calculo del momento ultimo de un puente de 2 vanos puente s

L1 L2

bs

t bs = 270

t = 20h

WDW = 0.33

bw

MU= 1,25MDC + 1,50MDW + 1,75MLLFy = 4200 = 0.9rinf = 7.5 cmrsup = 10.0 cm

CARGA VIVAUniforme Camin

WLL = 0.65 t/m 3.28 13.12P1 P2

S1 S2

Grup f'c S1 S2 L1 L2 bw h210 4.00 4.75 18.50 16.40 0.40 1.45

kg/cm2

CARGA MUERTA PESO PROPIO

WDC = 3.271 t/m

18.50 16.40

o o' 862.95 601.17M 0 125.856

Visos 30.26 30.26 26.82Vhip -6.80 6.80 7.67

Vtotal 23.45 37.06 34.50x/z 7.17 m 5.85

MDC max 84.08 t-m 56.05

CARGA MUERTA PESO PROPIO

WDW= 0.33 t/m

18.50 16.40

o o' 87.06 60.65M 0 12.70

Visos 3.053 3.053 2.71Vhip -0.69 0.69 0.77

Vtotal 2.366 3.74 3.48x/z 7.17 m 5.85

MDC max 8.483 t-m 5.654

CARGA VIVA Carga viva uniforme 1

WLL= 0.65 t/m

18.50 16.40

o o' 171.48 0.00M 0 14.74

Visos 6.01 6.01 0.00Vhip -0.80 0.80 0.90

Vtotal 5.22 6.81 0.90

x/z 7.17 m 5.85MDC max 20.69 t-m -5.26

Carga viva uniforme 2

WLL= 0.65

18.50 16.40

o o' 0.00 119.46M 0 10.27

Visos 0.00 0.00 5.33Vhip -0.56 0.56 0.63

Vtotal -0.56 0.56 5.96x/z 7.17 m 5.85

MDC max -3.98 t-m 16.40

Carga uniforme 3

WDW= 0.65 t/m

18.50 16.40

o o' 171.48 119.46M 0 25.01

Visos 6.01 6.01 5.33Vhip -1.35 1.35 1.52

Vtotal 4.66 7.36 6.85x/z 7.17 m 5.85

MDC max 16.71 t-m 11.14

CARGA VIVA CAMIN1er tramo posicin 1

7.17 11.334.00 4.75

P1 P2 P3

3.17 15.3311.92 6.58

18.50 16.40

P1 = 3.28 31.12 0.00P2 = 13.12 o' 246.49 0.00 oP3 = 13.12 282.01 0.00

559.62 0.00559.62

M 0 48.105Visos 15.42 15.42 0.00Vhip -2.60 2.60 2.93

Vtotal 12.82 18.02 2.93x/z 7.17 m 5.85

MDC max 78.79 t-m -17.17

1er tramo posicin 2

7.17 11.334.75 4.00

P3 P2 P1

2.42 16.0811.17 7.33

18.50 16.40

P3 = 13.12 96.23 0.00P2 = 13.12 o' 246.49 0.00 oP1 = 3.28 71.78 0.00

414.50 0.00414.50

M 0 35.63Visos 20.74 20.74 0.00Vhip -1.93 1.93 2.17

Vtotal 18.81 22.66 2.17x/z 7.17 m 5.85

MDC max 72.57 t-m -12.72

2do tramo posicin 1

10.554.00

P1

6.5515.30

18.50 16.40

P1 = 3.28 0 56.45P2 = 13.12 o' 0 183.18 oP3 = 13.12 0 39.41

0 279.04279.04

M 0 23.99Visos 0.00 0.00 21.98Vhip -1.30 1.30 1.46

Vtotal -1.30 1.30 23.45x/z 7.17 m 5.85

MDC max -9.30 t-m 57.80

2do tramo posicin 2

10.554.75

P3

5.8014.55

18.50 16.40

P3 = 13.12 0 221.29P2 = 13.12 o' 0 183.18 oP1 = 3.28 0 16.41

0 420.88420.88

M 0 36.18Visos 0.00 0.00 15.98Vhip -1.96 1.96 2.21

Vtotal -1.96 1.96 18.19x/z 7.17 m 5.85

MDC max -14.02 t-m 67.53

