Metodo Del Portal y Muto (1)

100 Ko= f´c= Ec= Ec=

300 21 21538.105766 Kn/mm2 2153.8105766 Kn K n/cm2

25 60 3.5

40 40

150

45 45 30 60

3.2

40 40

100 CREDI CREDITOS TOS APAR APAREDE EDESGA SGA DERECOS RESER"ADOS #

25

30 45 45

30 60 3.2

40 40

50

30 45 45

30 70

30

3.5 40 40

45 45 6

 Y

60

2.500 35 35

2.032

60

3.000 3.254

3.000 35 35

2.222

60

3.600 3.560

3.000 35 35

2.222

70

3.600 3.560

4.764 35 35

2.032

5

5.717 3.254

2.500 $c  %$ ' Do $ CD "c (0 (1 (2 (3  Y

2.032 1.354 0.404 63.2&6 51.&05 0.266 26.62&

$c  %$ ' Do $ CD "c (0 (1 (2 (3  Y

2.222 1.350 0.403 75.720 67.80& 0.266 66.558

$c

2.222

0.000

0.000

3.000 3.254 1.85& 0.482 63.2&6 &&.233 0.50& 50.&10

3.000

0.000

3.600

3.560 1.854 0.481 75.720 12&.666 0.50& 127.274

3.000

0.000 3.560

3.600

 %$ ' Do $ CD "c (0 (1 (2 (3  Y

1.747 0.466 75.720 78.44& 0.272 &5.106

0.000

$c 2.032  %$ 2.345 ' 0.655 Do 63.2&6 $ 84.202 CD 0.2&1 "c 116.236 (0 (1 (2 (3  Y 0.000

2.3&& 0.545 75.720 146.&&5 0.50& 178.206

4.764

0.000 3.254 3.220 0.713 63.2&6 146.804 0.507 202.656

0.000

5.717

1.1&1

1.303

1.303

1.1&1

1.1&1 2.771 0.581 63.2&6 43.782 0.225 22.461

1&4.&1&36 100

0.000 1.303 2.764 0.580 75.720 57.223 0.225 56.168

0.000 1.303

254.6&7725 250

3.576 0.641 75.720 63.257 0.21& 76.688

288.702082 350

0.000 1.1&1 4.800 0.77& 63.2&6 58.755 0.203 81.108

0.000

28&.760542 400

COE)ICIE*TES 0.167 0.455 0.200 0.545 0.367 1.000 65 3.568 2.275

65

28.571

1.225

137.143 35 3.568 1.&2

 

172.143

71.42& 1.28

176 &1.42& 3.568 1.76

267.42&

100

1.44

160 144 3.568 1.40

 

304.000

114.286

2.10

240 6

44.318

65 &7.5

65 2.250

53.182

42.857

28.571

117.370

172.143

205.714

137.143

52.5

35 2.250 140.844

107.143

71.42&

182.338

267.42& 264

176

137.143

&1.42& 2.250

218.805

150

100

207.273

304.000 240

160

216

144 2.250 248.727

171.42&

114.286

360

240 5

COE)ICIE*TES 0.167 0.455 0.200 0.545 0.367 1.000 &3.2007364 3.210 &3.2007364

26.62&

212.&86 0 3.210 212.&86

66.558

304.33& 0.000 3.240 304.33&

&5.1060817

406.827411 0 3.347 406.827

116.236

0 6

80.&&3

 

78.615028

178.184236

78.615028 2.764

&7.1&1

50.&10

22.461

185.126

17&.737

407.277

17&.737

0

0 2.764 222.151

127.274

56.168

25&.20&

245.402

570.25&

245.4016

0.000

0.000 2.7&5

311.050

178.205&18

76.688

322.407

283.878

70&.2&4877

283.877712

0

0 2.884 386.888

202.656

81.108

0

0 5

3.5 3.2 3.2 3.5

A+T,RAS 3.5 0 3.2 0 3.2 0 3.5 0

3.5 0 3.2 0 3.2 0 3.5 0

3.5 0 3.2 0 3.2 0 3.5 0

Kn 60 Ko= f´c= Ec= Ec=

&00 21 21538.105766 Kn/mm2 2153.8105766 Kn/cm2

  3.2

30 60 40 40

40

40 40 30 60

3.2

40 40

30 CREDITOS

30

30 40 40

30 60

30

APAREDESGA 3.2

40 40

20

40 40 30 60

30

3.5 40 40

40 40 6.5

60

30 60 40 40

60

40 40

60

0.741 0.&23

40 40

1.154

0.741

30 60 40 40

1.154

0.741

30 60

60

0.741 0.&23

40 40

40 40

1.154

0.741

30 60 40 40

5.2

0.&23

0.741 0.&23

40 40

1.154

0.677

5 $c 0.741  %$ 1.246 ' 0.384 Do 227.160 $ 64.5&5 CD 0.18& "c 11.353 (0 1.280 (1 0.000 (2 0.000 (3 0.000  Y 1.280

