DocumentDM

Prolongación Araurarias 80 • Indeco Animas • 91190 • Xalapa, Veracruz Tel. Oficina 228.202.1064

E-mail: [email protected]

Geotecnia • Hidrología • Diseño Estructural • Auscultación de Pavimentos • Supervisión de Obra • Arquitectura

Simbología y Definiciones

Strength I Estado limite de Esfuerzos I

Strength II Estado limite de Esfuerzos II

Strength III Estado limite de Esfuerzos III

Extreme I Estado limite de Evento Extremo I

Extreme II Estado limite de Evento Extremo II

Service I Estado limite de Servicio I

Sevice II Estado limite de Servicio II

DC Dead load of structural components…

Carga muerta de los componenetes estructurales y aditamentos no estructurales

EH horizontal earth pressure load

Carga de presión Horizontal de tierra

LL vehicular live load

Carga viva vehicular

IM vehicular dynamic load allowance

Carga dinamica permisible (impacto)

BR vehicular braking force

Fuerza de frenado

WA water load and stream pressure

Carga hidraulica y presión de flujo

WS wind load on structure

Carga de Viento sobre la estructura

EQx earthquake load

Carga de Sismo en el eje X

EQy earthquake load

Carga de sismo en el eje Y

Cargas, factores y estados limites obtenidos de AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS 2012




Dead load of structural components…

Carga muerta de los componenetes estructurales y aditamentos no estructurales

horizontal earth pressure load

Carga de presión Horizontal de tierra

vehicular live load

Carga viva vehicular

vehicular dynamic load allowance

Carga dinamica permisible (impacto)

vehicular braking force

Fuerza de frenado

water load and stream pressure

Carga hidraulica y presión de flujo

wind load on structure

Carga de Viento sobre la estructura

earthquake load

Carga de Sismo en el eje X

earthquake load

Carga de sismo en el eje Y

AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS




Diseño de Columnas

Cortante Momentos Carga Axial

Strength I Mx My

1.25DC+1.5EH+1.75LL+1.33IM+1.75BR+WA 6.55 0.16 14.02 192.35

Strenght II

1.25DC+1.3EH+1.35LL+1.33IM+1.35BR+WA 6.05 0.17 12.95 178.20

Strenght III

1.25DC+1.5EH+WA+1.4WS 5.84 0.12 12.59 127.15

Strenght IV

1.50DC+1.5EH+WA 4.85 0.15 10.56 148.81

Extreme I

5.15 2.39 11.01 144.68

Extreme II

4.95 7.67 10.57 144.31

Service I

DC+EH+LL+IM+BR+WA+0.3WS 4.86 0.13 11.06 140.21

Service II

DC+EH+1.3LL+1.3IM+1.3BR+WA 6.26 0.16 13.49 186.20

Condición más Desfavorable 6.55 7.67 14.02 192.35

ep:

Curvatura: Simple

45.46

50.69

K 0.70

Long. Efectiva 5.25

M. Inercia: 0.10

r: 0.30

A: 1.13

R de Esbeltez 12.25

Limite 1: 23.24

Limite 2: 40

Resumen de Elementos mecánicos obtenidos de RSA para cada una de las estados limites de carga establecidas en AASTHO 2012

1.25DC+1.5EH+0.5LL+0.5IM+0.5BR+WA+EQx+0.3EQy

1.25DC+1.5EH+0.5LL+0.5IM+0.5BR+WA+0.3EQx+EQy

Revisión de la Relación de Esbeltez para columnas sin desplazamiento lateral

M1:

M2:

𝑘𝑙/𝑟≤(34−12(𝑀_1/𝑀_2 )≤40




e

0.07

0.07

0.10

0.07

0.08

0.09

0.08

0.07

0.10

0.85




Diseño práctico

Elementos Mecánicos

Carga Axial: 192.35 ton e/D:

Momento: 163.50 ton-m 192350

Cortante: 6.55 ton 16349750

Diametro: 1.20 m 120

Peralte: 1 m 100

d/D 0.83 114.44

f'c: 250 Vs. 8C 22.57

f*c: 200 Vs. 10C 14.41

f''c: 170

fy: 4200

0.010

0.040 36 vs 32 vs 28 vs

0.010 0.016 0.014 0.013

0.25 0.40 0.35 0.31

K: 0.06

R: 0.04

Por la magnitud del momento flector se consideró conveniente establecer una excentricidad de 0.85, para generar un momento

flexionante mayor al que se obtuvo del analisis.

kg/cm2

ρmin:

ρmax:

ρGraf: ρProp:

qGraf: qProp:

K=𝑃/(𝐹_𝑟 𝐷^2 𝑓^′ 𝑐)R=𝑀/(𝐹_𝑟 𝐷^3 𝑓^′ 𝑐)𝐴_𝑠:ρπ𝑟^2

Q4

EL MOMENTO DE DISEÑO DEBE SER LA RAIZ CUADRADA DE LA SUMA DE LOS CUADRADOS DE LOS MOMENTOS







0.71

24 vs

0.011

0.27

Por la magnitud del momento flector se consideró conveniente establecer una excentricidad de 0.85, para generar un momento

flexionante mayor al que se obtuvo del analisis.







Dimensionado de Zuncho o Estribo

Ag1.44

Ac

0.0080

0.0049

Rige: 0.0080

Área de V. 1.27

Diametro: 1.27

S: 5.54 cm Rige: 5.54

Separación de Reglamento Separación Libre Máxima

16.7 cm5.00 cm

√fy Separación Libre Mínima

60.96 cm 4.00 cm

Separación de Estribos 4C

S: 108.58 cm

ρs:

850 Dvs

48 DVs

Se utilizaran 28 Vs 8C como refuerzo longitudinal con un angulo de separación de 13° repartidos en la circunferencia de la columna.

