3.- COLUMNAS --- ok.xlsx

T -

25

X6

0 Curve 1 0. degrees Curve 2 15. degreesP M3 M2 P M3

1 -340.7854 0.1326 0 -340.7854 0.13262 -340.7854 7.4955 0 -340.7854 6.08823 -340.7854 11.9781 0 -340.7854 11.71094 -340.7854 15.8304 0 -331.9851 16.33765 -322.9102 19.1245 0 -270.9666 19.94616 -274.3091 23.2371 0 -198.7776 21.05097 -248.8146 29.4823 0 -137.6598 22.26338 -202.1248 34.7355 0 -49.1763 19.82459 -92.3457 29.8166 0 48.4497 11.1092

10 6.0694 18.2284 0 111.159 3.061511 133.6314 -0.1918 0 133.6314 -0.1918

T -

25

X6

0 PUNTOCARGAS EN EL ANGULO ESFUERZOS

P (TN) M2 (TN-M) P (TN) M3 (TN-M)

1 340.785 0.133 340.785 0.133

2 340.785 9.389 340.785 2.350

3 336.541 21.485 336.541 6.042

4 253.133 33.388 253.133 10.739

5 180.010 39.543 180.010 12.266

6 114.616 42.080 114.616 11.435

7 65.775 46.771 65.775 11.852

8 5.413 44.480 5.413 10.700

9 -64.156 25.946 -64.156 6.698

10 -115.893 7.587 -115.893 2.253

11 -133.631 0.192 -133.631 -0.192

12 0.000 0.000

13 0.000 0.000

14 0.000 0.000

15 0.000 0.000

16 0.000 0.000

17 0.000 0.000

18 0.000 0.000

19 0.000 0.000

20 0.000 0.000

21 0.000 0.000

22 0.000 0.000

L -

60

X6


1 -349.5765 0.6676 -0.6676 -349.5765 0.66762 -338.9347 18.4737 6.5167 -349.5765 11.46983 -257.6368 26.4645 10.2587 -301.4081 20.39494 -187.9607 32.1162 14.2694 -222.8721 28.71745 -114.6038 35.7311 17.9405 -148.6474 33.7876 -45.9182 39.3823 18.1222 -78.947 37.90317 1.4956 43.5851 19.9539 -18.1136 44.9324

L -

60

X6

08 58.6531 46.3962 20.3685 48.7422 47.07619 115.6352 35.7294 14.0432 116.248 34.2443

10 160.2103 22.5749 9.0562 180.7083 16.018911 233.4125 -0.9654 0.9654 233.4125 -0.9654

L -

60

X6

0 PUNTOCARGAS EN EL ANGULO ESFUERZOS


1 349.577 0.944 349.577 0.668

2 349.577 13.038 349.577 8.513

3 349.577 23.349 349.577 13.884

4 279.566 33.380 279.566 19.853

5 216.399 40.572 216.399 26.482

6 138.226 45.764 138.226 33.430

7 74.383 53.416 74.383 41.876

8 -13.000 55.031 -13.000 46.029

9 -115.605 36.511 -115.605 31.453

10 -198.062 12.833 -198.062 10.292

11 -233.413 1.365 -233.413 -0.965

12 0.000 0.000

13 0.000 0.000

14 0.000 0.000

15 0.000 0.000

16 0.000 0.000

17 0.000 0.000

18 0.000 0.000

19 0.000 0.000

20 0.000 0.000

21 0.000 0.000

22 0.000 0.000

T=

60

x6


1 -270.113 -0.1324 0 -270.113 -0.13242 -270.113 9.3351 0 -270.113 7.27583 -270.113 15.0698 0 -270.113 14.23074 -258.0141 19.8273 0 -254.4299 19.69915 -231.5196 23.6736 0 -223.1756 23.67496 -200.7333 26.9889 0 -174.9213 26.25047 -191.0021 32.2671 0 -147.9926 29.33278 -158.1344 36.5351 0 -90.8134 28.64579 -79.4691 30.0402 0 -1.3629 16.9441

10 -2.8741 18.5892 0 64.4679 5.255511 89.775 0.1914 0 89.775 0.1914

T=

60

x6

0

PUNTOCARGAS EN EL ANGULO ESFUERZOS


1 270.113 0.132 270.113 -0.132

T=

60

x6

0 2 270.113 5.038 270.113 4.547

3 270.113 11.686 270.113 11.051

4 228.286 19.223 228.286 17.652

5 162.233 23.065 162.233 19.114

6 99.858 23.783 99.858 17.550

7 62.671 26.051 62.671 17.319

8 14.536 24.663 14.536 14.858

9 -37.495 14.697 -37.495 8.659

10 -74.231 5.147 -74.231 3.212

11 -89.775 0.191 -89.775 0.191

12 0.000 0.000

13 0.000 0.000

14 0.000 0.000

15 0.000 0.000

16 0.000 0.000

17 0.000 0.000

18 0.000 0.000

19 0.000 0.000

20 0.000 0.000

21 0.000 0.000

22 0.000 0.000

D =

60

Curve 1 0. degrees Curve 2 15. degreesP M3 M2 P M3

1 -372.4494 0 0 -372.4494 02 -372.4494 12.2897 0 -372.4494 11.92073 -372.018 20.2638 0 -370.9107 19.73364 -299.1601 27.9045 0 -298.9956 26.98035 -231.6239 33.9297 0 -230.4393 32.81026 -149.4173 38.3508 0 -148.0537 37.14677 -97.0388 43.7923 0 -95.7196 42.29128 -27.3563 44.593 0 -26.5937 43.14259 63.3359 31.2588 0 61.7481 30.3987

10 156.0455 12.3219 0 157.5746 11.529811 206.6128 0 0 206.6128 0

Ø =

60

PUNTOCARGAS EN EL ANGULO ESFUERZOS


1 372.449 0.000 372.449 0.000

2 372.449 12.591 372.449 8.903

3 369.830 20.455 369.830 14.464

4 298.752 27.991 298.752 19.793

5 232.329 33.979 232.329 24.027

6 151.485 38.428 151.485 27.173

7 99.622 43.999 99.622 31.112

8 31.499 45.161 31.499 31.934

9 -58.115 32.222 -58.115 22.784

10 -151.330 13.428 -151.330 9.495

Ø =

60

11 -206.613 0.000 -206.613 0.000

12 0.000 0.000

13 0.000 0.000

14 0.000 0.000

15 0.000 0.000

16 0.000 0.000

17 0.000 0.000

18 0.000 0.000

19 0.000 0.000

20 0.000 0.000

21 0.000 0.000

22 0.000 0.000

Curve 3 30. degrees Curve 4 45. degreesM2 P M3 M2 P M3 M2

0 -340.7854 0.1326 0 -340.7854 0.1326 02.3789 -340.7854 4.745 5.1075 -340.7854 2.35 9.09052.9335 -340.7854 11.2275 11.2845 -336.5413 6.0421 20.61815.7561 -275.4074 15.7094 21.3137 -253.1325 10.7386 31.6135

13.7828 -201.0472 15.9037 31.4593 -180.0101 12.2662 37.59222.36 -129.4062 14.6058 36.7763 -114.6155 11.435 40.4963

30.3373 -75.1381 14.6607 41.6514 -65.7746 11.8522 45.244333.3592 -2.9051 12.787 38.6228 -5.4126 10.7001 43.173322.3694 69.6956 7.4222 21.6831 64.1564 6.698 25.0668

8.3212 116.6082 2.2274 6.7598 115.8934 2.2527 7.24460 133.6314 -0.1918 0 133.6314 -0.1918 0

ESFUERZOS

M2 (TN-M)

0.000

9.091

20.618

31.614

37.592

40.496

45.244

43.173

25.067

7.245

0.000


-0.6676 -349.5765 0.6676 -0.6676 -349.5765 0.6676 -0.66768.8051 -349.5765 9.5864 9.1294 -349.5765 8.5132 9.8751

15.4041 -349.5765 15.9462 17.4725 -349.5765 13.8844 18.772220.3862 -257.1611 23.5214 25.3333 -279.5662 19.853 26.834922.4414 -181.5417 30.9426 26.709 -216.3992 26.4816 30.737222.7505 -107.3785 36.356 26.7467 -138.2256 33.4299 31.253624.1735 -43.707 43.8459 28.6679 -74.3827 41.8759 33.161

22.7629 35.524 47.0138 25.8296 12.9999 46.0293 30.161115.6241 116.6463 32.8648 16.9718 115.6048 31.4531 18.5406

