3. DISEÑO - VIGAS EJE X-X - PRIMER BLOQUE.xlsx

DISEÑO DE REFUERZO LONGITUDINAL POR FLEXION - VA-101 1. DATOS DE DISEÑO: F´c = fy =

210.00 Kg/cm² 4200 Kg/cm2

Ø barra = Ø estribo = recub. = d=

1/2 '' h=

3/8 '' 4.00 cm cm 54.41 cm

60.00 cm

b =

30.00 cm

2. MOMENTOS MAXIMOS - SAP 2000 (Ton (Ton .m) Mmax (-)

9.72 T-m

6.74 T-m

Mmax (+)

5.80 T-m

6.01 T-m

9.29 T-m

8.90 T-m

7.00 T-m

6.60 T-m

2

1

10.50 T-m

8.70 T-m

6.80 T-m

7.78 T-m

3

8.63 T-m

10.84 T-m

7.86 T-m

6.97 T-m

4

9.76 T-m

10.10 T-m

7.53 T-m

7.69 T-m

8.23 T-m

4.95 T-m 6

5

3. CALCULO DEL AREA DE ACERO MINIM O: ρ min =

0.002

As min =

3.94 cm²

2 Φ 5/8

Usar

As =

3.96 cm²

4. DETERMINACION DEL ACERO MAXIMO ρb = As max =

ρmax =

0.0217 26.55 cm²

5. CÁLCULO DEL ACERO 1 SUP 3.84 cm a= 4.90 cm² As = 1 INF 2.26 cm a= 2.88 cm² As =

2 SUP a= As =

3.67 cm 4.67 cm² 2.74 cm 3.49 cm²

2.88 cm²

0.0163

3 SUP a= As =

2 INF a= As =

6. AREA DE ACERO EN LOS APOYOS (cm2) 4.90 cm² SUP

INF

0.75. ρb

4.16 cm 5.31 cm²

4 SUP a= As =

3 INF a= As =

3.39 cm²

a= As =

3.94 cm2

2 Φ 5/8

EJE

As NECES.

As Min

4.30 cm 5.49 cm²

6 SUP a= As =

5 INF 3.08 cm

3.93 cm²

a= As =

2.95 cm 3.76 cm²

7 SUP

4.00 cm 5.10 cm²

a= As =

6 INF a= As =

3.85 cm²

a= As =

5.31 cm²

4.37 cm²

5.49 cm²

3.49 cm²

3.39 cm²

3.93 cm²

3.76 cm²

3

As =

3.96 cm2

COMBINACION DE ACERO

As PROPORC.

VERIF.

4

3.52 cm 4.49 cm²

7 INF 3.02 cm

4.67 cm²

7. COMBINACIONES DE ACERO PARA As NECESARIO As Min. =

a= As =

4 INF 2.66 cm

2

1

5 SUP

3.43 cm 4.37 cm²

5

2.27 cm 2.89 cm²

5.10 cm²

3.85 cm² 6

1 SUP

4.90 cm²

2 SUP 3 SUP

4.67 cm² 5.31 cm²

4 SUP

4.37 cm²

5 SUP 6 SUP 7 SUP 1 INF 2 INF 3 INF 4 INF 5 INF 6 INF 7 INF

5.49 cm² 5.10 cm² 4.49 cm² 2.88 cm² 3.49 cm² 3.39 cm² 3.93 cm² 3.76 cm² 3.85 cm² 2.89 cm²

Escoger Combinacion Escoger Combinacion Escoger Combinacion

1 Φ 1/2 + 2 Φ 5/8

5.25 cm²

Ok

1 Φ 5/8 + 1 Φ 3/4 2 Φ 1/2 + 1 Φ 3/4

4.83 cm² 5.43 cm²

Ok Ok

Escoger Combinacion Escoger Combinacion Escoger Combinacion Escoger Combinacion Colocar As Min Colocar As Min Colocar As Min Colocar As Min Colocar As Min Colocar As Min Colocar As Min