Momento negativo en el apoyo intermedio2 tramos, posicin 1

7.17 11.33 12.66 3.744.00 4.75 4.00 4.75

P1 P2 P3 P1 P2 P3

3.17 15.33 8.66 7.7411.92 6.58 17.41

18.50 16.40

P1 = 3.28 31.12 53.93P2 = 13.12 o' 246.49 127.14 oP3 = 13.12 282.01

559.62 181.08740.69

M 0 63.67Visos 15.42 15.42 21.98Vhip -3.44 3.44 3.88

Vtotal 11.98 18.86 25.87x/z 7.17 m 3.74

MDC max 72.76 t-m 5.37

2 tramos, posicin 2

7.17 11.33 12.66 3.744.75 4.00 4.75 4.00

P3 P2 P1 P3 P2 P1

2.42 16.08 7.91 8.4911.17 7.33 16.66

18.50 16.40

P3 = 13.12 96.23 222.87P2 = 13.12 o' 246.49 127.14 oP1 = 3.28 71.78

414.50 350.01764.51

M 0 65.72Visos 20.74 20.74 19.79Vhip -3.55 3.55 4.01

Vtotal 17.19 24.29 23.80x/z 7.17 m 3.74

MDC max 60.91 t-m 45.90

.. MOMENTOS MXIMOS DE CARGA VIVA

Momentos por carga uniforme

25.0120.69 16.40

Momentos por carga de camin

65.7278.79 67.53

Momentos por carga viva de camin + IMPACTO

IM= 1.3387.40

104.80 89.81

Momentos totales de carga viva + impacto

112.41125.49 106.21

RESMEN DE MOMENTOS DE LOS 3 ESTADOS DE CARGA

112.41312.70

125.86

84.08 56.058.48 5.65

125.49 106.21

MOMENTOS ULTIMOSMU = 1,25MDC + 1,50MDW + 1,75 MLL+IM

373.088337.429 264.409

ARMADURA

Armadura a flexin

Para Momento Positivof'c = 210

270 Fy= 4200bs= 270

20 bw= 40h= 145t= 20

145 137.5 = 0.9rinf= 7.5rsup= 10d(+) = 137.5

x x' 1 = 0.8540

MUL = x 0,85 fc bs 1 t (d - 1 t/2)MUL = 951.2247 t-m Muext

As calc =

b.) acero mnimo

Mcr = fr Ig/yt

fr = 2 yt = Ig =fr = 28.98 yt = 100.144231 Ig =

Mcr = 58.86 t-m

wmin = min = w f'c / Fy As min =wmin = 0.006 min = 0.00030613 As min =

As min = < min

c.) acero mximo

TRAMO A - Bc = (As Fy)/(0,85 f'c b ) t = 0,003 (dt - c)/cc = 7.421 t = 0.052586

0.052586 > 0,005

TRAMO B - Cc = (As Fy)/(0,85 f'c b ) t = 0,003 (dt - c)/cc = 5.772 t = 0.068467

0.068467 > 0,005

Para momento negativof'c = 210

270 Fy= 4200x x' bs= 270

20 bw= 40h= 145t= 20

145 135 = 0.9

^ )(

rinf= 7.5rsup= 10d(-) = 135

x x' 1 = 0.8540

MUL = x 0,85 fc bs 1 t (d - 1 t/2)MUL = 932.7901 t-m Muext < MUL Viga R de ancho bsMuext = 373.088 t-m

a.) acero calculado

w= frmula = w f'c / Fy As calc = bw dw= 0.3383121 = 0.0169156 As calc = 91.34

As calc = 12

b.) acero mnimo

Mcr = fr Ig/yt

fr = 2 yt = Ig =fr = 28.98 yt = 44.855769 Ig = 20336450.320513

Mcr = 131.40034

wmin = min = w f'c / Fy As min = bw dwmin = 0.0438514 min = 0.0021926 As min = 11.84

