Abacos Para Columnas

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DIAGRAMAS DE INTERACCION Pu - Mu A. Columnas Armadura Bordes Extremos fy = 420 MPa (1 - 16) 1 . f'c = 20 MPa γ = 0.8 2 . f'c = 25 MPa γ = 0.8 3 . f'c = 30 MPa γ = 0.8 4 . f'c = 35 MPa γ = 0.8 5 . f'c = 40 MPa γ = 0.8 6 . f'c = 45 MPa γ = 0.8 7 . f'c = 50 MPa γ = 0.8 8 . f'c = 55 MPa γ = 0.8 9 . f'c = 20 MPa γ = 0.9 10 . f'c = 25 MPa γ = 0.9 11 . f'c = 30 MPa γ = 0.9 12 . f'c = 35 MPa γ = 0.9 13 . f'c = 40 MPa γ = 0.9 14 . f'c = 45 MPa γ = 0.9 15 . f'c = 50 MPa γ = 0.9 16 . f'c = 55 MPa γ = 0.9 B. Columnas Armadura Perimetral fy = 420 MPa (17 - 32) 17 . f'c = 20 MPa γ = 0.8 18 . f'c = 25 MPa γ = 0.8 19 . f'c = 30 MPa γ = 0.8 20 . f'c = 35 MPa γ = 0.8 21 . f'c = 40 MPa γ = 0.8 22 . f'c = 45 MPa γ = 0.8 23 . f'c = 50 MPa γ = 0.8 24 . f'c = 55 MPa γ = 0.8 25 . f'c = 20 MPa γ = 0.9 26 . f'c = 25 MPa γ = 0.9 27 . f'c = 30 MPa γ = 0.9 28 . f'c = 35 MPa γ = 0.9 29 . f'c = 40 MPa γ = 0.9 30 . f'c = 45 MPa γ = 0.9 31 . f'c = 50 MPa γ = 0.9 32 . f'c = 55 MPa γ = 0.9

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Transcript of Abacos Para Columnas

DIAGRAMAS DE INTERACCION Pu - MuA. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Columnas Armadura Bordes Extremos fy = 420 MPa (1 - 16) = 0.8 f'c = 20 MPa = 0.8 f'c = 25 MPa = 0.8 f'c = 30 MPa = 0.8 f'c = 35 MPa = 0.8 f'c = 40 MPa = 0.8 f'c = 45 MPa = 0.8 f'c = 50 MPa = 0.8 f'c = 55 MPa f'c = 20 MPa f'c = 25 MPa f'c = 30 MPa f'c = 35 MPa f'c = 40 MPa f'c = 45 MPa f'c = 50 MPa f'c = 55 MPa = 0.9 = 0.9 = 0.9 = 0.9 = 0.9 = 0.9 = 0.9 = 0.9

. . . . . . . . . . . . . . . .

B. 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

. . . . . . . . . . . . . . . .

Columnas Armadura Perimetral fy = 420 MPa (17 - 32) = 0.8 f'c = 20 MPa = 0.8 f'c = 25 MPa = 0.8 f'c = 30 MPa = 0.8 f'c = 35 MPa = 0.8 f'c = 40 MPa = 0.8 f'c = 45 MPa = 0.8 f'c = 50 MPa = 0.8 f'c = 55 MPa f'c = 20 MPa f'c = 25 MPa f'c = 30 MPa f'c = 35 MPa f'c = 40 MPa f'c = 45 MPa f'c = 50 MPa f'c = 55 MPa = 0.9 = 0.9 = 0.9 = 0.9 = 0.9 = 0.9 = 0.9 = 0.9

C. 33 34 35 36 37 38 39 40

. . . . . . . .

Columnas Armadura Lateral fy = 420 MPa (33 - 40) = 0.8 f'c = 20 MPa = 0.8 f'c = 25 MPa = 0.8 f'c = 30 MPa = 0.8 f'c = 35 MPa f'c = 20 MPa f'c = 25 MPa f'c = 30 MPa f'c = 35 MPa = 0.9 = 0.9 = 0.9 = 0.9

D. 41 42 43 44 45 46 47 48

. . . . . . . .