8.3336 194.9891 11.3528 7.7532 198.0622 10.2921 7.66460.9654 233.4125 -0.9654 0.9654 233.4125 -0.9654 0.9654

ESFUERZOS

M2 (TN-M)

-0.668

9.875

18.772

26.835

30.737

31.254

33.161

30.161

18.541

7.665

0.965


0 -270.113 -0.1324 0 -270.113 -0.1324 00.7816 -270.113 5.5021 1.5005 -270.113 4.5469 2.16970.9161 -270.113 12.8859 2.1008 -270.113 11.0507 3.79941.0645 -248.5204 19.0918 2.6549 -228.2862 17.6524 7.61121.3308 -198.8363 22.7742 6.0935 -162.2332 19.1137 12.90944.3543 -137.7577 22.9248 10.6743 -99.858 17.5503 16.05018.3592 -97.3007 22.5348 16.3338 -62.6709 17.3191 19.4606

11.0359 -37.9533 19.4765 17.9631 -14.5363 14.8576 19.684910.4154 28.3718 10.8414 12.0135 37.4951 8.6587 11.8751

5.3898 72.4331 3.6146 4.3843 74.2308 3.2115 4.02230 89.775 0.1914 0 89.775 0.1914 0

ESFUERZOS

M2 (TN-M)

0.000

2.170

3.799

7.611

12.909

16.050

19.461

19.685

11.875

4.022

0.000


0 -372.4494 0 0 -372.4494 0 03.16 -372.4494 10.7533 6.2333 -372.4494 8.9029 8.9029

5.2746 -370.1936 17.7465 10.2417 -369.8302 14.4641 14.46417.2858 -298.8741 24.2684 13.9252 -298.7524 19.7927 19.79278.7314 -230.6353 29.3742 17.0489 -232.3293 24.0269 24.02699.9846 -148.7617 33.3445 19.2307 -151.485 27.1728 27.1728

11.3288 -96.6383 38.001 21.9115 -99.6217 31.1117 31.111711.3111 -28.0235 38.673 22.648 -31.4994 31.934 31.934

7.9925 60.6335 27.3726 15.8829 58.1152 22.7842 22.78423.3413 156.0023 10.857 5.9344 151.3295 9.4951 9.4951

0 206.6128 0 0 206.6128 0 0

ESFUERZOS

M2 (TN-M)

0.000

8.903

14.464

19.793

24.027

27.173

31.112

31.934

22.784

9.495

Curve 5 60. degrees Curve 6 75. degrees Curve 7P M3 M2 P M3 M2 P

-340.7854 0.1326 0 -340.7854 0.1326 0 -340.7854-340.7854 1.0554 10.8304 -340.7854 -0.3032 14.2481 -340.7854-340.7854 0.229 23.0821 -340.7854 -1.7723 25.1514 -339.7476-276.2461 3.5843 33.9153 -293.1089 -1.9291 33.9727 -297.5149-195.9688 8.3711 39.86 -219.9131 2.283 41.469 -240.9711-123.4246 9.5156 42.1601 -138.2652 6.6395 43.9494 -165.0416

-78.8181 10.0932 48.0763 -90.8556 8.2948 49.5674 -108.4754-21.1798 10.0375 48.0146 -36.5428 8.8738 51.6181 -50.682745.4506 6.5937 32.1244 28.8321 6.3833 37.6013 14.887

107.9 2.6972 10.5181 92.1013 2.931 17.0063 74.0225133.6314 -0.1918 0 133.6314 -0.1918 0 133.6314


-349.5765 0.6676 -0.6676 -349.5765 0.6676 -0.6676 -349.5765-349.5765 7.6742 10.877 -349.5765 7.1101 12.5352 -349.5765-349.5765 12.2433 20.0828 -349.5765 10.8014 20.7949 -349.5765-296.1788 17.1858 27.4394 -309.7355 14.5402 27.7494 -318.7381-241.2523 22.5891 32.5246 -262.9711 18.9239 33.5116 -279.6006-173.2048 28.734 35.8944 -204.0965 24.0675 38.7064 -229.2142-115.8775 38.0502 39.4453 -166.2221 31.6629 45.3318 -206.3032

-20.0026 43.2193 36.7 -79.7252 35.1975 46.9661 -152.1239102.4972 30.315 22.127 59.1582 26.8474 31.3629 -32.0039197.2972 10.3984 7.8998 182.1448 12.7855 10.8881 78.0947233.4125 -0.9654 0.9654 233.4125 -0.9654 0.9654 233.4125


-270.113 -0.1324 0 -270.113 -0.1324 0 -270.113-270.113 3.8183 3.8671 -270.113 -0.1534 5.6594 -270.113

-258.7923 8.271 9.756 -269.5795 0.2019 11.7568 -270.113-192.4226 12.4124 15.3208 -211.0741 3.5846 17.4977 -241.4721-129.1798 14.3876 17.5564 -149.0489 7.2518 20.0942 -186.6071

-73.42 13.6706 18.1608 -83.4211 10.2467 19.8539 -125.7676-41.0376 13.6057 20.1573 -47.4635 11.5954 21.2735 -85.5064

-1.8649 12.1486 19.6412 -10.5125 11.6844 21.3391 -30.348140.1592 7.4524 12.1509 29.9139 7.6685 14.9581 17.0499

74.958 3.0098 3.8895 67.1547 3.7032 5.9907 47.907289.775 0.1914 0 89.775 0.1914 0 89.775


-372.4494 0 0 -372.4494 0 0 -372.4494-372.4494 6.2333 10.7533 -372.4494 3.16 11.9207 -372.4494-370.1936 10.2417 17.7465 -370.9107 5.2746 19.7336 -372.018-298.8741 13.9252 24.2684 -298.9956 7.2858 26.9803 -299.1601-230.6353 17.0489 29.3742 -230.4393 8.7314 32.8102 -231.6239-148.7617 19.2307 33.3445 -148.0537 9.9846 37.1467 -149.4173

-96.6383 21.9115 38.001 -95.7196 11.3288 42.2912 -97.0388-28.0235 22.648 38.673 -26.5937 11.3111 43.1425 -27.356360.6335 15.8829 27.3726 61.7481 7.9925 30.3987 63.3359

156.0023 5.9344 10.857 157.5746 3.3413 11.5298 156.0455206.6128 0 0 206.6128 0 0 206.6128

90. degrees Curve 8 105. degrees Curve 9M3 M2 P M3 M2 P

0.1326 0 -340.7854 0.1326 0 -340.7854-1.6826 17.2461 -340.7854 -2.1938 14.2271 -340.7854-3.1206 26.8876 -340.7854 -3.8477 25.1451 -340.7854-4.5691 34.32 -303.2582 -5.5154 33.4257 -309.4569-3.2047 41.2822 -258.7836 -7.1751 39.3484 -262.9774

0.697 45.9128 -184.1227 -4.7448 44.958 -202.14355.3031 51.2657 -126.1491 -0.9422 51.6713 -146.57237.3883 54.1442 -48.5406 4.1702 52.1988 -60.96356.1889 41.7473 26.3925 3.8797 37.8241 36.80442.9993 23.9072 91.509 1.186 17.1836 107.3459

-0.1918 0 133.6314 -0.1918 0 133.6314


0.6676 -0.6676 -349.5765 0.6676 -0.6676 -349.57656.5389 14.0769 -349.5765 3.5153 11.0857 -349.57659.3292 21.0033 -349.5765 6.1468 18.782 -349.5765

12.3487 27.3307 -313.891 8.7545 25.5638 -293.963315.5951 33.2318 -266.24 10.4518 31.3983 -218.109219.5828 39.7152 -185.9796 8.4122 36.6389 -118.462723.1211 48.0946 -126.1584 5.6259 41.5511 -38.1838

24.0208 56.0168 -26.5338 -1.2318 41.5292 65.515816.9155 47.6253 99.8604 -6.6562 25.8105 155.0509

9.0485 31.0197 194.0865 -7.1104 8.605 207.3722-0.9654 0.9654 233.4125 -0.9654 0.9654 233.4125


-0.1324 0 -270.113 -0.1324 0 -270.113-2.5255 7.7057 -270.113 -2.8622 5.5716 -270.113

-4.562 12.063 -270.113 -5.405 10.8121 -270.113-5.1611 16.2606 -257.373 -7.9764 14.7418 -260.9579-2.2613 20.5273 -222.1943 -10.1898 17.9254 -226.64760.7192 22.4352 -161.8145 -8.6706 21.4433 -178.1114.6138 24.2811 -123.4949 -6.6913 24.8329 -145.87049.5243 23.6886 -63.2382 -2.9396 25.1034 -83.90048.2526 17.899 14.3007 1.4963 16.307 5.63194.8189 10.9723 67.1547 1.6798 5.9907 67.97320.1914 0 89.775 0.1914 0 89.775