As min = 2 < min

c.) acero mximo

c = (As Fy)/(0,85 f'c b ) t = 0,003 (dt - c)/cc = 66.79 t = 0.003064

0.003064 < 0,005

= 0,65 + 0,15 (dt/ c-1) = 0.803

a.) acero calculado

w= frmula = w f'c / Fy As calc = bw dw= 0.3958898 = 0.0197945 As calc = 106.89

^ )(

As calc = 14

b.) acero mnimo

Mcr = fr Ig/yt

fr = 2 yt = Ig =fr = 270.00 yt = 44.855769 Ig = 20336450.320513

Mcr = 1224.1105

wmin = min = w f'c / Fy As min = bw dwmin = 0.0492993 min = 0.002465 As min = 13.31

As min = 2 < min

c.) acero mximo

c = (As Fy)/(0,85 f'c b ) t = 0,003 (dt - c)/cc = 77.92 t = 0.002198

RESOLUCION MEDIANTE EL USO DE MATRICES

Datosf'c= 210 b = 270Fy= 4200 h = 145S1 = 4.00 WDC = 3.271S2 = 4.75 r inf = 7.5L1 = 18.50 r sup = 10L2 = 16.40 P1 = 3.28

P2 = 13.12P3 = 13.12

MF M'F k = 4EI / La = k/2

12 12 E = 12000 f'c = 1738.965I = 0.203365 m4

CARGA MUERTA DC

WDC = 3.271 t/m

WL2 WL2

^ )(

18.50 16.40

MF MF 93.29 -93.29 73.31k 76.46 76.46 86.25a 38.23 43.13

93.29 -19.98 k 76.46 162.72

a 38.23 43.13

RESOLUCION MATRICIAL DE GIROSUSANDO LA MATRIZ INVERSA

76.46 1 + 38.23 2 + 0.00 3 = -93.2938.23 1 + 162.72 2 + 43.13 3 = 19.98

0.00 1 + 43.13 2 + 86.25 3 = 73.31

R = -m

76.46 38.23 0.00R 38.23 162.72 43.13 -m

0.00 43.13 86.25

= -m

0.0151 -0.0041 0.0020-0.0041 0.0082 -0.0041 0.0020 -0.0041 0.0136

-1.3429 0.2455

MF

ai i + A + ad d + m = 0ai i + A + ad d = -m

R -1

R -1

0.00 -125.856 125.856

CARGA MUERTA DW

WDC = 0.33 t/m

18.50 16.40

MF MF 9.412 -9.41 7.40k 76.46 76.46 86.25a 38.23 43.13

9.412 -2.02 k 76.46 162.72

a 38.23 43.13


76.46 1 + 38.23 2 + 0.00 3 = -9.4138.23 1 + 162.72 2 + 43.13 3 = 2.02

0.00 1 + 43.13 2 + 86.25 3 = 7.40

R = -m

76.46 38.23 0.00R 38.23 162.72 43.13 -m

0.00 43.13 86.25

MF


= -m

0.0151 -0.0041 0.0020-0.0041 0.0082 -0.0041 0.0020 -0.0041 0.0136

-0.1355 0.0248

0.00 -12.697 12.697

CARGA VIVA WLL1

WDC = 0.65 t/m

18.50 16.40

MF MF 18.54 -18.54 0.00k 76.46 76.46 86.25a 38.23 43.13

18.54 -18.54 k 76.46 162.72

a 38.23 43.13


R -1

R -1

MF


76.46 1 + 38.23 2 + 0.00 3 = -18.5438.23 1 + 162.72 2 + 43.13 3 = 18.54

0.00 1 + 43.13 2 + 86.25 3 = 0.00

R = -m

76.46 38.23 0.00R 38.23 162.72 43.13 -m

0.00 43.13 86.25

= -m

0.0151 -0.0041 0.0020-0.0041 0.0082 -0.0041 0.0020 -0.0041 0.0136

-0.3564 0.2279

0.00 -14.741 14.741