Columnas Armadura Bordes Extremos fy = 280 MPa (41 - 48) = 0.8 f'c = 20 MPa = 0.8 f'c = 25 MPa = 0.8 f'c = 30 MPa = 0.8 f'c = 35 MPa f'c = 20 MPa f'c = 25 MPa f'c = 30 MPa f'c = 35 MPa = 0.9 = 0.9 = 0.9 = 0.9

E. 49 50 51 52 53 54 55 56

. . . . . . . .

Columnas Armadura Perimetral fy = 280 MPa (49 - 56) = 0.8 f'c = 20 MPa = 0.8 f'c = 25 MPa = 0.8 f'c = 30 MPa = 0.8 f'c = 35 MPa f'c = 20 MPa f'c = 25 MPa f'c = 30 MPa f'c = 35 MPa = 0.9 = 0.9 = 0.9 = 0.9

F. 57 58 59 60

. . . .

Columnas Armadura Lateral fy = 280 MPa (57 - 64) = 0.8 f'c = 20 MPa = 0.8 f'c = 25 MPa = 0.8 f'c = 30 MPa = 0.8 f'c = 35 MPa

61 62 63 64

. . . .

f'c = 20 MPa f'c = 25 MPa f'c = 30 MPa f'c = 35 MPa

= 0.9 = 0.9 = 0.9 = 0.9

G. 65 66 67 68 69 70 71 72

. . . . . . . .

Muros Armadura Uniformemente Distribuida fy = 420 MPa (65 - 72) = 1.0 f'c = 20 MPa = 1.0 f'c = 25 MPa = 1.0 f'c = 30 MPa = 1.0 f'c = 35 MPa = 1.0 f'c = 40 MPa = 1.0 f'c = 45 MPa = 1.0 f'c = 50 MPa = 1.0 f'c = 55 MPa

H. 73 74 75 76 77 78 79 80 . . . . . . . .

Muros Armadura Concentrada en Extremos w= 0.0025 fy = 420 MPa (73 - 80) = 0.9 f'c = 20 MPa = 0.9 f'c = 25 MPa = 0.9 f'c = 30 MPa = 0.9 f'c = 35 MPa = 0.9 f'c = 40 MPa = 0.9 f'c = 45 MPa = 0.9 f'c = 50 MPa = 0.9 f'c = 55 MPa

I. 81 82 83 84 85 86 87 88 . . . . . . . .

Muros Armadura Concentrada en Extremos w= 0.0050 fy = 420 MPa (81 - 88) = 0.9 f'c = 20 MPa = 0.9 f'c = 25 MPa = 0.9 f'c = 30 MPa = 0.9 f'c = 35 MPa = 0.9 f'c = 40 MPa = 0.9 f'c = 45 MPa = 0.9 f'c = 50 MPa = 0.9 f'c = 55 MPa

1- Diagrama de Interaccin Pu - Mu Columnas Armadura en Bordes Extremos1.4

g = 8%1.2

e/h = 0.1

0.2

0.3

0.4

h h b

7% 6% 0.5 fs = 0

1

5% 4%

e

Pu

Pu / (f'c Ag)

0.8

3% 2%

0.6

1% 1.0

fc = 20 MPa fy = 420 MPa = 0.8

0.4

fs = fy0.2

2.0

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Pu / (f'c Ag) * e/h

2- Diagrama de Interaccin Pu - Mu Columnas Armadura en Bordes Extremos1.2

g = 8% 7%1

e/h = 0.1

h 0.2 0.3 0.4 0.5 b h

6% 5%0.8

fs = 0 e

Pu

4% 3%

Pu / (f'c Ag)

