V.ca04 - Cálculo de Vigas

Dimensionamento de de seçã ( ) 25 ( ) 0.77

 KN  f   yk  fyk fyk (MPa) (MPa) = 250 cm2 Módulo Módulo de elasticid elasticidade ade (MPa) (MPa) = 210000

Domínio

sd

0.01

2

! 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.16 0.17 0.18 0.19 0.2 0.21 0.22 0.23 0.24 0.24 0.25 0.26 0.27 0.28 0.29 0.3 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.4 0.41 0.42 0.43 0.44

=

cd

0.000101 101 0.000204 204 0.000309 309 0.000417 417 0.000526 526 0.000638 638 0.000753 753 0.000 00087 0.000989 989 0.001111 0.00 0.0012 1236 36 0.001364 364 0.001494 494 0.001628 628 0.001765 765 0.00 0.0019 1905 05 0.002048 048 0.002195 195 0.002346 346 0.0025 0.002658 658 0.002821 821 0.002987 987 0.00 0.0031 3158 58 0.003333 0.003514 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035

 Kx 

sd

0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.009463 0.009 0.008569 0.008167 0.00779 0.007438 0.007106 0.006794 0.0065 0.006222 0.005959 0.005711 0.005474 0.00525 0.005037 0.004833 0.00464 0.004455

lim

ψ 

s

0.062068 068 0.123213 213 0.183335 335 0.242332 332 0.300092 092 0.356496 496 0.411416 416 0.464713 713 0.516242 242 0.565844 844 0.61 0.6133 3348 48 0.658574 574 0.701326 326 0.741392 392 0.778547 547 0.81 0.8125 2547 47 0.843137 137 0.870 87037 0.894737 737 0.916667 0.936508 508 0.954545 545 0.971014 014 0.98 0.9861 611 11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

0.0 0.0461 46185 0.0 0.0463 46371 0. 0.0465 46559 0.0 0.0467 46748 0.0 0.0469 46939 0. 0.0471 47131 0. 0.0473 47325 0.0 0.0475 47521 0.0 0.0477 47718 0. 0.0479 47917 0.04 0.0481 8117 17 0.0 0.0483 48319 0.0 0.0485 48523 0.0 0.0487 48729 0.0 0.0489 48936 0.04 0.0491 9145 45 0. 0.0493 49356 0.0 0.0495 49569 0.0 0.0497 49784 0.05 0.0 0.0502 50218 0.0 0.0504 50439 0.0 0.0506 50661 0. 0.0508 050885 85 0.051111 0.051339 0.05157 0.051802 0.052036 0.052273 0.052511 0.052752 0.052995 0.053241 0.053488 0.053738 0.053991 0.054245 0.054502 0.054762 0.055024 0.055288 0.055556 0.055825

13.5

15

24 2466. 66.918 918 62 623.8 3.8623 623 28 280.6 0.6477 477 15 159.8 9.8892 892 10 103.7 3.7133 133 73 73.05155 155 54.4804 42.37746 746 34 34.04964 964 28 28.07487 487 23.6 23.644 4436 36 20.2704 17 17.64469 469 15 15.56459 459 13 13.89254 254 12.5 12.532 3259 59 11 11.41622 622 10.48964 964 9. 9.708776 776 9.041825 8. 8.465627 627 7. 7.962899 899 7. 7.520487 487 7.12 7.1281 8199 99 6.77802 6.546422 6.332231 6.133585 5.948878 5.776721 5.615902 5.465361 5.324167 5.191498 5.066626 4.948905 4.837757 4.732667 4.633171 4.538853 4.449336 4.364281 4.28338 4.206351

22 2220.227 56 561.4761 252. 52.583 583 14 143.9003 93 93.34195 65.7 5.7464 464 49.03236 38.13971 30 30.64467 25 25.26738 21.2 21.279 7992 92 18.24336 15 15.88022 14 14.00813 12 12.50328 11.27 1.2793 933 3 10.2 0.2746 746 9.44068 068 8. 8.737 737898 8.137642 7. 7.619 619064 7. 7.166 166609 6. 6.768 768438 6.41 6.4153 5379 79 6.100218 5.89178 5.699008 5.520226 5.353991 5.199049 5.054312 4.918825 4.791751 4.672348 4.559964 4.454014 4.353981 4.2594 4.169854 4.084967 4.004403 3.927853 3.855042 3.785716

cd

0.0035

3

cd

0.0035

"

0.45 0.46 0.47 0.48 0.49 0.5 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.6 0.61 0.62 0.63 0.64 0.65 0.66 0.67 0.68 0.69 0.7 0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.78 0.79 0.8 0.81 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9 0.91 0.92 0.93 0.94 0.95 0.96

0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035

0.004278 0.004109 0.003947 0.003792 0.003643 0.0035 0.003363 0.003231 0.003104 0.002981 0.002864 0.00275 0.00264 0.002534 0.002432 0.002333 0.002238 0.002145 0.002056 0.001969 0.001885 0.001803 0.001724 0.001647 0.001572 0.0015 0.00143 0.001361 0.001295 0.00123 0.001167 0.001105 0.001045 0.000987 0.00093 0.000875 0.000821 0.000768 0.000717 0.000667 0.000618 0.00057 0.000523 0.000477 0.000433 0.000389 0.000346 0.000304 0.000263 0.000223 0.000184 0.000146

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

0.056098 0.056373 0.05665 0.056931 0.057214 0.0575 0.057789 0.058081 0.058376 0.058673 0.058974 0.059278 0.059585 0.059896 0.060209 0.060526 0.060847 0.06117 0.061497 0.061828 0.062162 0.0625 0.062842 0.063187 0.063536 0.063889 0.064246 0.064607 0.064972 0.065341 0.065714 0.066092 0.066474 0.06686 0.067251 0.067647 0.068047 0.068452 0.068862 0.069277 0.069697 0.070122 0.070552 0.070988 0.071429 0.071875 0.072327 0.072785 0.073248 0.073718 0.074194 0.074675

4.132939 4.062912 3.996055 3.932174 3.87109 3. 3.812636 3.756662 3.703027 3.651601 3.602264 3.554906 3.509422 3.465718 3.423703 3.383296 3.344418 3.306996 3. 3.270964 3.236259 3.202819 3.170591 3.139523 3.109564 3.080669 3.052795 3.025902 2.99995 2.974903 2.950728 2.927393 2.904866 2.883119 2.862125 2.841858 2.822293 2.803409 2.785182 2.767593 2.750621 2.734249 2.718457 2.70323 2.688552 2.674408 2.660783 2.647664 2.635038 2.622892 2.611216 2.599997 2.589227 2.578894

3.719645 3. 3.65662 3.59645 3.538957 3.483981 3.431373 3.380996 3.332724 3.286441 3.242038 3.199415 3.15848 3.119146 3.081333 3.044966 3.009976 2.976297 2.943868 2.912633 2.882537 2.853532 2.82557 2.798607 2.772602 2.747516 2.723312 2.699955 2.677413 2.655656 2.634653 2.614379 2.594807 2.575912 2.557672 2.540064 2.523068 2.506664 2.490834 2.475559 2.460824 2.446611 2.432907 2.419697 2.406967 2.394705 2.382898 2.371534 2.360603 2.350094 2.339998 2.330304 2.321004

cd

0.0035

3

cd

0.0035

"

0.45 0.46 0.47 0.48 0.49 0.5 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.6 0.61 0.62 0.63 0.64 0.65 0.66 0.67 0.68 0.69 0.7 0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.78 0.79 0.8 0.81 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9 0.91 0.92 0.93 0.94 0.95 0.96

0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035

0.004278 0.004109 0.003947 0.003792 0.003643 0.0035 0.003363 0.003231 0.003104 0.002981 0.002864 0.00275 0.00264 0.002534 0.002432 0.002333 0.002238 0.002145 0.002056 0.001969 0.001885 0.001803 0.001724 0.001647 0.001572 0.0015 0.00143 0.001361 0.001295 0.00123 0.001167 0.001105 0.001045 0.000987 0.00093 0.000875 0.000821 0.000768 0.000717 0.000667 0.000618 0.00057 0.000523 0.000477 0.000433 0.000389 0.000346 0.000304 0.000263 0.000223 0.000184 0.000146

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

0.056098 0.056373 0.05665 0.056931 0.057214 0.0575 0.057789 0.058081 0.058376 0.058673 0.058974 0.059278 0.059585 0.059896 0.060209 0.060526 0.060847 0.06117 0.061497 0.061828 0.062162 0.0625 0.062842 0.063187 0.063536 0.063889 0.064246 0.064607 0.064972 0.065341 0.065714 0.066092 0.066474 0.06686 0.067251 0.067647 0.068047 0.068452 0.068862 0.069277 0.069697 0.070122 0.070552 0.070988 0.071429 0.071875 0.072327 0.072785 0.073248 0.073718 0.074194 0.074675

4.132939 4.062912 3.996055 3.932174 3.87109 3. 3.812636 3.756662 3.703027 3.651601 3.602264 3.554906 3.509422 3.465718 3.423703 3.383296 3.344418 3.306996 3. 3.270964 3.236259 3.202819 3.170591 3.139523 3.109564 3.080669 3.052795 3.025902 2.99995 2.974903 2.950728 2.927393 2.904866 2.883119 2.862125 2.841858 2.822293 2.803409 2.785182 2.767593 2.750621 2.734249 2.718457 2.70323 2.688552 2.674408 2.660783 2.647664 2.635038 2.622892 2.611216 2.599997 2.589227 2.578894

3.719645 3. 3.65662 3.59645 3.538957 3.483981 3.431373 3.380996 3.332724 3.286441 3.242038 3.199415 3.15848 3.119146 3.081333 3.044966 3.009976 2.976297 2.943868 2.912633 2.882537 2.853532 2.82557 2.798607 2.772602 2.747516 2.723312 2.699955 2.677413 2.655656 2.634653 2.614379 2.594807 2.575912 2.557672 2.540064 2.523068 2.506664 2.490834 2.475559 2.460824 2.446611 2.432907 2.419697 2.406967 2.394705 2.382898 2.371534 2.360603 2.350094 2.339998 2.330304 2.321004

0.97 0.98 0.99 1

0.0035 0.0035 0.0035 0.0035

0.000108 7.14E-005 3.54E-005 0

1 1 1 1

0.075163 0.075658 0.076159 0.076667

2.568989 2. 2.31209 2.559503 2.303553 2.550429 2.295386 2.541757 2.287582

 retangular - Aço CA 25-A fck (MPa) 1#

20

21

25

30

35

"0

"5

50

1110.1133 280.73803 126.29148 71.950149 46.670976 32.873198 24.516182 19.069857 15.322336 12.63369 10.63996 9.1216802 7.9401096 7.0040638 6.2516417 5.6396664 5.137298 4.7203401 4.368949 4.0688212 3.8095321 3.5833047 3.3842191 3.2076897 3.0501089 2.9458899 2.8495039 2.7601131 2.6769953 2.5995247 2.5271561 2.4594127 2.3958753 2.3361741 2.2799818 2.2270071 2.1769906 2.1296999 2.0849268 2.0424837 2.0022013 1.9639266 1.9275208 1.8928578

951.52568 240.6326 108.24984 61.671556 40.003694 28.177027 21.01387 16.345591 13.133431 10.828877 9.1199657 7.818583 6.8058082 6.0034833 5.35855 4.8339998 4.4033982 4.0460058 3.7448134 3.487561 3.2653132 3.071404 2.9007592 2.7494483 2.6143791 2.5250485 2.4424319 2.3658112 2.2945674 2.228164 2.1661338 2.108068 2.0536074 2.002435 1.9542701 1.9088632 1.8659919 1.8254571 1.7870801 1.7507003 1.7161725 1.6833657 1.6521607 1.6224495

832.58497 210.55353 94.718607 53.962612 35.003232 24.654898 18.387136 14.302392 11.491752 9.4752674 7.97997 6.8412601 5.9550822 5.2530478 4.6887313 4.2297498 3.8529735 3.5402551 3.2767118 3.0516159 2.8571491 2.6874785 2.5381643 2.4057672 2.2875817 2.2094174 2.1371279 2.0700848 2.0077465 1.9496435 1.8953671 1.8445595 1.7969064 1.7521306 1.7099863 1.6702553 1.6327429 1.597275 1.5636951 1.5318627 1.501651 1.4729449 1.4456406 1.4196433

740.07553 187.15869 84.194317 47.966766 31.113984 21.915465 16.344121 12.713238 10.214891 8.4224599 7.0933067 6.0811201 5.2934064 4.6693759 4.1677611 3.7597776 3.4248653 3.1468934 2.9126327 2.7125475 2.5396881 2.3888698 2.2561461 2.1384598 2.033406 1.9639266 1.8996692 1.8400754 1.7846635 1.7330164 1.6847707 1.6396084 1.5972502 1.5574494 1.5199878 1.4846714 1.4513271 1.4198 1.3899512 1.3616558 1.3348009 1.3092844 1.2850139 1.2619052

666.06798 168.44282 75.774885 43.170089 28.002586 19.723919 14.709709 11.441914 9.1934018 7.5802139 6.383976 5.4730081 4.7640658 4.2024383 3.750985 3.3837999 3.0823788 2.832204 2.6213694 2.4412927 2.2857193 2.1499828 2.0305315 1.9246138 1.8300654 1.7675339 1.7097023 1.6560678 1.6061972 1.5597148 1.5162937 1.4756476 1.4375252 1.4017045 1.3679891 1.3362043 1.3061943 1.27782 1.2509561 1.2254902 1.2013208 1.178356 1.1565125 1.1357147

c 1850.189 467.8967 210.4858 119.9169 77.78496 54.78866 40.8603 31.78309 25.53723 21.05615 17.73327 15.2028 13.23352 11.67344 10.4194 9.399444 8.562163 7.867233 7.281582 6.781369 6.34922 5.972174 5.640365 5.346149 5.083515 4.909816 4.749173 4.600188 4.461659 4.332541 4.211927 4.099021 3.993125 3.893624 3.79997 3.711679 3.628318 3.5495 3.474878 3.404139 3.337002 3.273211 3.212535 3.154763

1665.17 421.1071 189.4372 107.9252 70.00646 49.3098 36.77427 28.60478 22.9835 18.95053 15.95994 13.68252 11.91016 10.5061 9.377463 8.4595 7.705947 7.08051 6.553424 6.103232 5.714298 5.374957 5.076329 4.811534 4.575163 4.418835 4.274256 4.14017 4.015493 3.899287 3.790734 3.689119 3.593813 3.504261 3.419973 3.340511 3.265486 3.19455 3.12739 3.063725 3.003302 2.94589 2.891281 2.839287

1585.8761 401.05433 180.41639 102.78593 66.672823 46.961711 35.023117 27.242652 21.889052 18.048128 15.199943 13.030972 11.343014 10.005805 8.9309167 8.0566663 7.3389971 6.743343 6.2413557 5.8126017 5.4421887 5.1190067 4.8345987 4.5824138 4.3572985 4.2084141 4.0707198 3.9430186 3.824279 3.7136067 3.610223 3.5134467 3.4226789 3.3373916 3.2571168 3.1814387 3.1099865 3.0424285 2.9784669 2.9178338 2.8602875 2.8056094 2.7536012 2.7040825

1332.136 336.88564 151.54977 86.340179 56.005171 39.447837 29.419418 22.883828 18.386804 15.160428 12.767952 10.946016 9.5281315 8.4048766 7.5019701 6.7675997 6.1647575 5.6644081 5.2427388 4.8825854 4.5714385 4.2999656 4.0610629 3.8492276 3.6601307 3.5350679 3.4194046 3.3121357 3.2123943 3.1194296 3.0325873 2.9512952 2.8750503 2.8034089 2.7359781 2.6724085 2.6123887 2.5556399 2.5019122 2.4509804 2.4026415 2.3567119 2.313025 2.2714293