0.677

0.&23

1.154

0.4 0 0 0 0.&23

0.741 2.804 0.584 227.160 &8.212 0.288 17.261 1.440   0.45 0.000 0 0.000 0 0.000 0 1.440 1.154

$c 0.741  %$ 1.246 ' 0.384 Do 227.160 $ 64.5&5 CD 0.18& "c 18.&22 (0 1.440   0.45 (1 0.000 0 (2 0.000 0 (3 0.000 0  Y 1.440 0.&23 $c

0.741

       

       

0.741 2.804 0.584 227.160 &8.212 0.288 28.76& 1.568   0.4& 0.000 0 0.000 0 0.000 0 1.568 1.154 0.741

 %$ 1.246 ' 0.384 Do 227.160 $ 64.5&5 CD 0.18& "c 24.5&8 (0 1.600 (1 0.000 (2 0.000 (3 0.000  Y 1.600 $c 0.677  %$ 1.363 ' 0.554 Do 18&.887 $ 71.241 CD 0.214 "c 32.12& (0 2.135   (1 0.000 (2 0.000 (3 0.000  Y 2.135

0.5 0 0 0 0.&23

0.61 0 0 0

       

       

2.804 0.584 227.160 &8.212 0.288 37.400 1.600 0.000 0.000 0.000 1.600 0.677 3.067 0.704 18&.887 &0.528 0.272 40.828 1.&25   0.000 0.000 0.000 1.&25

0.5 0 0 0 1.154

0.55 0 0 0

1.200 0.741

0.741 1.200

0.741

0.741 1.200

0.741

0.741 1.200

0.677

0.677

1.200 0.741 3.178 0.614 227.160 103.270 0.303 18.151 1.440   0.45 0.000 0 0.000 0 0.000 0 1.440 1.200 0.741 3.178 0.614 227.160 103.270 0.303 30.251 1.600 0.5 0.000 0 0.000 0 0.000 0 1.600 1.200 0.741

       

       

0.741 1.620 0.448 227.160 75.302 0.221 13.235 1.280 0.000 0.000 0.000 1.280 0.741 1.620 0.448 227.160 75.302 0.221 22.058 1.440 0.000 0.000 0.000 1.440 0.741

341.378 60.000 0.4 0 0 0

341.378 100.000   0.45 0 0 0

3.178 0.614 227.160 103.270 0.303 3&.326 1.600 0.5 0.000 0 0.000 0 0.000 0 1.600 1.200 0.677 3.476 0.726 18&.887 &3.371 0.281 42.110 2.275   0.65 0.000 0 0.000 0 0.000 0 2.275

       

       

1.620 0.448 227.160 75.302 0.221 28.676 1.600 0.000 0.000 0.000 1.600 0.677 1.772 0.602 18&.887 77.45& 0.233 34.&33 1.&&5 0.000 0.000 0.000 1.&&5

341.378 130.000 0.5 0 0 0

332.5&& 150.000   0.57 0 0 0

COE)ICIE*TES 0.154 0.444 0.1&2 0.556 0.346 1.000

0.1&2 0.4&0 0.200 0.510 0.3&2 1.000 24.&6 3.&00

2.08

24.&6

12.000 1.12

38.40 13.44 3.&00 1.&2

 

51.84

20.000 1.28

45.76 25.60 3.&00 1.76

71.36

26.000

1.44

42.00 37.44 3.&00 1.40

 

