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Dimensionamento de seção retangular - Aço CA 25-A25
fyk (MPa) = 2500.77
fck (MPa)Módulo de elasticidade (MPa) = 210000 13.5 15
Domínio Kx Ks Kc
0.01 2
0.01 0.000101 0.01 0.062068 0.046185 2466.918 2220.2270.02 0.000204 0.01 0.123213 0.046371 623.8623 561.47610.03 0.000309 0.01 0.183335 0.046559 280.6477 252.5830.04 0.000417 0.01 0.242332 0.046748 159.8892 143.90030.05 0.000526 0.01 0.300092 0.046939 103.7133 93.341950.06 0.000638 0.01 0.356496 0.047131 73.05155 65.74640.07 0.000753 0.01 0.411416 0.047325 54.4804 49.032360.08 0.00087 0.01 0.464713 0.047521 42.37746 38.139710.09 0.000989 0.01 0.516242 0.047718 34.04964 30.644670.1 0.001111 0.01 0.565844 0.047917 28.07487 25.26738
0.11 0.001236 0.01 0.613348 0.048117 23.64436 21.279920.12 0.001364 0.01 0.658574 0.048319 20.2704 18.243360.13 0.001494 0.01 0.701326 0.048523 17.64469 15.880220.14 0.001628 0.01 0.741392 0.048729 15.56459 14.008130.15 0.001765 0.01 0.778547 0.048936 13.89254 12.503280.16 0.001905 0.01 0.812547 0.049145 12.53259 11.279330.17 0.002048 0.01 0.843137 0.049356 11.41622 10.27460.18 0.002195 0.01 0.87037 0.049569 10.48964 9.440680.19 0.002346 0.01 0.894737 0.049784 9.708776 8.7378980.2 0.0025 0.01 0.916667 0.05 9.041825 8.137642
0.21 0.002658 0.01 0.936508 0.050218 8.465627 7.6190640.22 0.002821 0.01 0.954545 0.050439 7.962899 7.1666090.23 0.002987 0.01 0.971014 0.050661 7.520487 6.7684380.24 0.003158 0.01 0.986111 0.050885 7.128199 6.4153790.25 0.003333 0.01 1 0.051111 6.77802 6.1002180.26 0.003514 0.01 1 0.051339 6.546422 5.89178
0.0035 3
0.27 0.0035 0.009463 1 0.05157 6.332231 5.6990080.28 0.0035 0.009 1 0.051802 6.133585 5.5202260.29 0.0035 0.008569 1 0.052036 5.948878 5.3539910.3 0.0035 0.008167 1 0.052273 5.776721 5.199049
0.31 0.0035 0.00779 1 0.052511 5.615902 5.0543120.32 0.0035 0.007437 1 0.052752 5.465361 4.9188250.33 0.0035 0.007106 1 0.052995 5.324167 4.7917510.34 0.0035 0.006794 1 0.053241 5.191498 4.6723480.35 0.0035 0.0065 1 0.053488 5.066626 4.5599640.36 0.0035 0.006222 1 0.053738 4.948905 4.4540140.37 0.0035 0.005959 1 0.053991 4.837757 4.3539810.38 0.0035 0.005711 1 0.054245 4.732667 4.25940.39 0.0035 0.005474 1 0.054502 4.633171 4.1698540.4 0.0035 0.00525 1 0.054762 4.538853 4.084967
0.41 0.0035 0.005037 1 0.055024 4.449336 4.0044030.42 0.0035 0.004833 1 0.055288 4.364281 3.9278530.43 0.0035 0.00464 1 0.055556 4.28338 3.8550420.44 0.0035 0.004455 1 0.055825 4.206351 3.7857160.45 0.0035 0.004278 1 0.056098 4.132939 3.7196450.46 0.0035 0.004109 1 0.056373 4.062912 3.656620.47 0.0035 0.003947 1 0.05665 3.996055 3.59645
cd
sd
(Kx)lim
sd
f yk (KNcm2)=
0.0035 3