CARGA WLL2

WLL = 0.65 t/m

18.50 16.40

MF MF 0 0.00 14.57k 76.46 76.46 86.25a 38.23 43.13

0 14.57 k 76.46 162.72

a 38.23 43.13

R -1

R -1

MF


76.46 1 + 38.23 2 + 0.00 3 = 0.0038.23 1 + 162.72 2 + 43.13 3 = -14.57

0.00 1 + 43.13 2 + 86.25 3 = 14.57

R = -m

76.46 38.23 0.00R 38.23 162.72 43.13 -m

0.00 43.13 86.25

= -m

0.0151 -0.0041 0.0020-0.0041 0.0082 -0.0041 0.0020 -0.0041 0.0136

0.0895 -0.1791

0.00 -10.269 10.269

CARGA MUERTA DC

WDC = 0.65 t/m

18.50 16.40


R -1

R -1

MF MF 18.54 -18.54 14.57k 76.46 76.46 86.25a 38.23 43.13

18.54 -3.97 k 76.46 162.72

a 38.23 43.13


76.46 1 + 38.23 2 + 0.00 3 = -18.5438.23 1 + 162.72 2 + 43.13 3 = 3.97

0.00 1 + 43.13 2 + 86.25 3 = 14.57

R = -m

76.46 38.23 0.00R 38.23 162.72 43.13 -m

0.00 43.13 86.25

= -m

0.0151 -0.0041 0.0020-0.0041 0.0082 -0.0041 0.0020 -0.0041 0.0136

-0.2668 0.0488

0.00 -25.010 25.010

MF


R -1

R -1


7.17 11.334.00 4.75

P1 P2 P3

3.17 15.3311.92 6.58

18.50 16.40

Tramo 1MF MF P a b MF M'F

3.28 3.17 15.33 7.14 -1.4813.12 7.17 11.33 35.28 -22.3313.12 11.92 6.58 19.78 -35.840.00 0.00 0.000.00 0.00 0.00

62.21 -59.65

MF MF 62.21 -59.65 0.00k 76.46 76.46 86.25a 38.23 43.13

62.21 -59.65 k 76.46 162.72

a 38.23 43.13


76.46 1 + 38.23 2 + 0.00 3 = -62.21

MF


38.23 1 + 162.72 2 + 43.13 3 = 59.650.00 1 + 43.13 2 + 86.25 3 = 0.00

R = -m

76.46 38.23 0.00R 38.23 162.72 43.13 -m

0.00 43.13 86.25

= -m

0.0151 -0.0041 0.0020-0.0041 0.0082 -0.0041 0.0020 -0.0041 0.0136

-1.1853 0.7436

0.00 -48.105 48.105


7.17 11.334.75 4

P3 P2 P1

2.420 16.0811.17 7.33

18.50 16.40


13.12 2.42 16.08 23.99 -3.6113.12 7.17 11.33 35.28 -22.333.28 11.17 7.33 5.75 -8.760.00 0.00 0.000.00 0.00 0.00

R -1

R -1

65.02 -34.70

MF MF 65.02 -34.70 0.00k 76.46 76.46 86.25a 38.23 43.13

65.02 -34.70 k 76.46 162.72

a 38.23 43.13


76.46 1 + 38.23 2 + 0.00 3 = -65.0238.23 1 + 162.72 2 + 43.13 3 = 34.70

0.00 1 + 43.13 2 + 86.25 3 = 0.00

R = -m

76.46 38.23 0.00R 38.23 162.72 43.13 -m

0.00 43.13 86.25

= -m

0.0151 -0.0041 0.0020-0.0041 0.0082 -0.0041 0.0020 -0.0041 0.0136

-1.1258 0.5508

0.00 -35.630 35.630

MF


R -1

R -1

CARGA VIVA CAMIN2do tramo posicin 1

10.554

P1

6.5515.30

18.50 16.40


3.28 6.55 9.85 0.00 0.0013.12 10.55 5.85 0.00 0.0013.12 15.30 1.100.00 0.00 0.000.00 0.00 0.00