3.099704 3.047184 2.997041 2.949131 2.903317 2.859477 2.817496 2.77727 2.7387 2.701698 2.666179 2.632067 2.599288 2.567778 2.537472 2.508313 2.480247 2.453223 2.427194 2.402115 2.377944 2.354642 2.332173 2.310502 2.289597 2.269426 2.249962 2.231178 2.213046 2.195544 2.178649 2.162339 2.146593 2.131393 2.11672 2.102557 2.088887 2.075695 2.062966 2.050686 2.038843 2.027423 2.016414 2.005806 1.995587 1.985748 1.976278 1.967169 1.958412 1.949998 1.94192 1.93417

2.789734 2.742465 2.697337 2.654218 2.612985 2.573529 2.535747 2.499543 2.46483 2.431528 2.399561 2.36886 2.33936 2.311 2.283725 2.257482 2.232223 2.207901 2.184475 2.161903 2.140149 2.119178 2.098956 2.079452 2.060637 2.042484 2.024966 2.00806 1.991742 1.97599 1.960784 1.946105 1.931934 1.918254 1.905048 1.892301 1.879998 1.868125 1.856669 1.845618 1.834959 1.824681 1.814773 1.805225 1.796029 1.787173 1.778651 1.770452 1.762571 1.754998 1.747728 1.740753

2.6568893 2.6118717 2.5688926 2.5278263 2.4885576 2.4509804 2.4149969 2.3805171 2.3474575 2.3157411 2.2852964 2.2560571 2.2279615 2.2009522 2.1749759 2.1499828 2.1259263 2.1027629 2.0804519 2.0589553 2.0382373 2.0182645 1.9990053 1.9804302 1.9625113 1.9452225 1.9285391 1.9124379 1.8968968 1.8818953 1.8674136 1.8534334 1.8399372 1.8269085 1.8143315 1.8021915 1.7904744 1.779167 1.7682565 1.7577312 1.7475796 1.737791 1.7283551 1.7192623 1.7105034 1.7020697 1.6939529 1.686145 1.6786387 1.6714269 1.6645028 1.6578601

2.231787 2.1939722 2.1578698 2.1233741 2.0903884 2.0588235 2.0285974 1.9996344 1.9718643 1.9452225 1.919649 1.8950879 1.8714876 1.8487999 1.8269798 1.8059856 1.7857781 1.7663208 1.7475796 1.7295225 1.7121194 1.6953422 1.6791644 1.6635614 1.6485095 1.6339869 1.6199729 1.6064478 1.5933933 1.580792 1.5686275 1.5568841 1.5455473 1.5346031 1.5240384 1.5138408 1.5039985 1.4945002 1.4853355 1.4764942 1.4679669 1.4597444 1.4518183 1.4441804 1.4368229 1.4297386 1.4229204 1.4163618 1.4100565 1.4039986 1.3981824 1.3926025

1.8598225 1.8283102 1.7982248 1.7694784 1.7419903 1.7156863 1.6904979 1.666362 1.6432203 1.6210188 1.5997075 1.5792399 1.559573 1.5406666 1.5224832 1.504988 1.4881484 1.471934 1.4563163 1.4412687 1.4267661 1.4127851 1.3993037 1.3863011 1.3737579 1.3616558 1.3499774 1.3387065 1.3278278 1.3173267 1.3071895 1.2974034 1.2879561 1.2788359 1.270032 1.261534 1.2533321 1.2454169 1.2377796 1.2304118 1.2233057 1.2164537 1.2098486 1.2034836 1.1973524 1.1914488 1.185767 1.1803015 1.1750471 1.1699988 1.165152 1.1605021

1.5941336 1.567123 1.5413355 1.5166958 1.4931346 1.4705882 1.4489982 1.4283103 1.4084745 1.3894447 1.3711778 1.3536342 1.3367769 1.3205713 1.3049856 1.2899897 1.2755558 1.2616577 1.2482711 1.2353732 1.2229424 1.2109587 1.1994032 1.1882581 1.1775068 1.1671335 1.1571235 1.1474627 1.1381381 1.1291372 1.1204482 1.1120601 1.1039623 1.0961451 1.0885989 1.0813149 1.0742846 1.0675002 1.0609539 1.0546387 1.0485478 1.0426746 1.0370131 1.0315574 1.0263021 1.0212418 1.0163717 1.011687 1.0071832 1.0028561 0.9987017 0.9947161

1.3948669 1.3712326 1.3486686 1.3271088 1.3064927 1.2867647 1.2678734 1.2497715 1.2324152 1.2157641 1.1997806 1.18443 1.1696798 1.1554999 1.1418624 1.128741 1.1161113 1.1039505 1.0922373 1.0809515 1.0700746 1.0595889 1.0494778 1.0397258 1.0303184 1.0212418 1.012483 1.0040299 0.9958708 0.987995 0.9803922 0.9730526 0.965967 0.9591269 0.952524 0.9461505 0.9399991 0.9340626 0.9283347 0.9228089 0.9174793 0.9123403 0.9073864 0.9026127 0.8980143 0.8935866 0.8893253 0.8852261 0.8812853 0.8774991 0.873864 0.8703766

1.2398817 1.2188735 1.1988165 1.1796523 1.1613269 1.1437908 1.1269986 1.110908 1.0954802 1.0806792 1.0664717 1.0528266 1.0397153 1.027111 1.0149888 1.0033253 0.9920989 0.9812893 0.9708776 0.9608458 0.9511774 0.9418568 0.9328691 0.9242008 0.9158386 0.9077705 0.8999849 0.892471 0.8852185 0.8782178 0.8714597 0.8649356 0.8586374 0.8525573 0.846688 0.8410227 0.8355547 0.8302779 0.8251864 0.8202746 0.8155371 0.8109691 0.8065657 0.8023224 0.7982349 0.7942992 0.7905113 0.7868677 0.7833647 0.7799992 0.776768 0.7736681

1.1158935 1.0969861 1.0789349 1.0616871 1.0451942 1.0294118 1.0142987 0.9998172 0.9859322 0.9726113 0.9598245 0.947544 0.9357438 0.9243999 0.9134899 0.9029928 0.892889 0.8831604 0.8737898 0.8647612 0.8560597 0.8476711 0.8395822 0.8317807 0.8242548 0.8169935 0.8099864 0.8032239 0.7966967 0.790396 0.7843137 0.778442 0.7727736 0.7673016 0.7620192 0.7569204 0.7519992 0.7472501 0.7426677 0.7382471 0.7339834 0.7298722 0.7259091 0.7220902 0.7184114 0.7148693 0.7114602 0.7081809 0.7050283 0.7019993 0.6990912 0.6963012

1.926742 1.734067 1.6514928 1.3872539 1.919628 1.727665 1.645395 1.3821318 1.912822 1.72154 1.6395614 1.3772316 1.906318 1.715686 1.6339869 1.372549

1.1560449 1.1517765 1.147693 1.1437908

0.9908957 0.987237 0.9837369 0.9803922

0.8670337 0.8638324 0.8607698 0.8578431

0.7706966 0.767851 0.7651287 0.7625272

0.693627 0.6910659 0.6886158 0.6862745

  m   c   e    N    K   m   e   o    ã    t   s

  c    K   e   s    K   e    d   s   e    d   a    d    i   n   u   s    A

Dimensionamento de seçã ( ) 50 ( ) 0.$3 f   yk 

 KN 

fyk (MPa) = 500 Módulo de elasticidade (MPa) = ! Domínio 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 sd 0.13 2 0.01 0.14 0.15 0.16 0.17 0.18 0.19 0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.3 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.4 0.41 0.42 0.43 cd

cm2 210000

=

cd

0.000101 0.000204 0.000309 0.000417 0.000526 0.000638 0.000753 0.00087 0.000989 0.001111 0.001236 0.001364 0.001494 0.001628 0.001765 0.001905 0.002048 0.002195 0.002346 0.0025 0.002658 0.002821 0.002987 0.003158 0.003333 0.003514 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035

 Kx 

sd

0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.009463 0.009 0.008569 0.008167 0.00779 0.007438 0.007106 0.006794 0.0065 0.006222 0.005959 0.005711 0.005474 0.00525 0.005037 0.004833 0.00464

lim

ψ 

s

0.062068 0.123213 0.183335 0.242332 0.300092 0.356496 0.411416 0.464713 0.516242 0.565844 0.613348 0.658574 0.701326 0.741392 0.778547 0.812547 0.843137 0.87037 0.894737 0.916667 0.936508 0.954545 0.971014 0.986111 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

0.023092 0.023185 0.023279 0.023374 0.023469 0.023566 0.023663 0.02376 0.023859 0.023958 0.024059 0.02416 0.024262 0.024364 0.024468 0.024573 0.024678 0.024784 0.024892 0.025 0.025109 0.025219 0.02533 0.025442 0.025556 0.02567 0.025785 0.025901 0.026018 0.026136 0.026256 0.026376 0.026498 0.02662 0.026744 0.026869 0.026995 0.027123 0.027251 0.027381 0.027512 0.027644 0.027778

13.5

15

2466.918 623.8623 280.6477 159.8892 103.7133 73.05155 54.4804 42.37746 34.04964 28.07487 23.64436 20.2704 17.64469 15.56459 13.89254 12.53259 11.41622 10.48964 9.708776 9.041825 8.465627 7.962899 7.520487 7.128199 6.77802 6.546422 6.332231 6.133585 5.948878 5.776721 5.615902 5.465361 5.324167 5.191498 5.066626 4.948905 4.837757 4.732667 4.633171 4.538853 4.449336 4.364281 4.28338

2220.227 561.4761 252.583 143.9003 93.34195 65.7464 49.03236 38.13971 30.64467 25.26738 21.27992 18.24336 15.88022 14.00813 12.50328 11.27933 10.2746 9.44068 8.737898 8.137642 7.619064 7.166609 6.768438 6.415379 6.100218 5.89178 5.699008 5.520226 5.353991 5.199049 5.054312 4.918825 4.791751 4.672348 4.559964 4.454014 4.353981 4.2594 4.169854 4.084967 4.004403 3.927853 3.855042

cd

0.0035

3

cd

0.0035

"

0.44 0.45 0.46 0.47 0.48 0.49 0.5 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.6 0.61 0.62 0.63 0.64 0.65 0.66 0.67 0.68 0.69 0.7 0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.78 0.79 0.8 0.81 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9 0.91 0.92 0.93 0.94

0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035

0.004455 0.004278 0.004109 0.003947 0.003792 0.003643 0.0035 0.003363 0.003231 0.003104 0.002981 0.002864 0.00275 0.00264 0.002534 0.002432 0.002333 0.002238 0.002145 0.002056 0.001969 0.001885 0.001803 0.001724 0.001647 0.001572 0.0015 0.00143 0.001361 0.001295 0.00123 0.001167 0.001105 0.001045 0.000987 0.00093 0.000875 0.000821 0.000768 0.000717 0.000667 0.000618 0.00057 0.000523 0.000477 0.000433 0.000389 0.000346 0.000304 0.000263 0.000223

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

0.027913 0.028049 0.028186 0.028325 0.028465 0.028607 0.02875 0.028894 0.02904 0.029188 0.029337 0.029487 0.029639 0.029793 0.029948 0.030105 0.030263 0.030423 0.030585 0.030749 0.030914 0.031081 0.03125 0.031421 0.031593 0.031768 0.031944 0.032123 0.032303 0.032486 0.03267 0.032857 0.033046 0.033237 0.03343 0.033626 0.033824 0.034024 0.034226 0.034431 0.034639 0.034848 0.035061 0.035276 0.035494 0.035714 0.035938 0.036164 0.036392 0.036624 0.036859

4.206351 4.132939 4.062912 3.996055 3.932174 3.87109 3.812636 3.756662 3.703027 3.651601 3.602264 3.554906 3.509422 3.465718 3.423703 3.383296 3.344418 3.306996 3.270964 3.236259 3.202819 3.170591 3.139523 3.109564 3.080669 3.052795 3.025902 2.99995 2.974903 2.950728 2.927393 2.904866 2.883119 2.862125 2.841858 2.822293 2.803409 2.785182 2.767593 2.750621 2.734249 2.718457 2.70323 2.688552 2.674408 2.660783 2.647664 2.635038 2.622892 2.611216 2.599997

3.785716 3.719645 3.65662 3.59645 3.538957 3.483981 3.431373 3.380996 3.332724 3.286441 3.242038 3.199415 3.15848 3.119146 3.081333 3.044966 3.009976 2.976297 2.943868 2.912633 2.882537 2.853532 2.82557 2.798607 2.772602 2.747516 2.723312 2.699955 2.677413 2.655656 2.634653 2.614379 2.594807 2.575912 2.557672 2.540064 2.523068 2.506664 2.490834 2.475559 2.460824 2.446611 2.432907 2.419697 2.406967 2.394705 2.382898 2.371534 2.360603 2.350094 2.339998

0.95 0.96 0.97 0.98 0.99 1

0.0035 0.0035 0.0035 0.0035 0.0035 0.0035

0.000184 0.000146 0.000108 7.1E-005 3.5E-005 0

1 1 1 1 1 1

0.037097 0.037338 0.037582 0.037829 0.038079 0.038333

2.589227 2.578894 2.568989 2.559503 2.550429 2.541757

2.330304 2.321004 2.31209 2.303553 2.295386 2.287582

o retangular - Aço CA 50-A fck (MPa) 1#

20

21

25

30

35

"0

"5

50

1110.1133 280.73803 126.29148 71.950149 46.670976 32.873198 24.516182 19.069857 15.322336 12.63369 10.63996 9.1216802 7.9401096 7.0040638 6.2516417 5.6396664 5.137298 4.7203401 4.368949 4.0688212 3.8095321 3.5833047 3.3842191 3.2076897 3.0501089 2.9458899 2.8495039 2.7601131 2.6769953 2.5995247 2.5271561 2.4594127 2.3958753 2.3361741 2.2799818 2.2270071 2.1769906 2.1296999 2.0849268 2.0424837 2.0022013 1.9639266 1.9275208

951.52568 240.6326 108.24984 61.671556 40.003694 28.177027 21.01387 16.345591 13.133431 10.828877 9.1199657 7.818583 6.8058082 6.0034833 5.35855 4.8339998 4.4033982 4.0460058 3.7448134 3.487561 3.2653132 3.071404 2.9007592 2.7494483 2.6143791 2.5250485 2.4424319 2.3658112 2.2945674 2.228164 2.1661338 2.108068 2.0536074 2.002435 1.9542701 1.9088632 1.8659919 1.8254571 1.7870801 1.7507003 1.7161725 1.6833657 1.6521607

832.58497 210.55353 94.718607 53.962612 35.003232 24.654898 18.387136 14.302392 11.491752 9.4752674 7.97997 6.8412601 5.9550822 5.2530478 4.6887313 4.2297498 3.8529735 3.5402551 3.2767118 3.0516159 2.8571491 2.6874785 2.5381643 2.4057672 2.2875817 2.2094174 2.1371279 2.0700848 2.0077465 1.9496435 1.8953671 1.8445595 1.7969064 1.7521306 1.7099863 1.6702553 1.6327429 1.597275 1.5636951 1.5318627 1.501651 1.4729449 1.4456406

740.07553 187.15869 84.194317 47.966766 31.113984 21.915465 16.344121 12.713238 10.214891 8.4224599 7.0933067 6.0811201 5.2934064 4.6693759 4.1677611 3.7597776 3.4248653 3.1468934 2.9126327 2.7125475 2.5396881 2.3888698 2.2561461 2.1384598 2.033406 1.9639266 1.8996692 1.8400754 1.7846635 1.7330164 1.6847707 1.6396084 1.5972502 1.5574494 1.5199878 1.4846714 1.4513271 1.4198 1.3899512 1.3616558 1.3348009 1.3092844 1.2850139

666.06798 168.44282 75.774885 43.170089 28.002586 19.723919 14.709709 11.441914 9.1934018 7.5802139 6.383976 5.4730081 4.7640658 4.2024383 3.750985 3.3837999 3.0823788 2.832204 2.6213694 2.4412927 2.2857193 2.1499828 2.0305315 1.9246138 1.8300654 1.7675339 1.7097023 1.6560678 1.6061972 1.5597148 1.5162937 1.4756476 1.4375252 1.4017045 1.3679891 1.3362043 1.3061943 1.27782 1.2509561 1.2254902 1.2013208 1.178356 1.1565125

c 1850.189 467.8967 210.4858 119.9169 77.78496 54.78866 40.8603 31.78309 25.53723 21.05615 17.73327 15.2028 13.23352 11.67344 10.4194 9.399444 8.562163 7.867233 7.281582 6.781369 6.34922 5.972174 5.640365 5.346149 5.083515 4.909816 4.749173 4.600188 4.461659 4.332541 4.211927 4.099021 3.993125 3.893624 3.79997 3.711679 3.628318 3.5495 3.474878 3.404139 3.337002 3.273211 3.212535