0.48 0.0035 0.003792 1 0.056931 3.932174 3.5389570.49 0.0035 0.003643 1 0.057214 3.87109 3.4839810.5 0.0035 0.0035 1 0.0575 3.812636 3.431373
0.51 0.0035 0.003363 1 0.057789 3.756662 3.3809960.52 0.0035 0.003231 1 0.058081 3.703027 3.3327240.53 0.0035 0.003104 1 0.058376 3.651601 3.2864410.54 0.0035 0.002981 1 0.058673 3.602264 3.2420380.55 0.0035 0.002864 1 0.058974 3.554906 3.1994150.56 0.0035 0.00275 1 0.059278 3.509422 3.158480.57 0.0035 0.00264 1 0.059585 3.465718 3.1191460.58 0.0035 0.002534 1 0.059896 3.423703 3.0813330.59 0.0035 0.002432 1 0.060209 3.383296 3.0449660.6 0.0035 0.002333 1 0.060526 3.344418 3.009976
0.61 0.0035 0.002238 1 0.060847 3.306996 2.9762970.62 0.0035 0.002145 1 0.06117 3.270964 2.9438680.63 0.0035 0.002056 1 0.061497 3.236259 2.9126330.64 0.0035 0.001969 1 0.061828 3.202819 2.8825370.65 0.0035 0.001885 1 0.062162 3.170591 2.8535320.66 0.0035 0.001803 1 0.0625 3.139523 2.825570.67 0.0035 0.001724 1 0.062842 3.109564 2.7986070.68 0.0035 0.001647 1 0.063187 3.080669 2.7726020.69 0.0035 0.001572 1 0.063536 3.052795 2.7475160.7 0.0035 0.0015 1 0.063889 3.025902 2.723312
0.71 0.0035 0.00143 1 0.064246 2.99995 2.6999550.72 0.0035 0.001361 1 0.064607 2.974903 2.6774130.73 0.0035 0.001295 1 0.064972 2.950728 2.6556560.74 0.0035 0.00123 1 0.065341 2.927393 2.6346530.75 0.0035 0.001167 1 0.065714 2.904866 2.6143790.76 0.0035 0.001105 1 0.066092 2.883119 2.5948070.77 0.0035 0.001045 1 0.066474 2.862125 2.575912
0.0035 4
0.78 0.0035 0.000987 1 0.06686 2.841858 2.5576720.79 0.0035 0.00093 1 0.067251 2.822293 2.5400640.8 0.0035 0.000875 1 0.067647 2.803409 2.523068
0.81 0.0035 0.000821 1 0.068047 2.785182 2.5066640.82 0.0035 0.000768 1 0.068452 2.767593 2.4908340.83 0.0035 0.000717 1 0.068862 2.750621 2.4755590.84 0.0035 0.000667 1 0.069277 2.734249 2.4608240.85 0.0035 0.000618 1 0.069697 2.718457 2.4466110.86 0.0035 0.00057 1 0.070122 2.70323 2.4329070.87 0.0035 0.000523 1 0.070552 2.688552 2.4196970.88 0.0035 0.000477 1 0.070988 2.674408 2.4069670.89 0.0035 0.000433 1 0.071429 2.660783 2.3947050.9 0.0035 0.000389 1 0.071875 2.647664 2.382898
0.91 0.0035 0.000346 1 0.072327 2.635038 2.3715340.92 0.0035 0.000304 1 0.072785 2.622892 2.3606030.93 0.0035 0.000263 1 0.073248 2.611216 2.3500940.94 0.0035 0.000223 1 0.073718 2.599997 2.3399980.95 0.0035 0.000184 1 0.074194 2.589227 2.3303040.96 0.0035 0.000146 1 0.074675 2.578894 2.3210040.97 0.0035 0.000108 1 0.075163 2.568989 2.312090.98 0.0035 7.143E-05 1 0.075658 2.559503 2.3035530.99 0.0035 3.535E-05 1 0.076159 2.550429 2.295386
1 0.0035 0 1 0.076667 2.541757 2.287582
cd
cd
Dimensionamento de seção retangular - Aço CA 25-Afck (MPa)