1 Φ 5/8 + 1 Φ 3/4

4.83 cm²

Ok

2 Φ 3/4 1 Φ 1/2 + 2 Φ 5/8 1 Φ 5/8 + 1 Φ 3/4 2 Φ 5/8 2 Φ 5/8 2 Φ 5/8 2 Φ 5/8 2 Φ 5/8 2 Φ 5/8 2 Φ 5/8


Ok Ok Ok Ok Ok Ok Ok Ok Ok Ok

Falta As 1. Falta acero 2. El acero proporcioando no cumple con el As min

8. DISPOSICION FINAL DEL ACERO SUP

1 Φ 1/2 + 2 Φ 5/8

INF

2 Φ 5/8

1 Φ 5/8 + 1 Φ 3/4

2 Φ 5/8

1

2

2 Φ 1/2 + 1 Φ 3/4

1 Φ 5/8 + 1 Φ 3/4

2 Φ 5/8

2 Φ 5/8

3

2 Φ 3/4

1 Φ 1/2 + 2 Φ 51

2 Φ 5/8 5

4

UNIFORMIZANDO ACEROS - AGREGANDO BASTONES EJE

TENEMOS

As NECES.

As UNIFORME

As UNIF.

As FALTA

BASTON

As BASTÓN

1 SUP 2 SUP 3 SUP 4 SUP 5 SUP 6 SUP 7 SUP 1 INF 2 INF 3 INF 4 INF 5 INF 6 INF 7 INF

1 Φ 1/2 + 2 Φ 5/8 1 Φ 5/8 + 1 Φ 3/4 2 Φ 1/2 + 1 Φ 3/4 1 Φ 5/8 + 1 Φ 3/4 2 Φ 3/4 1 Φ 1/2 + 2 Φ 5/8 1 Φ 5/8 + 1 Φ 3/4 2 Φ 5/8 2 Φ 5/8 2 Φ 5/8 2 Φ 5/8 2 Φ 5/8 2 Φ 5/8 2 Φ 5/8

4.90 cm² 4.67 cm² 5.31 cm² 4.37 cm² 5.49 cm² 5.10 cm² 4.49 cm² 2.88 cm² 3.49 cm² 3.39 cm² 3.93 cm² 3.76 cm² 3.85 cm² 2.89 cm²

2 Φ 5/8 2 Φ 5/8 2 Φ 5/8 2 Φ 5/8 2 Φ 5/8 2 Φ 5/8 2 Φ 5/8 2 Φ 5/8 2 Φ 5/8 2 Φ 5/8 2 Φ 5/8 2 Φ 5/8 2 Φ 5/8 2 Φ 5/8


0.94 cm² 0.71 cm² 1.35 cm² 0.41 cm² 1.53 cm² 1.14 cm² 0.53 cm² No Falta No Falta No Falta No Falta No Falta No Falta No Falta

1 Φ 1/2 1 Φ 1/2 1 Φ 5/8 1 Φ 1/2 1 Φ 5/8 1 Φ 1/2 1 Φ 1/2

1.29 cm² 1.29 cm² 1.98 cm² 1.29 cm² 1.98 cm² 1.29 cm² 1.29 cm²

As PROPORC.

VERIF.


Ok Ok Ok Ok Ok Ok Ok Ok Ok Ok Ok Ok Ok Ok

2 Φ 5/8 6

8.94 Ton-m

5.83 Ton-m 7

4.49 cm²

2.89 cm² 7

Φ 5/8 + 1 Φ 3/4

2 Φ 5/8 7


Ø barra = Ø estribo = recub. = d=

210.00 Kg/cm² 4200 Kg/cm2

1/2 '' 3/8 '' 4.00 cm 54.41 cm

h=

60.00 cm

b =

30.00 cm

2. MOMENTOS MAXIMOS - SAP 2000 (Ton .m) Mmax (-)

12.13 T-m

9.43 T-m

Mmax (+)

9.01 T-m

8.34 T-m

10.62 T-m

11.72 T-m

9.19 T-m

8.46 T-m

2

1

12.00 T-m

11.30 T-m

9.12 T-m

9.57 T-m

3

10.50 T-m

12.75 T-m

10.35 T-m

8.86 T-m

4

11.94 T-m

12.24 T-m

9.69 T-m

9.90 T-m

10.40 T-m

7.48 T-m 6

5


0.002

As min =

3.94 cm²

2 Φ 5/8

Usar

As =

3.96 cm²


ρmax =

0.0217 26.55 cm²


2 SUP a= As =

4.21 cm 5.37 cm² 3.63 cm 4.62 cm²

4.53 cm²

0.0163

3 SUP a= As =

2 INF a= As =


INF

0.75. ρb

4.79 cm 6.10 cm²

4 SUP a= As =

3 INF a= As =

3.60 cm 4.59 cm²

5.73 cm² 4.10 cm 5.23 cm²

a= As =

4 INF a= As =

3.94 cm2

2 Φ 5/8

EJE

As NECES.

