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Diseño de Columnas según la norma ACI 318-08 por método PCA Columna :

Planilla Elaborada por: Univ. Edwin Santos Colque

frame COL-1

Datos de la columna L= 3.86 K= 0.9 Curvatura = Datos iniciales f'c = 210 fy = 4200 rec = 2.5 Pu = 77.59 Mux = 1.01 Muy = 0.622

Acero a Utilizar

Defina el Tipo de Seccion Rectangular b= cm. 30 t= cm. 45

m. 2

Diametro de Acero = Diametro del estribo =

Coef. Phi ( f ) =

0.65

𝑃𝑢≥0.10∗𝑓 ´𝑐∗𝐴𝑔 77.59

>=

28.35

CUMPLE

Preliminar.- Controlar el Pandeo

Paso 1.-

mm. mm.

Armado preliminar con 8 fierros n= 2

Kg/cm2 Kg/cm2 cm. T. Tm. Tm.

𝐾 ∗ 𝐿𝑢 𝑀1 ≤ 34 ± 12 ∗ 𝑟 𝑀2

f 12 f 8

𝐾 ∗ 𝐿𝑢 ≤ 22 𝑟

𝑂

8 f 12

45 cm Cumple Col. Corta

26.74 26.74

53.486 22

Asumir valor de B1

30

cm

0.65

B1 =

Paso 2.- Asumir relacion de Mx y My Si :

Mux > Muy

𝑀𝑢𝑦 𝑀𝑢𝑥 > 𝑀𝑜𝑥 𝑀𝑜𝑦

𝑀𝑜𝑥 = 𝑀𝑢𝑥 + 𝑀𝑢𝑦 ∗

𝑀𝑜𝑥 𝑀𝑜𝑦

Si :

Mux < Muy

𝑀𝑢𝑦 𝑀𝑢𝑥 < 𝑀𝑜𝑥 𝑀𝑜𝑦

𝑀𝑜𝑦 = 𝑀𝑢𝑦 + 𝑀𝑢𝑥 ∗

𝑀𝑜𝑦 1 − 𝐵1 ∗ 𝑀𝑜𝑥 𝐵1

∗

1 − 𝐵1 𝐵1

Paso 3.- Relacion Mox y Moy

𝑀𝑜𝑥 𝑡 ≅ 𝑀𝑜𝑦 𝑏

Rectangular

1.50 Calculo del Mox Asumido =

Paso 4.- Diseño Uniaxial Calculo de g =

𝑃𝑢 = ∅ ∗ 𝑓´𝑐 ∗ 𝑏 ∗ 𝑡

0.42

𝑀𝑜𝑥 = ∅ ∗ 𝑓´𝑐 ∗ 𝑏 ∗ 𝑡 2

0.018

𝑀𝑜𝑦 = ∅ ∗ 𝑓´𝑐 ∗ 𝑏 ∗ 𝑡 2

0.000

𝑔𝑥 =

𝑔𝑦 =

1.51

T.m.

0.7 ≤ 𝑔 ≤ 0.9

𝑡 − 2 ∗ 𝑟𝑒𝑐 − 2 ∗ ∅𝑒𝑠𝑡𝑟 − 2 ∗ ∅/2 = 𝑡

0.827

𝑏 − 2 ∗ 𝑟𝑒𝑐 − 2 ∗ ∅𝑒𝑠𝑡𝑟 − 2 ∗ ∅/2 = 𝑏

0.740

q =

0.05

de la Tabla nº

13

Resumen para ir a la tabla Coef. Pu = 0.42 Coef. Mu= 0.018 Ir a Tablas de fierros 8 Coef. gx = 0.83 Coef. gy = 0.74

Paso 5.-Calculo de la cuantia

𝜌=𝑞∗ Resultados Preliminares

f= Nro

As =

r=

f 12 8 9.05 0.007

𝑓´𝑐 𝑓𝑦

r=

0.003

cm2

𝜌=

𝐴𝑠𝑡 𝑏∗𝑡

Ast = Ast min =

3.38 13.50

cm2 cm2

Ast max = 108.00 cm2

mm. fierros

NO CUMPLE

NO CUMPLE

Acero suficiente, ir al Paso 6

Paso 6.-Calculo de Coef.x y Coef.y q= 𝑃𝑢 = ∅ ∗ 𝑓´𝑐 ∗ 𝑏 ∗ 𝑡

gx = gy =

Planilla Elaborada por: Univ. Edwin Santos Colque

0.13

Tabla

813 -9

0.42

Coef.x= Coef.y=

0.12 0.12

Momentos Reales Mox = Moy =

9.95 6.63

T.m. T.m.