0 0 -372.4494 0 0 -372.44940 12.2897 -372.4494 -3.16 11.9207 -372.44940 20.2638 -370.9107 -5.2746 19.7336 -370.19360 27.9045 -298.9956 -7.2858 26.9803 -298.87410 33.9297 -230.4393 -8.7314 32.8102 -230.63530 38.3508 -148.0537 -9.9846 37.1467 -148.76170 43.7923 -95.7196 -11.3288 42.2912 -96.63830 44.593 -26.5937 -11.3111 43.1425 -28.02350 31.2588 61.7481 -7.9925 30.3987 60.63350 12.3219 157.5746 -3.3413 11.5298 156.00230 0 206.6128 0 0 206.6128


0.1326 0 -340.7854 0.1326 0 -340.7854-2.50E+00 10.757 -340.7854 -2.5936 8.8104 -340.7854

-4.5061 22.8437 -340.7854 -5.1779 19.3379 -340.7854-6.514 32.1942 -316.2452 -7.5537 30.17 -311.1484-8.557 38.4705 -266.593 -10.0291 37.1621 -251.5319

-9.8077 42.841 -208.7184 -12.717 40.5934 -183.5901-8.0755 50.4623 -166.282 -15.6546 46.5723 -130.9236-3.5783 50.2197 -85.1992 -14.8467 45.9363 -49.11960.5397 32.9033 30.2968 -8.0883 27.2697 47.456

-0.2965 10.6827 111.4899 -1.8113 7.7238 115.9106-0.1918 0 133.6314 -0.1918 0 133.6314


0.6676 -0.6676 -349.5765 0.6676 -0.6676 -349.5765-1.59E-02 8.012 -349.5765 -5.4435 5.4435 -349.5765

1.3788 15.2498 -344.0262 -9.7933 9.7933 -349.57650.7632 22.1556 -246.0997 -14.3487 14.3487 -293.9633-2.749 26.618 -157.2362 -17.2914 17.2914 -218.1092

-7.1381 28.1163 -60.6381 -18.7273 18.7273 -118.4627-11.9306 29.54 19.7647 -20.2828 20.2828 -38.1838

-15.4796 26.6063 107.4267 -18.6318 18.6318 65.5158-12.0847 15.0199 172.882 -11.2947 11.2947 155.0509

-5.8764 5.9792 212.542 -4.9592 4.9592 207.3722-0.9654 0.9654 233.4125 -0.9654 0.9654 233.4125


-0.1324 0 -270.113 -0.1324 0 -270.113-2.9957 4.1252 -270.113 -3.4885 3.8007 -270.113-5.9972 9.4429 -270.113 -7.2324 8.8113 -270.113-9.0641 14.0756 -248.7637 -11.4287 13.7776 -229.431

-12.3663 16.8383 -205.8392 -15.7134 15.4883 -172.5566-15.1135 18.8087 -147.4909 -19.7973 14.6245 -110.8957-17.7132 21.6552 -101.1894 -24.5785 12.8548 -66.7567

-17.227 21.2401 -35.9069 -24.7609 8.7577 -20.1957-11.1651 12.1767 33.0042 -14.7908 3.8884 31.5597

-4.356 3.1359 74.2308 -4.8331 1.302 72.43310.1914 0 89.775 0.1914 0 89.775


0 0 -372.4494 0 0 -372.4494-6.2333 10.7533 -372.4494 -8.9029 8.9029 -372.4494

-10.2417 17.7465 -369.8302 -14.4641 14.4641 -370.1936-13.9252 24.2684 -298.7524 -19.7927 19.7927 -298.8741-17.0489 29.3742 -232.3293 -24.0269 24.0269 -230.6353-19.2307 33.3445 -151.485 -27.1728 27.1728 -148.7617-21.9115 38.001 -99.6217 -31.1117 31.1117 -96.6383

-22.648 38.673 -31.4994 -31.934 31.934 -28.0235-15.8829 27.3726 58.1152 -22.7842 22.7842 60.6335

-5.9344 10.857 151.3295 -9.4951 9.4951 156.00230 0 206.6128 0 0 206.6128


0.1326 0 -340.7854 0.1326 0 -340.7854-2.982 ### -340.7854 -4.2197 6.9801 -328.05

-6.1334 16.6949 -340.7854 -8.8234 15.3293 -256.6565-9.4648 27.854 -274.2574 -14.3862 22.1467 -184.1437

-12.7373 34.6695 -187.4898 -19.0239 22.6246 -107.2274-16.3036 35.2417 -107.7904 -21.3355 17.262 -35.0204-21.3756 34.8734 -47.4882 -24.0154 12.0782 -4.5599-23.5856 27.42 19.385 -23.779 5.816 40.6778-15.8858 12.1513 72.8431 -16.0941 1.3793 72.0454

-4.7907 1.9639 112.6136 -6.2239 0.9827 99.9109-0.1918 0 133.6314 -0.1918 0 133.6314


0.6676 -0.6676 -349.5765 0.6676 -0.6676 -349.5765-8.012 1.59E-02 -349.5765 -11.0857 -3.5153 -349.5765

-15.2498 -1.3788 -349.5765 -18.782 -6.1468 -349.5765-22.1556 -0.7632 -313.891 -25.5638 -8.7545 -318.7381

-26.618 2.749 -266.24 -31.3983 -10.4518 -279.6006-28.1163 7.1381 -185.9796 -36.6389 -8.4122 -229.2142

-29.54 11.9306 -126.1584 -41.5511 -5.6259 -206.3032

-26.6063 15.4796 -26.5338 -41.5292 1.2318 -152.1239-15.0199 12.0847 99.8604 -25.8105 6.6562 -32.0039

-5.9792 5.8764 194.0865 -8.605 7.1104 78.0947-0.9654 0.9654 233.4125 -0.9654 0.9654 233.4125


-0.1324 0 -270.113 -0.1324 0 -270.113-4.2634 3.4892 -270.113 -5.7465 3.3815 -266.2567-8.9656 8.1665 -256.6691 -13.0596 6.4334 -213.047

-14.7007 12.3904 -194.7246 -20.4038 6.6072 -158.5553-20.6889 11.0812 -136.515 -24.2157 5.1547 -104.6432-24.0945 7.7783 -81.9485 -25.5738 2.3403 -66.5998-27.4681 5.3066 -52.2102 -28.5914 1.6757 -45.0181-27.5454 3.1402 -17.3306 -28.7647 1.1045 -18.1334-17.5054 1.8206 24.5156 -20.0328 0.8965 17.3571

-5.468 1.3495 63.8616 -8.327 0.9666 47.90720.1914 0 89.775 0.1914 0 89.775


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-38.001 21.9115 -95.7196 -42.2912 11.3288 -97.0388-38.673 22.648 -26.5937 -43.1425 11.3111 -27.3563

-27.3726 15.8829 61.7481 -30.3987 7.9925 63.3359-10.857 5.9344 157.5746 -11.5298 3.3413 156.0455

0 0 206.6128 0 0 206.6128


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-9.8482 0 112.6136 -6.2239 -0.9827 115.9106-0.1918 0 133.6314 -0.1918 0 133.6314


0.6676 -0.6676 -349.5765 0.6676 -0.6676 -349.5765-14.0769 -6.5389 -349.5765 -12.5352 -7.1101 -349.5765-21.0033 -9.3292 -349.5765 -20.7949 -10.8014 -349.5765-27.3307 -12.3487 -309.7355 -27.7494 -14.5402 -296.1788-33.2318 -15.5951 -262.9711 -33.5116 -18.9239 -241.2523-39.7152 -19.5828 -204.0965 -38.7064 -24.0675 -173.2048-48.0946 -23.1211 -166.2221 -45.3318 -31.6629 -115.8775

-56.0168 -24.0208 -79.7252 -46.9661 -35.1975 -20.0026-47.6253 -16.9155 59.1582 -31.3629 -26.8474 102.4972-31.0197 -9.0485 182.1448 -10.8881 -12.7855 197.2972

-0.9654 0.9654 233.4125 -0.9654 0.9654 233.4125


-0.1324 0 -270.113 -0.1324 0 -270.113-12.6312 0 -270.113 -5.7465 -3.3815 -270.113-19.5521 0 -256.6691 -13.0596 -6.4334 -270.113