Así mismo se utilizaran estribos de Vs 4C a cada 15 cm.

ρ_𝑠:0.45(𝐴_𝑔/ 〖𝐴 _𝐶〗 _ −1) (𝑓^′′ 𝑐)/𝑓𝑦≥0.12 (𝑓^′′ 𝑐)/𝑓𝑦𝑆:((4𝐴_𝑒)/〖 ρ_𝑠 𝑑_𝑠〗 _ )

𝑆:((𝑎_𝑣 𝑓_𝑦𝑢 𝑑)/ 〖𝑉𝑢〗_ )

0 50 100 150 200 250 300 350 4000.0

200.0400.0600.0800.0

1,000.01,200.01,400.01,600.01,800.02,000.02,200.02,400.0

MOMENTO

CARG

A AX

IAL




Diagrama de Interacción para la Columna con el Armado Propuesto

0 50 100 150 200 250 300 350 4000.0

200.0400.0600.0800.0

1,000.01,200.01,400.01,600.01,800.02,000.02,200.02,400.0

MOMENTO

CARG

A AX

IAL



Geotecnia • Diseño Estructural • Proyecto Geométrico • Evaluación de Pavimentos • Hidrología • Supervisión de Obra

Diseño de Apoyo Central (Pila)Vs. # 4 Vs. # 5 Vs. # 6 Vs. # 8 Vs. # 10 Vs. # 12

Diametro: 1.3 1.6 1.9 2.5 3.2 3.8Área: 1.27 1.98 2.85 5.07 7.92 11.40

Diametro: 1.2 m f'c: 250

Vs. de Ref.: 8 f*c: 200

Vs. Zuncho: 4 f''c: 170

Recub.: 0.1 cm fy: 4200

Peralte: 1 m 0.003

0.0021

Pto. de Falla Balanceada Altura de Bloque de Esf.

58.82 cm a: 50.00 cmárea Comp. 4817.00

Fuerza de compresiónC: 696.06 ton

Xc: 0.25 cmNúmero de Varillas prop.: 40 10

9.00°

Distancias desde E.N.: X

50 10.00 48.82 0.00249 4200.00

49.38 10.62 48.21 0.00246 4200.00

47.55 12.45 46.38 0.00237 4200.00

44.55 15.45 43.37 0.00221 4200.00

40.45 19.55 39.27 0.00200 4005.99

35.36 24.64 34.18 0.00174 3486.24

29.39 30.61 28.21 0.00144 2877.70

22.70 37.30 21.52 0.00110 2195.35

15.45 44.55 14.27 0.00073 1455.99

7.82 52.18 6.65 0.00034 677.82

0.00 60.00 -1.18 -0.00006 -120.00

7.82 67.82 9.00 0.00046 917.82

15.45 75.45 16.63 0.00085 1695.99

22.70 82.70 23.88 0.00122 2435.35

29.39 89.39 30.57 0.00156 3117.70

35.36 95.36 36.53 0.00186 3726.24

40.45 100.45 41.63 0.00212 4200.00

44.55 104.55 45.73 0.00233 4200.00

47.55 107.55 48.73 0.00249 4200.00

kg/cm2

kg/cm2

kg/cm2

kg/cm2

εcu:

εy:

Cb:

Angulo de Separación Ѳ:

εn fn

D1:

D2:

D3:

D4:

D5:

D6:

D7:

D8:

D9:

D10:

D11:

D12:

D13:

D14:

D15:

D16:

D17:

D18:

D19:




49.38 109.38 50.56 0.00258 4200.00

50.00 110.00 51.18 0.00261 4200.00

D20:

D21:




Fza. (ton) Brazos (cm) Momentos21.28 50.00 10.64 Mo, Po: 0 2,485.542.56 49.38 21.02 Mb, Pb: 409.93 683.142.56 47.55 20.2442.56 44.55 18.9640.60 40.45 16.4235.33 35.36 12.4929.16 29.39 8.5722.25 22.70 5.0514.76 15.45 2.286.87 7.82 0.541.22 0.00 0.00-9.30 7.82 0.73-17.19 15.45 2.66-24.68 22.70 5.60-31.60 29.39 9.29-37.76 35.36 13.35-42.56 40.45 17.22-42.56 44.55 18.96-42.56 47.55 20.24-42.56 49.38 21.02-21.28 50.00 10.64683.15 409.93

-60.00-50.00

-40.00-30.00

-20.00-10.00

0.0010.00

20.0030.00

40.0050.00

60.00

0.00

10.00

20.00

30.00

40.00

50.00

60.00

70.00

80.00

90.00

100.00

110.00

120.00

130.00

140.00

Distribucion de Fuerzas

1,2

1,05




-60.00-50.00

-40.00-30.00

-20.00-10.00

0.0010.00

20.0030.00

40.0050.00

60.00

0.00

10.00

20.00

30.00

40.00

50.00

60.00

70.00

80.00

90.00

100.00

110.00

120.00

130.00

140.00


1,2

1,05





Diametro: 1.3 1.6 1.9 2.5 3.2 3.8 Diametro:Área: 1.27 1.98 2.85 5.07 7.92 11.40 Área:

Diametro: 1.2 m f'c: 250 Diametro:

Vs. de Ref.: 8 f*c: 200 Vs. de Ref.:

Vs. Zuncho: 4 f''c: 170 Vs. Zuncho:

Recub.: 0.1 cm fy: 4200 Recub.:

Peralte: 1 m 0.003 Peralte:

0.0021

Pto. Falla en Compresión Altura de Bloque de Esf. Pto. Falla en Tensión

99.00 cm a: 84.15 cmárea Comp. 8566.00

Fuerza de compresión Fuerza de compresiónC: 1,237.79 ton C:

Xc: 0.08 cm Xt:Número de Varillas prop.: 40 10 Número de Varillas prop.:

9.00°

Distancias desde E.N.: X Distancias desde E.N.:

50 10 89.00 0.00270 4200.00

49.38 10.62 88.38 0.00268 4200.00

47.55 12.45 86.55 0.00262 4200.00

44.55 15.45 83.55 0.00253 4200.00

40.45 19.55 79.45 0.00241 4200.00

35.36 24.64 74.36 0.00225 4200.00

29.39 30.61 68.39 0.00207 4144.80

22.70 37.30 61.70 0.00187 3739.37

15.45 44.55 54.45 0.00165 3300.05

7.82 52.18 46.82 0.00142 2837.68

0.00 60.00 39.00 0.00118 2363.64

7.82 67.82 31.18 0.00094 1889.59

15.45 75.45 23.55 0.00071 1427.22

22.70 82.70 16.30 0.00049 987.91

29.39 89.39 9.61 0.00029 582.47

35.36 95.36 3.64 0.00011 220.89

40.45 100.45 1.45 0.00305 4200.00

44.55 104.55 5.55 0.01166 4200.00

47.55 107.55 8.55 0.01796 4200.00

kg/cm2

kg/cm2

kg/cm2

kg/cm2

εcu:

εy:

Cc: Ct:

Angulo de Separación Ѳ: Angulo de Separación Ѳ:

εn fn

D1: D1:

D2: D2:

D3: D3:

D4: D4:

D5: D5:

D6: D6:

D7: D7:

D8: D8:

D9: D9:

D10: D10:

D11: D11:

D12: D12:

D13: D13:

D14: D14:

D15: D15:

D16: D16:

D17: D17:

D18: D18:

D19: D19:




49.38 109.38 10.38 0.02181 4200.00

50.00 110.00 11.00 0.02310 4200.00

D20: D20:

D21: D21:




Fza. (ton) Brazos (cm) Momentos Fza. (ton)21.28 50.00 10.64 Mo, Po: 0 2,485.5 20.2742.56 49.38 21.02 Mb, Pb: 409.93 683.1 39.2942.56 47.55 20.24 Mc, Pc: 326.20 1,498.2 35.5842.56 44.55 18.96 29.4942.56 40.45 17.22 21.1842.56 35.36 15.05 10.8542.00 29.39 12.34 1.2437.90 22.70 8.60 -4.4433.44 15.45 5.17 -8.8528.76 7.82 2.25 -13.4923.95 0.00 0.00 -18.2419.15 7.82 1.50 -23.0014.46 15.45 2.23 -27.6410.01 22.70 2.27 -32.045.90 29.39 1.73 -36.112.24 35.36 0.79 -39.74

-42.56 40.45 17.22 -42.56-42.56 44.55 18.96 -42.56-42.56 47.55 20.24 -42.56-42.56 49.38 21.02 -42.56-21.28 50.00 10.64 -21.28

1498.17 326.20 16.56

-60.00-50.00

-40.00-30.00

-20.00-10.00

0.0010.00

20.0030.00

40.0050.00

60.00

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140


1,2

1,05




-60.00-50.00

-40.00-30.00

-20.00-10.00

0.0010.00

20.0030.00

40.0050.00

60.00

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140


1,2

1,05





1.3 1.6 1.9 2.5 3.2 3.81.27 1.98 2.85 5.07 7.92 11.40

1.2 m f'c: 250

8 f*c: 200

4 f''c: 170

0.1 cm fy: 4200

1 m 0.003

0.0021ρ: 0.018

Pto. Falla en Tensión q: 0.443

30.00 cm Altura de Bloque de Esf.a: 25.50 cm

Fuerza de compresión área Comp. 1756.00253.74 ton

0.37 cmNúmero de Varillas prop.: 40 10

9.00°


50 10 20.00 0.00200 4000.00

49.38 10.62 19.38 0.00194 3876.88

47.55 12.45 17.55 0.00176 3510.57

44.55 15.45 14.55 0.00146 2910.07

40.45 19.55 10.45 0.00105 2090.17

35.36 24.64 5.36 0.00054 1071.07

29.39 30.61 -0.61 -0.00006 -122.15

22.70 37.30 7.30 0.00022 438.03

15.45 44.55 14.55 0.00044 872.95

7.82 52.18 22.18 0.00067 1330.70

0.00 60.00 30.00 0.00090 1800.00

7.82 67.82 37.82 0.00113 2269.30

15.45 75.45 45.45 0.00136 2727.05

22.70 82.70 52.70 0.00158 3161.97

29.39 89.39 59.39 0.00178 3563.36

35.36 95.36 65.36 0.00196 3921.32

40.45 100.45 70.45 0.00211 4200.00

44.55 104.55 74.55 0.00224 4200.00

47.55 107.55 77.55 0.00233 4200.00

kg/cm2

kg/cm2

kg/cm2

kg/cm2

εcu:

εy:


εn fn




49.38 109.38 79.38 0.00238 4200.00

50.00 110.00 80.00 0.00240 4200.00




Brazos (cm) Momentos50.00 10.13 Mo, Po: 0 2,485.549.38 19.40 Mc, Pc: 326.20 1,498.247.55 16.92 Mb, Pb: 409.93 683.144.55 13.14 Mt, Pt: 296.40 16.640.45 8.5735.36 3.8429.39 0.3622.70 1.0115.45 1.377.82 1.050.00 0.007.82 1.8015.45 4.2722.70 7.2729.39 10.6135.36 14.0540.45 17.2244.55 18.9647.55 20.2449.38 21.0250.00 10.64