18 20 21 25 30 35 40 45 50Kc
1850.189 1665.17 1585.8761 1332.136 1110.1133 951.52568 832.58497 740.07553 666.06798467.8967 421.1071 401.05433 336.88564 280.73803 240.6326 210.55353 187.15869 168.44282210.4858 189.4372 180.41639 151.54977 126.29148 108.24984 94.718607 84.194317 75.774885119.9169 107.9252 102.78593 86.340179 71.950149 61.671556 53.962612 47.966766 43.17008977.78496 70.00646 66.672823 56.005171 46.670976 40.003694 35.003232 31.113984 28.00258654.78866 49.3098 46.961711 39.447837 32.873198 28.177027 24.654898 21.915465 19.72391940.8603 36.77427 35.023117 29.419418 24.516182 21.01387 18.387136 16.344121 14.709709
31.78309 28.60478 27.242652 22.883828 19.069857 16.345591 14.302392 12.713238 11.44191425.53723 22.9835 21.889052 18.386804 15.322336 13.133431 11.491752 10.214891 9.193401821.05615 18.95053 18.048128 15.160428 12.63369 10.828877 9.4752674 8.4224599 7.580213917.73327 15.95994 15.199943 12.767952 10.63996 9.1199657 7.97997 7.0933067 6.38397615.2028 13.68252 13.030972 10.946016 9.1216802 7.818583 6.8412601 6.0811201 5.4730081
13.23352 11.91016 11.343014 9.5281315 7.9401096 6.8058082 5.9550822 5.2934064 4.764065811.67344 10.5061 10.005805 8.4048766 7.0040638 6.0034833 5.2530478 4.6693759 4.202438310.4194 9.377463 8.9309167 7.5019701 6.2516417 5.35855 4.6887313 4.1677611 3.750985
9.399444 8.4595 8.0566663 6.7675997 5.6396664 4.8339998 4.2297498 3.7597776 3.38379998.562163 7.705947 7.3389971 6.1647575 5.137298 4.4033982 3.8529735 3.4248653 3.08237887.867233 7.08051 6.743343 5.6644081 4.7203401 4.0460058 3.5402551 3.1468934 2.8322047.281582 6.553424 6.2413557 5.2427388 4.368949 3.7448134 3.2767118 2.9126327 2.62136946.781369 6.103232 5.8126017 4.8825854 4.0688212 3.487561 3.0516159 2.7125475 2.44129276.34922 5.714298 5.4421887 4.5714385 3.8095321 3.2653132 2.8571491 2.5396881 2.2857193
5.972174 5.374957 5.1190067 4.2999656 3.5833047 3.071404 2.6874785 2.3888698 2.14998285.640365 5.076329 4.8345987 4.0610629 3.3842191 2.9007592 2.5381643 2.2561461 2.03053155.346149 4.811534 4.5824138 3.8492276 3.2076897 2.7494483 2.4057672 2.1384598 1.92461385.083515 4.575163 4.3572985 3.6601307 3.0501089 2.6143791 2.2875817 2.033406 1.83006544.909816 4.418835 4.2084141 3.5350679 2.9458899 2.5250485 2.2094174 1.9639266 1.76753394.749173 4.274256 4.0707198 3.4194046 2.8495039 2.4424319 2.1371279 1.8996692 1.70970234.600188 4.14017 3.9430186 3.3121357 2.7601131 2.3658112 2.0700848 1.8400754 1.65606784.461659 4.015493 3.824279 3.2123943 2.6769953 2.2945674 2.0077465 1.7846635 1.60619724.332541 3.899287 3.7136067 3.1194296 2.5995247 2.228164 1.9496435 1.7330164 1.55971484.211927 3.790734 3.610223 