-23.794 0 -194.7246 -20.4038 -6.6072 -229.431-25.5094 0 -136.515 -24.2157 -5.1547 -172.5566

-26.316 0 -81.9485 -25.5738 -2.3403 -110.8957-28.5445 0 -52.2102 -28.5914 -1.6757 -66.7567-29.4818 0 -17.3306 -28.7647 -1.1045 -20.1957

-22.351 0 24.5156 -20.0328 -0.8965 31.5597-13.4802 0 63.8616 -8.327 -0.9666 72.4331

0.1914 0 89.775 0.1914 0 89.775


0 0 -372.4494 0 0 -372.4494-12.2897 0 -372.4494 -11.9207 -3.16 -372.4494-20.2638 0 -370.9107 -19.7336 -5.2746 -370.1936-27.9045 0 -298.9956 -26.9803 -7.2858 -298.8741-33.9297 0 -230.4393 -32.8102 -8.7314 -230.6353-38.3508 0 -148.0537 -37.1467 -9.9846 -148.7617-43.7923 0 -95.7196 -42.2912 -11.3288 -96.6383

-44.593 0 -26.5937 -43.1425 -11.3111 -28.0235-31.2588 0 61.7481 -30.3987 -7.9925 60.6335-12.3219 0 157.5746 -11.5298 -3.3413 156.0023

0 0 206.6128 0 0 206.6128


0.1326 0 -340.7854 0.1326 0 -340.7854-2.982 -7.8081 -340.7854 -2.5936 -8.8104 -340.7854

-6.1334 -16.6949 -340.7854 -5.1779 -19.3379 -340.7854-9.4648 -27.854 -316.2452 -7.5537 -30.17 -309.4569

-12.7373 -34.6695 -266.593 -10.0291 -37.1621 -262.9774-16.3036 -35.2417 -208.7184 -12.717 -40.5934 -202.1435-21.3756 -34.8734 -166.282 -15.6546 -46.5723 -146.5723-23.5856 -27.42 -85.1992 -14.8467 -45.9363 -60.9635-15.8858 -12.1513 30.2968 -8.0883 -27.2697 36.8044

-4.7907 -1.9639 111.4899 -1.8113 -7.7238 107.3459-0.1918 0 133.6314 -0.1918 0 133.6314


0.6676 -0.6676 -349.5765 0.6676 -0.6676 -349.5765-10.877 -7.6742 -349.5765 -9.8751 -8.5132 -349.5765

-20.0828 -12.2433 -349.5765 -18.7722 -13.8844 -349.5765-27.4394 -17.1858 -279.5662 -26.8349 -19.853 -257.1611-32.5246 -22.5891 -216.3992 -30.7372 -26.4816 -181.5417-35.8944 -28.734 -138.2256 -31.2536 -33.4299 -107.3785-39.4453 -38.0502 -74.3827 -33.161 -41.8759 -43.707

-36.7 -43.2193 12.9999 -30.1611 -46.0293 35.524-22.127 -30.315 115.6048 -18.5406 -31.4531 116.6463-7.8998 -10.3984 198.0622 -7.6646 -10.2921 194.9891-0.9654 0.9654 233.4125 -0.9654 0.9654 233.4125


-0.1324 0 -270.113 -0.1324 0 -270.113-4.2634 -3.4892 -270.113 -3.4885 -3.8007 -270.113-8.9656 -8.1665 -270.113 -7.2324 -8.8113 -270.113

-14.7007 -12.3904 -248.7637 -11.4287 -13.7776 -260.9579-20.6889 -11.0812 -205.8392 -15.7134 -15.4883 -226.6476-24.0945 -7.7783 -147.4909 -19.7973 -14.6245 -178.111-27.4681 -5.3066 -101.1894 -24.5785 -12.8548 -145.8704-27.5454 -3.1402 -35.9069 -24.7609 -8.7577 -83.9004-17.5054 -1.8206 33.0042 -14.7908 -3.8884 5.6319

-5.468 -1.3495 74.2308 -4.8331 -1.302 67.97320.1914 0 89.775 0.1914 0 89.775


0 0 -372.4494 0 0 -372.4494-10.7533 -6.2333 -372.4494 -8.9029 -8.9029 -372.4494-17.7465 -10.2417 -369.8302 -14.4641 -14.4641 -370.1936-24.2684 -13.9252 -298.7524 -19.7927 -19.7927 -298.8741-29.3742 -17.0489 -232.3293 -24.0269 -24.0269 -230.6353-33.3445 -19.2307 -151.485 -27.1728 -27.1728 -148.7617

-38.001 -21.9115 -99.6217 -31.1117 -31.1117 -96.6383-38.673 -22.648 -31.4994 -31.934 -31.934 -28.0235

-27.3726 -15.8829 58.1152 -22.7842 -22.7842 60.6335-10.857 -5.9344 151.3295 -9.4951 -9.4951 156.0023

0 0 206.6128 0 0 206.6128


0.1326 0 -340.7854 0.1326 0 -340.7854-2.5031 -10.757 -340.7854 -2.1938 -14.2271 -340.7854-4.5061 -22.8437 -340.7854 -3.8477 -25.1451 -339.7476

-6.514 -32.1942 -303.2582 -5.5154 -33.4257 -297.5149-8.557 -38.4705 -258.7836 -7.1751 -39.3484 -240.9711

-9.8077 -42.841 -184.1227 -4.7448 -44.958 -165.0416-8.0755 -50.4623 -126.1491 -0.9422 -51.6713 -108.4754-3.5783 -50.2197 -48.5406 4.1702 -52.1988 -50.68270.5397 -32.9033 26.3925 3.8797 -37.8241 14.887

-0.2965 -10.6827 91.509 1.186 -17.1836 74.0225-0.1918 0 133.6314 -0.1918 0 133.6314


0.6676 -0.6676 -349.5765 0.6676 -0.6676 -349.5765-9.1294 -9.5864 -349.5765 -8.8051 -11.4698 -338.9347

-17.4725 -15.9462 -301.4081 -15.4041 -20.3949 -257.6368-25.3333 -23.5214 -222.8721 -20.3862 -28.7174 -187.9607

-26.709 -30.9426 -148.6474 -22.4414 -33.787 -114.6038-26.7467 -36.356 -78.947 -22.7505 -37.9031 -45.9182-28.6679 -43.8459 -18.1136 -24.1735 -44.9324 1.4956

-25.8296 -47.0138 48.7422 -22.7629 -47.0761 58.6531-16.9718 -32.8648 116.248 -15.6241 -34.2443 115.6352

-7.7532 -11.3528 180.7083 -8.3336 -16.0189 160.2103-0.9654 0.9654 233.4125 -0.9654 0.9654 233.4125


-0.1324 0 -270.113 -0.1324 0 -270.113-2.9957 -4.1252 -270.113 -2.8622 -5.5716 -270.113-5.9972 -9.4429 -270.113 -5.405 -10.8121 -270.113-9.0641 -14.0756 -257.373 -7.9764 -14.7418 -241.4721

-12.3663 -16.8383 -222.1943 -10.1898 -17.9254 -186.6071-15.1135 -18.8087 -161.8145 -8.6706 -21.4433 -125.7676-17.7132 -21.6552 -123.4949 -6.6913 -24.8329 -85.5064

-17.227 -21.2401 -63.2382 -2.9396 -25.1034 -30.3481-11.1651 -12.1767 14.3007 1.4963 -16.307 17.0499

-4.356 -3.1359 67.1547 1.6798 -5.9907 47.90720.1914 0 89.775 0.1914 0 89.775


0 0 -372.4494 0 0 -372.4494-6.2333 -10.7533 -372.4494 -3.16 -11.9207 -372.4494

-10.2417 -17.7465 -370.9107 -5.2746 -19.7336 -372.018-13.9252 -24.2684 -298.9956 -7.2858 -26.9803 -299.1601-17.0489 -29.3742 -230.4393 -8.7314 -32.8102 -231.6239-19.2307 -33.3445 -148.0537 -9.9846 -37.1467 -149.4173-21.9115 -38.001 -95.7196 -11.3288 -42.2912 -97.0388

-22.648 -38.673 -26.5937 -11.3111 -43.1425 -27.3563-15.8829 -27.3726 61.7481 -7.9925 -30.3987 63.3359

-5.9344 -10.857 157.5746 -3.3413 -11.5298 156.04550 0 206.6128 0 0 206.6128


0.1326 0 -340.7854 0.1326 0 -340.7854-1.6826 -17.2461 -340.7854 -0.3032 -14.2481 -340.7854-3.1206 -26.8876 -340.7854 -1.7723 -25.1514 -340.7854-4.5691 -34.32 -293.1089 -1.9291 -33.9727 -276.2461-3.2047 -41.2822 -219.9131 2.283 -41.469 -195.9688