As Min

6.50 cm²

6 SUP a= As =

5 INF 3.83 cm 4.88 cm²

7 SUP 4.89 cm

6.23 cm²

a= As =

6 INF a= As =

3.92 cm 4.99 cm²

5.73 cm²

6.50 cm²

4.62 cm²

4.59 cm²

5.23 cm²

4.88 cm²

3

As =

3.96 cm2


As PROPORC.

VERIF.

4

4.85 cm 6.18 cm²

7 INF a= As =

6.10 cm²


5.10 cm

5.37 cm²

2

1

5 SUP a= As =

4.49 cm

5

3.28 cm 4.18 cm²

6.23 cm²

4.99 cm² 6

1 SUP

6.17 cm²

2 SUP 3 SUP

5.37 cm² 6.10 cm²

4 SUP

5.73 cm²



Escoger Combinacion Escoger Combinacion Escoger Combinacion

2 Φ 1/2 + 2 Φ 5/8

6.54 cm²

Ok

2 Φ 1/2 + 1 Φ 3/4 2 Φ 1/2 + 2 Φ 5/8

5.43 cm² 6.54 cm²

Ok Ok

Escoger Combinacion Escoger Combinacion Escoger Combinacion Escoger Combinacion Escoger Combinacion Escoger Combinacion Escoger Combinacion Escoger Combinacion Escoger Combinacion Escoger Combinacion Escoger Combinacion

3 Φ 1/2 + 1 Φ 5/8

5.85 cm²

Ok

1 Φ 1/2 + 2 Φ 3/4 2 Φ 1/2 + 2 Φ 5/8 2 Φ 1/2 + 2 Φ 5/8 2 Φ 1/2 + 1 Φ 5/8 1 Φ 5/8 + 1 Φ 3/4 1 Φ 5/8 + 1 Φ 3/4 2 Φ 3/4 1 Φ 1/2 + 2 Φ 5/8 1 Φ 1/2 + 2 Φ 5/8 2 Φ 1/2 + 1 Φ 5/8





2 Φ 1/2 + 2 Φ 5/8

INF

2 Φ 1/2 + 1 Φ 5/8

2 Φ 1/2 + 1 Φ 3/4

1 Φ 5/8 + 1 Φ 3/4

1

2

2 Φ 1/2 + 2 Φ 5/8

3 Φ 1/2 + 1 Φ 5/8

1 Φ 5/8 + 1 Φ 3/4

2 Φ 3/4

3

1 Φ 1/2 + 2 Φ 3/4

1 Φ 1/2 + 2 Φ 5/8 5

4

UNIFORMIZANDO ACEROS - AGREGANDO BASTONES EJE

TENEMOS

As NECES.

As UNIFORME

As UNIF.

As FALTA

BASTON

As BASTÓN

As PROPORC.

VERIF.


2 Φ 1/2 + 2 Φ 5/8 2 Φ 1/2 + 1 Φ 3/4 2 Φ 1/2 + 2 Φ 5/8 3 Φ 1/2 + 1 Φ 5/8 1 Φ 1/2 + 2 Φ 3/4 2 Φ 1/2 + 2 Φ 5/8 2 Φ 1/2 + 2 Φ 5/8 2 Φ 1/2 + 1 Φ 5/8 1 Φ 5/8 + 1 Φ 3/4 1 Φ 5/8 + 1 Φ 3/4 2 Φ 3/4 1 Φ 1/2 + 2 Φ 5/8 1 Φ 1/2 + 2 Φ 5/8 2 Φ 1/2 + 1 Φ 5/8