3.0325873 2.5271561 2.1661338 1.8953671 1.6847707 1.51629374.099021 3.689119 3.5134467 2.9512952 2.4594127 2.108068 1.8445595 1.6396084 1.47564763.993125 3.593813 3.4226789 2.8750503 2.3958753 2.0536074 1.7969064 1.5972502 1.43752523.893624 3.504261 3.3373916 2.8034089 2.3361741 2.002435 1.7521306 1.5574494 1.40170453.79997 3.419973 3.2571168 2.7359781 2.2799818 1.9542701 1.7099863 1.5199878 1.3679891
3.711679 3.340511 3.1814387 2.6724085 2.2270071 1.9088632 1.6702553 1.4846714 1.33620433.628318 3.265486 3.1099865 2.6123887 2.1769906 1.8659919 1.6327429 1.4513271 1.3061943
3.5495 3.19455 3.0424285 2.5556399 2.1296999 1.8254571 1.597275 1.4198 1.277823.474878 3.12739 2.9784669 2.5019122 2.0849268 1.7870801 1.5636951 1.3899512 1.25095613.404139 3.063725 2.9178338 2.4509804 2.0424837 1.7507003 1.5318627 1.3616558 1.22549023.337002 3.003302 2.8602875 2.4026415 2.0022013 1.7161725 1.501651 1.3348009 1.20132083.273211 2.94589 2.8056094 2.3567119 1.9639266 1.6833657 1.4729449 1.3092844 1.1783563.212535 2.891281 2.7536012 2.313025 1.9275208 1.6521607 1.4456406 1.2850139 1.15651253.154763 2.839287 2.7040825 2.2714293 1.8928578 1.6224495 1.4196433 1.2619052 1.13571473.099704 2.789734 2.6568893 2.231787 1.8598225 1.5941336 1.3948669 1.2398817 1.11589353.047184 2.742465 2.6118717 2.1939722 1.8283102 1.567123 1.3712326 1.2188735 1.09698612.997041 2.697337 2.5688926 2.1578698 1.7982248 1.5413355 1.3486686 1.1988165 1.0789349
2.949131 2.654218 2.5278263 2.1233741 1.7694784 1.5166958 1.3271088 1.1796523 1.06168712.903317 2.612985 2.4885576 2.0903884 1.7419903 1.4931346 1.3064927 1.1613269 1.04519422.859477 2.573529 2.4509804 2.0588235 1.7156863 1.4705882 1.2867647 1.1437908 1.02941182.817496 2.535747 2.4149969 2.0285974 1.6904979 1.4489982 1.2678734 1.1269986 1.01429872.77727 2.499543 2.3805171 1.9996344 1.666362 1.4283103 1.2497715 1.110908 0.99981722.7387 2.46483 2.3474575 1.9718643 1.6432203 1.4084745 1.2324152 1.0954802 0.9859322
2.701698 2.431528 2.3157411 1.9452225 1.6210188 1.3894447 1.2157641 1.0806792 0.97261132.666179 2.399561 2.2852964 1.919649 1.5997075 1.3711778 1.1997806 1.0664717 0.95982452.632067 2.36886 2.2560571 1.8950879 1.5792399 1.3536342 1.18443 1.0528266 0.9475442.599288 2.33936 2.2279615 1.8714876 1.559573 1.3367769 1.1696798 1.0397153 0.93574382.567778 2.311 2.2009522 1.8487999 1.5406666 1.3205713 1.1554999 1.027111 0.92439992.537472 2.283725 2.1749759 1.8269798 1.5224832 1.3049856 1.1418624 1.0149888 0.91348992.508313 2.257482 2.1499828 1.8059856 1.504988 1.2899897 1.128741 1.0033253 0.90299282.480247 2.232223 2.1259263 1.7857781 1.4881484 1.2755558 1.1161113 0.9920989 0.8928892.453223 