0.00 0.00

MF MF 0.00 0.00 26.29k 76.46 76.46 86.25a 38.23 43.13

0 26.29 k 76.46 162.72

a 38.23 43.13


76.46 1 + 38.23 2 + 0.00 3 = 0.0038.23 1 + 162.72 2 + 43.13 3 = -26.29

0.00 1 + 43.13 2 + 86.25 3 = 49.51

MF


R = -m

76.46 38.23 0.00R 38.23 162.72 43.13 -m

0.00 43.13 86.25

= -m

0.0151 -0.0041 0.0020-0.0041 0.0082 -0.0041 0.0020 -0.0041 0.0136

0.2091 -0.4183

0.00 -23.986 23.986

CARGA VIVA CAMIN2do tramo posicin 2

10.554.75

P3

5.8014.55

18.50 16.40


13.12 5.80 10.60 0.00 0.0013.12 10.55 5.85 0.00 0.003.28 14.55 1.850.00 0.00 0.000.00 0.00 0.00

0.00 0.00

R -1

R -1

MF MF 0.00 0.00 50.03k 76.46 76.46 86.25a 38.23 43.13

0 50.03 k 76.46 162.72

a 38.23 43.13


76.46 1 + 38.23 2 + 0.00 3 = 0.0038.23 1 + 162.72 2 + 43.13 3 = -50.03

0.00 1 + 43.13 2 + 86.25 3 = 53.92

R = -m

76.46 38.23 0.00R 38.23 162.72 43.13 -m

0.00 43.13 86.25

= -m

0.0151 -0.0041 0.0020-0.0041 0.0082 -0.0041 0.0020 -0.0041 0.0136

0.3154 -0.6309

0.00 -36.179 36.179

MF


R -1

R -1

MOMENTO NEGATIVO EN EL APOYO INTERMEDIO posicin 1

7.17 11.33 12.664.00 4.75 4

P1 P2 P3 P1

3.17 15.33 8.6611.92 6.58

18.50 16.40

Tramo 1 Tramo 2 Tramo 1MF MF P a b a b MF M'F

3.28 3.17 15.33 8.66 7.74 7.14 -1.4813.12 7.17 11.33 12.66 3.74 35.28 -22.3313.12 11.92 6.58 19.78 -35.840.00 0.00 0.000.00 0.00 0.00

62.21 -59.65

MF MF 62.21 -59.65 14.96k 76.46 76.46 86.25a 38.23 43.13

62.21 -44.68 k 76.46 162.72

a 38.23 43.13


76.46 1 + 38.23 2 + 0.00 3 = -62.2138.23 1 + 162.72 2 + 43.13 3 = 44.68

0.00 1 + 43.13 2 + 86.25 3 = 36.32

MF


R = -m

76.46 38.23 0.00R 38.23 162.72 43.13 -m

0.00 43.13 86.25

= -m

0.0151 -0.0041 0.0020-0.0041 0.0082 -0.0041 0.0020 -0.0041 0.0136

-1.0496 0.4722

0.00 -63.670 63.670

posicin 2

7.17 11.33 12.664.75 4 4.75

P3 P2 P1 P3

2.42 16.08 7.9111.17 7.33

18.50 16.40

Tramo 1 Tramo 2 Tramo 1MF MF P a b a b MF M'F

13.12 2.42 16.08 7.91 8.49 23.99 -3.6113.12 7.17 11.33 12.66 3.74 35.28 -22.333.28 11.17 7.33 0 0 5.75 -8.760.00 0.00 0.000.00 0.00 0.00