1665.1699 421.10705 189.43721 107.92522 70.006464 49.309797 36.774273 28.604785 22.983504 18.950535 15.95994 13.68252 11.910164 10.506096 9.3774626 8.4594996 7.7059469 7.0805101 6.5534235 6.1032318 5.7142982 5.374957 5.0763286 4.8115345 4.5751634 4.4188348 4.2742558 4.1401696 4.0154929 3.899287 3.7907341 3.689119 3.5938129 3.5042612 3.4199726 3.3405107 3.2654859 3.1945499 3.1273902 3.0637255 3.0033019 2.9458899 2.8912812

1585.8761 401.05433 180.41639 102.78593 66.672823 46.961711 35.023117 27.242652 21.889052 18.048128 15.199943 13.030972 11.343014 10.005805 8.9309167 8.0566663 7.3389971 6.743343 6.2413557 5.8126017 5.4421887 5.1190067 4.8345987 4.5824138 4.3572985 4.2084141 4.0707198 3.9430186 3.824279 3.7136067 3.610223 3.5134467 3.4226789 3.3373916 3.2571168 3.1814387 3.1099865 3.0424285 2.9784669 2.9178338 2.8602875 2.8056094 2.7536012

1332.136 336.88564 151.54977 86.340179 56.005171 39.447837 29.419418 22.883828 18.386804 15.160428 12.767952 10.946016 9.5281315 8.4048766 7.5019701 6.7675997 6.1647575 5.6644081 5.2427388 4.8825854 4.5714385 4.2999656 4.0610629 3.8492276 3.6601307 3.5350679 3.4194046 3.3121357 3.2123943 3.1194296 3.0325873 2.9512952 2.8750503 2.8034089 2.7359781 2.6724085 2.6123887 2.5556399 2.5019122 2.4509804 2.4026415 2.3567119 2.313025

3.154763 3.099704 3.047184 2.997041 2.949131 2.903317 2.859477 2.817496 2.77727 2.7387 2.701698 2.666179 2.632067 2.599288 2.567778 2.537472 2.508313 2.480247 2.453223 2.427194 2.402115 2.377944 2.354642 2.332173 2.310502 2.289597 2.269426 2.249962 2.231178 2.213046 2.195544 2.178649 2.162339 2.146593 2.131393 2.11672 2.102557 2.088887 2.075695 2.062966 2.050686 2.038843 2.027423 2.016414 2.005806 1.995587 1.985748 1.976278 1.967169 1.958412 1.949998

2.8392866 2.7897338 2.7424653 2.6973372 2.6542176 2.6129855 2.5735294 2.5357468 2.4995429 2.4648304 2.4315282 2.3995612 2.3688599 2.3393595 2.3109998 2.2837247 2.2574819 2.2322226 2.207901 2.1844745 2.1619031 2.1401492 2.1191777 2.0989556 2.0794517 2.0606369 2.0424837 2.0249661 2.0080598 1.9917417 1.97599 1.9607843 1.9461051 1.9319341 1.9182539 1.9050481 1.892301 1.8799981 1.8681253 1.8566694 1.8456178 1.8349586 1.8246805 1.8147729 1.8052255 1.7960286 1.7871732 1.7786505 1.7704523 1.7625707 1.7549982

2.7040825 2.6568893 2.6118717 2.5688926 2.5278263 2.4885576 2.4509804 2.4149969 2.3805171 2.3474575 2.3157411 2.2852964 2.2560571 2.2279615 2.2009522 2.1749759 2.1499828 2.1259263 2.1027629 2.0804519 2.0589553 2.0382373 2.0182645 1.9990053 1.9804302 1.9625113 1.9452225 1.9285391 1.9124379 1.8968968 1.8818953 1.8674136 1.8534334 1.8399372 1.8269085 1.8143315 1.8021915 1.7904744 1.779167 1.7682565 1.7577312 1.7475796 1.737791 1.7283551 1.7192623 1.7105034 1.7020697 1.6939529 1.686145 1.6786387 1.6714269

2.2714293 2.231787 2.1939722 2.1578698 2.1233741 2.0903884 2.0588235 2.0285974 1.9996344 1.9718643 1.9452225 1.919649 1.8950879 1.8714876 1.8487999 1.8269798 1.8059856 1.7857781 1.7663208 1.7475796 1.7295225 1.7121194 1.6953422 1.6791644 1.6635614 1.6485095 1.6339869 1.6199729 1.6064478 1.5933933 1.580792 1.5686275 1.5568841 1.5455473 1.5346031 1.5240384 1.5138408 1.5039985 1.4945002 1.4853355 1.4764942 1.4679669 1.4597444 1.4518183 1.4441804 1.4368229 1.4297386 1.4229204 1.4163618 1.4100565 1.4039986

1.8928578 1.8598225 1.8283102 1.7982248 1.7694784 1.7419903 1.7156863 1.6904979 1.666362 1.6432203 1.6210188 1.5997075 1.5792399 1.559573 1.5406666 1.5224832 1.504988 1.4881484 1.471934 1.4563163 1.4412687 1.4267661 1.4127851 1.3993037 1.3863011 1.3737579 1.3616558 1.3499774 1.3387065 1.3278278 1.3173267 1.3071895 1.2974034 1.2879561 1.2788359 1.270032 1.261534 1.2533321 1.2454169 1.2377796 1.2304118 1.2233057 1.2164537 1.2098486 1.2034836 1.1973524 1.1914488 1.185767 1.1803015 1.1750471 1.1699988

1.6224495 1.5941336 1.567123 1.5413355 1.5166958 1.4931346 1.4705882 1.4489982 1.4283103 1.4084745 1.3894447 1.3711778 1.3536342 1.3367769 1.3205713 1.3049856 1.2899897 1.2755558 1.2616577 1.2482711 1.2353732 1.2229424 1.2109587 1.1994032 1.1882581 1.1775068 1.1671335 1.1571235 1.1474627 1.1381381 1.1291372 1.1204482 1.1120601 1.1039623 1.0961451 1.0885989 1.0813149 1.0742846 1.0675002 1.0609539 1.0546387 1.0485478 1.0426746 1.0370131 1.0315574 1.0263021 1.0212418 1.0163717 1.011687 1.0071832 1.0028561

1.4196433 1.3948669 1.3712326 1.3486686 1.3271088 1.3064927 1.2867647 1.2678734 1.2497715 1.2324152 1.2157641 1.1997806 1.18443 1.1696798 1.1554999 1.1418624 1.128741 1.1161113 1.1039505 1.0922373 1.0809515 1.0700746 1.0595889 1.0494778 1.0397258 1.0303184 1.0212418 1.012483 1.0040299 0.9958708 0.987995 0.9803922 0.9730526 0.965967 0.9591269 0.952524 0.9461505 0.9399991 0.9340626 0.9283347 0.9228089 0.9174793 0.9123403 0.9073864 0.9026127 0.8980143 0.8935866 0.8893253 0.8852261 0.8812853 0.8774991

1.2619052 1.2398817 1.2188735 1.1988165 1.1796523 1.1613269 1.1437908 1.1269986 1.110908 1.0954802 1.0806792 1.0664717 1.0528266 1.0397153 1.027111 1.0149888 1.0033253 0.9920989 0.9812893 0.9708776 0.9608458 0.9511774 0.9418568 0.9328691 0.9242008 0.9158386 0.9077705 0.8999849 0.892471 0.8852185 0.8782178 0.8714597 0.8649356 0.8586374 0.8525573 0.846688 0.8410227 0.8355547 0.8302779 0.8251864 0.8202746 0.8155371 0.8109691 0.8065657 0.8023224 0.7982349 0.7942992 0.7905113 0.7868677 0.7833647 0.7799992

1.1357147 1.1158935 1.0969861 1.0789349 1.0616871 1.0451942 1.0294118 1.0142987 0.9998172 0.9859322 0.9726113 0.9598245 0.947544 0.9357438 0.9243999 0.9134899 0.9029928 0.892889 0.8831604 0.8737898 0.8647612 0.8560597 0.8476711 0.8395822 0.8317807 0.8242548 0.8169935 0.8099864 0.8032239 0.7966967 0.790396 0.7843137 0.778442 0.7727736 0.7673016 0.7620192 0.7569204 0.7519992 0.7472501 0.7426677 0.7382471 0.7339834 0.7298722 0.7259091 0.7220902 0.7184114 0.7148693 0.7114602 0.7081809 0.7050283 0.7019993

1.94192 1.93417 1.926742 1.919628 1.912822 1.906318

1.747728 1.7407531 1.7340674 1.7276648 1.7215395 1.7156863

1.6645028 1.6578601 1.6514928 1.645395 1.6395614 1.6339869

1.3981824 1.3926025 1.3872539 1.3821318 1.3772316 1.372549

1.165152 1.1605021 1.1560449 1.1517765 1.147693 1.1437908

0.9987017 0.9947161 0.9908957 0.987237 0.9837369 0.9803922

0.873864 0.8703766 0.8670337 0.8638324 0.8607698 0.8578431

0.776768 0.7736681 0.7706966 0.767851 0.7651287 0.7625272

0.6990912 0.6963012 0.693627 0.6910659 0.6886158 0.6862745

  m   c   e    N    K   m   e   o    ã    t

  s   e   c    K   e   s    K   e    d   s   e    d   a    d    i   n   u   s    A

Dimensionamento de de seçã ( ) $0 ( ) 0.5# f   yk 

 KN 

fyk fyk (MPa) (MPa) = $00 cm2 Módulo Módulo de elasticida elasticidade de (MPa) (MPa) = 210000 Domínio

sd

0.01

2

cd

0.0035

3

! 0.01 0.01 0.02 0.02 0.03 0.04 0.04 0.05 0.05 0.06 0.07 0.08 0.09 0.09 0.1 0.1 0.11 0.12 0.13 0.13 0.14 0.14 0.15 0.16 0.16 0.17 0.18 0.19 0.19 0.2 0.21 0.21 0.22 0.22 0.23 0.23 0.24 0.24 0.25 0.26 0.27 0.28 0.29 0.3 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.4 0.41 0.42 0.43 0.44

=

cd

0.00 0.0001 0101 01 0.00 0.0002 0204 04 0.00030 0309 0.00 0.0004 0417 17 0.00 0.0005 0526 26 0.00063 0638 0.00075 0753 0.00087 0.00 0.0009 0989 89 0.001111 0.00 0.0012 1236 36 0.00136 1364 0.00 0.0014 1494 94 0.00 0.0016 1628 28 0.00176 1765 0.00 0.0019 1905 05 0.00204 2048 0.00219 2195 0.00 0.0023 2346 46 0.0025 0.00 0.0026 2658 58 0.00 0.0028 2821 21 0.00 0.0029 2987 87 0.00 0.0031 3158 58 0.003333 0.003514 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035

 Kx 

sd

0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.009463 0.009 0.008569 0.008167 0.00779 0.007438 0.007106 0.006794 0.0065 0.006222 0.005959 0.005711 0.005474 0.00525 0.005037 0.004833 0.00464 0.004455

lim

ψ 

s

0.06 0.0620 2068 68 0.12 0.1232 3213 13 0.183 183335 0.24 0.2423 2332 32 0.30 0.3000 0092 92 0.356 356496 0.411 411416 0.464713 0.51 0.5162 6242 42 0.565 565844 0.61 0.6133 3348 48 0.658 658574 0.70 0.7013 1326 26 0.74 0.7413 1392 92 0.778 778547 0.81 0.8125 2547 47 0.843 843137 0.87037 037 0.89 0.8947 4737 37 0.916667 0.93 0.9365 6508 08 0.95 0.9545 4545 45 0.97 0.9710 1014 14 0.98 0.9861 611 11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

0.01 0.0192 9244 44 0.01 0.0193 9321 21 0.01939 9399 0.01 0.0194 9478 78 0.01 0.0195 9558 58 0.01963 9638 0.01971 9719 0.0198 0.01 0.0198 9882 82 0.01996 9965 0.02 0.0200 0049 49 0.02013 0133 0.02 0.0202 0218 18 0.02 0.0203 0304 04 0.02039 0.02 0.0204 0477 77 0.02056 0565 0.0 0.02065 0654 0.02 0.0207 0743 43 0.020833 0.02 0.0209 0924 24 0.02 0.0210 1016 16 0.02 0.021 1109 109 0.0 0.021 2120 202 2 0.021296 0.021391 0.021487 0.021584 0.021682 0.02178 0.02188 0.02198 0.022081 0.022184 0.022287 0.022391 0.022496 0.022602 0.022709 0.022817 0.022927 0.023037 0.023148 0.023261

13.5

15

2466 2466..918 918 623. 623.86 8623 23 280.6 0.6477 477 159. 159.88 8892 92 103. 103.71 7133 33 73.05155 155 54.4804 42.37746 34.0 34.049 4964 64 28.07487 487 23.6 23.644 4436 36 20.2704 17.6 17.644 4469 69 15.5 15.564 6459 59 13.89254 254 12.5 12.532 3259 59 11 11.41622 622 10.48964 964 9.70 9.7087 8776 76 9.041825 8.46 8.4656 5627 27 7.96 7.9628 2899 99 7.52 7.5204 0487 87 7.12 7.1281 8199 99 6.77802 6.546422 6.332231 6.133585 5.948878 5.776721 5.615902 5.465361 5.324167 5.191498 5.066626 4.948905 4.837757 4.732667 4.633171 4.538853 4.449336 4.364281 4.28338 4.206351

2220 2220.2 .227 27 561. 561.47 4761 61 252. 52.583 583 143. 143.90 9003 03 93.3 93.341 4195 95 65.7 5.7464 464 49.03236 38.13971 30.6 30.644 4467 67 25.26738 21.2 21.279 7992 92 18.24336 15.8 15.880 8022 22 14.0 14.008 0813 13 12.50328 11.27 1.2793 933 3 10.2 0.2746 746 9.4 9.44068 068 8.73 8.7378 7898 98 8.137642 7.61 7.6190 9064 64 7.16 7.1666 6609 09 6.76 6.7684 8438 38 6.41 6.4153 5379 79 6.100218 5.89178 5.699008 5.520226 5.353991 5.199049 5.054312 4.918825 4.791751 4.672348 4.559964 4.454014 4.353981 4.2594 4.169854 4.084967 4.004403 3.927853 3.855042 3.785716

cd

0.0035

"

0.45 0.46 0.47 0.48 0.49 0.5 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.6 0.61 0.62 0.63 0.64 0.65 0.66 0.67 0.68 0.69 0.7 0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.78 0.79 0.8 0.81 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9 0.91 0.92 0.93 0.94 0.95

0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035

0.004278 0.004109 0.003947 0.003792 0.003643 0.0035 0.003363 0.003231 0.003104 0.002981 0.002864 0.00275 0.00264 0.002534 0.002432 0.002333 0.002238 0.002145 0.002056 0.001969 0.001885 0.001803 0.001724 0.001647 0.001572 0.0015 0.00143 0.001361 0.001295 0.00123 0.001167 0.001105 0.001045 0.000987 0.00093 0.000875 0.000821 0.000768 0.000717 0.000667 0.000618 0.00057 0.000523 0.000477 0.000433 0.000389 0.000346 0.000304 0.000263 0.000223 0.000184

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

0.023374 0.023489 0.023604 0.023721 0.023839 0.023958 0.024079 0.0242 0.024323 0.024447 0.024573 0.024699 0.024827 0.024957 0.025087 0.025219 0.025353 0.025488 0.025624 0.025762 0.025901 0.026042 0.026184 0.026328 0.026473 0.02662 0.026769 0.026919 0.027072 0.027225 0.027381 0.027538 0.027697 0.027859 0.028021 0.028186 0.028353 0.028522 0.028693 0.028865 0.02904 0.029217 0.029397 0.029578 0.029762 0.029948 0.030136 0.030327 0.03052 0.030716 0.030914