2.207901 2.1027629 1.7663208 1.471934 1.2616577 1.1039505 0.9812893 0.88316042.427194 2.184475 2.0804519 1.7475796 1.4563163 1.2482711 1.0922373 0.9708776 0.87378982.402115 2.161903 2.0589553 1.7295225 1.4412687 1.2353732 1.0809515 0.9608458 0.86476122.377944 2.140149 2.0382373 1.7121194 1.4267661 1.2229424 1.0700746 0.9511774 0.85605972.354642 2.119178 2.0182645 1.6953422 1.4127851 1.2109587 1.0595889 0.9418568 0.84767112.332173 2.098956 1.9990053 1.6791644 1.3993037 1.1994032 1.0494778 0.9328691 0.83958222.310502 2.079452 1.9804302 1.6635614 1.3863011 1.1882581 1.0397258 0.9242008 0.83178072.289597 2.060637 1.9625113 1.6485095 1.3737579 1.1775068 1.0303184 0.9158386 0.82425482.269426 2.042484 1.9452225 1.6339869 1.3616558 1.1671335 1.0212418 0.9077705 0.81699352.249962 2.024966 1.9285391 1.6199729 1.3499774 1.1571235 1.012483 0.8999849 0.80998642.231178 2.00806 1.9124379 1.6064478 1.3387065 1.1474627 1.0040299 0.892471 0.80322392.213046 1.991742 1.8968968 1.5933933 1.3278278 1.1381381 0.9958708 0.8852185 0.79669672.195544 1.97599 1.8818953 1.580792 1.3173267 1.1291372 0.987995 0.8782178 0.7903962.178649 1.960784 1.8674136 1.5686275 1.3071895 1.1204482 0.9803922 0.8714597 0.78431372.162339 1.946105 1.8534334 1.5568841 1.2974034 1.1120601 0.9730526 0.8649356 0.7784422.146593 1.931934 1.8399372 1.5455473 1.2879561 1.1039623 0.965967 0.8586374 0.77277362.131393 1.918254 1.8269085 1.5346031 1.2788359 1.0961451 0.9591269 0.8525573 0.76730162.11672 1.905048 1.8143315 1.5240384 1.270032 1.0885989 0.952524 0.846688 0.7620192
2.102557 1.892301 1.8021915 1.5138408 1.261534 1.0813149 0.9461505 0.8410227 0.75692042.088887 1.879998 1.7904744 1.5039985 1.2533321 1.0742846 0.9399991 0.8355547 0.75199922.075695 1.868125 1.779167 1.4945002 1.2454169 1.0675002 0.9340626 0.8302779 0.74725012.062966 1.856669 1.7682565 1.4853355 1.2377796 1.0609539 0.9283347 0.8251864 0.74266772.050686 1.845618 1.7577312 1.4764942 1.2304118 1.0546387 0.9228089 0.8202746 0.73824712.038843 1.834959 1.7475796 1.4679669 1.2233057 1.0485478 0.9174793 0.8155371 0.73398342.027423 1.824681 1.737791 1.4597444 1.2164537 1.0426746 0.9123403 0.8109691 0.72987222.016414 1.814773 1.7283551 1.4518183 1.2098486 1.0370131 0.9073864 0.8065657 0.72590912.005806 1.805225 1.7192623 1.4441804 1.2034836 1.0315574 0.9026127 0.8023224 0.72209021.995587 1.796029 1.7105034 1.4368229 1.1973524 1.0263021 0.8980143 0.7982349 0.71841141.985748 1.787173 1.7020697 1.4297386 1.1914488 1.0212418 0.8935866 0.7942992 0.71486931.976278 1.778651 1.6939529 1.4229204 1.185767 1.0163717 0.8893253 0.7905113 0.71146021.967169 1.770452 1.686145 1.4163618 1.1803015 1.011687 0.8852261 0.7868677 0.70818091.958412 1.762571 1.6786387 1.4100565 1.1750471 1.0071832 0.8812853 0.7833647 0.70502831.949998 1.754998 1.6714269 1.4039986 1.1699988 1.0028561 0.8774991 0.7799992 0.70199931.94192 1.747728 1.6645028 1.3981824 1.165152 0.9987017 0.873864 0.776768 0.69909121.93417 1.740753 1.6578601 1.3926025 1.1605021 0.9947161 0.8703766 0.7736681 0.6963012