0.697 -45.9128 -138.2652 6.6395 -43.9494 -123.42465.3031 -51.2657 -90.8556 8.2948 -49.5674 -78.81817.3883 -54.1442 -36.5428 8.8738 -51.6181 -21.17986.1889 -41.7473 28.8321 6.3833 -37.6013 45.45062.9993 -23.9072 92.1013 2.931 -17.0063 107.9

-0.1918 0 133.6314 -0.1918 0 133.6314


0.6676 -0.6676 -349.5765 0.6676 -0.6676 -349.5765-6.5167 -18.4737 -349.5765 1.0661 -10.1563 -349.5765

-10.2587 -26.4645 -332.5611 1.511 -17.677 -349.5765-14.2694 -32.1162 -245.8619 -1.81 -26.1266 -297.8284-17.9405 -35.7311 -165.4009 -5.9284 -32.0078 -223.2638-18.1222 -39.3823 -74.5742 -9.6733 -35.6752 -123.7858-19.9539 -43.5851 -9.274 -13.9527 -41.4638 -46.3775

-20.3685 -46.3962 67.735 -15.5976 -42.7224 54.9414-14.0432 -35.7294 136.1019 -10.4989 -29.6636 147.5777

-9.0562 -22.5749 192.3878 -3.7453 -12.2801 207.3722-0.9654 0.9654 233.4125 -0.9654 0.9654 233.4125


-0.1324 0 -270.113 -0.1324 0 -270.113-2.5255 -7.7057 -270.113 -0.1534 -5.6594 -270.113

-4.562 -12.063 -269.5795 0.2019 -11.7568 -258.7923-5.1611 -16.2606 -211.0741 3.5846 -17.4977 -192.4226-2.2613 -20.5273 -149.0489 7.2518 -20.0942 -129.17980.7192 -22.4352 -83.4211 10.2467 -19.8539 -73.424.6138 -24.2811 -47.4635 11.5954 -21.2735 -41.03769.5243 -23.6886 -10.5125 11.6844 -21.3391 -1.86498.2526 -17.899 29.9139 7.6685 -14.9581 40.15924.8189 -10.9723 67.1547 3.7032 -5.9907 74.9580.1914 0 89.775 0.1914 0 89.775


0 0 -372.4494 0 0 -372.44940 -12.2897 -372.4494 3.16 -11.9207 -372.44940 -20.2638 -370.9107 5.2746 -19.7336 -370.19360 -27.9045 -298.9956 7.2858 -26.9803 -298.87410 -33.9297 -230.4393 8.7314 -32.8102 -230.63530 -38.3508 -148.0537 9.9846 -37.1467 -148.76170 -43.7923 -95.7196 11.3288 -42.2912 -96.63830 -44.593 -26.5937 11.3111 -43.1425 -28.02350 -31.2588 61.7481 7.9925 -30.3987 60.63350 -12.3219 157.5746 3.3413 -11.5298 156.00230 0 206.6128 0 0 206.6128


0.1326 0 -340.7854 0.1326 0 -340.78541.0554 -10.8304 -340.7854 2.35 -9.0905 -340.7854

0.229 -23.0821 -336.5413 6.0421 -20.6181 -340.78543.5843 -33.9153 -253.1325 10.7386 -31.6135 -275.40748.3711 -39.86 -180.0101 12.2662 -37.592 -201.04729.5156 -42.1601 -114.6155 11.435 -40.4963 -129.4062

10.0932 -48.0763 -65.7746 11.8522 -45.2443 -75.138110.0375 -48.0146 -5.4126 10.7001 -43.1733 -2.9051

6.5937 -32.1244 64.1564 6.698 -25.0668 69.69562.6972 -10.5181 115.8934 2.2527 -7.2446 116.6082

-0.1918 0 133.6314 -0.1918 0 133.6314


0.6676 -0.6676 -349.5765 0.6676 -0.6676 -349.57653.6029 -7.3677 -349.5765 5.4419 -5.4419 -349.57656.3066 -12.0952 -349.5765 8.6919 -8.6919 -349.5765

8.108 -18.1043 -341.1552 12.5698 -12.5698 -297.82847.6643 -24.4919 -263.9797 16.4822 -16.4822 -223.26384.7128 -29.6187 -180.3732 19.5898 -19.5898 -123.78581.0743 -35.1653 -112.7455 23.0628 -23.0628 -46.3775

-4.0493 -36.7616 -9.5746 23.2263 -23.2263 54.9414-4.8785 -23.2303 109.8012 14.3568 -14.3568 147.5777-1.8107 -7.4062 191.6715 5.0998 -5.0998 207.3722-0.9654 0.9654 233.4125 -0.9654 0.9654 233.4125


-0.1324 0 -270.113 -0.1324 0 -270.1133.8183 -3.8671 -270.113 4.5469 -2.1697 -270.113

8.271 -9.756 -270.113 11.0507 -3.7994 -270.11312.4124 -15.3208 -228.2862 17.6524 -7.6112 -248.520414.3876 -17.5564 -162.2332 19.1137 -12.9094 -198.836313.6706 -18.1608 -99.858 17.5503 -16.0501 -137.757713.6057 -20.1573 -62.6709 17.3191 -19.4606 -97.300712.1486 -19.6412 -14.5363 14.8576 -19.6849 -37.9533

7.4524 -12.1509 37.4951 8.6587 -11.8751 28.37183.0098 -3.8895 74.2308 3.2115 -4.0223 72.43310.1914 0 89.775 0.1914 0 89.775


0 0 -372.4494 0 0 -372.44946.2333 -10.7533 -372.4494 8.9029 -8.9029 -372.4494

10.2417 -17.7465 -369.8302 14.4641 -14.4641 -370.193613.9252 -24.2684 -298.7524 19.7927 -19.7927 -298.874117.0489 -29.3742 -232.3293 24.0269 -24.0269 -230.635319.2307 -33.3445 -151.485 27.1728 -27.1728 -148.761721.9115 -38.001 -99.6217 31.1117 -31.1117 -96.6383

22.648 -38.673 -31.4994 31.934 -31.934 -28.023515.8829 -27.3726 58.1152 22.7842 -22.7842 60.6335

5.9344 -10.857 151.3295 9.4951 -9.4951 156.00230 0 206.6128 0 0 206.6128

330. degrees Curve 24 345. degreesM3 M2 P M3 M2

0.1326 0 -340.7854 0.1326 04.745 -5.1075 -340.7854 6.0882 -2.3789

11.2275 -11.2845 -340.7854 11.7109 -2.933515.7094 -21.3137 -331.9851 16.3376 -5.756115.9037 -31.4593 -270.9666 19.9461 -13.782814.6058 -36.7763 -198.7776 21.0509 -22.3614.6607 -41.6514 -137.6598 22.2633 -30.3373

12.787 -38.6228 -49.1763 19.8245 -33.35927.4222 -21.6831 48.4497 11.1092 -22.36942.2274 -6.7598 111.159 3.0615 -8.3212

-0.1918 0 133.6314 -0.1918 0


0.6676 -0.6676 -349.5765 0.6676 -0.66767.3677 -3.6029 -349.5765 10.1563 -1.0661

12.0952 -6.3066 -332.5611 17.677 -1.51118.1043 -8.108 -245.8619 26.1266 1.8124.4919 -7.6643 -165.4009 32.0078 5.928429.6187 -4.7128 -74.5742 35.6752 9.673335.1653 -1.0743 -9.274 41.4638 13.9527

36.7616 4.0493 67.735 42.7224 15.597623.2303 4.8785 136.1019 29.6636 10.4989

7.4062 1.8107 192.3878 12.2801 3.7453-0.9654 0.9654 233.4125 -0.9654 0.9654


-0.1324 0 -270.113 -0.1324 05.5021 -1.5005 -270.113 7.2758 -0.7816

12.8859 -2.1008 -270.113 14.2307 -0.916119.0918 -2.6549 -254.4299 19.6991 -1.064522.7742 -6.0935 -223.1756 23.6749 -1.330822.9248 -10.6743 -174.9213 26.2504 -4.354322.5348 -16.3338 -147.9926 29.3327 -8.359219.4765 -17.9631 -90.8134 28.6457 -11.035910.8414 -12.0135 -1.3629 16.9441 -10.4154