4.132939 4.062912 3.996055 3.932174 3.87109 3.812636 3.756662 3.703027 3.651601 3.602264 3.554906 3.509422 3.465718 3.423703 3.383296 3.344418 3.306996 3.270964 3.236259 3.202819 3.170591 3.139523 3.109564 3.080669 3.052795 3.025902 2.99995 2.974903 2.950728 2.927393 2.904866 2.883119 2.862125 2.841858 2.822293 2.803409 2.785182 2.767593 2.750621 2.734249 2.718457 2.70323 2.688552 2.674408 2.660783 2.647664 2.635038 2.622892 2. 2.611216 2.599997 2.589227

3.719645 3. 3.65662 3. 3.59645 3.538957 3.483981 3.431373 3.380996 3.332724 3.286441 3.242038 3.199415 3.15848 3.119146 3.081333 3.044966 3.009976 2.976297 2.943868 2.912633 2.882537 2.853532 2. 2.82557 2.798607 2.772602 2.747516 2.723312 2.699955 2.677413 2.655656 2.634653 2.614379 2.594807 2.575912 2.557672 2.540064 2.523068 2.506664 2.490834 2.475559 2.460824 2.446611 2.432907 2.419697 2.406967 2.394705 2.382898 2.371534 2.360603 2.350094 2.339998 2.330304

0.96 0.97 0.98 0.99 1

0.0035 0.0035 0.0035 0.0035 0.0035

0.000146 0.000108 7.1E-005 3.5E-005 0

1 1 1 1 1

0.031115 0.031318 0.031524 0.031733 0.031944

2.578894 2.568989 2.559503 2.550429 2.541757

2.321004 2.31209 2.303553 2.295386 2.287582

o retangular - Aço CA 60-A fck (MPa) 1#

20

21

25

30

35

"0

"5

50

1110.1133 280.73803 126.29148 71.950149 46.670976 32.873198 24.516182 19.069857 15.322336 12.63369 10.63996 9.1216802 7.9401096 7.0040638 6.2516417 5.6396664 5.137298 4.7203401 4.368949 4.0688212 3.8095321 3.5833047 3.3842191 3.2076897 3.0501089 2.9458899 2.8495039 2.7601131 2.6769953 2.5995247 2.5271561 2.4594127 2.3958753 2.3361741 2.2799818 2.2270071 2.1769906 2.1296999 2.0849268 2.0424837 2.0022013 1.9639266 1.9275208 1.8928578

951.52568 240.6326 108.24984 61.671556 40.003694 28.177027 21.01387 16.345591 13.133431 10.828877 9.1199657 7.818583 6.8058082 6.0034833 5.35855 4.8339998 4.4033982 4.0460058 3.7448134 3.487561 3.2653132 3.071404 2.9007592 2.7494483 2.6143791 2.5250485 2.4424319 2.3658112 2.2945674 2.228164 2.1661338 2.108068 2.0536074 2.002435 1.9542701 1.9088632 1.8659919 1.8254571 1.7870801 1.7507003 1.7161725 1.6833657 1.6521607 1.6224495

832.58497 210.55353 94.718607 53.962612 35.003232 24.654898 18.387136 14.302392 11.491752 9.4752674 7.97997 6.8412601 5.9550822 5.2530478 4.6887313 4.2297498 3.8529735 3.5402551 3.2767118 3.0516159 2.8571491 2.6874785 2.5381643 2.4057672 2.2875817 2.2094174 2.1371279 2.0700848 2.0077465 1.9496435 1.8953671 1.8445595 1.7969064 1.7521306 1.7099863 1.6702553 1.6327429 1.597275 1.5636951 1.5318627 1.501651 1.4729449 1.4456406 1.4196433

740.07553 187.15869 84.194317 47.966766 31.113984 21.915465 16.344121 12.713238 10.214891 8.4224599 7.0933067 6.0811201 5.2934064 4.6693759 4.1677611 3.7597776 3.4248653 3.1468934 2.9126327 2.7125475 2.5396881 2.3888698 2.2561461 2.1384598 2.033406 1.9639266 1.8996692 1.8400754 1.7846635 1.7330164 1.6847707 1.6396084 1.5972502 1.5574494 1.5199878 1.4846714 1.4513271 1.4198 1.3899512 1.3616558 1.3348009 1.3092844 1.2850139 1.2619052

666.06798 168.44282 75.774885 43.170089 28.002586 19.723919 14.709709 11.441914 9.1934018 7.5802139 6.383976 5.4730081 4.7640658 4.2024383 3.750985 3.3837999 3.0823788 2.832204 2.6213694 2.4412927 2.2857193 2.1499828 2.0305315 1.9246138 1.8300654 1.7675339 1.7097023 1.6560678 1.6061972 1.5597148 1.5162937 1.4756476 1.4375252 1.4017045 1.3679891 1.3362043 1.3061943 1.27782 1.2509561 1.2254902 1.2013208 1.178356 1.1565125 1.1357147

c 1850.189 467.8967 210.4858 119.9169 77.78496 54.78866 40.8603 31.78309 25.53723 21.05615 17.73327 15.2028 13.23352 11.67344 10.4194 9.399444 8.562163 7.867233 7.281582 6.781369 6.34922 5.972174 5.640365 5.346149 5.083515 4.909816 4.749173 4.600188 4.461659 4.332541 4.211927 4.099021 3.993125 3.893624 3.79997 3.711679 3.628318 3.5495 3.474878 3.404139 3.337002 3.273211 3.212535 3.154763

1665.1699 421.10705 189.43721 107.92522 70.006464 49.309797 36.774273 28.604785 22.983504 18.950535 15.95994 13.68252 11.910164 10.506096 9.3774626 8.4594996 7.7059469 7.0805101 6.5534235 6.1032318 5.7142982 5.374957 5.0763286 4.8115345 4.5751634 4.4188348 4.2742558 4.1401696 4.0154929 3.899287 3.7907341 3.689119 3.5938129 3.5042612 3.4199726 3.3405107 3.2654859 3.1945499 3.1273902 3.0637255 3.0033019 2.9458899 2.8912812 2.8392866

1585.8761 401.05433 180.41639 102.78593 66.672823 46.961711 35.023117 27.242652 21.889052 18.048128 15.199943 13.030972 11.343014 10.005805 8.9309167 8.0566663 7.3389971 6.743343 6.2413557 5.8126017 5.4421887 5.1190067 4.8345987 4.5824138 4.3572985 4.2084141 4.0707198 3.9430186 3.824279 3.7136067 3.610223 3.5134467 3.4226789 3.3373916 3.2571168 3.1814387 3.1099865 3.0424285 2.9784669 2.9178338 2.8602875 2.8056094 2.7536012 2.7040825

1332.136 336.88564 151.54977 86.340179 56.005171 39.447837 29.419418 22.883828 18.386804 15.160428 12.767952 10.946016 9.5281315 8.4048766 7.5019701 6.7675997 6.1647575 5.6644081 5.2427388 4.8825854 4.5714385 4.2999656 4.0610629 3.8492276 3.6601307 3.5350679 3.4194046 3.3121357 3.2123943 3.1194296 3.0325873 2.9512952 2.8750503 2.8034089 2.7359781 2.6724085 2.6123887 2.5556399 2.5019122 2.4509804 2.4026415 2.3567119 2.313025 2.2714293

3.099704 3.047184 2.997041 2.949131 2.903317 2.859477 2.817496 2.77727 2.7387 2.701698 2.666179 2.632067 2.599288 2.567778 2.537472 2.508313 2.480247 2.453223 2.427194 2.402115 2.377944 2.354642 2.332173 2.310502 2.289597 2.269426 2.249962 2.231178 2.213046 2.195544 2.178649 2.162339 2.146593 2.131393 2.11672 2.102557 2.088887 2.075695 2.062966 2.050686 2.038843 2.027423 2.016414 2.005806 1.995587 1.985748 1.976278 1.967169 1.958412 1.949998 1.94192

2.7897338 2.7424653 2.6973372 2.6542176 2.6129855 2.5735294 2.5357468 2.4995429 2.4648304 2.4315282 2.3995612 2.3688599 2.3393595 2.3109998 2.2837247 2.2574819 2.2322226 2.207901 2.1844745 2.1619031 2.1401492 2.1191777 2.0989556 2.0794517 2.0606369 2.0424837 2.0249661 2.0080598 1.9917417 1.97599 1.9607843 1.9461051 1.9319341 1.9182539 1.9050481 1.892301 1.8799981 1.8681253 1.8566694 1.8456178 1.8349586 1.8246805 1.8147729 1.8052255 1.7960286 1.7871732 1.7786505 1.7704523 1.7625707 1.7549982 1.747728

2.6568893 2.6118717 2.5688926 2.5278263 2.4885576 2.4509804 2.4149969 2.3805171 2.3474575 2.3157411 2.2852964 2.2560571 2.2279615 2.2009522 2.1749759 2.1499828 2.1259263 2.1027629 2.0804519 2.0589553 2.0382373 2.0182645 1.9990053 1.9804302 1.9625113 1.9452225 1.9285391 1.9124379 1.8968968 1.8818953 1.8674136 1.8534334 1.8399372 1.8269085 1.8143315 1.8021915 1.7904744 1.779167 1.7682565 1.7577312 1.7475796 1.737791 1.7283551 1.7192623 1.7105034 1.7020697 1.6939529 1.686145 1.6786387 1.6714269 1.6645028

2.231787 2.1939722 2.1578698 2.1233741 2.0903884 2.0588235 2.0285974 1.9996344 1.9718643 1.9452225 1.919649 1.8950879 1.8714876 1.8487999 1.8269798 1.8059856 1.7857781 1.7663208 1.7475796 1.7295225 1.7121194 1.6953422 1.6791644 1.6635614 1.6485095 1.6339869 1.6199729 1.6064478 1.5933933 1.580792 1.5686275 1.5568841 1.5455473 1.5346031 1.5240384 1.5138408 1.5039985 1.4945002 1.4853355 1.4764942 1.4679669 1.4597444 1.4518183 1.4441804 1.4368229 1.4297386 1.4229204 1.4163618 1.4100565 1.4039986 1.3981824

1.8598225 1.8283102 1.7982248 1.7694784 1.7419903 1.7156863 1.6904979 1.666362 1.6432203 1.6210188 1.5997075 1.5792399 1.559573 1.5406666 1.5224832 1.504988 1.4881484 1.471934 1.4563163 1.4412687 1.4267661 1.4127851 1.3993037 1.3863011 1.3737579 1.3616558 1.3499774 1.3387065 1.3278278 1.3173267 1.3071895 1.2974034 1.2879561 1.2788359 1.270032 1.261534 1.2533321 1.2454169 1.2377796 1.2304118 1.2233057 1.2164537 1.2098486 1.2034836 1.1973524 1.1914488 1.185767 1.1803015 1.1750471 1.1699988 1.165152

1.5941336 1.567123 1.5413355 1.5166958 1.4931346 1.4705882 1.4489982 1.4283103 1.4084745 1.3894447 1.3711778 1.3536342 1.3367769 1.3205713 1.3049856 1.2899897 1.2755558 1.2616577 1.2482711 1.2353732 1.2229424 1.2109587 1.1994032 1.1882581 1.1775068 1.1671335 1.1571235 1.1474627 1.1381381 1.1291372 1.1204482 1.1120601 1.1039623 1.0961451 1.0885989 1.0813149 1.0742846 1.0675002 1.0609539 1.0546387 1.0485478 1.0426746 1.0370131 1.0315574 1.0263021 1.0212418 1.0163717 1.011687 1.0071832 1.0028561 0.9987017

1.3948669 1.3712326 1.3486686 1.3271088 1.3064927 1.2867647 1.2678734 1.2497715 1.2324152 1.2157641 1.1997806 1.18443 1.1696798 1.1554999 1.1418624 1.128741 1.1161113 1.1039505 1.0922373 1.0809515 1.0700746 1.0595889 1.0494778 1.0397258 1.0303184 1.0212418 1.012483 1.0040299 0.9958708 0.987995 0.9803922 0.9730526 0.965967 0.9591269 0.952524 0.9461505 0.9399991 0.9340626 0.9283347 0.9228089 0.9174793 0.9123403 0.9073864 0.9026127 0.8980143 0.8935866 0.8893253 0.8852261 0.8812853 0.8774991 0.873864

1.2398817 1.2188735 1.1988165 1.1796523 1.1613269 1.1437908 1.1269986 1.110908 1.0954802 1.0806792 1.0664717 1.0528266 1.0397153 1.027111 1.0149888 1.0033253 0.9920989 0.9812893 0.9708776 0.9608458 0.9511774 0.9418568 0.9328691 0.9242008 0.9158386 0.9077705 0.8999849 0.892471 0.8852185 0.8782178 0.8714597 0.8649356 0.8586374 0.8525573 0.846688 0.8410227 0.8355547 0.8302779 0.8251864 0.8202746 0.8155371 0.8109691 0.8065657 0.8023224 0.7982349 0.7942992 0.7905113 0.7868677 0.7833647 0.7799992 0.776768

1.1158935 1.0969861 1.0789349 1.0616871 1.0451942 1.0294118 1.0142987 0.9998172 0.9859322 0.9726113 0.9598245 0.947544 0.9357438 0.9243999 0.9134899 0.9029928 0.892889 0.8831604 0.8737898 0.8647612 0.8560597 0.8476711 0.8395822 0.8317807 0.8242548 0.8169935 0.8099864 0.8032239 0.7966967 0.790396 0.7843137 0.778442 0.7727736 0.7673016 0.7620192 0.7569204 0.7519992 0.7472501 0.7426677 0.7382471 0.7339834 0.7298722 0.7259091 0.7220902 0.7184114 0.7148693 0.7114602 0.7081809 0.7050283 0.7019993 0.6990912

1.93417 1.926742 1.919628 1.912822 1.906318

1.7407531 1.7340674 1.7276648 1.7215395 1.7156863

1.6578601 1.6514928 1.645395 1.6395614 1.6339869

1.3926025 1.3872539 1.3821318 1.3772316 1.372549

1.1605021 1.1560449 1.1517765 1.147693 1.1437908

0.9947161 0.9908957 0.987237 0.9837369 0.9803922

0.8703766 0.8670337 0.8638324 0.8607698 0.8578431

0.7736681 0.7706966 0.767851 0.7651287 0.7625272

0.6963012 0.693627 0.6910659 0.6886158 0.6862745

  m   c   e    N    K   m   e   o    ã    t

  e   c    K   e   s    K   e    d   s   e    d   a    d    i   n   u   s    A

Dimensionamento de seção retangular - Aço CA 25-B ( ) 25 ( ) 0.5"

 KN  f   yk  fyk (MPa) = 250 cm2 Módulo de elasticidade (MPa) = 210000

Domínio

sd

0.01

2

cd

0.0035

3

cd

0.0035

"

! 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.3 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.4 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.5 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.6 0.61 0.62 0.63 0.64 0.65 0.66 0.67 0.68 0.69 0.7 0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.78 0.79 0.8 0.81 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1

=

cd

0.000101 0.000204 0.000309 0.000417 0.000526 0.000638 0.000753 0.00087 0.000989 0.001111 0.001236 0.001364 0.001494 0.001628 0.001765 0.001905 0.002048 0.002195 0.002346 0.0025 0.002658 0.002821 0.002987 0.003158 0.003333 0.003514 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035

 Kx 

sd

0.00319 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.009463 0.009 0.008569 0.008167 0.00779 0.007438 0.007106 0.006794 0.0065 0.006222 0.005959 0.005711 0.005474 0.00525 0.005037 0.004833 0.00464 0.004455 0.004278 0.004109 0.003947 0.003792 0.003643 0.0035 0.003363 0.003231 0.003104 0.002981 0.002864 0.00275 0.00264 0.002534 0.002432 0.002333 0.002238 0.002145 0.002056 0.001969 0.001885 0.001803 0.001724 0.001647 0.001572 0.0015 0.00143 0.001361 0.001295 0.00123 0.001167 0.001105 0.001045 0.000987 0.00093 0.000875 0.000821 0.000768 0.000717 0.000667 0.000618 0.00057 0.000523 0.000477 0.000433 0.000389 0.000346 0.000304 0.000263 0.000223 0.000184 0.000146 0.000108 7.14E-005 3.54E-005 0

fck (MPa)

lim

ψ  0.062068 0.123213 0.183335 0.242332 0.300092 0.356496 0.411416 0.464713 0.516242 0.565844 0.613348 0.658574 0.701326 0.741392 0.778547 0.812547 0.843137 0.87037 0.894737 0.916667 0.936508 0.954545 0.971014 0.986111 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