296.40

-60.00-50.00

-40.00-30.00

-20.00-10.00

0.0010.00

20.0030.00

40.0050.00

60.00

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140


1,2

1,05




-60.00-50.00

-40.00-30.00

-20.00-10.00

0.0010.00

20.0030.00

40.0050.00

60.00

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140


1,2

1,05




0 50 100 150 200 250 300 350 400 4500.0

500.0

1,000.0

1,500.0

2,000.0

2,500.0

3,000.0

192.35





Diametro: 1.3 1.6 1.9 2.5 3.2 3.8Área: 1.27 1.98 2.85 5.07 7.92 11.40


Vs. de Ref.: 8 f*c: 200


Recub.: 0.07 cm fy: 4200

Peralte: 1.06 m 0.003

0.0021


62.35 cm a: 53.00 cmárea Comp. 4817.00



10.00°


53 7 55.35 0.00266 4200.00

52.19 7.81 54.55 0.00262 4200.00

49.80 10.20 52.16 0.00251 4200.00

45.90 14.10 48.25 0.00232 4200.00

40.60 19.40 42.95 0.00207 4133.24

34.07 25.93 36.42 0.00175 3504.63

26.50 33.50 28.85 0.00139 2776.42

18.13 41.87 20.48 0.00099 1970.72

9.20 50.80 11.56 0.00056 1112.02

0.00 60.00 2.35 0.00011 226.42

9.20 69.20 6.85 0.00033 659.19

18.13 78.13 15.77 0.00076 1517.89

26.50 86.50 24.15 0.00116 2323.58

34.07 94.07 31.71 0.00153 3051.80

40.60 100.60 38.25 0.00184 3680.41

45.90 105.90 43.55 0.00210 4190.31

49.80 109.80 47.45 0.00228 4200.00

52.19 112.19 49.84 0.00240 4200.00

53.00 113.00 50.65 0.00244 4200.00

kg/cm2

kg/cm2

kg/cm2

kg/cm2

εcu:

εy:

Cb:


εn fn

D1:

D2:

D3:

D4:

D5:

D6:

D7:

D8:

D10:

D11:

D12:

D13:

D14:

D15:

D16:

D17:

D18:

D19:

D20:




Fza. (ton) Brazos (cm) Momentos21.28 53.00 11.28 Mo, Po: 0 2,400.442.56 52.19 22.22 Mb, Pb: 409.41 721.442.56 49.80 21.2042.56 45.90 19.5441.89 40.60 17.0135.52 34.07 12.1028.14 26.50 7.4619.97 18.13 3.6211.27 9.20 1.042.29 0.00 0.00-6.68 9.20 0.61-15.38 18.13 2.79-23.55 26.50 6.24-30.93 34.07 10.54-37.30 40.60 15.14-42.47 45.90 19.49-42.56 49.80 21.20-42.56 52.19 22.22-21.28 53.00 11.28721.39 409.41

-60.00 -50.00 -40.00 -30.00 -20.00 -10.00 0.00 10.00 20.00 30.00 40.00 50.00 60.000

10

20

30

40

50

60

70

80

90

100

110

120

130

140


1,2

1,05




-60.00 -50.00 -40.00 -30.00 -20.00 -10.00 0.00 10.00 20.00 30.00 40.00 50.00 60.000

10

20

30

40

50

60

70

80

90

100

110

120

130

140


1,2

1,05





Diametro: 1.3 1.6 1.9 2.5 3.2 3.8Área: 1.27 1.98 2.85 5.07 7.92 11.40


Vs. de Ref.: 8 f*c: 200


Recub.: 0.07 cm fy: 4200

Peralte: 1.06 m 0.003

0.0021

Pto. Falla en Compresión Altura de Bloque de Esf.

100.00 cm a: 85.00 cmárea Comp. 8566.00

Fuerza de compresiónC: 1,237.79 ton


10.00°


53 7 93.00 0.00279 4200.00

52.19 7.81 92.19 0.00277 4200.00

49.80 10.20 89.80 0.00269 4200.00

45.90 14.10 85.90 0.00258 4200.00

40.60 19.40 80.60 0.00242 4200.00

34.07 25.93 74.07 0.00222 4200.00

26.50 33.50 66.50 0.00200 3990.00

18.13 41.87 58.13 0.00174 3487.62

9.20 50.80 49.20 0.00148 2952.20

0.00 60.00 40.00 0.00120 2400.00

9.20 69.20 30.80 0.00092 1847.80

18.13 78.13 21.87 0.00066 1312.38

26.50 86.50 13.50 0.00041 810.00

34.07 94.07 5.93 0.00018 355.94

40.60 100.60 0.60 0.00021 420.25

45.90 105.90 5.90 0.00206 4129.54

49.80 109.80 9.80 0.00343 4200.00

52.19 112.19 12.19 0.00427 4200.00

53.00 113.00 13.00 0.00455 4200.00

kg/cm2

kg/cm2

kg/cm2

kg/cm2

εcu:

εy:

Cc:


εn fn

D1:

D2:

D3:

D4:

D5:

D6:

D7:

D8:

D10:

D11:

D12:

D13:

D14:

D15:

D16:

D17:

D18:

D19:

D20:




Fza. (ton) Brazos (cm) Momentos21.28 53.00 11.28 Mo, Po: 0 2,400.442.56 52.19 22.22 Mb, Pb: 409.41 721.442.56 49.80 21.20 Mc, Pc: 339.02 1,493.242.56 45.90 19.5442.56 40.60 17.2842.56 34.07 14.5040.44 26.50 10.7235.34 18.13 6.4129.92 9.20 2.7524.32 0.00 0.0018.73 9.20 1.7213.30 18.13 2.418.21 26.50 2.183.61 34.07 1.23-4.26 40.60 1.73-41.85 45.90 19.21-42.56 49.80 21.20-42.56 52.19 22.22-21.28 53.00 11.28

1493.23 339.02

-60.00 -50.00 -40.00 -30.00 -20.00 -10.00 0.00 10.00 20.00 30.00 40.00 50.00 60.000

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1,2

1,05




-60.00 -50.00 -40.00 -30.00 -20.00 -10.00 0.00 10.00 20.00 30.00 40.00 50.00 60.000