2 Φ 5/8 2 Φ 5/8 2 Φ 5/8 2 Φ 5/8 2 Φ 5/8 2 Φ 5/8 2 Φ 5/8 2 Φ 5/8 2 Φ 5/8 2 Φ 5/8 2 Φ 5/8 2 Φ 5/8 2 Φ 5/8 2 Φ 5/8



2 Φ 1/2 1 Φ 5/8 2 Φ 1/2 1 Φ 5/8 2 Φ 1/2 2 Φ 1/2 2 Φ 1/2 1 Φ 1/2 1 Φ 1/2 1 Φ 1/2 1 Φ 1/2 1 Φ 1/2 1 Φ 1/2 1 Φ 1/2




2 Φ 1/2 + 2 Φ 5

1 Φ 1/2 + 2 Φ 5/8 6

12.14 Ton-m

8.34 Ton-m 7

6.18 cm²

4.18 cm² 7

Φ 1/2 + 2 Φ 5/8

Φ 1/2 + 1 Φ 5/8 7


Ø barra = Ø estribo =

210.00 Kg/cm² 4200 Kg/cm2

recub. = d=

1/2 '' 3/8 '' 4.00 cm 24.41 cm

h=

30.00 cm

b =

30.00 cm


1.90 T-m

1.20 T-m

Mmax (+)

1.00 T-m

0.89 T-m

1.08 T-m

1.86 T-m

0.47 T-m

0.50 T-m

2

1

3

3. CALCULO DEL AREA DE ACERO MINIMO: ρ min = As min =

0.002 1.77 cm²

2 Φ 1/2

Usar

As =

2.58 cm²


ρmax =

0.0217 11.91 cm²


2 SUP a= As =

1.04 cm 1.33 cm² 0.77 cm 0.98 cm²

1.10 cm²

0.0163

3 SUP a= As =

2 INF a= As =


INF

0.75. ρb

1.64 cm 2.09 cm²

3 INF a= As =

0.43 cm 0.55 cm²

1.33 cm²

2.09 cm²

0.98 cm²

0.55 cm² 3

2

1


1.77 cm2

2 Φ 1/2

EJE

As NECES.

As Min

As =

2.58 cm2


As PROPORC.

VERIF.

1 SUP

2.13 cm²

2 SUP 3 SUP 1 INF 2 INF 3 INF

1.33 cm² 2.09 cm² 1.10 cm² 0.98 cm² 0.55 cm²

Colocar As Min Colocar As Min Colocar As Min Colocar As Min Colocar As Min Colocar As Min

2 Φ 1/2

2.58 cm²

Ok

2 Φ 1/2 2 Φ 1/2 2 Φ 1/2 2 Φ 1/2 2 Φ 1/2

2.58 cm² 2.58 cm² 2.58 cm² 2.58 cm² 2.58 cm²

Ok Ok Ok Ok Ok



2 Φ 1/2

INF

2 Φ 1/2

2 Φ 1/2

2 Φ 1/2

2 Φ 1/2

1

2 Φ 1/2

2

3

UNIFORMIZANDO ACEROS - AGREGANDO B ASTONES EJE

TENEMOS

As NECES.

As UNIFORME

As UNIF.

As FALTA

1 SUP 2 SUP 3 SUP 1 INF 2 INF 3 INF

2 Φ 1/2 2 Φ 1/2 2 Φ 1/2 2 Φ 1/2 2 Φ 1/2 2 Φ 1/2

2.13 cm² 1.33 cm² 2.09 cm² 1.10 cm² 0.98 cm² 0.55 cm²

2 Φ 1/2 2 Φ 1/2 2 Φ 1/2 2 Φ 1/2 2 Φ 1/2 2 Φ 1/2

2.58 cm² 2.58 cm² 2.58 cm² 2.58 cm² 2.58 cm² 2.58 cm²

No Falta No Falta No Falta No Falta No Falta No Falta

BASTON

As BASTÓN

As PROPORC.

VERIF.