3.6146 -4.3843 64.4679 5.2555 -5.38980.1914 0 89.775 0.1914 0


0 0 -372.4494 0 010.7533 -6.2333 -372.4494 11.9207 -3.1617.7465 -10.2417 -370.9107 19.7336 -5.274624.2684 -13.9252 -298.9956 26.9803 -7.285829.3742 -17.0489 -230.4393 32.8102 -8.731433.3445 -19.2307 -148.0537 37.1467 -9.9846

38.001 -21.9115 -95.7196 42.2912 -11.328838.673 -22.648 -26.5937 43.1425 -11.3111

27.3726 -15.8829 61.7481 30.3987 -7.992510.857 -5.9344 157.5746 11.5298 -3.3413

0 0 206.6128 0 0

I N T E R A C C I O N C O L U M N A S

DATOS PARA DISEÑO DE COLUMNA TIPO "T" - 50 x 90

23.16 Tn 75.32 Tn

16.78 Tn 65.49 Tn

11.42 Tn 66.42 Tn

1.03 Tn 37.23 Tn

1.78 Tn 38.17 Tn

75.32 Tn

20 Ø 5/8" Ø =

PPP = MUX

=

PCM = MUY

=

PCV = MUR =

PSX = eX =

PSY = eY =

PU = eT =

As =

0 5 10 15 20 25 30 35 40 45 50

-200

-100

0

100

200

300

400

VERIFICACION DE COLUMNA TIPO "T" 50x90

DIAGRAMA DE INTERACCION DE COLUMNA

ESFUERZO


DATOS PARA DISEÑO DE COLUMNA TIPO "L" - 60 x 60

17.32 Tn 39.79 Tn

5.54 Tn 39.21 Tn

4.58 Tn 44.59 Tn

3.93 Tn 25.49 Tn

8.23 Tn 30.87 Tn

44.59 Tn

12 Ø 3/4" Ø =

PPP = MUX

=

PCM = MUY

=

PCV = MUR =

PSX = eX =

PSY = eY =

PU

= eT =

As =

0 10 20 30 40 50 60

-300

-200

-100

0

100

200

300

400

VERIFICACION DE COLUMNA TIPO "L" 60x60


ESFUERZO


DATOS PARA DISEÑO DE COLUMNA TIPO "T" 60 x 60

12.58 Tn 28.40 Tn

4.72 Tn 24.83 Tn

2.46 Tn 24.96 Tn

0.10 Tn 15.70 Tn

0.21 Tn 15.83 Tn

28.40 Tn

12 Ø 3/4" Ø =

PPP = MUX

=

PCM = MUY

=

PCV = MUR

=

PSX = eX =

PSY = eY =

PU

= eT =

As =

0 10 20 30 40 50 60

-300

-200

-100

0

100

200

300

400



ESFUERZO

0 5 10 15 20 25 30

-150

-100

-50

0

50

100

150

200

250

300



ESFUERZO


DATOS PARA DISEÑO DE COLUMNA CIRCULAR D = 0.60

10.97 Tn 20.09 Tn

1.68 Tn 18.96 Tn

1.40 Tn 19.83 Tn

1.12 Tn 12.78 Tn

1.82 Tn 13.65 Tn

20.09 Tn

16 Ø 5/8" Ø =

PPP = MUX

=

PCM = MUY

=

PCV = MUR

=

PSX = eX =

PSY = eY =

PU

= eT =

As =

0 5 10 15 20 25 30

-150

-100

-50

0

50

100

150

200

250

300



ESFUERZO

0 5 10 15 20 25 30 35 40 45 50

-300

-200

-100

0

100

200

300

400

500

VERIFICACION COLUMNA CIRCULAR Ø=60


ESFUERZO


0 5 10 15 20 25 30 35 40 45 50

-300

-200

-100

0

100

200

300

400

500



ESFUERZO


10.86 Tn

37.72 Tn

39.25 Tn-m

0.144 m

0.501 m

0.521 m

16.0617 °

0 5 10 15 20 25 30 35 40 45 50

-200

-100

0

100

200

300

400



ESFUERZO


17.50 Tn

13.55 Tn

22.13 Tn-m

0.392 m

0.304 m

0.496 m

52.2499 °

0 10 20 30 40 50 60

-300

-200

-100

0

100

200

300

400



ESFUERZO


6.18 Tn

10.09 Tn

11.83 Tn-m

0.218 m

0.355 m

0.417 m

31.4870 °

0 10 20 30 40 50 60

-300

-200

-100

0

100

200

300

400



ESFUERZO

0 5 10 15 20 25 30

-150

-100

-50

0

50

100

150

200

250

300



ESFUERZO


16.97 Tn

25.69 Tn

30.79 Tn-m

0.845 m

1.279 m

1.533 m

33.4475 °

0 5 10 15 20 25 30

-150

-100

-50

0

50

100

150

200

250

300



ESFUERZO

0 5 10 15 20 25 30 35 40 45 50

-300

-200

-100

0

100

200

300

400

500



ESFUERZO


0 5 10 15 20 25 30 35 40 45 50

-300

-200

-100

0

100

200

300

400

500



ESFUERZO

DISEÑO DE COLUMNAS SUJETAS A FLEXOCOMPRESION BIAXIAL

DISEÑO DE COLUMNAS POR CARGA AXIAL

DISEÑO POR FLEXOCOMPRESION BIAXIAL

METODO DE CARGAS RECIPROCAS DE BRESLER

β 0.85Ø 0.65

f'c = 210.00

fy = 4200.00

0.0800

0.0100

COLUMNA RECTANGULAR (25x25)

t =

25 c

m

25 cm

25 cm

d = 19 cm

Ag = 625 cm²

Pu = 12.89 Tn

0.91 Tn-m

0.37 Tn-m

b = 25 cm

45.00 °Mu = 0.982 Tn-m

22.13 ° ESTA DENTRO DE LOS ANGULOS

Coeficiente Adimencional de Entrada a los Diagramas de Interacción a 0°0.0300.10

Coeficiente Adimencional de Entrada a los Diagramas de Interacción a 45.00 °0.0300.10

Factores de dimención del nucleo para los ejes principales0.60

Datos Para Diseño a Flexión :

Kg/cm2

Kg/cm2

ρmax =

ρmin =

Datos : PPP =

b = PCM =

t = PCV =

PSX =

PSY =

PU1 =

Cargas : PU2 =

PU3 =

MUX = PU4 =

MUY = PU5 =

Resultados :β =

α =

x =y =

x =y =

gx =

�=��/(�∗�)

� =∅∗(0.85 ^′ ∗ ) )_� ∗� � (��−�� +��∗��

1 ≤1/(1 +1 −1 )/�_� /�_�� /�_�� /�_�

� =0.85 ^′ ∗ )_� ∗� � (��−�� +��∗��

�� : ≥0.1 ^′ �_� ∗� �∗��

X

Y

0.600.60

Del grafico de INTERACCION a 0°: ρ= 0.010Del grafico de INTERACCION a 45.00° : ρ= 0.010

ρ= 0.010As = 6.25 cm²

Usar 08 de Ø= 1/2'' As = 10.13 cm²

19.837 Tn1.400 Tn-m0.569 Tn-m

18.420 Tn > 13.125 Tn Verifica

152.317 Tn76.250 Tn Del diagrama de Interacción76.250 Tn Del diagrama de Interacción

1

19.837 Tn < 50.854 Tn Verifica

gy =

g =

Pn =Mnx =Mny =

a.- VERIFICACION POR EL METODO DE LAS CARGAS RECIPROCAS DE BRESLER

Po =Pox =Poy =

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

-40

-30

-20

-10

0

10

20

30

40

50

60

70

80

90

100

COLUMNA (25 x 25)

DIAGRAMA DE INTERACCION DE COLUMNA ESFUERZO




5.63 Tn

1.53 Tn

1.69 Tn

0.00 Tn

0.02 Tn

12.89 Tn

10.64 Tn

10.66 Tn

6.44 Tn

6.47 Tn

Coeficiente Adimencional de Entrada a los Diagramas de Interacción a 45.00 °

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

-40

-30

-20

-10

0

10

20

30

40

50

60

70

80

90

100

COLUMNA (25 x 25)






β 0.85Ø 0.65

f'c = 210.00

fy = 4200.00

0.0800

0.0100


t =

40 c

m

25 cm

40 cm

d = 34 cm

Ag = 1000 cm²

Pu = 11.26 Tn

4.10 Tn-m

0.10 Tn-m

b = 25 cm

57.99 °Mu = 4.101 Tn-m






Kg/cm2

Kg/cm2

ρmax =

ρmin =

Datos : PPP =

b = PCM =

t = PCV =

PSX =

PSY =

PU1 =

Cargas : PU2 =

PU3 =

MUX = PU4 =

MUY = PU5 =

Resultados :β =

α =

x =y =

x =y =

gx =

�=��/(�∗�)