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1,2

1,05





Diametro: 1.3 1.6 1.9 2.5 3.2 3.8Área: 1.27 1.98 2.85 5.07 7.92 11.40


Vs. de Ref.: 8 f*c: 200


Recub.: 0.07 cm fy: 4200

Peralte: 1.06 m 0.003

0.0021ρ: 0.016



Fuerza de compresión área Comp. 1756.00C: 253.74 ton

Xt: 0.40 cmNúmero de Varillas prop.: 36 9

10.00°


53 7 23.00 0.00230 4200.00

52.19 7.81 22.19 0.00222 4200.00

49.80 10.20 19.80 0.00198 3960.74

45.90 14.10 15.90 0.00159 3179.87

40.60 19.40 10.60 0.00106 2120.07

34.07 25.93 4.07 0.00041 813.55

26.50 33.50 3.50 0.00010 193.42

18.13 41.87 11.87 0.00033 656.14

9.20 50.80 20.80 0.00057 1149.29

0.00 60.00 30.00 0.00083 1657.89

9.20 69.20 39.20 0.00108 2166.50

18.13 78.13 48.13 0.00133 2659.65

26.50 86.50 56.50 0.00156 3122.37

34.07 94.07 64.07 0.00177 3540.59

40.60 100.60 70.60 0.00195 3901.60

45.90 105.90 75.90 0.00210 4194.44

49.80 109.80 79.80 0.00221 4200.00

52.19 112.19 82.19 0.00227 4200.00

53.00 113.00 83.00 0.00229 4200.00

kg/cm2

kg/cm2

kg/cm2

kg/cm2

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Ct:


εn fn

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Fza. (ton) Brazos (cm) Momentos21.28 53.00 11.28 Mo, Po: 0 2,400.442.56 52.19 22.22 Mc, Pc: 339.02 1,493.240.14 49.80 19.99 Mb, Pb: 409.41 721.432.23 45.90 14.79 Mt, Pt: 302.51 77.721.49 40.60 8.72 Mf,Pf 937.4 0.08.24 34.07 2.81-1.96 26.50 0.52-6.65 18.13 1.21-11.65 9.20 1.07-16.80 0.00 0.00-21.96 9.20 2.02-26.95 18.13 4.89-31.64 26.50 8.39-35.88 34.07 12.22-39.54 40.60 16.05-42.51 45.90 19.51-42.56 49.80 21.20-42.56 52.19 22.22-21.28 53.00 11.2877.74 302.51

-60.00 -50.00 -40.00 -30.00 -20.00 -10.00 0.00 10.00 20.00 30.00 40.00 50.00 60.000

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1,2

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-60.00 -50.00 -40.00 -30.00 -20.00 -10.00 0.00 10.00 20.00 30.00 40.00 50.00 60.000

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0 100 200 300 400 500 600 700 800 900 10000.0

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Diametro: 1.3 1.6 1.9 2.5 3.2 3.8Área: 1.27 1.98 2.85 5.07 7.92 11.40


Vs. de Ref.: 8 f*c: 200


Recub.: 0.07 cm fy: 4200

Peralte: 1.06 m 0.003

0.0021


62.35 cm a: 53.00 cmárea Comp. 4817.00



11.25°


53 7 55.35 0.00266 4200.00

51.98 8.02 54.33 0.00261 4200.00

48.97 11.03 51.32 0.00247 4200.00

44.07 15.93 46.42 0.00223 4200.00

37.48 22.52 39.83 0.00192 3832.66

29.45 30.55 31.80 0.00153 3059.82

20.28 39.72 22.64 0.00109 2178.10

10.34 49.66 12.69 0.00061 1221.38

0.00 60.00 2.35 0.00011 226.42

10.34 70.34 7.99 0.00038 768.55

20.28 80.28 17.93 0.00086 1725.27

29.45 89.45 27.09 0.00130 2606.99

37.48 97.48 35.12 0.00169 3379.83

44.07 104.07 41.71 0.00201 4014.08

48.97 108.97 46.61 0.00224 4200.00

51.98 111.98 49.63 0.00239 4200.00

53.00 113.00 50.65 0.00244 4200.00

kg/cm2

kg/cm2

kg/cm2

kg/cm2

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Fza. (ton) Brazos (cm) Momentos21.28 53.00 11.28 Mo, Po: 0 2,315.342.56 51.98 22.13 Mb, Pb: 384.04 718.642.56 48.97 20.8442.56 44.07 18.7638.84 37.48 14.5631.01 29.45 9.1322.07 20.28 4.4812.38 10.34 1.282.29 0.00 0.00-7.79 10.34 0.81

-17.48 20.28 3.55-26.42 29.45 7.78-34.25 37.48 12.84-40.68 44.07 17.93-42.56 48.97 20.84-42.56 51.98 22.13-21.28 53.00 11.28718.59 384.04

-60.00 -50.00 -40.00 -30.00 -20.00 -10.00 0.00 10.00 20.00 30.00 40.00 50.00 60.000

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1,2

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-60.00 -50.00 -40.00 -30.00 -20.00 -10.00 0.00 10.00 20.00 30.00 40.00 50.00 60.000