0.83 0.74

Paso 7.-Calculo de B1 Real q=

𝑃𝑂 = 0.85 ∗ 𝑓´𝑐 ∗ 𝐴𝑔 + 𝐴𝑔 ∗ 𝑓𝑦

Po =

De la Fig. Nº

6

278.98

Ton.

B1 =

0.63

Paso 8.-Calculo de la relacion real de Momentos 𝑀𝑢𝑥 0.10 = 𝑀𝑜𝑥 Utilizar la Ecuacion 𝑀𝑢𝑦 0.09 = 𝑀𝑜𝑦 Resultado =

0.78

A

0.13

𝑃𝑢 = 𝑃𝑂

0.278

𝑀𝑢𝑥 𝑀𝑢𝑦 1 − 𝐵1 + ∗ =1 𝑀𝑜𝑥 𝑀𝑜𝑦 𝐵1

A 0.78

𝑀𝑢𝑦 𝑀𝑢𝑥 1 − 𝐵1 + ∗ =1 𝑀𝑜𝑦 𝑀𝑜𝑥 𝐵1

B 0.15

Ok pero Revisar

Entonces usar :

8

f 12

Paso 9.- Calculo del espaciamiento a) zona de confinamiento

10 18

𝑡 = 4 6 ∗ ∅𝑙𝑜𝑛𝑔. =

𝑆≤

𝑆𝑥 = 𝑆𝑥 =

b) zona intermedia 11.25 7.2

13

10 18 𝑆 ≤ 15

cm.

13

35 − 𝑕𝑥 ≤ 10 + = 3 10𝑐𝑚 ≤ 𝑆𝑥 ≤ 15𝑐𝑚

𝑏 = 2 6 ∗ ∅𝑙𝑜𝑛𝑔. = 15𝑐𝑚

15 7.2 15

15

cm.

10 10

13 10

Entonces usar :

f 12

8

para

b x t = 30 cm x 30 cm

Paso 10.- Calculo de la longitud por confinamiento Lo

40 58 45

𝑡= 𝐿 = 6 45𝑐𝑚

𝐿𝑜 ≥

45

Armado Definitivo : 64.33

65.00

cm.

45 Usar Estribos

Paso 11.- Calculo del acero de refuerzo transversal

5cm.

a) zona de confinamiento

Lo,(cm)=

𝐴𝑔 𝑓´𝑐 −1 ∗ = 𝐴𝑠𝑕 𝑓𝑦 𝑓´𝑐 0.09 ∗ 𝑆 ∗ 𝑏𝑐 ∗ = 𝑓𝑦

0.3 ∗ 𝑆 ∗ 𝑏𝑐 ∗ 𝐴𝑠𝑕 =

65.00

f 12 c 13

1.75

cm2 2.00 usar:

1.50

m.

f 6 c/15

cm2 Lo,(cm)=

Usar :

f 12

Usar :

f 6

5cm.

65.00

f 12 c 13

b) zona intermedia

𝐴𝑣𝑚𝑖𝑛 ≥

3.5 ∗ 𝑏𝑤 ∗ 𝑆 = 𝑓𝑦

0.38 0.56

cm2 cm2

Planilla Elaborada por: Univ. Edwin Santos Colque b,(cm)= 30

Para estribo de construccion utilizar : t,(cm)=

f 6 c/15 en una longitud:

2.00

m.