0.6

2% 1% 1.0

fc = 25 MPa fy = 420 MPa = 0.8

0.4

fs = fy0.2

2.0

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Pu / (f'c Ag) * e/h

3- Diagrama de Interaccin Pu - Mu Columnas Armadura en Bordes Extremos1.2

e/h = 0.1 g = 8% 7% 6%0.8

0.2

0.3

h 0.4 b h

1

0.5 fs = 0 e

Pu

5% 4%

Pu / (f'c Ag)

3%0.6

2% 1% 1.0

fc = 30 MPa fy = 420 MPa = 0.8

0.4

fs = fy0.2

2.0

0 0 0.1 0.2 0.3 Pu / (f'c Ag) * e/h 0.4 0.5 0.6

4- Diagrama de Interaccin Pu - Mu Columnas Armadura en Bordes Extremos1

g = 8% 7%0.8

e/h = 0.1 0.2 0.3 0.4 b fs = 0

h h

6% 5% 4% 3% 0.5

e

Pu

0.6 Pu / (f'c Ag)

2% 1%

0.4

fc = 35 MPa fy = 420 MPa = 0.81.0 fs = fy

0.2

2.0

0 0 0.1 0.2 Pu / (f'c Ag) * e/h 0.3 0.4 0.5

5- Diagrama de Interaccin Pu - Mu Columnas Armadura en Bordes Extremos1

e/h = 0.1 0.2 g = 8%0.8

h 0.3 b 0.4 fs = 0 0.5 e Pu h

7% 6% 5% 4% 3% 2% 1%

0.6 Pu / (f'c Ag)

0.4

fc = 40 MPa fy = 420 MPa = 0.81.0 fs = fy

0.2

2.0

0 0 0.1 0.2 Pu / (f'c Ag) * e/h 0.3 0.4

6- Diagrama de Interaccin Pu - Mu Columnas Armadura en Bordes Extremos1

h e/h = 0.1 0.2 0.3 b 0.4 e fs = 0 0.5 Pu h

0.8

g = 8% 7% 6% 5% 4%

0.6 Pu / (f'c Ag)

3% 2% 1%

0.4

fc = 45 MPa fy = 420 MPa = 0.81.0 fs = fy

0.2

2.0

0 0 0.1 0.2 Pu / (f'c Ag) * e/h 0.3 0.4

7- Diagrama de Interaccin Pu - Mu Columnas Armadura en Bordes Extremos1

h e/h = 0.1 h 0.2 0.3 b

0.8

g = 8% 7% 6% 5% 4% 3% 2% 1% 0.4 fs = 0 0.5 e Pu

0.6 Pu / (f'c Ag)

0.4

fc = 50 MPa fy = 420 MPa = 0.81.0

0.2

fs = fy 2.0

0 0 0.1 0.2 Pu / (f'c Ag) * e/h 0.3 0.4

8- Diagrama de Interaccin Pu - Mu Columnas Armadura en Bordes Extremos1

h h e/h = 0.1 0.2 0.3 b

0.8

g = 8% 7% 6% 5% 4% 3% 2% 1% 0.4 e Pu

0.6 Pu / (f'c Ag)

fs = 0

0.5

0.4

fc = 55 MPa fy = 420 MPa = 0.81.0 fs = fy 2.0

0.2

0 0 0.1 0.2 Pu / (f'c Ag) * e/h 0.3 0.4

9- Diagrama de Interaccin Pu - Mu Columnas Armadura en Bordes Extremos1.4

g = 8%1.2

e/h = 0.1

0.2

0.3

0.4 0.5 b

h h

7% 6%

1

5% 4%

fs = 0 e

Pu

Pu / (f'c Ag)

0.8

3% 2%

0.6

1%

1.0

fc = 20 MPa fy = 420 MPa = 0.9

0.4

fs = fy0.2

2.0

0 0 0.1 0.2 0.3 0.4 Pu / (f'c Ag) * e/h 0.5 0.6 0.7 0.8

10- Diagrama de Interaccin Pu - Mu Columnas Armadura en Bordes Extremos1.4

e/h = 0.11.2

0.2

0.3

0.4

h h b

g = 8%1

7% 6% 5% fs = 0

0.5 e Pu

Pu / (f'c Ag)