�_ =∅∗(0.85� ∗�^′ ∗ � (��−��) )+��∗��

1/�_� ≤1/(1/�_�� +1/�_�� −1/�_� )

�_ =0.85� ∗�^′ ∗ � (��−��)+��∗��

�� : �_ ≥0.1� ∗�^′ �∗��

X

Y

0.700.70


ρ= 0.010As = 10.00 cm²

Usar 06 de Ø= 5/8'' As = 11.88 cm²

17.319 Tn6.308 Tn-m0.154 Tn-m

16.082 Tn > 21.000 Tn CORREGIR



gy =

g =

Pn =Mnx =Mny =


Po =Pox =Poy =

0.00.5

1.01.5

2.02.5

3.03.5

4.04.5

5.05.5

6.06.5

7.07.5

8.08.5

9.09.5

10.010.5

11.011.5

12.012.5

13.013.5

-70-60-50-40-30-20-10

0102030405060708090

100110120130140150160170

COLUMNA (25 x 40)





3.22 Tn

1.03 Tn

1.53 Tn

0.49 Tn

4.41 Tn

8.56 Tn

7.34 Tn

11.26 Tn

4.32 Tn

8.24 Tn


0.00.5

1.01.5

2.02.5

3.03.5

4.04.5

5.05.5

6.06.5

7.07.5

8.08.5

9.09.5

10.010.5

11.011.5

12.012.5

13.013.5

-70-60-50-40-30-20-10

0102030405060708090

100110120130140150160170

COLUMNA (25 x 40)






β 0.85Ø 0.65

f'c = 210.00

fy = 4200.00

0.0800

0.0100

PLACA L (60x60)

t =

60 c

m

60 cm

60 cm

d = 54 cm

Ag = 3600 cm²

Pu = 56.87 Tn

4.10 Tn-m

0.10 Tn-m

b = 60 cm

45.00 °Mu = 4.101 Tn-m






Kg/cm2

Kg/cm2

ρmax =

ρmin =

Datos : PPP =

b = PCM =

t = PCV =

PSX =

PSY =

PU1 =

Cargas : PU2 =

PU3 =

MUX = PU4 =

MUY = PU5 =

Resultados :β =

α =

x =y =

x =y =

gx =

�=��/(�∗�)

�_ =∅∗(0.85� ∗�^′ ∗ � (��−��) )+��∗��

1/�_� ≤1/(1/�_�� +1/�_�� −1/�_� )

�_ =0.85� ∗�^′ ∗ � (��−��)+��∗��

�� : �_ ≥0.1� ∗�^′ �∗��

X

Y

0.800.80


ρ= 0.010As = 36.00 cm²

Usar 12 de Ø= 3/4'' As = 34.20 cm²

87.486 Tn6.308 Tn0.154 Tn-m



87.486 Tn < 170.618 Tn Verifica

gy =

g =

Pn =Mnx =Mny =


Po =Pox =Poy =

-5.0 0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0

-200

-100

0

100

200

300

400

PLACA L (60X60)




PLACA L (60x60)

22.06 Tn

9.16 Tn

7.74 Tn

3.57 Tn

3.82 Tn

56.87 Tn

50.34 Tn

50.59 Tn

31.67 Tn

31.92 Tn


-5.0 0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0

-200

-100

0

100

200

300

400

PLACA L (60X60)






β 0.85Ø 0.65

f'c = 210.00

fy = 4200.00

0.0800

0.0100

COLUMNA (25x60)

t =

60 c

m

25 cm

60 cm

d = 54 cm

Ag = 1500 cm²

Pu = 13.25 Tn

5.74 Tn-m

0.74 Tn-m

b = 25 cm

67.38 °Mu = 5.788 Tn-m






Kg/cm2

Kg/cm2

ρmax =

ρmin =

Datos : PPP =

b = PCM =

t = PCV =

PSX =

PSY =

PU1 =

Cargas : PU2 =

PU3 =

MUX = PU4 =

MUY = PU5 =

Resultados :β =

α =

x =y =

x =y =

gx =

�=��/(�∗�)

�_ =∅∗(0.85� ∗�^′ ∗ � (��−��) )+��∗��

1/�_� ≤1/(1/�_�� +1/�_�� −1/�_� )

�_ =0.85� ∗�^′ ∗ � (��−��)+��∗��

�� : �_ ≥0.1� ∗�^′ �∗��

X

Y

0.800.70


ρ= 0.010As = 15.00 cm²

Usar 12 de Ø= 5/8'' As = 23.75 cm²

20.383 Tn8.831 Tn-m1.138 Tn-m

18.927 Tn > 31.500 Tn CORREGIR



gy =

g =

Pn =Mnx =Mny =


Po =Pox =Poy =

0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0

-100

0

100

200

300

COLUMNA (25 x 60)




COLUMNA (25x60)

4.94 Tn

2.01 Tn

2.07 Tn

0.11 Tn

0.46 Tn

13.25 Tn

10.87 Tn

11.22 Tn

6.37 Tn

6.72 Tn


0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0

-100

0

100

200

300

COLUMNA (25 x 60)






β 0.85Ø 0.65

f'c = 210.00

fy = 4200.00

0.0800

0.0100

PLACA (25x90)

t =

90 c

m

25 cm

90 cm

d = 84 cm

Ag = 2250 cm²

Pu = 136.66 Tn

16.68 Tn-m

12.77 Tn-m

b = 25 cm

74.48 °Mu = 21.007 Tn-m






Kg/cm2

Kg/cm2

ρmax =

ρmin =

Datos : PPP =

b = PCM =

t = PCV =

PSX =

PSY =

PU1 =

Cargas : PU2 =

PU3 =

MUX = PU4 =

MUY = PU5 =

Resultados :β =

α =

x =y =

x =y =

gx =

�=��/(�∗�)

�_ =∅∗(0.85� ∗�^′ ∗ � (��−��) )+��∗��

1/�_� ≤1/(1/�_�� +1/�_�� −1/�_� )

�_ =0.85� ∗�^′ ∗ � (��−��)+��∗��

�� : �_ ≥0.1� ∗�^′ �∗��

X

Y

0.900.80


ρ= 0.010As = 22.50 cm²

Usar 14 de Ø= 5/8'' As = 27.71 cm²

210.238 Tn25.662 Tn-m19.646 Tn-m

195.221 Tn > 47.250 Tn Verifica


210.238 Tn < 234.516 Tn Verifica

gy =

g =

Pn =Mnx =Mny =


Po =Pox =Poy =

0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0 55.0 60.0 65.0 70.0 75.0

-200

-100

0

100

200

300

400

PLACA (25 x 90)




PLACA (25x90)

29.30 Tn

11.80 Tn

14.98 Tn

10.16 Tn

70.30 Tn

83.01 Tn

76.52 Tn

136.66 Tn

47.15 Tn

107.29 Tn


0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0 55.0 60.0 65.0 70.0 75.0

-200

-100

0

100

200

300

400

PLACA (25 x 90)






β 0.85Ø 0.65

f'c = 210.00

fy = 4200.00

0.0800

0.0100

PLACA T (50x90)

t =

53 c

m

53 cm

53 cm

d = 47 cm

Ag = 2809 cm²

Pu = 63.91 Tn

10.27 Tn-m

16.36 Tn-m

b = 53 cm

45.00 °Mu = 19.316 Tn-m

57.88 ° CORREGIR





Kg/cm2

Kg/cm2

ρmax =

ρmin =

Datos : PPP =

b = PCM =

t = PCV =

PSX =

PSY =

PU1 =

Cargas : PU2 =

PU3 =

MUX = PU4 =

MUY = PU5 =

Resultados :β =

α =

x =y =

x =y =

gx =

�=��/(�∗�)

�_ =∅∗(0.85� ∗�^′ ∗ � (��−��) )+��∗��

1/�_� ≤1/(1/�_�� +1/�_�� −1/�_� )

�_ =0.85� ∗�^′ ∗ � (��−��)+��∗��

�� : �_ ≥0.1� ∗�^′ �∗��

X

Y

0.800.80


ρ= 0.010As = 28.09 cm²

Usar 20 de Ø= 5/8'' As = 39.59 cm²

98.318 Tn15.800 Tn-m25.169 Tn-m



98.318 Tn < 100.814 Tn Verifica

gy =

g =

Pn =Mnx =Mny =


Po =Pox =Poy =

0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0 55.0 60.0 65.0 70.0 75.0 80.0