45

Usar armadura de:

8 f 12

Diametro Masa en mm. Kg/m

3 5 6 7 8 10 12 14 16 18 20 22 24 25 26 28 30 32 34 36 38 40 45 50

0.056 0.154 0.222 0.302 0.395 0.617 0.888 1.21 1.58 2 2.47 2.98 3.55 4.17 4.83 5.55 6.31 7.13 7.99 8.9 9.87 12.48 15.41

Numero de Barras

1

2

3

4

5

6

7

8

9

10

0.07 0.20 0.28 0.03 0.50 0.79 1.13 1.54 2.01 2.54 3.14 3.80 4.52 4.91 5.31 6.16 7.07 8.04 9.08 10.18 11.34 12.57 15.90 19.63

0.14 0.39 0.57 0.77 1.01 1.57 2.26 3.08 4.02 5.09 6.28 7.60 9.05 9.82 10.62 12.32 14.14 16.08 18.16 20.36 22.68 25.13 31.81 39.27

0.21 0.59 0.85 1.15 1.51 2.36 3.39 4.62 6.03 7.63 9.42 11.40 13.57 14.73 15.93 18.47 21.21 24.13 27.24 30.54 34.02 37.70 47.71 58.90

0.28 0.79 1.13 1.54 2.01 3.14 4.52 6.16 8.04 10.18 12.57 15.21 18.10 19.63 21.24 24.63 28.27 32.17 36.32 40.72 45.36 50.27 63.62 78.54

0.35 0.98 1.41 1.92 2.51 3.93 5.65 7.70 10.05 12.72 15.71 19.01 22.62 24.54 26.55 30.79 35.34 40.21 45.40 50.89 56.71 62.83 79.52 98.17

0.42 1.18 1.70 2.31 3.02 4.71 6.79 9.24 12.06 15.27 18.85 22.81 27.14 29.45 31.86 36.95 42.41 48.25 54.48 61.07 68.05 75.40 95.4 117.8

0.49 1.37 1.98 2.69 3.52 5.50 7.92 10.78 14.07 17.81 21.99 26.61 31.67 34.36 37.17 43.10 49.48 56.30 63.55 71.25 79.39 87.96 111.3 137.4

0.57 1.57 2.26 3.08 4.02 6.28 9.05 12.32 16.08 20.36 25.13 30.41 36.19 39.27 42.47 49.26 56.55 64.34 72.63 81.43 90.73 100.5 127.2 157.1

0.64 1.77 2.54 3.46 4.52 7.07 10.18 13.85 18.10 22.90 28.27 34.21 40.72 44.18 47.78 55.42 63.62 72.38 81.71 91.6 102.1 113.1 143.1 176.7

0.71 1.96 2.83 3.85 5.03 7.85 11.31 15.39 20.11 25.45 31.42 38.01 45.24 49.09 53.09 61.58 70.69 80.42 90.79 101.8 113.4 125.7 159.0 196.3

Separacion cm. 7 7.5 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 13 13.5 14 14.5 15 15.5 16 16.5 17 17.5 18 18.5 19 19.5 20 20.5 21 21.5 22 22.5 23 23.5 24 24.5 25 25.5 26 26.5 27 27.5 28 28.5 29 29.5 30

Areas para 100 cm. De ancho cm`2 Diametros ( mm. ) 6 4.00 3.73 3.50 3.29 3.11 2.95 2.80 2.67 2.55 2.43 2.33 2.24 2.15 2.07 2.00 1.93 1.87 1.81 1.75 1.70 1.65 1.60 1.56 1.51 1.47 1.44 1.40 1.37 1.33 1.30 1.27 1.24 1.22 1.19 1.17 1.14 1.12 1.10 1.08 1.06 1.04 1.02 1.00 0.98 0.97 0.95 0.93

8 7.14 6.67 6.25 5.88 5.56 5.26 5.00 4.76 4.55 4.35 4.17 4.00 3.85 3.70 3.57 3.45 3.33 3.23 3.13 3.03 2.94 2.86 2.78 2.70 2.63 2.56 2.50 2.44 2.38 2.33 2.27 2.22 2.17 2.13 2.08 2.04 2.00 1.96 1.92 1.89 1.85 1.82 1.79 1.75 1.72 1.69 1.67