65.02 -34.70

R -1

R -1

MF MF 65.02 -34.70 36.45k 76.46 76.46 86.25a 38.23 43.13

65.02 1.74 k 76.46 162.72

a 38.23 43.13


76.46 1 + 38.23 2 + 0.00 3 = -65.0238.23 1 + 162.72 2 + 43.13 3 = -1.74

0.00 1 + 43.13 2 + 86.25 3 = 55.15

R = -m

76.46 38.23 0.00R 38.23 162.72 43.13 -m

0.00 43.13 86.25

= -m

0.0151 -0.0041 0.0020-0.0041 0.0082 -0.0041 0.0020 -0.0041 0.0136

-0.8635 0.0261

0.00 -65.717 65.717

MF


R -1

R -1

H

13.12P3

WDC3.271

026.82-7.6719.15

m t-m

02.71

-0.771.93

m t-m

00.00

-0.90-0.90

m t-m

t/m

05.33

-0.634.70

m t-m

05.33

-1.523.81

m t-m

00.00

-2.93-2.93

m t-m

00.00

-2.17-2.17

m t-m

5.854.75

P2 P3

9.851.10

021.98-1.4620.52

m t-m

5.854.00

P2 P1

10.601.85

015.98-2.2113.78

m t-m

3.74

7.74-1.01

021.98-3.8818.10

m t-m

3.74

P2 P1

8.49-0.26

019.79-4.0115.78

m t-m

MLL + IMMDWMDC

MDCMDW

MLL + IM

Muext

7 32 mm

20336450.3205

bs d11.36

2 32 mm

0,003 (dt - c)/c

No hace faltadisminuir

0,003 (dt - c)/c

No hace faltadisminuir

Muext < MUL Viga R de ancho bs

32 mm

20336450.320513

11.84 32 mm

0,003 (dt - c)/c

Se debe disminuir

32 mm

20336450.320513

13.31 32 mm

0,003 (dt - c)/c

t/m2

-73.3186.25

-73.3186.25

-93.319.9873.31

-1.34290.24555

0.7272

0.7272

0.00

-7.4086.25

-7.4086.25

-9.42.027.40

-0.13550.024770.07336

0.0734

0.00

0.0086.25

0.0086.25

-18.518.54

0.00

-0.35640.22786-0.1139

-0.1139

0.00

-14.5786.25

-14.5786.25

0.0-14.5714.57

0.08953-0.17910.25844

0.2584

0.00

-14.5786.25

-14.5786.25

-18.53.97

14.57

-0.26680.048790.14451

0.1445

0.00

Tramo 2MF M'F

0.00 0.000.00 0.00

0.00 0.00

0.0086.25

0.0086.25

-62.259.60.00

-1.18530.74361-0.3718

-0.3718

0.00

Tramo 2MF M'F

0.00 0.000.00 0.00

0.00 0.00

0.0086.25

0.0086.25

-65.034.70.00

-1.12580.55078-0.2754

-0.2754

0.00

5.854.75

P2 P3

9.851.10

Tramo 2MF M'F

7.75 -5.1517.63 -31.80.91 -12.600.00 0.000.00 0.0026.29 -49.51

-49.5186.25

-49.5186.25

0.0-26.349.51

0.20913-0.41830.7831

0.7831

0.00

5.854

P2 P1

10.601.85

Tramo 2MF M'F

31.79 -17.3817.63 -31.80.61 -4.780.00 0.000.00 0.0050.03 -53.92

-53.9286.25

-53.9286.25

0.0-50.053.92

0.31544-0.63090.94057

0.9406

0.00

3.74

P2 P3

7.74

Tramo 2MF M'F

6.33 -7.088.64 -29.20.00 0.00

0.00 0.000.00 0.00

14.96 -36.32

-36.3286.25

-36.3286.25

-62.244.7

36.32

-1.04960.472190.18497

0.1850

0.00

3.744.75

P2 P1

8.49

Tramo 2MF M'F

27.81 -25.918.64 -29.20.00 0.000.00 0.000.00 0.0036.45 -55.15

-55.1586.25

-55.1586.25

-65.0-1.7

55.15

-0.86350.026140.62635

0.6263

0.00

Hoja1

calculo del momento ultimo de un puente de 2 vanos puente s

Documents