7&.44

30.000

2.10

63.00 6.500

16.64

18.35 37.44

37.44 2.763

2.167

20.80

1&.0&

18.000

18.000

34.560

38.118 57.60

57.60

20.16

20.16 2.763

2.167

43.20

3&.64

30.000

30.000

47.573

52.471 68.64

68.64

38.40

38.40 2.763

2.167

5&.47

54.57

3&.000

3&.000

52.&60

58.412 63.00  

56.16

63.00 56.160 2.763

66.20

2.167 60.75

45.000

45.000

&4.50

&4.50 5.200

5

24.&6 24.&6

12.000

51.840 38.40 13.44

20.000

71.360 45.76 25.60

26.000

7&.440 42.00 37.44

30.000

63.00

COE)ICIE*TES 0.154 0.444 0.1&2 0.556 0.346 1.000

0.1&2 0.4&0 0.200 0.510 0.3&2 1.000 21.7&8 4.014

21.7&8

11.353

33.303 14.532 3.8&& 47.835

18.&22

3&.358 27.248 3.823 66.605

24.5&8

43.856 3&.358 3.&08 83.214

32.12&

68.5&5 6.500

13.502

15.65&

30.380

31.&45 2.6&7

1.&53

16.878

16.286

17.261

18.151

31.&15

36.538

46.&51

48.401

24.857

26.137 2.714

2.026

3&.8&3

38.000

28.76&

30.251

46.644

54.570

5&.840

62.&22

45.110

48.401 2.686

2.111

58.305

56.753

37.400

3&.326

55.175

5&.840

56.131

64.304  

51.585 62.&22 2.867

68.&6&

1.861 58.376

40.828

42.110

78.5&3

&5.800 5.200

5

25.411 25.411

3.20 3.20 3.20 3.50

13.235

55.763 38.822 16.&41

22.058

77.645 45.881 31.764

28.676

&8.456 52.575 45.881

1.&2 1.28 1.76 1.44 1.60 1.60 1.37 2.14

A+T,RAS 1.76 1.44 1.63 1.57 1.60 1.60 1.58 1.&3

34.&33

6&.6&2

1.76 1.44 1.60 1.60 1.60 1.60 1.23 2.28

1.&2 1.28 1.76 1.44 1.60 1.60 1.51 2.00

+= -C- = -C"=

6.50 m

55.82 K*m 23.26 K*m C- C"

-S=

24 K*/m2 10 K*/m2

7&.44 K*/m

-S=

&1  0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.&0 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.&0 2.00 2.10 2.20 2.30 2.40 2.50 2.60 2.70

-C- 55.82 47.74 3&.&0 32.2& 24.&3 17.81 10.&3 4.2& 2.11 8.28 14.20 1&.88 25.32 30.52 35.4& 40.21 44.6& 48.&3 52.&3 56.70 60.22 63.50 66.54 6&.34 71.&0 74.23 76.31 78.15

-C" 23.26 20.80 18.44 16.18 14.02 11.&5 &.&& 8.13 6.37 4.71 3.15 1.6& 0.33 0.&3 2.10 3.16 4.12 4.&8 5.74 6.40 6.&6 7.42 7.78 8.04 8.21 8.27 8.23 8.0&

1.4-C-1.7 -S -C" 7&.44 117.6& 77.40 102.1& 75.37 87.20 73.33 72.71 71.30 58.73 6&.26 45.26 67.22 32.2& 65.1& 1&.83 63.15 7.87 61.12 3.58 5&.08 14.52 57.04 24.&6 55.01 34.8& 52.&7 44.32 50.&4 53.24 48.&0 61.66 46.86 6&.56 44.83 76.&7 42.7& 83.86 40.76 &0.25 38.72 &6.14 36.68 101.52 34.65 106.3& 32.61 110.76 30.58 114.62 28.54 117.&7 26.50 120.82 24.47 123.16

2.80 2.&0 3.00 3.10 3.20 3.30 3.40 3.50 3.60 3.70 3.80 3.&0 4.00 4.10 4.20 4.30 4.40 4.50 4.60 4.70 4.80 4.&0 5.00 5.10 5.20 5.30 5.40 5.50 5.60 5.70 5.80 5.&0 6.00 6.10 6.20 6.30 6.40 6.50

7&.75 81.11 82.24 83.12 83.76 84.16 84.32 84.24 83.&3 83.37 82.57 81.53 80.25 78.74 76.&8 74.&8 72.74 70.26 67.54 64.5& 61.3& 57.&5 54.27 50.35 46.20 41.80 37.16 32.28 27.16 21.81 16.21 10.37 4.2& 2.03 8.5& 15.38 22.42 2&.70

7.85 7.51 7.07 6.53 5.8& 5.16 4.32 3.38 2.34 1.20 0.04 1.38 2.82 4.36 5.&& 7.73 &.57 11.51 13.55 15.6& 17.&3 20.27 22.71 25.25 27.88 30.62 33.46 36.40 3&.44 42.58 45.82 4&.16 52.60 56.13 5&.77 63.51 67.35 71.2&

22.43 20.40 18.36 16.32 14.2& 12.25 10.22 8.18 6.14 4.11 2.07 0.04 2.00 4.04 6.07 8.11 10.14 12.18 14.22 16.25 18.2& 20.32 22.36 24.40 26.43 28.47 30.50 32.54 34.58 36.61 38.65 40.68 42.72 44.76 46.7& 48.83 50.86 52.&0

125.00 126.33 127.15 127.47 127.28 126.5& 125.3& 123.68 121.47 118.76 115.53 111.80 107.57 102.83 &7.58 &1.82 85.56 78.80 71.53 63.75 55.47 46.68 37.38 27.58 17.27 6.46 4.86 16.6& 2&.02 41.86 55.20 6&.05 83.41 &8.27 113.63 12&.51 145.8& 162.77

200.00 150.00 100.00 50.00 0.00 0.00

1.00

2.00

3.