2.58 cm² 2.58 cm² 2.58 cm² 2.58 cm² 2.58 cm² 2.58 cm²

Ok Ok Ok Ok Ok Ok


Ø barra =

210.00 Kg/cm² 4200 Kg/cm2

Ø estribo = recub. = d=

1/2 '' h=

3/8 '' 4.00 cm 44.41 cm

50.00 cm

b =

30.00 cm


2.29 T-m

1.78 T-m

Mmax (+)

1.31 T-m

1.25 T-m

2.48 T-m

3.52 T-m

2.81 T-m

1.68 T-m

2

1

2.96 T-m

3.14 T-m

2.33 T-m

2.29 T-m

3

2.28 T-m

4.25 T-m

3.24 T-m

1.71 T-m

4

2.75 T-m

3.14 T-m

2.21 T-m

2.24 T-m

2.27 T-m

2.04 T-m 6

5


0.002

As min =

3.22 cm²

3 Φ 1/2

Usar

As =

3.87 cm²


ρmax =

0.0217 21.67 cm²


2 SUP a= As =

1.17 cm 1.50 cm² 1.33 cm 1.70 cm²

0.79 cm²

0.0163

3 SUP a= As =

2 INF a= As =


INF

0.75. ρb

1.68 cm 2.14 cm²

4 SUP a= As =

3 INF a= As =

a= As =

1.54 cm

a= As =

4 INF 1.10 cm

1.41 cm²

a= As =

3.22 cm2

3 Φ 1/2

EJE

As NECES.

As Min

6 SUP a= As =

5 INF 1.96 cm²

1.04 cm 1.33 cm²

7 SUP

1.49 cm 1.90 cm²

a= As =

6 INF a= As =

1.35 cm²

a= As =

1.90 cm²

2.59 cm²

1.70 cm²

1.41 cm²

1.96 cm²

1.33 cm²

3

As =

3.87 cm2


As PROPORC.

VERIF.

4

1.68 cm 2.14 cm²

7 INF 1.06 cm

2.14 cm²


2.03 cm 2.59 cm²

1.50 cm²

2

1

5 SUP

1.49 cm 1.90 cm²

5

0.57 cm 0.73 cm²

1.90 cm²

1.35 cm² 6

1 SUP

1.38 cm²

2 SUP 3 SUP

1.50 cm² 2.14 cm²

4 SUP

1.90 cm²



Colocar As Min Colocar As Min Colocar As Min

3 Φ 1/2

3.87 cm²

Ok

3 Φ 1/2 3 Φ 1/2

3.87 cm² 3.87 cm²

Ok Ok

Colocar As Min Colocar As Min Colocar As Min Colocar As Min Colocar As Min Colocar As Min Colocar As Min Colocar As Min Colocar As Min Colocar As Min Colocar As Min

3 Φ 1/2

3.87 cm²

Ok

3 Φ 1/2 3 Φ 1/2 3 Φ 1/2 3 Φ 1/2 3 Φ 1/2 3 Φ 1/2 3 Φ 1/2 3 Φ 1/2 3 Φ 1/2 3 Φ 1/2





3 Φ 1/2

INF

3 Φ 1/2

3 Φ 1/2

3 Φ 1/2

1

2

3 Φ 1/2

3 Φ 1/2

3 Φ 1/2

3 Φ 1/2

3

3 Φ 1/2

3 Φ 1/2

3 Φ 1/2 5

4

UNIFORMIZANDO ACEROS - AGREGANDO B ASTONES EJE

TENEMOS

As NECES.

As UNIFORME

As UNIF.

As FALTA


3 Φ 1/2 3 Φ 1/2 3 Φ 1/2 3 Φ 1/2 3 Φ 1/2 3 Φ 1/2 3 Φ 1/2 3 Φ 1/2 3 Φ 1/2 3 Φ 1/2 3 Φ 1/2 3 Φ 1/2 3 Φ 1/2 3 Φ 1/2


3 Φ 1/2 3 Φ 1/2 3 Φ 1/2 3 Φ 1/2 3 Φ 1/2 3 Φ 1/2 3 Φ 1/2 3 Φ 1/2 3 Φ 1/2 3 Φ 1/2 3 Φ 1/2 3 Φ 1/2 3 Φ 1/2 3 Φ 1/2


No Falta No Falta No Falta No Falta No Falta No Falta No Falta No Falta No Falta No Falta No Falta No Falta No Falta No Falta

BASTON

As BASTÓN

As PROPORC.

VERIF.