13.5

15

1#

20

21

s 0.046185   2466.918 0.046371   623.8623 0.046559   280.6477 0.046748   159.8892 0.046939   103.7133 0.047131   73.05155 0.047325   54.4804 0.047521   42.37746 0.047718   34.04964 0.047917   28.07487 0.048117   23.64436 0.048319   20.2704 0.048523   17.64469 0.048729   15.56459 0.048936 13.89254 0.049145 12.53259 0.049356   11.41622 0 .049569 10.48964 0.049784   9.708776 0.05 9.041825 0.050218   8.465627 0.050439   7.962899 0.050661   7.520487 0.050885   7.128199 0.051111 6.77802 0.051339   6.546422 0.05157 6.332231 0.051802   6.133585 0.052036   5.948878 0.052273   5.776721 0.052511   5.615902 0.052752   5.465361 0.052995   5.324167 0.053241   5.191498 0.053488   5.066626 0.053738   4.948905 0.053991   4.837757 0.054245 4.732667 0.054502   4.633171 0.054762 4.538853 0.055024   4.449336 0.055288   4.364281 0.055556 4.28338 0.055825   4.206351 0.056098   4.132939 0.056373   4.062912 0.05665   3.996055 0.056931   3.932174 0.057214   3.87109 0.0575 3.812636 0.057789   3.756662 0.058081   3.703027 0.058376 3.651601 0.058673   3.602264 0.05736 3.554906 0.058032   3.509422 0.058706   3.465718 0.059383 3.423703 0.060063   3.383296 0.060747   3.344418 0.061434   3.306996 0.062124   3.270964 0.062819   3.236259 0.063518   3.202819 0.064222   3.170591 0.06493 3.139523 0.065643   3.109564 0.066362   3.080669 0.067086   3.052795 0.067816   3.025902 0.068552 2.99995 0.069294   2.974903 0.070043   2.950728 0.070798   2.927393 0.071561   2.904866 0.072331   2.883119 0.073108   2.862125 0.073893   2.841858 0.074687   2.822293 0.075489   2.803409 0.076299   2.785182 0.077119   2.767593 0.077948   2.750621 0.069277   2.734249 0.069697   2.718457 0.070122   2.70323 0.070552   2.688552 0.070988   2.674408 0.071429   2.660783 0.071875   2.647664 0.072327   2.635038 0.072785   2.622892 0.073248   2.611216 0.073718   2.599997 0.074194   2.589227 0.074675   2.578894 0.075163   2.568989 0.075658   2.559503 0.076159   2.550429 0.076667   2.541757

25

30

35

"0

"5

50

1110.113 280.738 126.2915 71.95015 46.67098 32.8732 24.51618 19.06986 15.32234 12.63369 10.63996 9.12168 7.94011 7.004064 6.251642 5.639666 5.137298 4.72034 4.368949 4.068821 3.809532 3.583305 3.384219 3.20769 3.050109 2.94589 2.849504 2.760113 2.676995 2.599525 2.527156 2.459413 2.395875 2.336174 2.279982 2.227007 2.176991 2.1297 2.084927 2.042484 2.002201 1.963927 1.927521 1.892858 1.859823 1.82831 1.798225 1.769478 1.74199 1.715686 1.690498 1.666362 1.64322 1.621019 1.599707 1.57924 1.559573 1.540667 1.522483 1.504988 1.488148 1.471934 1.456316 1.441269 1.426766 1.412785 1.399304 1.386301 1.373758 1.361656 1.349977 1.338707 1.327828 1.317327 1.30719 1.297403 1.287956 1.278836 1.270032 1.261534 1.253332 1.245417 1.23778 1.230412 1.223306 1.216454 1.209849 1.203484 1.197352 1.191449 1.185767 1.180302 1.175047 1.169999 1.165152 1.160502 1.156045 1.151777 1.147693 1.143791

951.5257 240.6326 108.2498 61.67156 40.00369 28.17703 21.01387 16.34559 13.13343 10.82888 9.119966 7.818583 6.805808 6.003483 5.35855 4.834 4.403398 4.046006 3.744813 3.487561 3.265313 3.071404 2.900759 2.749448 2.614379 2.525048 2.442432 2.365811 2.294567 2.228164 2.166134 2.108068 2.053607 2.002435 1.95427 1.908863 1.865992 1.825457 1.78708 1.7507 1.716173 1.683366 1.652161 1.62245 1.594134 1.567123 1.541336 1.516696 1.493135 1.470588 1.448998 1.42831 1.408475 1.389445 1.371178 1.353634 1.336777 1.320571 1.304986 1.28999 1.275556 1.261658 1.248271 1.235373 1.222942 1.210959 1.199403 1.188258 1.177507 1.167134 1.157123 1.147463 1.138138 1.129137 1.120448 1.11206 1.103962 1.096145 1.088599 1.081315 1.074285 1.0675 1.060954 1.054639 1.048548 1.042675 1.037013 1.031557 1.026302 1.021242 1.016372 1.011687 1.007183 1.002856 0.998702 0.994716 0.990896 0.987237 0.983737 0.980392

832.585 210.5535 94.71861 53.96261 35.00323 24.6549 18.38714 14.30239 11.49175 9.475267 7.97997 6.84126 5.955082 5.253048 4.688731 4.22975 3.852973 3.540255 3.276712 3.051616 2.857149 2.687479 2.538164 2.405767 2.287582 2.209417 2.137128 2.070085 2.007746 1.949643 1.895367 1.844559 1.796906 1.752131 1.709986 1.670255 1.632743 1.597275 1.563695 1.531863 1.501651 1.472945 1.445641 1.419643 1.394867 1.371233 1.348669 1.327109 1.306493 1.286765 1.267873 1.249771 1.232415 1.215764 1.199781 1.18443 1.16968 1.1555 1.141862 1.128741 1.116111 1.103951 1.092237 1.080952 1.070075 1.059589 1.049478 1.039726 1.030318 1.021242 1.012483 1.00403 0.995871 0.987995 0.980392 0.973053 0.965967 0.959127 0.952524 0.946151 0.939999 0.934063 0.928335 0.922809 0.917479 0.91234 0.907386 0.902613 0.898014 0.893587 0.889325 0.885226 0.881285 0.877499 0.873864 0.870377 0.867034 0.863832 0.86077 0.857843

740.0755 187.1587 84.19432 47.96677 31.11398 21.91547 16.34412 12.71324 10.21489 8.42246 7.093307 6.08112 5.293406 4.669376 4.167761 3.759778 3.424865 3.146893 2.912633 2.712547 2.539688 2.38887 2.256146 2.13846 2.033406 1.963927 1.899669 1.840075 1.784664 1.733016 1.684771 1.639608 1.59725 1.557449 1.519988 1.484671 1.451327 1.4198 1.389951 1.361656 1.334801 1.309284 1.285014 1.261905 1.239882 1.218873 1.198817 1.179652 1.161327 1.143791 1.126999 1.110908 1.09548 1.080679 1.066472 1.052827 1.039715 1.027111 1.014989 1.003325 0.992099 0.981289 0.970878 0.960846 0.951177 0.941857 0.932869 0.924201 0.915839 0.907771 0.899985 0.892471 0.885219 0.878218 0.87146 0.864936 0.858637 0.852557 0.846688 0.841023 0.835555 0.830278 0.825186 0.820275 0.815537 0.810969 0.806566 0.802322 0.798235 0.794299 0.790511 0.786868 0.783365 0.779999 0.776768 0.773668 0.770697 0.767851 0.765129 0.762527

666.068 168.4428 75.77489 43.17009 28.00259 19.72392 14.70971 11.44191 9.193402 7.580214 6.383976 5.473008 4.764066 4.202438 3.750985 3.3838 3.082379 2.832204 2.621369 2.441293 2.285719 2.149983 2.030531 1.924614 1.830065 1.767534 1.709702 1.656068 1.606197 1.559715 1.516294 1.475648 1.437525 1.401704 1.367989 1.336204 1.306194 1.27782 1.250956 1.22549 1.201321 1.178356 1.156512 1.135715 1.115894 1.096986 1.078935 1.061687 1.045194 1.029412 1.014299 0.999817 0.985932 0.972611 0.959824 0.947544 0.935744 0.9244 0.91349 0.902993 0.892889 0.88316 0.87379 0.864761 0.85606 0.847671 0.839582 0.831781 0.824255 0.816993 0.809986 0.803224 0.796697 0.790396 0.784314 0.778442 0.772774 0.767302 0.762019 0.75692 0.751999 0.74725 0.742668 0.738247 0.733983 0.729872 0.725909 0.72209 0.718411 0.714869 0.71146 0.708181 0.705028 0.701999 0.699091 0.696301 0.693627 0.691066 0.688616 0.686275

c 2220.227 561.4761 252.583 143.9003 93.34195 65.7464 49.03236 38.13971 30.64467 25.26738 21.27992 18.24336 15.88022 14.00813 12.50328 11.27933 10.2746 9.44068 8.737898 8.137642 7.619064 7.166609 6.768438 6.415379 6.100218 5.89178 5.699008 5.520226 5.353991 5.199049 5.054312 4.918825 4.791751 4.672348 4.559964 4.454014 4.353981 4.2594 4.169854 4.084967 4.004403 3.927853 3.855042 3.785716 3.719645 3.65662 3.59645 3.538957 3.483981 3.431373 3.380996 3.332724 3.286441 3.242038 3.199415 3.15848 3.119146 3.081333 3.044966 3.009976 2.976297 2.943868 2.912633 2.882537 2.853532 2.82557 2.798607 2.772602 2.747516 2.723312 2.699955 2.677413 2.655656 2.634653 2.614379 2.594807 2.575912 2.557672 2.540064 2.523068 2.506664 2.490834 2.475559 2.460824 2.446611 2.432907 2.419697 2.406967 2.394705 2.382898 2.371534 2.360603 2.350094 2.339998 2.330304 2.321004 2.31209 2.303553 2.295386 2.287582

1850.189 467.8967 210.4858 119.9169 77.78496 54.78866 40.8603 31.78309 25.53723 21.05615 17.73327 15.2028 13.23352 11.67344 10.4194 9.399444 8.562163 7.867233 7.281582 6.781369 6.34922 5.972174 5.640365 5.346149 5.083515 4.909816 4.749173 4.600188 4.461659 4.332541 4.211927 4.099021 3.993125 3.893624 3.79997 3.711679 3.628318 3.5495 3.474878 3.404139 3.337002 3.273211 3.212535 3.154763 3.099704 3.047184 2.997041 2.949131 2.903317 2.859477 2.817496 2.77727 2.7387 2.701698 2.666179 2.632067 2.599288 2.567778 2.537472 2.508313 2.480247 2.453223 2.427194 2.402115 2.377944 2.354642 2.332173 2.310502 2.289597 2.269426 2.249962 2.231178 2.213046 2.195544 2.178649 2.162339 2.146593 2.131393 2.11672 2.102557 2.088887 2.075695 2.062966 2.050686 2.038843 2.027423 2.016414 2.005806 1.995587 1.985748 1.976278 1.967169 1.958412 1.949998 1.94192 1.93417 1.926742 1.919628 1.912822 1.906318

1665.17 421.1071 189.4372 107.9252 70.00646 49.3098 36.77427 28.60478 22.9835 18.95053 15.95994 13.68252 11.91016 10.5061 9.377463 8.4595 7.705947 7.08051 6.553424 6.103232 5.714298 5.374957 5.076329 4.811534 4.575163 4.418835 4.274256 4.14017 4.015493 3.899287 3.790734 3.689119 3.593813 3.504261 3.419973 3.340511 3.265486 3.19455 3.12739 3.063725 3.003302 2.94589 2.891281 2.839287 2.789734 2.742465 2.697337 2.654218 2.612985 2.573529 2.535747 2.499543 2.46483 2.431528 2.399561 2.36886 2.33936 2.311 2.283725 2.257482 2.232223 2.207901 2.184475 2.161903 2.140149 2.119178 2.098956 2.079452 2.060637 2.042484 2.024966 2.00806 1.991742 1.97599 1.960784 1.946105 1.931934 1.918254 1.905048 1.892301 1.879998 1.868125 1.856669 1.845618 1.834959 1.824681 1.814773 1.805225 1.796029 1.787173 1.778651 1.770452 1.762571 1.754998 1.747728 1.740753 1.734067 1.727665 1.72154 1.715686

1585.876 401.0543 180.4164 102.7859 66.67282 46.96171 35.02312 27.24265 21.88905 18.04813 15.19994 13.03097 11.34301 10.00581 8.930917 8.056666 7.338997 6.743343 6.241356 5.812602 5.442189 5.119007 4.834599 4.582414 4.357298 4.208414 4.07072 3.943019 3.824279 3.713607 3.610223 3.513447 3.422679 3.337392 3.257117 3.181439 3.109987 3.042428 2.978467 2.917834 2.860288 2.805609 2.753601 2.704083 2.656889 2.611872 2.568893 2.527826 2.488558 2.45098 2.414997 2.380517 2.347458 2.315741 2.285296 2.256057 2.227961 2.200952 2.174976 2.149983 2.125926 2.102763 2.080452 2.058955 2.038237 2.018264 1.999005 1.98043 1.962511 1.945223 1.928539 1.912438 1.896897 1.881895 1.867414 1.853433 1.839937 1.826908 1.814331 1.802191 1.790474 1.779167 1.768257 1.757731 1.74758 1.737791 1.728355 1.719262 1.710503 1.70207 1.693953 1.686145 1.678639 1.671427 1.664503 1.65786 1.651493 1.645395 1.639561 1.633987

1332.136 336.8856 151.5498 86.34018 56.00517 39.44784 29.41942 22.88383 18.3868 15.16043 12.76795 10.94602 9.528132 8.404877 7.50197 6.7676 6.164758 5.664408 5.242739 4.882585 4.571439 4.299966 4.061063 3.849228 3.660131 3.535068 3.419405 3.312136 3.212394 3.11943 3.032587 2.951295 2.87505 2.803409 2.735978 2.672409 2.612389 2.55564 2.501912 2.45098 2.402642 2.356712 2.313025 2.271429 2.231787 2.193972 2.15787 2.123374 2.090388 2.058824 2.028597 1.999634 1.971864 1.945223 1.919649 1.895088 1.871488 1.8488 1.82698 1.805986 1.785778 1.766321 1.74758 1.729522 1.712119 1.695342 1.679164 1.663561 1.64851 1.633987 1.619973 1.606448 1.593393 1.580792 1.568627 1.556884 1.545547 1.534603 1.524038 1.513841 1.503998 1.4945 1.485335 1.476494 1.467967 1.459744 1.451818 1.44418 1.436823 1.429739 1.42292 1.416362 1.410057 1.403999 1.398182 1.392602 1.387254 1.382132 1.377232 1.372549

  m   c   e    N    K   m   e   o    ã    t   s   e   c    K   e   s    K   e    d   s   e    d   a    d    i   n   u   s    A

Dimensionamento de seção ( ) 50 ( ) 0."$

 KN  f   yk  fyk (MPa) = 500 cm2 Módulo de elasticidade (MPa) = 210000

Domínio

sd

0.01

2

cd

0.0035

3

! 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.3 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.4 0.41 0.42 0.43 0.44

=

cd

0.000101 0.000204 0.000309 0.000417 0.000526 0.000638 0.000753 0.00087 0.000989 0.001111 0.001236 0.001364 0.001494 0.001628 0.001765 0.001905 0.002048 0.002195 0.002346 0.0025 0.002658 0.002821 0.002987 0.003158 0.003333 0.003514 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035