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1,2

1,05





Diametro: 1.3 1.6 1.9 2.5 3.2 3.8Área: 1.27 1.98 2.85 5.07 7.92 11.40


Vs. de Ref.: 8 f*c: 200


Recub.: 0.07 cm fy: 4200

Peralte: 1.06 m 0.003

0.0021


95.00 cm a: 80.75 cmárea Comp. 8094.00



11.25°


53 7 88.00 0.00278 4200.00

51.98 8.02 86.98 0.00275 4200.00

48.97 11.03 83.97 0.00265 4200.00

44.07 15.93 79.07 0.00250 4200.00

37.48 22.52 72.48 0.00229 4200.00

29.45 30.55 64.45 0.00204 4070.22

20.28 39.72 55.28 0.00175 3491.51

10.34 49.66 45.34 0.00143 2863.57

0.00 60.00 35.00 0.00111 2210.53

10.34 70.34 24.66 0.00078 1557.49

20.28 80.28 14.72 0.00046 929.54

29.45 89.45 5.55 0.00018 350.83

37.48 97.48 2.48 0.00047 945.63

44.07 104.07 9.07 0.00173 3462.29

48.97 108.97 13.97 0.00267 4200.00

51.98 111.98 16.98 0.00324 4200.00

53.00 113.00 18.00 0.00344 4200.00

kg/cm2

kg/cm2

kg/cm2

kg/cm2

εcu:

εy:

Cc:


εn fn

D1:

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D5:

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D18:

D19:

D20:




Fza. (ton) Brazos (cm) Momentos21.28 53.00 11.28 Mo, Po: 0 2,315.342.56 51.98 22.13 Mb, Pb: 384.04 718.642.56 48.97 20.84 Mc, Pc: 336.83 1,366.942.56 44.07 18.7642.56 37.48 15.9541.25 29.45 12.1535.38 20.28 7.1829.02 10.34 3.0022.40 0.00 0.0015.78 10.34 1.639.42 20.28 1.913.56 29.45 1.05-9.58 37.48 3.59

-35.09 44.07 15.46-42.56 48.97 20.84-42.56 51.98 22.13-21.28 53.00 11.28

1366.85 336.83

-60.00-50.00-40.00-30.00-20.00-10.00 0.00 10.00 20.00 30.00 40.00 50.00 60.000

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1,2

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-60.00-50.00-40.00-30.00-20.00-10.00 0.00 10.00 20.00 30.00 40.00 50.00 60.000

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130

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1,05





Diametro: 1.3 1.6 1.9 2.5 3.2 3.8Área: 1.27 1.98 2.85 5.07 7.92 11.40


Vs. de Ref.: 8 f*c: 200


Recub.: 0.07 cm fy: 4200

Peralte: 1.06 m 0.003

0.0021ρ: 0.014





11.25°


53 7 15.00 0.00205 4090.91

51.98 8.02 13.98 0.00191 3813.17

48.97 11.03 10.97 0.00150 2990.62

44.07 15.93 6.07 0.00083 1654.88

37.48 22.52 0.52 0.00001 26.17

29.45 30.55 8.55 0.00021 427.74

20.28 39.72 17.72 0.00044 885.89

10.34 49.66 27.66 0.00069 1383.01

0.00 60.00 38.00 0.00095 1900.00

10.34 70.34 48.34 0.00121 2416.99

20.28 80.28 58.28 0.00146 2914.11

29.45 89.45 67.45 0.00169 3372.26

37.48 97.48 75.48 0.00189 3773.83

44.07 104.07 82.07 0.00205 4103.39

48.97 108.97 86.97 0.00217 4200.00

51.98 111.98 89.98 0.00225 4200.00

53.00 113.00 91.00 0.00228 4200.00

kg/cm2

kg/cm2

kg/cm2

kg/cm2

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εn fn

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Fza. (ton) Brazos (cm) Momentos20.73 53.00 10.99 Mo, Po: 0 2,315.338.64 51.98 20.09 Mc, Pc: 336.83 1,366.930.31 48.97 14.84 Mb, Pb: 384.04 718.616.77 44.07 7.39 Mt, Pt: 234.34 -52.4-0.27 37.48 0.10 Mf,Pf 856.2 0.0-4.33 29.45 1.28-8.98 20.28 1.82

-14.02 10.34 1.45-19.25 0.00 0.00-24.49 10.34 2.53-29.53 20.28 5.99-34.17 29.45 10.06-38.24 37.48 14.33-41.58 44.07 18.33-42.56 48.97 20.84-42.56 51.98 22.13-21.28 53.00 11.28-52.42 234.34

-60.00-50.00-40.00-30.00-20.00-10.00 0.00 10.00 20.00 30.00 40.00 50.00 60.000

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Distribucion de Fuerzas1,2

1,05




-60.00-50.00-40.00-30.00-20.00-10.00 0.00 10.00 20.00 30.00 40.00 50.00 60.000

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100

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120

130

140

Distribucion de Fuerzas1,2

1,05




0 100 200 300 400 500 600 700 800 900

-500.0

0.0

500.0

1,000.0

1,500.0

2,000.0

2,500.0




Diseño de Apoyo Extremo Tigra I


Vs. de Ref.: 8C f*c: 200

Vs. Zuncho: 4C f''c: 170

Recub.: 0.07 cm fy: 4200

Peralte: 1.06 m 0.003

0.0021


62.35 cm a: 53.00 cmárea Comp. 4817.00



12.86°


53 7 55.35 0.00266 4200.00

51.67 8.33 54.02 0.00260 4200.00

47.75 12.25 50.10 0.00241 4200.00

41.44 18.56 43.79 0.00211 4200.00

33.04 26.96 35.40 0.00170 3406.21

23.00 37.00 25.35 0.00122 2439.22

11.79 48.21 14.15 0.00068 1361.27

0.00 60.00 2.35 0.00011 226.42

11.79 71.79 9.44 0.00045 908.44

23.00 83.00 20.64 0.00099 1986.39

33.04 93.04 30.69 0.00148 2953.38

41.44 101.44 39.08 0.00188 3760.93

47.75 107.75 45.40 0.00218 4200.00

51.67 111.67 49.32 0.00237 4200.00

53.00 113.00 50.65 0.00244 4200.00

kg/cm2

kg/cm2

kg/cm2

kg/cm2

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εy:

Cb:


εn fn

D1:

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D3:

D4:

D5:

D6:

D7:

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D14:

D15:

D16:

D17:

D18:

D19:

D20:




Fza. (ton) Brazos (cm) Momentos21.28 53.00 11.28 Mo, Po: 0 2,230.142.56 51.67 21.99 Mb, Pb: 359.40 716.642.56 47.75 20.3242.56 41.44 17.6434.52 33.04 11.4124.72 23.00 5.6813.80 11.79 1.632.29 0.00 0.00-9.21 11.79 1.09

-20.13 23.00 4.63-29.93 33.04 9.89-38.11 41.44 15.79-42.56 47.75 20.32-42.56 51.67 21.99-21.28 53.00 11.28716.57 359.40

-60.00 -50.00 -40.00 -30.00 -20.00 -10.00 0.00 10.00 20.00 30.00 40.00 50.00 60.000

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1,2

1,05








Recub.: 0.07 cm fy: 4200

Peralte: 1.06 m 0.003

0.0021


90.00 cm a: 76.50 cmárea Comp. 7610.00



12.86°


53 7 83.00 0.00277 4200.00

51.67 8.33 81.67 0.00272 4200.00

47.75 12.25 77.75 0.00259 4200.00

41.44 18.56 71.44 0.00238 4200.00

33.04 26.96 63.04 0.00210 4200.00

23.00 37.00 53.00 0.00177 3533.06

11.79 48.21 41.79 0.00139 2786.24

0.00 60.00 30.00 0.00100 2000.00

11.79 71.79 18.21 0.00061 1213.76

23.00 83.00 7.00 0.00023 466.94

33.04 93.04 3.04 0.00040 799.30

41.44 101.44 11.44 0.00150 3002.23

47.75 107.75 17.75 0.00233 4200.00

51.67 111.67 21.67 0.00284 4200.00

53.00 113.00 23.00 0.00302 4200.00

kg/cm2

kg/cm2

kg/cm2

kg/cm2

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εy:

Cc:


εn fn

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D2:

D3:

D4:

D5:

D6:

D7:

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D15:

D16:

D17:

D18:

D19:

D20:




Fza. (ton) Brazos (cm) Momentos21.28 53.00 11.28 Mo, Po: 0 2,230.142.56 51.67 21.99 Mb, Pb: 359.40 716.642.56 47.75 20.32 Mc, Pc: 330.48 1,247.642.56 41.44 17.6442.56 33.04 14.0735.80 23.00 8.2328.24 11.79 3.3320.27 0.00 0.0012.30 11.79 1.454.73 23.00 1.09-8.10 33.04 2.68

-30.43 41.44 12.61-42.56 47.75 20.32-42.56 51.67 21.99-21.28 53.00 11.28

1247.59 330.48

-60.00 -50.00 -40.00 -30.00 -20.00 -10.00 0.00 10.00 20.00 30.00 40.00 50.00 60.000

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1,2

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Recub.: 0.07 cm fy: 4200

Peralte: 1.06 m 0.003

0.0021ρ: 0.013





12.86°


53 7 18.00 0.00216 4200.00

51.67 8.33 16.67 0.00200 4001.08

47.75 12.25 12.75 0.00153 3060.32

41.44 18.56 6.44 0.00077 1544.90

33.04 26.96 1.96 0.00005 101.37

23.00 37.00 12.00 0.00031 622.44

11.79 48.21 23.21 0.00060 1203.29

0.00 60.00 35.00 0.00091 1814.81

11.79 71.79 46.79 0.00121 2426.34

23.00 83.00 58.00 0.00150 3007.19

33.04 93.04 68.04 0.00176 3528.26

41.44 101.44 76.44 0.00198 3963.40

47.75 107.75 82.75 0.00215 4200.00

51.67 111.67 86.67 0.00225 4200.00

53.00 113.00 88.00 0.00228 4200.00

kg/cm2

kg/cm2

kg/cm2

kg/cm2

εcu:

εy:

Ct:


εn fn

D1:

D2:

D3:

D4:

D5:

D6:

D7:

D8:

D14:

D15:

D16:

D17:

D18:

D19:

D20:




Fza. (ton) Brazos (cm) Momentos21.28 53.00 11.28 Mo, Po: 0 2,230.140.55 51.67 20.95 Mc, Pc: 330.48 1,247.631.01 47.75 14.81 Mb, Pb: 359.40 716.615.66 41.44 6.49 Mt, Pt: 232.91 31.9-1.03 33.04 0.34-6.31 23.00 1.45

-12.19 11.79 1.44-18.39 0.00 0.00-24.59 11.79 2.90-30.48 23.00 7.01-35.76 33.04 11.82-40.17 41.44 16.64-42.56 47.75 20.32-42.56 51.67 21.99-21.28 53.00 11.2831.87 232.91

-60.00 -50.00 -40.00 -30.00 -20.00 -10.00 0.00 10.00 20.00 30.00 40.00 50.00 60.000

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140


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-60.00 -50.00 -40.00 -30.00 -20.00 -10.00 0.00 10.00 20.00 30.00 40.00 50.00 60.000

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Diagrama de Interacción de la Columna Analizada

0 50 100 150 200 250 300 350 4000.0

500.0

1,000.0

1,500.0

2,000.0

2,500.0







Recub.: 0.07 cm fy: 4200

Peralte: 1.06 m 0.003

0.0021


62.35 cm a: 53.00 cmárea Comp. 4817.00



15.00°


53 7 55.35 0.00266 4200.00

51.19 8.81 53.55 0.00258 4200.00

45.90 14.10 48.25 0.00232 4200.00

37.48 22.52 39.83 0.00192 3832.66

26.50 33.50 28.85 0.00139 2776.42

13.72 46.28 16.07 0.00077 1546.39

0.00 60.00 2.35 0.00011 226.4213.72 73.72 11.36 0.00055 1093.56

26.50 86.50 24.15 0.00116 2323.58

37.48 97.48 35.12 0.00169 3379.83

45.90 105.90 43.55 0.00210 4190.31

51.19 111.19 48.84 0.00235 4200.00

53.00 113.00 50.65 0.00244 4200.00

kg/cm2

kg/cm2

kg/cm2

kg/cm2

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εy:

Cb:


εn fn

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D19:

D20:




Fza. (ton) Brazos (cm) Momentos21.28 53.00 11.28 Mo, Po: 0 2,145.042.56 51.19 21.79 Mb, Pb: 334.38 712.242.56 45.90 19.5438.84 37.48 14.5628.14 26.50 7.4615.67 13.72 2.152.29 0.00 0.00

-11.08 13.72 1.52-23.55 26.50 6.24-34.25 37.48 12.84-42.47 45.90 19.49-42.56 51.19 21.79-21.28 53.00 11.28712.22 334.38

-60.00 -50.00 -40.00 -30.00 -20.00 -10.00 0.00 10.00 20.00 30.00 40.00 50.00 60.000

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140


1,2

1,05




0




Recub.: 0.07 cm fy: 4200

Peralte: 1.06 m 0.003

0.0021


90.00 cm a: 76.50 cmárea Comp. 7610.00



15.00°


53 7 83.00 0.00277 4200.00

51.19 8.81 81.19 0.00271 4200.00

45.90 14.10 75.90 0.00253 4200.00

37.48 22.52 67.48 0.00225 4200.00

26.50 33.50 56.50 0.00188 3766.67

13.72 46.28 43.72 0.00146 2914.49

0.00 60.00 30.00 0.00100 2000.0013.72 73.72 16.28 0.00054 1085.51

26.50 86.50 3.50 0.00012 233.33

37.48 97.48 7.48 0.00098 1962.62

45.90 105.90 15.90 0.00209 4173.58

51.19 111.19 21.19 0.00278 4200.00

53.00 113.00 23.00 0.00302 4200.00

kg/cm2

kg/cm2

kg/cm2

kg/cm2

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εy:

Cc:


εn fn

D1:

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D3:

D4:

D5:

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D15:

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D18:

D19:

D20:




Fza. (ton) Brazos (cm) Momentos21.28 53.00 11.28 Mo, Po: 0 2,145.042.56 51.19 21.79 Mb, Pb: 334.38 712.242.56 45.90 19.54 Mc, Pc: 306.99 1,223.942.56 37.48 15.9538.17 26.50 10.1229.54 13.72 4.0520.27 0.00 0.0011.00 13.72 1.512.36 26.50 0.63

-19.89 37.48 7.45-42.30 45.90 19.41-42.56 51.19 21.79-21.28 53.00 11.28

1223.93 306.99

-60.00 -50.00 -40.00 -30.00 -20.00 -10.00 0.00 10.00 20.00 30.00 40.00 50.00 60.000

10

20

30

40

50

60

70

80

90

100

110

120

130

140


1,2

1,05




0




Recub.: 0.07 cm fy: 4200

Peralte: 1.06 m 0.003

0.0021ρ: 0.011





15.00°


53 7 18.00 0.00216 4200.00

51.19 8.81 16.19 0.00194 3886.58

45.90 14.10 10.90 0.00131 2615.84

37.48 22.52 2.48 0.00006 128.42

26.50 33.50 8.50 0.00022 440.74

13.72 46.28 21.28 0.00055 1103.54

0.00 60.00 35.00 0.00091 1814.8113.72 73.72 48.72 0.00126 2526.09

26.50 86.50 61.50 0.00159 3188.89

37.48 97.48 72.48 0.00188 3758.05

45.90 105.90 80.90 0.00210 4194.78

51.19 111.19 86.19 0.00223 4200.00

53.00 113.00 88.00 0.00228 4200.00

kg/cm2

kg/cm2

kg/cm2

kg/cm2

εcu:

εy:

Ct:


εn fn

D1:

D2:

D3:

D4:

D5:

D5:

D15:

D16:

D17:

D18:

D19:

D20:




Fza. (ton) Brazos (cm) Momentos21.28 53.00 11.28 Mo, Po: 0 2,145.039.39 51.19 20.16 Mc, Pc: 306.99 1,223.926.51 45.90 12.17 Mb, Pb: 334.38 712.21.30 37.48 0.49 Mt, Pt: 209.94 50.8-4.47 26.50 1.18

-11.18 13.72 1.53-18.39 0.00 0.00-25.60 13.72 3.51-32.32 26.50 8.56-38.08 37.48 14.27-42.51 45.90 19.51-42.56 51.19 21.79-21.28 53.00 11.2850.77 209.94

-60.00 -50.00 -40.00 -30.00 -20.00 -10.00 0.00 10.00 20.00 30.00 40.00 50.00 60.000

10

20

30

40

50

60

70

80

90

100

110

120

130

140


1,2

1,05




Diagrama de Interacción de la Columna Analizada

0 50 100 150 200 250 300 350 4000.0

500.0

1,000.0

1,500.0

2,000.0

2,500.0

0 50 100 150 200 250 300 350 400 450

-200.0

0.0

200.0

400.0

600.0

800.0

1,000.0

1,200.0

1,400.0

1,600.0

1,800.0

2,000.0

2,200.0

2,400.0

2,600.0

36 vs32 vs28 vsE.M.20 Vs

CURVATURA K

Simple 0.50

Doble 0.70

1.00

1.00

2.00

2.00

10.0010.6212.4515.4519.5524.6430.6137.3044.5552.1860.0067.8275.4582.7089.3995.36

100.45104.55107.55109.38110.00

397.73451.53621.18934.13

1416.022086.182948.613991.265181.856481.917833.569183.6710470.911650.6

12680.0513533.25614195.8714665.2214941.9515034.69

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