0.8

4% 3%

0.6

2% 1% 1.0

fc = 25 MPa fy = 420 MPa = 0.9

0.4

fs = fy0.2

2.0

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Pu / (f'c Ag) * e/h

11- Diagrama de Interaccin Pu - Mu Columnas Armadura en Bordes Extremos1.2

e/h = 0.1 g = 8% 7% 6%0.8

0.2

0.3

0.4

h h b

1

0.5 fs = 0 e Pu

5% 4%

Pu / (f'c Ag)

3%0.6

2% 1% 1.0 fs = fy

fc = 30 MPa fy = 420 MPa = 0.9

0.4

2.00.2

0 0 0.1 0.2 0.3 Pu / (f'c Ag) * e/h 0.4 0.5 0.6

12- Diagrama de Interaccin Pu - Mu Columnas Armadura en Bordes Extremos1

g = 8% 7%0.8

e/h = 0.1 0.2 0.3 0.4 0.5 b fs = 0

h h

6% 5% 4%

e

Pu

0.6 Pu / (f'c Ag)

3% 2% 1% 1.0

0.4

fc = 35 MPa fy = 420 MPa = 0.9

fs = fy0.2

2.0

0 0 0.1 0.2 0.3 Pu / (f'c Ag) * e/h 0.4 0.5 0.6

13- Diagrama de Interaccin Pu - Mu Columnas Armadura en Bordes Extremos1

h e/h = 0.1 g = 8% 0.2 0.3 0.4 b h

0.8

7% 6% 5% 4% 3% 2% 1% fs = 0 0.5

e

Pu

0.6 Pu / (f'c Ag)

0.4

fc = 40 MPa fy = 420 MPa = 0.91.0 fs = fy

0.2

2.0

0 0 0.1 0.2 Pu / (f'c Ag) * e/h 0.3 0.4 0.5

14- Diagrama de Interaccin Pu - Mu Columnas Armadura en Bordes Extremos1

h e/h = 0.1 0.2 0.3 0.4 g = 8% 7% 6% 5% 4% 3% 2% 1% fs = 0 b h

0.8

0.5

e

Pu

0.6 Pu / (f'c Ag)

0.4

fc = 45 MPa fy = 420 MPa = 0.91.0 fs = fy

0.2

2.0

0 0 0.1 0.2 Pu / (f'c Ag) * e/h 0.3 0.4 0.5

15- Diagrama de Interaccin Pu - Mu Columnas Armadura en Bordes Extremos1

h e/h = 0.1 0.2 0.3 b h

0.8

0.6 Pu / (f'c Ag)

g = 8% 7% 6% 5% 4% 3% 2% 1%

0.4 e fs = 0 0.5 Pu

0.4

fc = 50 MPa fy = 420 MPa = 0.91.0 fs = fy

0.2

2.0

0 0 0.1 0.2 Pu / (f'c Ag) * e/h 0.3 0.4

16- Diagrama de Interaccin Pu - Mu Columnas Armadura en Bordes Extremos1

h h e/h = 0.1 0.2 0.3 b

0.8

g = 8% 7% 6% 5% 4% 3% 2% 1%

0.4 e

Pu

0.6 Pu / (f'c Ag)

fs = 0

0.5

0.4

fc = 55 MPa fy = 420 MPa = 0.91.0 fs = fy

0.2

2.0

0 0 0.1 0.2 Pu / (f'c Ag) * e/h 0.3 0.4

17- Diagrama de Interaccin Pu - Mu Columnas Armadura Perimetral1.4

g = 8%1.2

e/h = 0.1

0.2 0.3 b fs = 0

h h

7% 6%

1

5% 0.4 4%

e

Pu

Pu / (f'c Ag)