-300

-200

-100

0

100

200

300

400

500

PLACA T (50x 90)




PLACA T (50x90)

23.12 Tn

10.81 Tn

9.65 Tn

0.03 Tn

2.40 Tn

63.91 Tn

52.09 Tn

54.46 Tn

30.57 Tn

32.94 Tn


0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0 55.0 60.0 65.0 70.0 75.0 80.0

-300

-200

-100

0

100

200

300

400

500

PLACA T (50x 90)






β 0.85Ø 0.65

f'c = 210.00

fy = 4200.00

0.0800

0.0100

PLACA T (50x120)

t =

55 c

m

55 cm

55 cm

d = 49 cm

Ag = 3025 cm²

Pu = 102.90 Tn

51.78 Tn-m

20.19 Tn-m

b = 55 cm

45.00 °Mu = 55.577 Tn-m






Kg/cm2

Kg/cm2

ρmax =

ρmin =

Datos : PPP =

b = PCM =

t = PCV =

PSX =

PSY =

PU1 =

Cargas : PU2 =

PU3 =

MUX = PU4 =

MUY = PU5 =

Resultados :β =

α =

x =y =

x =y =

gx =

�=��/(�∗�)

�_ =∅∗(0.85� ∗�^′ ∗ � (��−��) )+��∗��

1/�_� ≤1/(1/�_�� +1/�_�� −1/�_� )

�_ =0.85� ∗�^′ ∗ � (��−��)+��∗��

�� : �_ ≥0.1� ∗�^′ �∗��

X

Y

0.800.80


ρ= 0.010As = 30.25 cm²

Usar 24 de Ø= 5/8'' As = 47.50 cm²

158.314 Tn79.662 Tn-m31.062 Tn-m

147.006 Tn > 63.525 Tn Verifica


158.314 Tn < 251.144 Tn Verifica

gy =

g =

Pn =Mnx =Mny =


Po =Pox =Poy =

0.05.0

10.015.0

20.025.0

30.035.0

40.045.0

50.055.0

60.065.0

70.075.0

80.085.0

90.095.0

100.0105.0

110.0115.0

120.0125.0

130.0135.0

140.0

-300

-200

-100

0

100

200

300

400

500

600

700

PLACA (50 x 120)




PLACA T (50x120)

33.88 Tn

17.11 Tn

18.54 Tn

0.37 Tn

9.55 Tn

102.90 Tn

82.65 Tn

91.83 Tn

46.26 Tn

55.44 Tn


0.05.0

10.015.0

20.025.0

30.035.0

40.045.0

50.055.0

60.065.0

70.075.0

80.085.0

90.095.0

100.0105.0

110.0115.0

120.0125.0

130.0135.0

140.0

-300

-200

-100

0

100

200

300

400

500

600

700

PLACA (50 x 120)






β 0.85Ø 0.65

f'c = 210.00

fy = 4200.00

0.0800

0.0100


t =

25 c

m

90 cm

25 cm

d = 19 cm

Ag = 2250 cm²

Pu = 34.99 Tn

8.50 Tn-m

0.55 Tn-m

b = 90 cm

15.52 °Mu = 8.518 Tn-m






Kg/cm2

Kg/cm2

ρmax =

ρmin =

Datos : PPP =

b = PCM =

t = PCV =

PSX =

PSY =

PU1 =

Cargas : PU2 =

PU3 =

MUX = PU4 =

MUY = PU5 =

Resultados :β =

α =

x =y =

x =y =

gx =

�=��/(�∗�)

�_ =∅∗(0.85� ∗�^′ ∗ � (��−��) )+��∗��

1/�_� ≤1/(1/�_�� +1/�_�� −1/�_� )

�_ =0.85� ∗�^′ ∗ � (��−��)+��∗��

�� : �_ ≥0.1� ∗�^′ �∗��

X

Y

0.600.80


ρ= 0.010As = 22.50 cm²

Usar 14 de Ø= 5/8'' As = 27.71 cm²

53.827 Tn13.077 Tn-m0.846 Tn-m



53.827 Tn < 248.687 Tn Verifica

gy =

g =

Pn =Mnx =Mny =


Po =Pox =Poy =

0.0 10.0 20.0 30.0 40.0 50.0 60.0

-140-120-100

-80-60-40-20

020406080

100120140160180200220240260280300320340360

COLUMNA (25 x 90)





14.84 Tn

3.68 Tn

3.44 Tn

3.39 Tn

6.03 Tn

31.77 Tn

31.68 Tn

34.99 Tn

20.90 Tn

24.21 Tn

0.01570.000628796


0.0 10.0 20.0 30.0 40.0 50.0 60.0

-140-120-100

-80-60-40-20

020406080

100120140160180200220240260280300320340360

COLUMNA (25 x 90)






β 0.85Ø 0.65

f'c = 210.00

fy = 4200.00

0.0800

0.0100

COLUMNA RECTANGULAR (60x60)t

= 6

0 c

m

60 cm

60 cm

d = 54 cm

Ag = 3600 cm²

Pu = 61.55 Tn

31.96 Tn-m

27.66 Tn-m

b = 60 cm

45.00 °Mu = 42.267 Tn-m






Kg/cm2

Kg/cm2

ρmax =

ρmin =

Datos : PPP =

b = PCM =

t = PCV =

PSX =

PSY =

PU1 =

Cargas : PU2 =

PU3 =

MUX = PU4 =

MUY = PU5 =

Resultados :β =

α =

x =y =

x =y =

gx =

�=��/(�∗�)

�_ =∅∗(0.85� ∗�^′ ∗ � (��−��) )+��∗��

1/�_� ≤1/(1/�_�� +1/�_�� −1/�_� )

�_ =0.85� ∗�^′ ∗ � (��−��)+��∗��

�� : �_ ≥0.1� ∗�^′ �∗��

X

Y

0.800.80


ρ= 0.010As = 36.00 cm²

Usar 08 de Ø= 5/8''As = 38.64 cm²

Usar 08 de Ø= 3/4''

94.685 Tn49.169 Tn-m42.554 Tn-m

102.575 Tn > 75.600 Tn Verifica


94.685 Tn < 341.316 Tn Verifica

gy =

g =

Pn =Mnx =Mny =


Po =Pox =Poy =

0 10 20 30 40 50 60 70 80 90

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

450

500

550

600

650

COLUMNA (60 x 60)





20.44 Tn

9.51 Tn

8.90 Tn

2.50 Tn

10.38 Tn

57.06 Tn

51.69 Tn

61.55 Tn

30.08 Tn

39.94 Tn


0 10 20 30 40 50 60 70 80 90

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

450

500

550

600

650

COLUMNA (60 x 60)


DISEÑO DE NUDOS (VIGA - COLUMNA)

MOMENTO RESISTENTE DE LA VIGA

Ø = 0.90 (FLEXION)f'c = 210 kg/cm2fy = 4200 kg/cm2b = 25 cmh = 60 cmd = 51 cm

11.64 cm20.00910.1826

20.02 Tn-m

MOMENTO RESISTENTE DE LA COLUMNA

50.00 Tn-m ( Del diagrama de interaccion)Ø = 0.75

37.50 Tn-m

20.02 Tn-m <= 28.13 Tn-m OK !!!

CORTANTE RESISTENTE EN EL NUDO

Ø = 0.85 (CORTANTE)90 cm25 cm

d = 50 cm5.07 cm2

S = 7.5 cm3750.00 cm2

291.63 Tn

CORTANTE ACTUANTE EN EL NUDO

11.64 cm2 (De la viga)

5.70 cm2 (De la viga)

11071 kg (Del analisis estrcutural)

79.96 Tn

As =ρ =ω =

MRV =

MC =

MRC =

1.- VERIFICACION DE MOMENTOS

b =bW =

AV =

AJ =

VR =

As1 =

As2 =

VCOL =

VU =

2.- VERIFICACION DE CORTANTES

�=��/(�∗�)

�=�∗ / ^′ �� (�)� ;

� <=3/4_�� ∗�_�� OK !!!

�_��=∅∗�^′ �∗�∗�^2 (1−0.59 )∗� ∗�

�_�=1.2∗√ ^′ )(� � ∗�_�

�_�=1.25 1 2 )−∗��(�_� +�_� �_��

� <_� =�_� OK !!!

79.96 Tn <= 291.63 Tn OK !!!

DISEÑO DE NUDOS (VIGA - COLUMNA)

3.- COLUMNAS --- ok.xlsx

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Transcript of 3.- COLUMNAS --- ok.xlsx