 Kx 

sd

0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.009463 0.009 0.008569 0.008167 0.00779 0.007438 0.007106 0.006794 0.0065 0.006222 0.005959 0.005711 0.005474 0.00525 0.005037 0.004833 0.00464 0.004455

lim

ψ  0.062068 0.123213 0.183335 0.242332 0.300092 0.356496 0.411416 0.464713 0.516242 0.565844 0.613348 0.658574 0.701326 0.741392 0.778547 0.812547 0.843137 0.87037 0.894737 0.916667 0.936508 0.954545 0.971014 0.986111 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

13.5

15

s 0.023092   2466.918 0.023185   623.8623 0.023279 280.6477 0.023374   159.8892 0.023469   103.7133 0.023566 73.05155 0.023663   54.4804 0.02376 42.37746 0.023859   34.04964 0.023958   28.07487 0.024059   23.64436 0.02416   20.2704 0.024262   17.64469 0.024364   15.56459 0.024468   13.89254 0.024573   12.53259 0.024678   11.41622 0.024784 10.48964 0.024892   9.708776 0.025 9.041825 0.025109   8.465627 0.025219   7.962899 0.02533 7.520487 0.025442   7.128199 0.025556   6.77802 0.02567   6.546422 0.025785   6.332231 0.025901   6.133585 0.026018   5.948878 0.026136   5.776721 0.026256   5.615902 0.026376   5.465361 0.026498   5.324167 0.02662 5.191498 0.026744   5.066626 0.026869   4.948905 0.026995   4.837757 0.027123 4.732667 0.027251   4.633171 0.027381   4.538853 0.027512   4.449336 0.027644   4.364281 0.027778   4.28338 0.027913   4.206351

2220.227 561.4761 252.583 143.9003 93.34195 65.7464 49.03236 38.13971 30.64467 25.26738 21.27992 18.24336 15.88022 14.00813 12.50328 11.27933 10.2746 9.44068 8.737898 8.137642 7.619064 7.166609 6.768438 6.415379 6.100218 5.89178 5.699008 5.520226 5.353991 5.199049 5.054312 4.918825 4.791751 4.672348 4.559964 4.454014 4.353981 4.2594 4.169854 4.084967 4.004403 3.927853 3.855042 3.785716

cd

0.0035

"

0.45 0.46 0.47 0.48 0.49 0.5 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.6 0.61 0.62 0.63 0.64 0.65 0.66 0.67 0.68 0.69 0.7 0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.78 0.79 0.8 0.81 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9 0.91 0.92 0.93 0.94 0.95

0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035

0.004278 0.004109 0.003947 0.003792 0.003643 0.0035 0.003363 0.003231 0.003104 0.002981 0.002864 0.00275 0.00264 0.002534 0.002432 0.002333 0.002238 0.002145 0.002056 0.001969 0.001885 0.001803 0.001724 0.001647 0.001572 0.0015 0.00143 0.001361 0.001295 0.00123 0.001167 0.001105 0.001045 0.000987 0.00093 0.000875 0.000821 0.000768 0.000717 0.000667 0.000618 0.00057 0.000523 0.000477 0.000433 0.000389 0.000346 0.000304 0.000263 0.000223 0.000184

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

0.028049   4.132939 0.028186 4.062912 0.026236 3.996055 0.026518   3.932174 0.0268 3.87109 0.027082   3.812636 0.027366   3.756662 0.027649   3.703027 0.027934   3.651601 0.028219   3.602264 0.028506   3.554906 0.028793 3.509422 0.029082   3.465718 0.029372   3.423703 0.029664   3.383296 0.029956   3.344418 0.030251   3.306996 0.030546   3.270964 0.030844   3.236259 0.031143   3.202819 0.031445   3.170591 0.031748 3.139523 0.032053   3.109564 0.03236 3.080669 0.032669   3.052795 0.032981   3.025902 0.033295   2.99995 0.032303   2.974903 0.032486   2.950728 0.03267 2.927393 0.032857   2.904866 0.033046   2.883119 0.033237   2.862125 0.03343 2.841858 0.033626   2.822293 0.033824   2.803409 0.034024   2.785182 0.034226   2.767593 0.034431   2.750621 0.034639   2.734249 0.034848   2.718457 0.035061   2.70323 0.035276   2.688552 0.035494   2.674408 0.035714   2.660783 0.035938   2.647664 0.036164   2.635038 0.036392   2.622892 0.036624   2.611216 0.036859   2.599997 0.037097   2.589227

3.719645 3.65662 3.59645 3.538957 3.483981 3.431373 3.380996 3.332724 3.286441 3.242038 3.199415 3.15848 3.119146 3.081333 3.044966 3.009976 2.976297 2.943868 2.912633 2.882537 2.853532 2.82557 2.798607 2.772602 2.747516 2.723312 2.699955 2.677413 2.655656 2.634653 2.614379 2.594807 2.575912 2.557672 2.540064 2.523068 2.506664 2.490834 2.475559 2.460824 2.446611 2.432907 2.419697 2.406967 2.394705 2.382898 2.371534 2.360603 2.350094 2.339998 2.330304

0.96 0.97 0.98 0.99 1

0.0035 0.0035 0.0035 0.0035 0.0035

0.000146 0.000108 7.1E-005 3.5E-005 0

1 1 1 1 1

0.037338   2.578894 0.037582 2.568989 0.037829   2.559503 0.038079   2.550429 0.038333   2.541757

Equação a!a dete!minação da tensão a " 0.001 # " -0.0343 $ensão c " 0.31239 53.9805 0.31938 0.32607 0.3325 0.33868 0.34462 0.35033 0.35583 0.36114 0.36625 0.37118 0.37595 0.38055 0.385 0.3893 0.39347 0.3975 0.40141 0.40519 0.40886 0.41243 0.41588 0.41924 0.4225 0.42567

53.6717 53.3712 53.0786 52.7934 52.5155 52.2443 51.9796 51.7211 51.4685 51.2216 50.98 50.7436 50.5122 50.2854 50.0632 49.8454 49.6317 49.422 49.2162 49.014 48.8155 48.6203 48.4284 48.2397

%a&o! da de'eomação no in(cio do t!ec)o a!a#*&ico 0.0014493

2.321004 2.31209 2.303553 2.295386 2.287582

 retangular - Aço CA 50-B fck (MPa) 1#

20

21

25

30

35

"0

"5

50

1110.113 280.738 126.2915 71.95015 46.67098 32.8732 24.51618 19.06986 15.32234 12.63369 10.63996 9.12168 7.94011 7.004064 6.251642 5.639666 5.137298 4.72034 4.368949 4.068821 3.809532 3.583305 3.384219 3.20769 3.050109 2.94589 2.849504 2.760113 2.676995 2.599525 2.527156 2.459413 2.395875 2.336174 2.279982 2.227007 2.176991 2.1297 2.084927 2.042484 2.002201 1.963927 1.927521 1.892858

951.5257 240.6326 108.2498 61.67156 40.00369 28.17703 21.01387 16.34559 13.13343 10.82888 9.119966 7.818583 6.805808 6.003483 5.35855 4.834 4.403398 4.046006 3.744813 3.487561 3.265313 3.071404 2.900759 2.749448 2.614379 2.525048 2.442432 2.365811 2.294567 2.228164 2.166134 2.108068 2.053607 2.002435 1.95427 1.908863 1.865992 1.825457 1.78708 1.7507 1.716173 1.683366 1.652161 1.62245

832.585 210.5535 94.71861 53.96261 35.00323 24.6549 18.38714 14.30239 11.49175 9.475267 7.97997 6.84126 5.955082 5.253048 4.688731 4.22975 3.852973 3.540255 3.276712 3.051616 2.857149 2.687479 2.538164 2.405767 2.287582 2.209417 2.137128 2.070085 2.007746 1.949643 1.895367 1.844559 1.796906 1.752131 1.709986 1.670255 1.632743 1.597275 1.563695 1.531863 1.501651 1.472945 1.445641 1.419643

740.0755 187.1587 84.19432 47.96677 31.11398 21.91547 16.34412 12.71324 10.21489 8.42246 7.093307 6.08112 5.293406 4.669376 4.167761 3.759778 3.424865 3.146893 2.912633 2.712547 2.539688 2.38887 2.256146 2.13846 2.033406 1.963927 1.899669 1.840075 1.784664 1.733016 1.684771 1.639608 1.59725 1.557449 1.519988 1.484671 1.451327 1.4198 1.389951 1.361656 1.334801 1.309284 1.285014 1.261905

666.068 168.4428 75.77489 43.17009 28.00259 19.72392 14.70971 11.44191 9.193402 7.580214 6.383976 5.473008 4.764066 4.202438 3.750985 3.3838 3.082379 2.832204 2.621369 2.441293 2.285719 2.149983 2.030531 1.924614 1.830065 1.767534 1.709702 1.656068 1.606197 1.559715 1.516294 1.475648 1.437525 1.401704 1.367989 1.336204 1.306194 1.27782 1.250956 1.22549 1.201321 1.178356 1.156512 1.135715

c 1850.189 467.8967 210.4858 119.9169 77.78496 54.78866 40.8603 31.78309 25.53723 21.05615 17.73327 15.2028 13.23352 11.67344 10.4194 9.399444 8.562163 7.867233 7.281582 6.781369 6.34922 5.972174 5.640365 5.346149 5.083515 4.909816 4.749173 4.600188 4.461659 4.332541 4.211927 4.099021 3.993125 3.893624 3.79997 3.711679 3.628318 3.5495 3.474878 3.404139 3.337002 3.273211 3.212535 3.154763

1665.17 421.1071 189.4372 107.9252 70.00646 49.3098 36.77427 28.60478 22.9835 18.95053 15.95994 13.68252 11.91016 10.5061 9.377463 8.4595 7.705947 7.08051 6.553424 6.103232 5.714298 5.374957 5.076329 4.811534 4.575163 4.418835 4.274256 4.14017 4.015493 3.899287 3.790734 3.689119 3.593813 3.504261 3.419973 3.340511 3.265486 3.19455 3.12739 3.063725 3.003302 2.94589 2.891281 2.839287

1585.876 401.0543 180.4164 102.7859 66.67282 46.96171 35.02312 27.24265 21.88905 18.04813 15.19994 13.03097 11.34301 10.00581 8.930917 8.056666 7.338997 6.743343 6.241356 5.812602 5.442189 5.119007 4.834599 4.582414 4.357298 4.208414 4.07072 3.943019 3.824279 3.713607 3.610223 3.513447 3.422679 3.337392 3.257117 3.181439 3.109987 3.042428 2.978467 2.917834 2.860288 2.805609 2.753601 2.704083

1332.136 336.8856 151.5498 86.34018 56.00517 39.44784 29.41942 22.88383 18.3868 15.16043 12.76795 10.94602 9.528132 8.404877 7.50197 6.7676 6.164758 5.664408 5.242739 4.882585 4.571439 4.299966 4.061063 3.849228 3.660131 3.535068 3.419405 3.312136 3.212394 3.11943 3.032587 2.951295 2.87505 2.803409 2.735978 2.672409 2.612389 2.55564 2.501912 2.45098 2.402642 2.356712 2.313025 2.271429

  m   c   e    N    K   m   e   o    ã    t

3.099704 3.047184 2.997041 2.949131 2.903317 2.859477 2.817496 2.77727 2.7387 2.701698 2.666179 2.632067 2.599288 2.567778 2.537472 2.508313 2.480247 2.453223 2.427194 2.402115 2.377944 2.354642 2.332173 2.310502 2.289597 2.269426 2.249962 2.231178 2.213046 2.195544 2.178649 2.162339 2.146593 2.131393 2.11672 2.102557 2.088887 2.075695 2.062966 2.050686 2.038843 2.027423 2.016414 2.005806 1.995587 1.985748 1.976278 1.967169 1.958412 1.949998 1.94192

2.789734 2.742465 2.697337 2.654218 2.612985 2.573529 2.535747 2.499543 2.46483 2.431528 2.399561 2.36886 2.33936 2.311 2.283725 2.257482 2.232223 2.207901 2.184475 2.161903 2.140149 2.119178 2.098956 2.079452 2.060637 2.042484 2.024966 2.00806 1.991742 1.97599 1.960784 1.946105 1.931934 1.918254 1.905048 1.892301 1.879998 1.868125 1.856669 1.845618 1.834959 1.824681 1.814773 1.805225 1.796029 1.787173 1.778651 1.770452 1.762571 1.754998 1.747728

2.656889 2.611872 2.568893 2.527826 2.488558 2.45098 2.414997 2.380517 2.347458 2.315741 2.285296 2.256057 2.227961 2.200952 2.174976 2.149983 2.125926 2.102763 2.080452 2.058955 2.038237 2.018264 1.999005 1.98043 1.962511 1.945223 1.928539 1.912438 1.896897 1.881895 1.867414 1.853433 1.839937 1.826908 1.814331 1.802191 1.790474 1.779167 1.768257 1.757731 1.74758 1.737791 1.728355 1.719262 1.710503 1.70207 1.693953 1.686145 1.678639 1.671427 1.664503

2.231787 2.193972 2.15787 2.123374 2.090388 2.058824 2.028597 1.999634 1.971864 1.945223 1.919649 1.895088 1.871488 1.8488 1.82698 1.805986 1.785778 1.766321 1.74758 1.729522 1.712119 1.695342 1.679164 1.663561 1.64851 1.633987 1.619973 1.606448 1.593393 1.580792 1.568627 1.556884 1.545547 1.534603 1.524038 1.513841 1.503998 1.4945 1.485335 1.476494 1.467967 1.459744 1.451818 1.44418 1.436823 1.429739 1.42292 1.416362 1.410057 1.403999 1.398182

1.859823 1.82831 1.798225 1.769478 1.74199 1.715686 1.690498 1.666362 1.64322 1.621019 1.599707 1.57924 1.559573 1.540667 1.522483 1.504988 1.488148 1.471934 1.456316 1.441269 1.426766 1.412785 1.399304 1.386301 1.373758 1.361656 1.349977 1.338707 1.327828 1.317327 1.30719 1.297403 1.287956 1.278836 1.270032 1.261534 1.253332 1.245417 1.23778 1.230412 1.223306 1.216454 1.209849 1.203484 1.197352 1.191449 1.185767 1.180302 1.175047 1.169999 1.165152

1.594134 1.567123 1.541336 1.516696 1.493135 1.470588 1.448998 1.42831 1.408475 1.389445 1.371178 1.353634 1.336777 1.320571 1.304986 1.28999 1.275556 1.261658 1.248271 1.235373 1.222942 1.210959 1.199403 1.188258 1.177507 1.167134 1.157123 1.147463 1.138138 1.129137 1.120448 1.11206 1.103962 1.096145 1.088599 1.081315 1.074285 1.0675 1.060954 1.054639 1.048548 1.042675 1.037013 1.031557 1.026302 1.021242 1.016372 1.011687 1.007183 1.002856 0.998702

1.394867 1.371233 1.348669 1.327109 1.306493 1.286765 1.267873 1.249771 1.232415 1.215764 1.199781 1.18443 1.16968 1.1555 1.141862 1.128741 1.116111 1.103951 1.092237 1.080952 1.070075 1.059589 1.049478 1.039726 1.030318 1.021242 1.012483 1.00403 0.995871 0.987995 0.980392 0.973053 0.965967 0.959127 0.952524 0.946151 0.939999 0.934063 0.928335 0.922809 0.917479 0.91234 0.907386 0.902613 0.898014 0.893587 0.889325 0.885226 0.881285 0.877499 0.873864

1.239882 1.218873 1.198817 1.179652 1.161327 1.143791 1.126999 1.110908 1.09548 1.080679 1.066472 1.052827 1.039715 1.027111 1.014989 1.003325 0.992099 0.981289 0.970878 0.960846 0.951177 0.941857 0.932869 0.924201 0.915839 0.907771 0.899985 0.892471 0.885219 0.878218 0.87146 0.864936 0.858637 0.852557 0.846688 0.841023 0.835555 0.830278 0.825186 0.820275 0.815537 0.810969 0.806566 0.802322 0.798235 0.794299 0.790511 0.786868 0.783365 0.779999 0.776768