3 Φ 1/2 6

3.52 Ton-m

1.21 Ton-m 7

2.14 cm²

0.73 cm² 7

3 Φ 1/2

3 Φ 1/2 7

COMBINACIONES DE ACEROS COMERCIALES

1/2 - 3/8"

Area (cm2)

b min (cm)

1/2 - 3/4"

Area (cm2)

b min (cm)

Peso

Area

2 Φ 3/8

1.420

14.34

1 Φ 1/2 + 1 Φ 3/4

4.140

15.62

ACEROS COMERCIALES DIAMETRO

BARRA N°

pulg

cm

Kg/m

cm2

1 Φ 1/2 + 1 Φ 3/8

2.000

14.66

2 Φ 1/2 + 1 Φ 3/4

5.430

19.43

3

1 Φ 3/8

0.95

0.559

0.71

3 Φ 3/8

2.130

17.83

2 Φ 3/4

5.700

16.26

4

1 Φ 1/2

1.27

0.993

1.29

2 Φ 1/2

2.580

14.98

1 Φ 1/2 + 2 Φ 3/4

6.990

20.07

5

1 Φ 5/8

1.59

1.552

1.98

1 Φ 1/2 + 2 Φ 3/8

2.710

18.15

3 Φ 3/4

8.550

20.71

6

1 Φ 3/4

1.91

2.235

2.85

4 Φ 3/8

2.840

21.32

2 Φ 1/2 + 2 Φ 3/4

8.280

23.88

7

1 Φ 7/8

2.22

3.042

3.88

2 Φ 1/2 + 1 Φ 3/8

3.290

18.47

4 Φ 3/4

11.400

25.16

8

1Φ1

2.54

3.973

5.1

3 Φ 1/2

3.870

18.79

9

1 Φ 1 1/8

2.86

5.028

6.45

2 Φ 1/2 + 2 Φ 3/8

4.000

21.96

5/8 - 3/4"

Area (cm2)

b min (cm)

10

1 Φ 1 1/4

3.18

6.207

8.19

3 Φ 1/2 + 1 Φ 3/8

4.580

22.28

1 Φ 5/8 + 1 Φ 3/4

4.830

15.94

11

1 Φ 1 3/8

3.49

7.511

9.58

4 Φ 1/2

5.160

22.60

2 Φ 5/8 + 1 Φ 3/4

6.810

20.07

12

1 Φ 1 1/2

3.81

8.938

11.4

1 Φ 5/8 + 2 Φ 3/4

7.680

20.39

COMBINACIONES RECOMENDADAS

1/2 - 5/8"

Area (cm2)

b min (cm)

3 Φ 5/8 + 1 Φ 3/4

8.790

24.200

1 Φ 1/2 + 1 Φ 5/8

3.270

15.30

2 Φ 5/8 + 2 Φ 3/4

9.660

24.520

3.960

15.62

1 Φ 5/8 + 3 Φ 3/4

10.530

24.840

4.560

19.11

1/2 - 3/8"

1/2 - 5/8"

1/2 - 3/4"

Evitando tener diametros

2 Φ 5/8

5/8 - 3/4"

5/8 - 1"

5/8 - 3/4"

excesivamente diferentes

2 Φ 1/2 + 1 Φ 5/8 1 Φ 1/2 + 2 Φ 5/8

5.250

19.43

5/8 - 1"

Area (cm2)

b min (cm)

5/8 - 3/4"

Area (cm2)

b min (cm)

3 Φ 1/2 + 1 Φ 5/8

5.850

22.92

1 Φ 1 + 1 Φ 5/8

7.080

16.57

1 Φ 3/4 + 1 Φ 1

7.950

16.89

3 Φ 5/8

5.940

19.75

2Φ1

10.200

17.52

1 Φ 1 + 2 Φ 3/4

10.800

21.34

2 Φ 1/2 + 2 Φ 5/8

6.540

23.24

2 Φ 1+ 1 Φ 5/8

12.180

21.65

7.230

23.56

2 Φ 1+ 2 Φ 5/8

14.160

25.78

7.920

23.88

3Φ1

15.300

22.60

2 Φ 1 + 1 Φ 3/4

13.050

21.97

1 Φ 1/2 + 3 Φ 5/8

2 Φ 1+ 2 Φ 3/4

15.900

26.42

4 Φ 5/8

3. DISEÑO - VIGAS EJE X-X - PRIMER BLOQUE.xlsx

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