50.00 100.00 150.00

-C-= -C"=

2&.70 K*m 71.2& K*m

52.& K*/m

&4

&4

&5

&5

1.25-C- 1.25-C- -C"-S -C"-S 0.&-C--S 0.&-C--S 178.2& 1&.41 12&.68 2&.20 163.08 8.27 120.37 34.44 148.2& 2.45 111.27 3&.46 133.&2 12.74 102.40 44.27 11&.&8 22.61 &3.74 48.86 106.47 32.05 85.2& 53.23 &3.38 41.07 77.06 57.3& 80.71 4&.66 6&.05 61.33 68.47 57.83 61.25 65.06 56.66 65.57 53.67 68.56 45.27 72.8& 46.30 71.86 34.30 7&.78 3&.15 74.&4 23.76 86.25 32.22 77.80 13.65 &2.2& 25.50 80.44 3.&6 &7.&1 1&.00 82.87 5.30 103.10 12.71 85.0& 14.14 107.87 6.64 87.08 22.56 112.22 0.7& 88.87 30.55 116.13 4.85 &0.43 38.11 11&.63 10.27 &1.78 45.25 122.6& 15.48 &2.&2 51.&7 125.34 20.46 &3.83 58.26 127.55 25.24 &4.53 64.12 12&.35 2&.80 &5.02 6&.56 130.71 34.14 &5.2& 74.58 131.66 38.26 &5.34 7&.17 132.17 42.17 &5.18 83.33 132.27 45.87 &4.80

-A *EG

178.2& 163.08 148.2& 133.&2 11&.&8 106.47 &3.38 80.71 68.47 56.66 46.30 3&.15 32.22 25.50 1&.00 12.71 6.64 0.7& 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

-A POS

2&.20 34.44 3&.46 44.27 48.86 53.23 57.3& 61.33 65.06 68.56 72.8& 7&.78 86.25 &2.2& &7.&1 103.10 107.87 112.22 116.13 11&.63 122.6& 125.34 127.55 12&.35 130.71 131.66 132.17 132.27

87.07 &0.38 &3.27 &5.74 &7.78 &&.3& 100.58 101.35 101.6& 101.60 101.0& 100.16 &8.80 &7.01 &4.80 &2.17 8&.10 85.62 81.71 77.37 72.61 67.43 61.82 55.78 4&.32 42.44 35.13 27.3& 1&.23 10.65 1.63 7.80 17.66 27.&5 38.66 4&.7& 61.35 73.34

00

4.00

131.&3 131.18 12&.&& 128.3& 126.35 123.&0 121.02 117.71 113.&8 10&.82 105.24 100.23 &4.80 88.&4 82.66 75.&5 68.82 61.26 53.28 44.87 36.04 26.78 17.10 6.&& 3.54 14.50 25.88 37.6& 4&.&2 62.58 75.66 8&.17 103.10 117.46 132.24 147.45 163.08 17&.14

5.00

6.00

4&.34 52.61 55.65 58.48 61.10 63.4& 65.67 67.64 6&.3& 70.&2 72.24 73.34 74.23 74.&0 75.35 75.5& 75.61 75.42 75.01 74.38 73.54 72.48 71.21 6&.71 68.01 66.0& 63.&5 61.5& 5&.02 56.24 53.23 50.02 46.58 42.&3 3&.07 34.&8 30.68 26.17

7.00

Comn K  Comn +

&4.21 &3.40 &2.37 &1.13 8&.67 88.00 86.11 84.00 81.68 7&.14 76.3& 73.41 70.23 66.83 63.21 5&.37 55.32 51.06 46.57 41.88 36.&6 31.83 26.4& 20.&2 15.14 &.15 2.&4 3.4& 10.13 16.&& 24.06 31.35 38.86 46.58 54.52 62.67 71.04 7&.63

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 3.54 14.50 25.88 37.6& 4&.&2 62.58 75.66 8&.17 103.10 117.46 132.24 147.45 163.08 17&.14

131.&3 131.18 12&.&& 128.3& 127.28 126.5& 125.3& 123.68 121.47 118.76 115.53 111.80 107.57 102.83 &7.58 &2.17 8&.10 85.62 81.71 77.37 73.54 72.48 71.21 6&.71 68.01 66.0& 63.&5 61.5& 5&.02 56.24 53.23 50.02 46.58 42.&3 3&.07 34.&8 30.68 26.17