1.115894 1.096986 1.078935 1.061687 1.045194 1.029412 1.014299 0.999817 0.985932 0.972611 0.959824 0.947544 0.935744 0.9244 0.91349 0.902993 0.892889 0.88316 0.87379 0.864761 0.85606 0.847671 0.839582 0.831781 0.824255 0.816993 0.809986 0.803224 0.796697 0.790396 0.784314 0.778442 0.772774 0.767302 0.762019 0.75692 0.751999 0.74725 0.742668 0.738247 0.733983 0.729872 0.725909 0.72209 0.718411 0.714869 0.71146 0.708181 0.705028 0.701999 0.699091

  e   c    K   e   s    K   e    d   s   e    d   a    d    i   n   u   s    A

1.93417 1.926742 1.919628 1.912822 1.906318

1.740753 1.734067 1.727665 1.72154 1.715686

1.65786 1.651493 1.645395 1.639561 1.633987

1.392602 1.387254 1.382132 1.377232 1.372549

1.160502 1.156045 1.151777 1.147693 1.143791

0.994716 0.990896 0.987237 0.983737 0.980392

0.870377 0.867034 0.863832 0.86077 0.857843

0.773668 0.770697 0.767851 0.765129 0.762527

0.696301 0.693627 0.691066 0.688616 0.686275

Dimensionamento de seção ( ) $0 ( ) 0."" f   yk 

 KN 

fyk (MPa) = $00 cm 2 Módulo de elasticidade (MPa) = 210000 Domínio

sd

0.01

2

cd

0.0035

3

! 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.3 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.4 0.41 0.42 0.43 0.44

=

cd

0.000101 0.000204 0.000309 0.000417 0.000526 0.000638 0.000753 0.00087 0.000989 0.001111 0.001236 0.001364 0.001494 0.001628 0.001765 0.001905 0.002048 0.002195 0.002346 0.0025 0.002658 0.002821 0.002987 0.003158 0.003333 0.003514 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035

 Kx 

sd

0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.009463 0.009 0.008569 0.008167 0.00779 0.007438 0.007106 0.006794 0.0065 0.006222 0.005959 0.005711 0.005474 0.00525 0.005037 0.004833 0.00464 0.004455

lim

ψ  0.062068 0.123213 0.183335 0.242332 0.300092 0.356496 0.411416 0.464713 0.516242 0.565844 0.613348 0.658574 0.701326 0.741392 0.778547 0.812547 0.843137 0.87037 0.894737 0.916667 0.936508 0.954545 0.971014 0.986111 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

13.5

15

s 0.019244   2466.918 0.019321   623.8623 0.019399 280.6477 0.019478   159.8892 0.019558   103.7133 0.019638 73.05155 0.019719   54.4804 0.0198 42.37746 0.019882   34.04964 0.019965   28.07487 0.020049   23.64436 0.020133   20.2704 0.020218   17.64469 0.020304   15.56459 0.02039   13.89254 0.020477   12.53259 0.020565   11.41622 0.020654 10.48964 0.020743   9.708776 0.020833   9.041825 0.020924   8.465627 0.021016   7.962899 0.021109   7.520487 0.021202   7.128199 0.021296   6.77802 0.021391 6.546422 0.021487   6.332231 0.021584   6.133585 0.021682   5.948878 0.02178   5.776721 0.02188   5.615902 0.02198   5.465361 0.022081   5.324167 0.022184   5.191498 0.022287   5.066626 0.022391   4.948905 0.022496   4.837757 0.022602 4.732667 0.022709   4.633171 0.022817   4.538853 0.022927   4.449336 0.023037   4.364281 0.023148   4.28338 0.023261   4.206351

2220.227 561.4761 252.583 143.9003 93.34195 65.7464 49.03236 38.13971 30.64467 25.26738 21.27992 18.24336 15.88022 14.00813 12.50328 11.27933 10.2746 9.44068 8.737898 8.137642 7.619064 7.166609 6.768438 6.415379 6.100218 5.89178 5.699008 5.520226 5.353991 5.199049 5.054312 4.918825 4.791751 4.672348 4.559964 4.454014 4.353981 4.2594 4.169854 4.084967 4.004403 3.927853 3.855042 3.785716

cd

0.0035

"

0.45 0.46 0.47 0.48 0.49 0.5 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.6 0.61 0.62 0.63 0.64 0.65 0.66 0.67 0.68 0.69 0.7 0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.78 0.79 0.8 0.81 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9 0.91 0.92 0.93 0.94 0.95

0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035

0.004278 0.004109 0.003947 0.003792 0.003643 0.0035 0.003363 0.003231 0.003104 0.002981 0.002864 0.00275 0.00264 0.002534 0.002432 0.002333 0.002238 0.002145 0.002056 0.001969 0.001885 0.001803 0.001724 0.001647 0.001572 0.0015 0.00143 0.001361 0.001295 0.00123 0.001167 0.001105 0.001045 0.000987 0.00093 0.000875 0.000821 0.000768 0.000717 0.000667 0.000618 0.00057 0.000523 0.000477 0.000433 0.000389 0.000346 0.000304 0.000263 0.000223 0.000184

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

0.021252   4.132939 0.021474 4.062912 0.021695 3.996055 0.021917   3.932174 0.022139   3.87109 0.022362   3.812636 0.022585   3.756662 0.022808   3.703027 0.023033   3.651601 0.023258   3.602264 0.023483   3.554906 0.02371   3.509422 0.023937   3.465718 0.024166   3.423703 0.024395   3.383296 0.024626   3.344418 0.024858   3.306996 0.025091   3.270964 0.025325   3.236259 0.025561   3.202819 0.025798   3.170591 0.026036 3.139523 0.026276   3.109564 0.026328   3.080669 0.026473   3.052795 0.02662   3.025902 0.026769   2.99995 0.026919   2.974903 0.027072   2.950728 0.027225   2.927393 0.027381   2.904866 0.027538   2.883119 0.027697   2.862125 0.027859   2.841858 0.028021   2.822293 0.028186   2.803409 0.028353   2.785182 0.028522   2.767593 0.028693   2.750621 0.028865   2.734249 0.02904   2.718457 0.029217   2.70323 0.029397   2.688552 0.029578   2.674408 0.029762   2.660783 0.029948   2.647664 0.030136   2.635038 0.030327   2.622892 0.03052   2.611216 0.030716   2.599997 0.030914   2.589227

3.719645 3.65662 3.59645 3.538957 3.483981 3.431373 3.380996 3.332724 3.286441 3.242038 3.199415 3.15848 3.119146 3.081333 3.044966 3.009976 2.976297 2.943868 2.912633 2.882537 2.853532 2.82557 2.798607 2.772602 2.747516 2.723312 2.699955 2.677413 2.655656 2.634653 2.614379 2.594807 2.575912 2.557672 2.540064 2.523068 2.506664 2.490834 2.475559 2.460824 2.446611 2.432907 2.419697 2.406967 2.394705 2.382898 2.371534 2.360603 2.350094 2.339998 2.330304

0.96 0.97 0.98 0.99 1

0.0035 0.0035 0.0035 0.0035 0.0035

0.000146 0.000108 7.1E-005 3.5E-005 0

1 1 1 1 1

0.031115   2.578894 0.031318 2.568989 0.031524   2.559503 0.031733   2.550429 0.031944   2.541757

Equação a!a dete!minação da tensão a" 0 # " -0.029 $ensão c " 0.31239 65.9903 0.31938 0.32607 0.3325 0.33868 0.34462 0.35033 0.35583 0.36114 0.36625 0.37118 0.37595 0.38055 0.385 0.3893 0.39347 0.3975 0.40141 0.40519 0.40886 0.41243 0.41588 0.41924

65.6299 65.2796 64.9388 64.607 64.2837 63.9687 63.6614 63.3616 63.0689 62.7829 62.5035 62.2303 61.963 61.7015 61.4454 61.1946 60.9489 60.7079 60.4717 60.2399 60.0125 59.7892

%a&o! da de'eomação no in(cio do t!ec)o a!a#*&ico 0.0017391

2.321004 2.31209 2.303553 2.295386 2.287582

 retangular - Aço CA 60-B fck (MPa) 1#

20

21

1850.189 467.8967 210.4858 119.9169 77.78496 54.78866 40.8603 31.78309 25.53723 21.05615 17.73327 15.2028 13.23352 11.67344 10.4194 9.399444 8.562163 7.867233 7.281582 6.781369 6.34922 5.972174 5.640365 5.346149 5.083515 4.909816 4.749173 4.600188 4.461659 4.332541 4.211927 4.099021 3.993125 3.893624 3.79997 3.711679 3.628318 3.5495 3.474878 3.404139 3.337002 3.273211 3.212535 3.154763

1665.17 421.1071 189.4372 107.9252 70.00646 49.3098 36.77427 28.60478 22.9835 18.95053 15.95994 13.68252 11.91016 10.5061 9.377463 8.4595 7.705947 7.08051 6.553424 6.103232 5.714298 5.374957 5.076329 4.811534 4.575163 4.418835 4.274256 4.14017 4.015493 3.899287 3.790734 3.689119 3.593813 3.504261 3.419973 3.340511 3.265486 3.19455 3.12739 3.063725 3.003302 2.94589 2.891281 2.839287

1585.876 401.0543 180.4164 102.7859 66.67282 46.96171 35.02312 27.24265 21.88905 18.04813 15.19994 13.03097 11.34301 10.00581 8.930917 8.056666 7.338997 6.743343 6.241356 5.812602 5.442189 5.119007 4.834599 4.582414 4.357298 4.208414 4.07072 3.943019 3.824279 3.713607 3.610223 3.513447 3.422679 3.337392 3.257117 3.181439 3.109987 3.042428 2.978467 2.917834 2.860288 2.805609 2.753601 2.704083

25 c 1332.136 336.8856 151.5498 86.34018 56.00517 39.44784 29.41942 22.88383 18.3868 15.16043 12.76795 10.94602 9.528132 8.404877 7.50197 6.7676 6.164758 5.664408 5.242739 4.882585 4.571439 4.299966 4.061063 3.849228 3.660131 3.535068 3.419405 3.312136 3.212394 3.11943 3.032587 2.951295 2.87505 2.803409 2.735978 2.672409 2.612389 2.55564 2.501912 2.45098 2.402642 2.356712 2.313025 2.271429

30

35

"0

"5

25

1110.113 280.738 126.2915 71.95015 46.67098 32.8732 24.51618 19.06986 15.32234 12.63369 10.63996 9.12168 7.94011 7.004064 6.251642 5.639666 5.137298 4.72034 4.368949 4.068821 3.809532 3.583305 3.384219 3.20769 3.050109 2.94589 2.849504 2.760113 2.676995 2.599525 2.527156 2.459413 2.395875 2.336174 2.279982 2.227007 2.176991 2.1297 2.084927 2.042484 2.002201 1.963927 1.927521 1.892858

951.5257 240.6326 108.2498 61.67156 40.00369 28.17703 21.01387 16.34559 13.13343 10.82888 9.119966 7.818583 6.805808 6.003483 5.35855 4.834 4.403398 4.046006 3.744813 3.487561 3.265313 3.071404 2.900759 2.749448 2.614379 2.525048 2.442432 2.365811 2.294567 2.228164 2.166134 2.108068 2.053607 2.002435 1.95427 1.908863 1.865992 1.825457 1.78708 1.7507 1.716173 1.683366 1.652161 1.62245

832.585 210.5535 94.71861 53.96261 35.00323 24.6549 18.38714 14.30239 11.49175 9.475267 7.97997 6.84126 5.955082 5.253048 4.688731 4.22975 3.852973 3.540255 3.276712 3.051616 2.857149 2.687479 2.538164 2.405767 2.287582 2.209417 2.137128 2.070085 2.007746 1.949643 1.895367 1.844559 1.796906 1.752131 1.709986 1.670255 1.632743 1.597275 1.563695 1.531863 1.501651 1.472945 1.445641 1.419643

740.0755 187.1587 84.19432 47.96677 31.11398 21.91547 16.34412 12.71324 10.21489 8.42246 7.093307 6.08112 5.293406 4.669376 4.167761 3.759778 3.424865 3.146893 2.912633 2.712547 2.539688 2.38887 2.256146 2.13846 2.033406 1.963927 1.899669 1.840075 1.784664 1.733016 1.684771 1.639608 1.59725 1.557449 1.519988 1.484671 1.451327 1.4198 1.389951 1.361656 1.334801 1.309284 1.285014 1.261905

1332.136 336.8856 151.5498 86.34018 56.00517 39.44784 29.41942 22.88383 18.3868 15.16043 12.76795 10.94602 9.528132 8.404877 7.50197 6.7676 6.164758 5.664408 5.242739 4.882585 4.571439 4.299966 4.061063 3.849228 3.660131 3.535068 3.419405 3.312136 3.212394 3.11943 3.032587 2.951295 2.87505 2.803409 2.735978 2.672409 2.612389 2.55564 2.501912 2.45098 2.402642 2.356712 2.313025 2.271429

  m   c   e    N    K   m   e   o    ã    t   s

3.099704 3.047184 2.997041 2.949131 2.903317 2.859477 2.817496 2.77727 2.7387 2.701698 2.666179 2.632067 2.599288 2.567778 2.537472 2.508313 2.480247 2.453223 2.427194 2.402115 2.377944 2.354642 2.332173 2.310502 2.289597 2.269426 2.249962 2.231178 2.213046 2.195544 2.178649 2.162339 2.146593 2.131393 2.11672 2.102557 2.088887 2.075695 2.062966 2.050686 2.038843 2.027423 2.016414 2.005806 1.995587 1.985748 1.976278 1.967169 1.958412 1.949998 1.94192

2.789734 2.742465 2.697337 2.654218 2.612985 2.573529 2.535747 2.499543 2.46483 2.431528 2.399561 2.36886 2.33936 2.311 2.283725 2.257482 2.232223 2.207901 2.184475 2.161903 2.140149 2.119178 2.098956 2.079452 2.060637 2.042484 2.024966 2.00806 1.991742 1.97599 1.960784 1.946105 1.931934 1.918254 1.905048 1.892301 1.879998 1.868125 1.856669 1.845618 1.834959 1.824681 1.814773 1.805225 1.796029 1.787173 1.778651 1.770452 1.762571 1.754998 1.747728

2.656889 2.611872 2.568893 2.527826 2.488558 2.45098 2.414997 2.380517 2.347458 2.315741 2.285296 2.256057 2.227961 2.200952 2.174976 2.149983 2.125926 2.102763 2.080452 2.058955 2.038237 2.018264 1.999005 1.98043 1.962511 1.945223 1.928539 1.912438 1.896897 1.881895 1.867414 1.853433 1.839937 1.826908 1.814331 1.802191 1.790474 1.779167 1.768257 1.757731 1.74758 1.737791 1.728355 1.719262 1.710503 1.70207 1.693953 1.686145 1.678639 1.671427 1.664503

2.231787 2.193972 2.15787 2.123374 2.090388 2.058824 2.028597 1.999634 1.971864 1.945223 1.919649 1.895088 1.871488 1.8488 1.82698 1.805986 1.785778 1.766321 1.74758 1.729522 1.712119 1.695342 1.679164 1.663561 1.64851 1.633987 1.619973 1.606448 1.593393 1.580792 1.568627 1.556884 1.545547 1.534603 1.524038 1.513841 1.503998 1.4945 1.485335 1.476494 1.467967 1.459744 1.451818 1.44418 1.436823 1.429739 1.42292 1.416362 1.410057 1.403999 1.398182

1.859823 1.82831 1.798225 1.769478 1.74199 1.715686 1.690498 1.666362 1.64322 1.621019 1.599707 1.57924 1.559573 1.540667 1.522483 1.504988 1.488148 1.471934 1.456316 1.441269 1.426766 1.412785 1.399304 1.386301 1.373758 1.361656 1.349977 1.338707 1.327828 1.317327 1.30719 1.297403 1.287956 1.278836 1.270032 1.261534 1.253332 1.245417 1.23778 1.230412 1.223306 1.216454 1.209849 1.203484 1.197352 1.191449 1.185767 1.180302 1.175047 1.169999 1.165152