10 11.29 10.53 9.88 9.29 8.78 8.32 7.90 7.52 7.18 6.87 6.58 6.32 6.08 5.85 5.64 5.45 5.27 5.10 4.94 4.79 4.65 4.51 4.39 4.27 4.16 4.05 3.95 3.85 3.76 3.67 3.59 3.51 3.43 3.36 3.29 3.22 3.16 3.10 3.04 2.98 2.93 2.87 2.82 2.77 2.72 2.68 2.63

12 16.14 15.07 14.13 13.29 12.56 11.89 11.30 10.76 10.27 9.83 9.42 9.04 8.69 8.37 8.07 7.79 7.53 7.29 7.06 6.85 6.65 6.46 6.28 6.11 5.95 5.79 5.65 5.51 5.38 5.26 5.14 5.02 4.91 4.81 4.71 4.61 4.52 4.43 4.35 4.26 4.19 4.11 4.04 3.96 3.90 3.83 3.77

14 22.00 20.53 19.25 18.12 17.11 16.21 15.40 14.67 14.00 13.39 12.83 12.32 11.85 11.41 11.00 10.62 10.27 9.94 9.63 9.33 9.06 8.80 8.56 8.32 8.11 7.90 7.70 7.51 7.33 7.16 7.00 6.84 6.70 6.55 6.42 6.29 6.16 6.04 5.92 5.81 5.70 5.60 5.50 5.40 5.31 5.22 5.13

16 28.71 26.80 25.13 23.65 22.33 21.16 20.10 19.14 18.27 17.48 16.75 16.08 15.46 14.89 14.36 13.86 13.40 12.97 12.56 12.18 11.82 11.49 11.17 10.86 10.58 10.31 10.05 9.80 9.57 9.35 9.14 8.93 8.74 8.55 8.38 8.20 8.04 7.88 7.73 7.58 7.44 7.31 7.18 7.05 6.93 6.81 6.70

18 36.29 33.87 31.75 29.88 28.22 26.74 25.40 24.19 23.09 22.09 21.17 20.32 19.54 18.81 18.14 17.52 16.93 16.39 15.88 15.39 14.94 14.51 14.11 13.73 13.37 13.03 12.70 12.39 12.10 11.81 11.55 11.29 11.04 10.81 10.58 10.37 10.16 9.96 9.77 9.58 9.41 9.24 9.07 8.91 8.76 8.61 8.47

20 44.86 41.87 39.25 36.94 34.89 33.05 31.40 29.90 28.55 27.30 26.17 25.12 24.15 23.26 22.43 21.66 20.93 20.26 19.63 19.03 18.47 17.94 17.44 16.97 16.53 16.10 15.70 15.32 14.95 14.60 14.27 13.96 13.65 13.36 13.08 12.82 12.56 12.31 12.08 11.85 11.63 11.42 11.21 11.02 10.83 10.64 10.47

22 54.29 50.67 47.50 44.71 42.22 40.00 38.00 36.19 34.55 33.04 31.67 30.40 29.23 28.15 27.14 26.21 25.33 24.52 23.75 23.03 22.35 21.71 21.11 20.54 20.00 19.49 19.00 18.54 18.10 17.67 17.27 16.89 16.52 16.17 15.83 15.51 15.20 14.90 14.62 14.34 14.07 13.82 13.57 13.33 13.10 12.88 12.67

24 64.57 60.27 56.50 53.18 50.22 47.58 45.20 43.05 41.09 39.30 37.67 36.16 34.77 33.48 32.29 31.17 30.13 29.16 28.25 27.39 26.59 25.83 25.11 24.43 23.79 23.18 22.60 22.05 21.52 21.02 20.55 20.09 19.65 19.23 18.83 18.45 18.08 17.73 17.38 17.06 16.74 16.44 16.14 15.86 15.59 15.32 15.07

25 70.14 65.47 61.38 57.76 54.56 51.68 49.10 46.76 44.64 42.70 40.92 39.28 37.77 36.37 35.07 33.86 32.73 31.68 30.69 29.76 28.88 28.06 27.28 26.54 25.84 25.18 24.55 23.95 23.38 22.84 22.32 21.82 21.35 20.89 20.46 20.04 19.64 19.25 18.88 18.53 18.19 17.85 17.54 17.23 16.93 16.64 16.37