1.926742 1.734067 1.6514928 1.3872539 1.1560449 0.9908957 0.8670337 0.7706966 0.6936271.919628 1.727665 1.645395 1.3821318 1.1517765 0.987237 0.8638324 0.767851 0.69106591.912822 1.72154 1.6395614 1.3772316 1.147693 0.9837369 0.8607698 0.7651287 0.68861581.906318 1.715686 1.6339869 1.372549 1.1437908 0.9803922 0.8578431 0.7625272 0.6862745
As
unid
ades
de
Ks
e K
c es
tão
em K
N e
cm
Dimensionamento de seção retangular - Aço CA 50-A50
fyk (MPa) = 5000.63
fck (MPa)Módulo de elasticidade (MPa) = 210000 13.5 15
Domínio Kx Ks Kc
0.01 2
0.01 0.000101 0.01 0.062068 0.023092 2466.918 2220.2270.02 0.000204 0.01 0.123213 0.023185 623.8623 561.47610.03 0.000309 0.01 0.183335 0.023279 280.6477 252.5830.04 0.000417 0.01 0.242332 0.023374 159.8892 143.90030.05 0.000526 0.01 0.300092 0.023469 103.7133 93.341950.06 0.000638 0.01 0.356496 0.023566 73.05155 65.74640.07 0.000753 0.01 0.411416 0.023663 54.4804 49.032360.08 0.00087 0.01 0.464713 0.02376 42.37746 38.139710.09 0.000989 0.01 0.516242 0.023859 34.04964 30.644670.1 0.001111 0.01 0.565844 0.023958 28.07487 25.26738
0.11 0.001236 0.01 0.613348 0.024059 23.64436 21.279920.12 0.001364 0.01 0.658574 0.02416 20.2704 18.243360.13 0.001494 0.01 0.701326 0.024262 17.64469 15.880220.14 0.001628 0.01 0.741392 0.024364 15.56459 14.008130.15 0.001765 0.01 0.778547 0.024468 13.89254 12.503280.16 0.001905 0.01 0.812547 0.024573 12.53259 11.279330.17 0.002048 0.01 0.843137 0.024678 11.41622 10.27460.18 0.002195 0.01 0.87037 0.024784 10.48964 9.440680.19 0.002346 0.01 0.894737 0.024892 9.708776 8.7378980.2 0.0025 0.01 0.916667 0.025 9.041825 8.137642
0.21 0.002658 0.01 0.936508 0.025109 8.465627 7.6190640.22 0.002821 0.01 0.954545 0.025219 7.962899 7.1666090.23 0.002987 0.01 0.971014 0.02533 7.520487 6.7684380.24 0.003158 0.01 0.986111 0.025442 7.128199 6.4153790.25 0.003333 0.01 1 0.025556 6.77802 6.1002180.26 0.003514 0.01 1 0.02567 6.546422 5.89178
0.0035 3
0.27 0.0035 0.009463 1 0.025785 6.332231 5.6990080.28 0.0035 0.009 1 0.025901 6.133585 5.5202260.29 0.0035 0.008569 1 0.026018 5.948878 5.3539910.3 0.0035 0.008167 1 0.026136 5.776721 5.199049