0.8

3% 2%

0.5

0.6

1%

fc = 20 MPa fy = 420 MPa = 0.81.0 fs = fy

0.4

0.2

2.0

0 0 0.1 0.2 Pu / (f'c Ag) * e/h 0.3 0.4 0.5

18- Diagrama de Interaccin Pu - Mu Columnas Armadura Perimetral1.4

e/h = 0.11.2

h 0.2 0.3 b h

g = 8%1

7% 6% 5% fs = 0 0.4 e

Pu

Pu / (f'c Ag)

0.8

4% 3% 0.5

0.6

2% 1%

fc = 25 MPa fy = 420 MPa = 0.81.0

0.4

fs = fy0.2

2.0

0 0 0.1 0.2 Pu / (f'c Ag) * e/h 0.3 0.4 0.5

19- Diagrama de Interaccin Pu - Mu Columnas Armadura Perimetral1.2

h e/h = 0.1 0.2 0.3 b h

1

g = 8% 7% 6% fs = 0

0.8

5% 4% 0.4

e

Pu

Pu / (f'c Ag)

3%0.6

2% 1%

0.5

fc = 30 MPa fy = 420 MPa = 0.8

0.4

fs = fy0.2

1.0

2.0

0 0 0.1 0.2 Pu / (f'c Ag) * e/h 0.3 0.4

20- Diagrama de Interaccin Pu - Mu Columnas Armadura Perimetral1.2

h e/h = 0.1 0.2 0.3 g = 8% 7% 6% 5% 4% 3% e fs = 0 0.4 Pu b h

1

0.8

Pu / (f'c Ag)

0.6

0.5

2% 1%

fc = 35 MPa fy = 420 MPa = 0.81.0 fs = fy

0.4

0.2

2.0

0 0 0.1 0.2 Pu / (f'c Ag) * e/h 0.3 0.4

21- Diagrama de Interaccin Pu - Mu Columnas Armadura Perimetral1

h e/h = 0.1 g = 8% 0.2 0.3 b 0.4 fs = 0 e 0.5 Pu h

0.8

7% 6% 5% 4% 3% 2% 1%

0.6 Pu / (f'c Ag)

0.4

fc = 40 MPa fy = 420 MPa = 0.81.0

fs = fy0.2

2.0

0 0 0.1 0.2 Pu / (f'c Ag) * e/h 0.3 0.4

22- Diagrama de Interaccin Pu - Mu Columnas Armadura Perimetral1

h e/h = 0.1 g = 8% 7% 6% 5% 4% 3% 2% 1% fs = 0 0.4 0.3 e Pu 0.2 b h

0.8

0.6 Pu / (f'c Ag)

0.50.4

fc = 45 MPa fy = 420 MPa = 0.8

fs = fy0.2

1.0

2.0

0 0 0.1 Pu / (f'c Ag) * e/h 0.2 0.3

23- Diagrama de Interaccin Pu - Mu Columnas Armadura Perimetral1

h h e/h = 0.1 0.2 b

0.8

g = 8% 7% 6% 5% 4% 3% 2% 1% 0.3 e fs = 0 0.4 Pu

0.6 Pu / (f'c Ag)

0.50.4

fc = 50 MPa fy = 420 MPa = 0.8

fs = fy0.2

1.0

2.00 0 0.1 Pu / (f'c Ag) * e/h 0.2 0.3

24- Diagrama de Interaccin Pu - Mu Columnas Armadura Perimetral1

h h e/h = 0.1 0.2 b

0.8

g = 8% 7% 6% 5% 4% 3% 2% 1%

0.3 e Pu

0.6 Pu / (f'c Ag)

fs = 0

0.4

0.50.4

fc = 55 MPa fy = 420 MPa = 0.8

0.2

fs = fy

1.0

2.0

0 0 0.1 Pu / (f'c Ag) * e/h 0.2 0.3

25- Diagrama de Interaccin Pu - Mu Columnas Armadura Perimetral1.4

g = 8%1.2

e/h = 0.1

0.2

0.3

h h b

7% 6% fs = 0 0.4

1

5% 4% 0.5

e

Pu

Pu / (f'c Ag)

