.72

1.5 = 1.5 0.8 200 35 65 = 38,608.03

Vu < 1.5

1 =

2=

65

2= 32.5

2 =

0.3 =

2 0.71 (4200)

0.3 200 (35)= 40.16

=

=

5 2.85 2

40 65 = 0.0063 < 0.015

= 0.2 + 20

= 0.8 0.2 + 200.0063 200 35 65 = 8390.81

3 =

=

0.8 20.71 4200 (65)

16460 8390.81= 38.41

Rige S = 30 cm



ARMADO DE LA TRABE



Trabe 3 nivel

DISEO A FLEXION

CM + CVMAX




CM + CVINT + SISMO

Diagrama de momento

Datos:

fc = 250 kg/cm2

fy = 4200 kg/cm2

f*c = 0.8 fc = 0.8( 250 kg/cm2) = 200 kg/cm2

fc = 0.85 f*c = 0.85( 200 kg/cm2) =170 kg/cm2

h = 50 cm

b= 25 cm

d= 45 cm

=0.7

=

0.7 250 /2

4200 /2= 0.0026

= 0.75

6000 16000 +

= 170

4200

6000 0.85

6000 + 4200

= 0.0152



Mu(+) = 1.4 (4.45 ton-m) = 6.23 ton-m

= 1 1 2

2= 1 1

2(6.23)(100)(1000)

0.9 25 452 (170)= 0.0840

=

=

0.0840 170

4200= 0.0034

bien

As = b d = 0.0034( 25 cm)(45 cm) = 3.82 cm2

# =

=

3.82

1.98= 1.93 2 5/8

Mu(+) = 1.1 (8.63 ton-m) = 12.08 ton-m

= 1 1 2

2= 1 1

2(12.08)(100)(1000)

0.9 25 452 (170)= 0.1705

=

=

0.1705 170

4200= 0.0069

As = b d = 0.0069( 25 cm)(45 cm) = 7.76 cm2 As= 7.76 cm2 2(1.98 cm2) = 3.80 cm2

# =

=

3.80

1.98 = 1.92 2 5/8

Mu(-) = 1.1 (12.10 ton-m) = 16.94 ton-m

= 1 1 2

2= 1 1

2(16.94)(100)(1000)

0.9 25 452 (170)= 0.2499

=

=

0.2499 170

4200= 0.0101

bien

As = b d = 0.0101( 25 cm)(45 cm) = 11.38 cm2

# =

=

11.38

2.85= 3.99 4 3/4

Mu(-) = 1.1 (13.58 ton-m) = 19.01 ton-m

= 1 1 2

2= 1 1

2(19.01)(100)(1000)

0.9 25 452 (170)= 0.2855

=

=

0.2855 170

4200= 0.0116

As = b d = 0.0116( 25 cm)(45 cm) = 13.05 cm2 As= 13.05 cm2 4(2.85 cm2) = 1.65 cm2

# =

=

1.65

1.27 = 1.30 2 1/2



DISEO POR CORTANTE

CM + CVMAX


CM + CVINT + SISMO





2.5 = 2.5 0.8 200 25 45 = 31,819.81

1.5 = 1.5 0.8 200 25 45 = 19,091.88

Vu < 1.5

1 =

2=

45

2= 22.5

2 =

0.3 =

2 0.71 (4200)

0.3 200 (25)= 56.23

=

=

4 2.85 2 + 2(1.272)

25 45 = 0.0124 < 0.015

= 0.2 + 20

= 0.8 0.2 + 200.0124 200 35 65 = 5702.11

Rige S = 20 cm


2.5 = 2.5 0.8 200 25 45 = 31,819.81

1.5 = 1.5 0.8 200 25 45 = 19,091.88

Vu < 1.5

1 =

2=

45

2= 22.5

2 =

0.3 =

2 0.71 (4200)

0.3 200 (25)= 56.23

=

=

4 2.85 2 + 2(1.272)

25 45 = 0.0124 < 0.015

= 0.2 + 20

= 0.8 0.2 + 200.0124 200 35 65 = 5702.11

3 =

=

0.8 20.71 4200 (45)

10580 5702.11= 43.98

Rige S = 20 cm



ARMADO DE LA TRABE



DISEO DE COLUMNAS

Cortantes de entrepiso



COLUMNAS



CARGAS AXIALES

CARGA AXIAL TOTAL = 371.71 TON UNIDAD EN TONELADAS



DISEO DE LA COLUMNA 1

FUERZAS Y MOMENTOS INTERNOS CAUSADOS POR LA

GRAVEDAD Y POR EL SISMO.

DIRECCION DESPLAZAMIENTOS (CM)

POR SISMO CM + Cmi

X 0.46 0

Y 0.17 0.01

DIRECCION X

Debido a cargas verticales

H = 3.5 m 0.7/2 =3.15 m = 315 cm

Rigidez

Kv= 2858.33

K c= 1488.10

A = 1.04

B = 0

K= 0.63

H= K H = 0.63(315 cm) = 204.75 cm

r = 0.3 (70 cm) = 21 cm

=

204.75

21= 9.75



34 121

2= 34 12

0.16

0.33= 28.18

=

204.75

21= 9.75 < 28.18

PUEDE DESPRECIARSE LOS EFECTOS DE ESBELTES

Fa = 1



Debido a fuerzas laterales

0.08(

)

0.46(2)

350 0.08(

71.07

1.1 371.71)