1.594134 1.567123 1.541336 1.516696 1.493135 1.470588 1.448998 1.42831 1.408475 1.389445 1.371178 1.353634 1.336777 1.320571 1.304986 1.28999 1.275556 1.261658 1.248271 1.235373 1.222942 1.210959 1.199403 1.188258 1.177507 1.167134 1.157123 1.147463 1.138138 1.129137 1.120448 1.11206 1.103962 1.096145 1.088599 1.081315 1.074285 1.0675 1.060954 1.054639 1.048548 1.042675 1.037013 1.031557 1.026302 1.021242 1.016372 1.011687 1.007183 1.002856 0.998702

1.394867 1.371233 1.348669 1.327109 1.306493 1.286765 1.267873 1.249771 1.232415 1.215764 1.199781 1.18443 1.16968 1.1555 1.141862 1.128741 1.116111 1.103951 1.092237 1.080952 1.070075 1.059589 1.049478 1.039726 1.030318 1.021242 1.012483 1.00403 0.995871 0.987995 0.980392 0.973053 0.965967 0.959127 0.952524 0.946151 0.939999 0.934063 0.928335 0.922809 0.917479 0.91234 0.907386 0.902613 0.898014 0.893587 0.889325 0.885226 0.881285 0.877499 0.873864

1.239882 1.218873 1.198817 1.179652 1.161327 1.143791 1.126999 1.110908 1.09548 1.080679 1.066472 1.052827 1.039715 1.027111 1.014989 1.003325 0.992099 0.981289 0.970878 0.960846 0.951177 0.941857 0.932869 0.924201 0.915839 0.907771 0.899985 0.892471 0.885219 0.878218 0.87146 0.864936 0.858637 0.852557 0.846688 0.841023 0.835555 0.830278 0.825186 0.820275 0.815537 0.810969 0.806566 0.802322 0.798235 0.794299 0.790511 0.786868 0.783365 0.779999 0.776768

2.231787 2.193972 2.15787 2.123374 2.090388 2.058824 2.028597 1.999634 1.971864 1.945223 1.919649 1.895088 1.871488 1.8488 1.82698 1.805986 1.785778 1.766321 1.74758 1.729522 1.712119 1.695342 1.679164 1.663561 1.64851 1.633987 1.619973 1.606448 1.593393 1.580792 1.568627 1.556884 1.545547 1.534603 1.524038 1.513841 1.503998 1.4945 1.485335 1.476494 1.467967 1.459744 1.451818 1.44418 1.436823 1.429739 1.42292 1.416362 1.410057 1.403999 1.398182

  e   c    K   e   s    K   e    d   s   e    d   a    d    i   n   u   s    A

1.93417 1.926742 1.919628 1.912822 1.906318

1.740753 1.734067 1.727665 1.72154 1.715686

1.65786 1.651493 1.645395 1.639561 1.633987

1.392602 1.387254 1.382132 1.377232 1.372549

1.160502 1.156045 1.151777 1.147693 1.143791

0.994716 0.990896 0.987237 0.983737 0.980392

0.870377 0.867034 0.863832 0.86077 0.857843

0.773668 0.770697 0.767851 0.765129 0.762527

1.392602 1.387254 1.382132 1.377232 1.372549

Programa para o cálculo da área de aço em vigas de Concreto Armado ados de entrad

1º PAVIMENTO bw (cm) = 12

VIGA

f ck  ( MPa )

V 08 Momento &ositi'o  Mk 

30

 M d ( kN  .  cm ) = 14420

Escola o Aço

bw

' d

=

103.00

CA 25 -

CA 50 -

CA 60 -

CA 25 - B

CA 50 - B

CA 60 -

Para seus dados tem-se dmin !cm" # Adote um valor para

%$k%.m

41.877

0.6

As

Voc !s"# "$%b%&'%do o om*+o 3. O ,%&o$ -%$% % d!o$m%/o o ONETO  +5%& % 0.3500%

&esultados'

#&c5&o d! Ps+.

ψ  = 1

#&c5&o d! c. #&c5&o d! s.

c = 1.0499 s = 0.03026

#&c5&o d! d. #&c5&o d! As.

d = 42.3 cm As = 10.262 cm:

O ,%&o$ -%$% % d!o$m%/o o AO  +5%& % 0.2333%

Espaçamentos m(nimos e%igidos

Vertical

 Bitolas usuais Bitola usual

Horizontal

Dimensão máxima dos grãos - dmáx (mm)

19

16 Caso seu dmáx (mm) não esteja entre os dados, digite-o aqui:

Sua seção contará com 6 eV  

 barras de aço submetidas ao esforço de tração. Totalizando:

min

=

Bitola usual

12.064 cm² de área.

¿ ¿ {¿ {¿ ¿ ¿

0.76

e V  =

2

Seriam

2 1.6 0.9

φ 0,5 d máx

Armadura m(nima de tração - )B-*

 A S

≥

2 cm

eh

2 1.6 2.28

≥

cm φ 1,2 d más 2

¿ ¿ {¿ { ¿ ¿ ¿

2 cm

eh =

2.28 cm

 barras.

10

Colocação das +arras na seção E"$! com o ,%&o$ d% cob!$"5$% ;; !m cm< 2

3

Sua seção contará com

fileiras de

5%& o d+>m!"$o do !s"$+bo 5"+&+?%do (mm)< 6.3

2

cent#metros" uma da outra na $orizontal.

 barras disostas na base da ner!ura" searadas

2.0

%stas estarão searadas de

3.54

cent#metros"

na !ertical.

Cálculo da altura !" da viga  &'mero de barras na fileira inferior 

2

 &'mero de fileiras com o n'mero máximo de barras 

Dist ância (cm) do centr óide da armadura de aço à base da viga.

3 0

 &'mero de barras ue comletam o total de barras tracionadas  &'mero total de fileiras na $orizontal

3

@5% ,+% d!,! "!$ o m*+mo Ado"%$!mos

49.6 0

c!"*m!"$os d! %&"5$%. c!"*m!"$os 

7.030

Programa para o cálculo da área de aço em vigas

d;

Dados geom

bw bw (cm) = 1 d; (cm) = 4

σ ' sd

( kN / cm ) =

  *abela

Escol



d

'

As;

CA 25 - A

CA 50 - A

CA 25 - B

CA 50 - B

Dados

As  M d ( kN .  cm ) = 30000

5+d%do com %s 5+d%d!s

+bser!ação,

+ !alor de c ara seus dados  igual a

f ck  ( MPa )  =

 Área de aço da armadura de tração - As  Área de aço da armadura de Compressã

1.2

 Bitolas %scol$a a bitola ara /s (mm)

4om este !alor de c (ara o fc5 dese6ado)" !á at a tabela ao lado e col$a o !alor de x mais r7ximo e digite-o no esaço abaixo.

16

Sua seção contará com 9  barras de aço submetidas ao esforço de tração. Totalizando: 18.096 cm² de área.

0.123

Espaçamentos Vertical Dimensão máxima Caso seu dmáx (mm) não esteja ent

Armadura m(nima de tração - )B-* min

 A S

=

1.12 Seriam

Bitola usual 16

 

eV  

≥

2 1.6 0.9

2 cm

φ 0,5 d máx ¿ ¿ {¿ {¿ ¿ ¿

2

barras.

e V 

=

2 cm

Colocação das +arras na seção

E"$! com o ,%&o$ d% cob!$"5$% ;c; !m cm< 2.

5%& o d+>m!

2

2

Sua seção contará com fileiras de

5.80

cent#metros"

 barras disostas na base da ner!ura

uma da outra na $orizontal.

%stas estarão s

cent#metros" na !ertical.

Cálculo da altura !" da viga  &'mero de barras na fileira inferior 

2

 &'mero de fileiras com o n'mero máximo de barras 

4 1

 &'mero de barras ue comletam o total de barras tracionadas  &'mero total de fileiras na $orizontal



@5% ,+% d!,! "!$ o m*+mo

60.20

c!"*m!"$os

e Concreto Armado ,tricos da seção

σ ' sd

%a&o!es de σ ' sd ( KN  / cm2 )

d (cm) = 0 ( kN / cm2 ) = 43. ao lado

+e&ação d,d

a o Aço

 

0.05 0.1 0.15 0.2

CA 60 - A CA 60 - B

A 50 A

A 50 / 40.5

43.5

39.1 37.5 35.5

 ec.nicos K

Kc

0.01

1332.136

0.02

336.8856

0.03

151.5498

0.04

86.34018

0.05

56.00517

0.06 0.07

39.44784 29.41942

0.08

22.88383

0.09

18.3868

0.1

15.16043

0.11

12.76795

0.12

10.94602

0.13

9.528132

0.14

8.404877

 m(nimos e%igidos Horizontal

0.15

7.50197

0.16

6.7676

dos grãos - dmáx (mm)

0.17

6.164758

0.18

5.664408

0.19

5.242739

0.2

4.882585

0.21

4.571439

0.22

4.299966

0.23

4.061063

0.24 0.25 0.26 0.27 0.28 0.29

3.849228 3.660131 3.535068 3.419405 3.312136 3.212394

0.3

3.11943

dm+ (cm) 9.182

 ( MPa )  = 2

k 

17.448 cm  4.291 cm 

= o-As' =  

usuais %scol$a a bitola ara /s8 (mm) 10

Sua seção contará com 6  barras de aço submetidas ao esforço de comressão. Totalizando: 4.712 cm² de área.

19

e os dados, digite-o aqui: eh

2 1.6 2.28

≥

cm φ 1,2 d más 2

¿ ¿ {¿ { ¿ ¿ ¿

eh =

2.28 cm

$o do !s"$+bo 5"+&+?%do (mm)< 

" searadas

earadas de

2.0

0.31

3.032587

0.32

2.951295

0.33

2.87505

0.34 0.35 0.36 0.37

2.803409 2.735978 2.672409 2.612389

0.38

2.55564

0.39

2.501912

Distância (cm) do centróide da armadura de aço à base da viga.

0.4

2.45098

0.41

2.402642

10.200

0.42

2.356712

0.43

2.313025

0.44 0.45

2.271429 2.231787

0.46

2.193972

0.47 0.48 0.49 0.5 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.6 0.61 0.62 0.63 0.64 0.65 0.66 0.67 0.68 0.69 0.7 0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.78

2.15787 2.123374 2.090388 2.058824 2.028597 1.999634 1.971864 1.945223 1.919649 1.895088 1.871488 1.8488 1.82698 1.805986 1.785778 1.766321 1.74758 1.729522 1.712119 1.695342 1.679164 1.663561 1.64851 1.633987 1.619973 1.606448 1.593393 1.580792 1.568627 1.556884 1.545547 1.534603

 d! %&"5$%.

0.79 0.8 0.81 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1

1.524038 1.513841 1.503998 1.4945 1.485335 1.476494 1.467967 1.459744 1.451818 1.44418 1.436823 1.429739 1.42292 1.416362 1.410057 1.403999 1.398182 1.392602 1.387254 1.382132 1.377232 1.372549

2

(

' sd  KN  / cm

50

dc " 21413.01

Aço A 25 A

K &im 0.77

e&ta d " 8586.994

A 50 A

0.63

A 60 A

0.58

A 60

A 25 /

0.54

46.9

A 50 / A 60 /

0.46 0.44

2

)

44.9 42.4 39

Kc do !o#&e 1.25 K adotado a!a o 0.628

Kc a!a os c& 1.751272 s m e 0.030716 &cu&o da dist!i#uição 2.907216

2

Esaçamento )o!iont 5.8 Nme!o de 'i&ei!as )o!i 4 /a!!as que so#!am 1 Nme!o de 'i&ei!as )o!i 5

Kc &im 1.54554728 1.75127212

Kc&im 1.751272 0.628

/ito&as usuais  10

1.84879986

Aço usado

12.5

1.94522253

A

16

2.19397222 2.27142931

As

As,

As min

3

1

3

20 22.2 25.4

ma 1.6 1 1.6 8.677851 5.463918 0.559529 !o#&ema

9

6

1

imensão dos a!eados u&os

Ks2

9.5 0.023

15 19

s 0.022989

38 50

das #a!!as

a& !ea&

iontais com&etas

iontais no tota&

3

1.9

1.6

Aço uti&i 16

 Aço uti&i 2 10

rograma para o cálculo do momento má%imo em vigas

d;

Dados de entr

bw

' (cm) = 0

f ck  ( MPa )  = 2

/ual o tipo de A1 u

'

d



As;

CA 25 - A

CA 50 - A

CA 25 - B

CA 50 - B

/ual o tipo de armaçã

As

Armadura Simples

5%"%s b%$$%s o$%m 5"+&+?%d%s % %$m%d5$% d! 5%"%s b%$$%s o$%m 5"+&+?%d%s % %$m%d5$% d! 5%& % b+"o&% do AO s5bm!"+do % "$%/oB

5%& % b+"o&% do AO s5bm

20

5%& o ,%&o$ d% cob!$"5$% d! coc$!"o ;; (cm)B

2

5%& o "%m%'o do %$!%do 5"+&+?%do (mm)B

5%& o ,%&o$ d% !s-!ss5$ Caso seu dmáx (mm) não esteja en

15

4normaçes so+re a colocação das armaduras d Armadura de tração - Cálculo de d

5%& o Cm!$o d! b%$$%s d% +&!+$% +!$+o$B

2 P%$

5%"%s ,!?!s !s"% m!sm% +&!+$% s! $!-!"!B

0

5%"%s b%$$%s sob$%m +so&%d%s sob$! !s"%s +&!+$%sB NCm!$o "o"%& d! +&!+$%s % 'o$+?o"%&

1

2 Armadura de compressão - Cálculo de d'

5%& o Cm!$o d! b%$$%s d% +&!+$% s5-!$+o$B

2 P%

%$5%"%s ,!?!s !s"% m!sm% +&!+$% s! $!-!"!B

0

5%"%s b%$$%s sob$%m +so&%d%s sob$! !s"%s +&!+$%sB NCm!$o "o"%& d! +&!+$%s % 'o$+?o"%&

0

1 d89d

!&%/o d;Dd

0.0

4/ :0 /

0.0: 0.=

 &a tabela ao lado egue o !alor de

2 σ ' sd  ( kN / cm ) = 43.

0.=:

;<.:

0.2

O mom!"o m#+mo s5-o$"%do -!&% ,+%  d! 14394.3 FN.cm 14.39  ".m

de Concreto Armad da

bw (cm) = 12  

tiliado3 CA 60 - A CA 60 - B

o da viga3 a Simples

 

"$%/oB

3

 

com-$!ssoB

0

"+do % com-$!ssoB % do !s"$+bo (mm)B tre os dados, digite-o aqui:

aço na viga

 s!5s d%dos d ,%&!

4.833 c!"*m!"$os.

s!5s d%dos d; ,%&!

10



c!"*m!"$os.

4/ :0 B

4/ 10

;0.:

;1.>

<>.=

;;.>


;2.;

<:.:

<>

o5

2

50

Esco&)idos

 Aço

K &im

Kc &im

K &im

Kc&im

A 25 A

0.77

1.5455473

0.628

1.751272

A 50 A A 60 A

0.63 0.58

1.7512721 1.8487999

A 25 / A 50 / A 60 /

0.54 0.46 0.44

1.9452225 2.1939722 2.2714293

Ks &imite Ks2 Ks,

Aço usado A

/ito&as usuais mm 10 12.5

Aço uti&i

Aço uti&i 2

4 2

1 1

As 9.424777961

As, 0

16 20 22.2 25.4

0.0307158 0.023 0.0229885

imensão dos a!eados

e&ta d " 0 dc " 14394.298

9.5 15 19

:%A;
25 38 50

2

1.5

Esco&)ida 1 A!madu!a >im&es

1

2 A!madu!a u&a

 A!madu!a de $!ação n" N" n," n,," Esaçamento @e!tica&

2 0 1 2

&cu&o da dist?ncia d 1.666667

A!madu!a de om!essão

2 2 0.75

n" 2 N" 0

2

n," 0

:%0=

n,," 1

:%0=

&cu&o da dist?ncia d

cent!*ide in'e!io! ao est!i#o in'e!io! 

cent!*ide sue!io! ao est!i#o in'e!io!