0.8

3% 2%

0.6

1%

fc = 20 MPa fy = 420 MPa = 0.91.0 fs = fy 2.0

0.4

0.2

0 0 0.1 0.2 0.3 Pu / (f'c Ag) * e/h 0.4 0.5 0.6

26- Diagrama de Interaccin Pu - Mu Columnas Armadura Perimetral1.4

e/h = 0.11.2

0.2 0.3

h h b

g = 8% 7%1

6% 5%

fs = 0 0.4

e

Pu

Pu / (f'c Ag)

0.8

4% 3% 0.5

0.6

2% 1%

fc = 25 MPa fy = 420 MPa = 0.91.0 fs = fy

0.4

0.2

2.0

0 0 0.1 0.2 Pu / (f'c Ag) * e/h 0.3 0.4 0.5

27- Diagrama de Interaccin Pu - Mu Columnas Armadura Perimetral1.2

h e/h = 0.1 g = 8% 7% 6% fs = 0 e 0.5 0.4 Pu 0.2 0.3 b h

1

0.8

5% 4%

Pu / (f'c Ag)

3%0.6

2% 1%

fc = 30 MPa fy = 420 MPa = 0.9fs = fy 1.0

0.4

0.2

2.0

0 0 0.1 0.2 Pu / (f'c Ag) * e/h 0.3 0.4 0.5

28- Diagrama de Interaccin Pu - Mu Columnas Armadura Perimetral1.2

e/h = 0.1

h 0.2 0.3 b h

1

g = 8% 7%0.8

6% 5% 4%

fs = 0 0.4

e

Pu

Pu / (f'c Ag)

0.6

3% 2% 1%

0.5

fc = 35 MPa fy = 420 MPa = 0.9fs = fy 1.0

0.4

0.2

2.0

0 0 0.1 0.2 Pu / (f'c Ag) * e/h 0.3 0.4

29- Diagrama de Interaccin Pu - Mu Columnas Armadura Perimetral1

h e/h = 0.1 g = 8% 0.2 0.3 b fs = 0 0.4 e 0.5 Pu h

0.8

7% 6% 5% 4% 3% 2% 1%

0.6 Pu / (f'c Ag)

0.4

fc = 40 MPa fy = 420 MPa = 0.9fs = fy 1.0

0.2

2.0

0 0 0.1 0.2 Pu / (f'c Ag) * e/h 0.3 0.4

30- Diagrama de Interaccin Pu - Mu Columnas Armadura Perimetral1

h h e/h = 0.1 0.2 0.3 b 0.4 fs = 0 0.5 e Pu g = 8% 7% 6% 5% 4% 3% 2% 1%

0.8

0.6 Pu / (f'c Ag)

0.4

fc = 45 MPa fy = 420 MPa = 0.9fs = fy 1.0

0.2

2.0

0 0 0.1 0.2 Pu / (f'c Ag) * e/h 0.3 0.4

31- Diagrama de Interaccin Pu - Mu Columnas Armadura Perimetral1

h e/h = 0.1 0.2 b h

0.8

g = 8% 7% 6% 5% 4% 3% 2% 1%

0.3 e fs = 0 0.4 Pu

0.6 Pu / (f'c Ag)

0.50.4

fc = 50 MPa fy = 420 MPa = 0.9

fs = fy0.2

1.0

2.0

0 0 0.1 Pu / (f'c Ag) * e/h 0.2 0.3

32- Diagrama de Interaccin Pu - Mu Columnas Armadura Perimetral1

h h e/h = 0.1 0.2 b

0.8

g = 8% 7% 6% 5% 4% 3% 2% 1%

0.3 e Pu

0.6 Pu / (f'c Ag)

fs = 0

0.4 0.5

0.4

fc = 55 MPa fy = 420 MPa = 0.9

fs = fy0.2

1.0

2.0

0 0 0.1 Pu / (f'c Ag) * e/h 0.2 0.3