0.0026 0.0139

Puede despreciarse los efectos de esbeltez

DIRECCION Y

Debido a cargas verticales

H = 3.5 m 0.7/2 =3.15 m = 315 cm

Rigidez

Kv= 1633.33

K c= 1488.10

A = 1.82

B = 0

K= 0.65

H= K H = 0.65(315 cm) = 204.75 cm

r = 0.3 (70 cm) = 21 cm

=

204.75

21= 9.75

34 121

2= 34 12

1.31

3.19= 29.07

=

204.75

21= 9.75 < 29.07

PUEDE DESPRECIARSE LOS EFECTOS DE ESBELTES

Fa = 1



Debido a fuerzas laterales

0.08(

)

0.17(2)

350 0.08(

71.07

1.1 371.71)

0.0010 0.0139

Puede despreciarse los efectos de esbeltez

CARGAS DE DISEO

a) CM + CV

Pu = 1.4 (20.68) =40. 53 TON

Mx = 1.4(0.38) = 0.53 TON-m

My= 1.4(3.39) = 4.75 TON-m

a) CM + CVi + SISMO

Pu = 1.1 (19.46) = 21.41 TON

Mx = 1.1(19.37) = 21.31TON-m

My= 1.1(5.04) = 5.54 TON-m



Datos:

fc = 250 kg/cm2

fy = 4200 kg/cm2

f*c = 0.8 fc = 0.8( 250 kg/cm2) = 200 kg/cm2

fc = 0.85 f*c = 0.85( 200 kg/cm2) =170 kg/cm2

h = 50 cm

b= 50 cm

=20

= 0.004762

= 0.06

ex = ey = 0.05 (0.50)=0.025 m

Mex= Mey = 0.025(40.23) = 1.01 Ton m

Rige Mex

Mex= Mey = 0.025(21.41) = 0.54 Ton m

a) CM + CV

eje x

=

1.0140.530.50

= 0.050

=

45

50= 0.9

= 0.01

=

=

0.01(4200)

170= 0.25

K= 0.72

PUx= 0.72( 0.8)(50)(50)(250)= 360,000 kg= 360 ton

eje y

=

4.7540.530.50

= 0.23

=

45

50= 0.9

= 0.01

=

=

0.01(4200)

170= 0.25

K= 0.5

PUx= 0.5( 0.8)(50)(50)(250)= 250,000 kg= 250 ton

Po=0.8(( 8x5.07)(4200)+(50x50)(170))= 476,281.60 kg

Po= 476.28 ton



= 1

360+

1

250

1

476.28 1

= 213.76 > 40.53



COLUMNA CIRCULAR

CARGAS DE DISEO

Pu = 1.1 (31.28) =34.41 TON

Mx = 1.1(6.76) = 7.44 TON-m

My= 1.1(15.05) = 16.56TON-m

= 7.442 + 16.562 = 18.15

d= 45- 2(5)= 35 CM

=

35

45= 0.78 0.8

=

18.1534.410.45

= 1.17

= 34410

0.8 4545 250 = 0.08

q= 0

=20

= 0.004762

As= 0.004762(1590.43)=7.57 cm2

# =

=

7.57

1.27= 5.96 6 1/2

Zunchos

Ag = 1590.43 cm2

Ac = 1194.59 cm2

s= 0.45(1590.43/1194.59 -1)(250/4200)=0.0089

0.12 fc/fy = 0.12(250/4200)=0.0071

=4

s ds=

4(0.71)

0.0089(39)= 8.18

S mx. = 7 cm



Diseo de losa 1

Tablero critico I

Mu=1.4(419)(855.3)(10-4

)(4)=200.68 kg/m

=0.7

=

0.7 250 /2

4200 /2= 0.0026

= 0.75

6000 16000 +

= 170

4200

6000 0.85

6000 + 4200 = 0.0152

= 1 1 2

2= 1 1

2(200.68)(100)

0.9 100 102 (170)= . 0132

=

=

0.0132 170

4200= 0.0005

As = b d = 0.0026( 100 cm)(10 cm) = 2.60 cm2

=

100 =

0.71

2.60= 27.31 25

Diseo de losa 2

Tablero critico 2

Mu=1.4(506)( 694.60)(10-4

)(4.5)(0.72)= 45.55 kg/m

=0.7

=

0.7 250 /2

4200 /2= 0.0026

= 0.75

6000 16000 +

= 170

4200

6000 0.85

6000 + 4200 = 0.0152

= 1 1 2

2= 1 1

2(45.55)(100)

0.9 12 162 (170)= 0.0436

=

=

0.0436 170

4200= 0.0018

As = b d = 0.0026( 12 cm)(16 cm) = 0.50 cm2

# =

=

0.50

0.71= 0.70 2 3/8



DISEO DE LOS PERNOS DE CORTANTES

Claro de 7 m

Separacin entre trabes = 2.25 m

IR 14 x 34

A= 64. 5 cm

bf= 17. 1 cm

tf = 1.16 cm

capa de compresin = 6 cm

Hs= 10.12 cm

Dimetro del perno = 7/8 =2.22 cm

Wr= 17.41 cm

q=7600 kg

= 0.85

1

17.41

6.35

10.12

6.35 1 = 1.38

F= 1

qlosacero= 1(7600 kg)=7600 kg

be1= 700/4= 175 cm

be2= 17.1+ 207.9=225 cm

be3=17.1+2(8x6)=113.1 cm

be =113.1 cm

Ac=113.1 cm(6cm)=678.6 m2

Vh1= 0.85(250)(678.6)=144,202.50 kg

Vh2= 64.5(3515/2)=113358.75 kg

Vh=113358.75 kg

Np=113358.75/7600= 14 .92

15 pernos para un claro de 3.5 metros

Separacin de pernos=350/14.92=23.45 cm

Usar dos pernos a cada 31.66 cm

PROYECTO

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