0.31 0.0035 0.00779 1 0.026256 5.615902 5.0543120.32 0.0035 0.007437 1 0.026376 5.465361 4.9188250.33 0.0035 0.007106 1 0.026498 5.324167 4.7917510.34 0.0035 0.006794 1 0.02662 5.191498 4.6723480.35 0.0035 0.0065 1 0.026744 5.066626 4.5599640.36 0.0035 0.006222 1 0.026869 4.948905 4.4540140.37 0.0035 0.005959 1 0.026995 4.837757 4.3539810.38 0.0035 0.005711 1 0.027123 4.732667 4.25940.39 0.0035 0.005474 1 0.027251 4.633171 4.1698540.4 0.0035 0.00525 1 0.027381 4.538853 4.084967
0.41 0.0035 0.005037 1 0.027512 4.449336 4.0044030.42 0.0035 0.004833 1 0.027644 4.364281 3.9278530.43 0.0035 0.00464 1 0.027778 4.28338 3.8550420.44 0.0035 0.004455 1 0.027913 4.206351 3.7857160.45 0.0035 0.004278 1 0.028049 4.132939 3.7196450.46 0.0035 0.004109 1 0.028186 4.062912 3.656620.47 0.0035 0.003947 1 0.028325 3.996055 3.59645
cd
sd
cd
(Kx)lim
sd
f yk (KNcm2)=
0.0035 3
0.48 0.0035 0.003792 1 0.028465 3.932174 3.5389570.49 0.0035 0.003643 1 0.028607 3.87109 3.4839810.5 0.0035 0.0035 1 0.02875 3.812636 3.431373
0.51 0.0035 0.003363 1 0.028894 3.756662 3.3809960.52 0.0035 0.003231 1 0.02904 3.703027 3.3327240.53 0.0035 0.003104 1 0.029188 3.651601 3.2864410.54 0.0035 0.002981 1 0.029337 3.602264 3.2420380.55 0.0035 0.002864 1 0.029487 3.554906 3.1994150.56 0.0035 0.00275 1 0.029639 3.509422 3.158480.57 0.0035 0.00264 1 0.029793 3.465718 3.1191460.58 0.0035 0.002534 1 0.029948 3.423703 3.0813330.59 0.0035 0.002432 1 0.030105 3.383296 3.0449660.6 0.0035 0.002333 1 0.030263 3.344418 3.009976
0.61 0.0035 0.002238 1 0.030423 3.306996 2.9762970.62 0.0035 0.002145 1 0.030585 3.270964 2.9438680.63 0.0035 0.002056 1 0.030749 3.236259 2.912633
0.0035 4
0.64 0.0035 0.001969 1 0.030914 3.202819 2.8825370.65 0.0035 0.001885 1 0.031081 3.170591 2.8535320.66 0.0035 0.001803 1 0.03125 3.139523 2.825570.67 0.0035 0.001724 1 0.031421 3.109564 2.7986070.68 0.0035 0.001647 1 0.031593 3.080669 2.7726020.69 0.0035 0.001572 1 0.031768 3.052795 2.7475160.7 0.0035 0.0015 1 0.031944 3.025902 2.723312
0.71 0.0035 0.00143 1 0.032123 2.99995 2.6999550.72 0.0035 0.001361 1 0.032303 2.974903 2.6774130.73 0.0035 0.001295 1 0.032486 2.950728 2.6556560.74 0.0035 0.00123 1 0.03267 2.927393 2.6346530.75 0.0035 0.001167 1 0.032857 2.904866 2.6143790.76 0.0035 0.001105 1 0.033046 2.883119 2.5948070.77 0.0035 0.001045 1 0.033237 2.862125 2.5759120.78 0.0035 0.000987 1 0.03343 2.841858 2.5576720.79 0.0035 0.00093 1 0.033626 2.822293 2.5400640.8 0.0035 0.000875 1 0.033824 2.803409 2.523068
0.81 0.0035 0.000821 1 0.034024 2.785182 2.5066640.82 0.0035 0.000768 1 0.034226 2.767593 2.4908340.83 0.0035 0.000717 1 0.034431 2.750621 2.4755590.84 0.0035 0.000667 1 0.034639 2.734249 2.4608240.85 0.0035 0.000618 1 0.034848 2.718457 2.4466110.86 0.0035 0.00057 1 0.035061 2.70323 2.4329070.87 0.0035 0.000523 1 0.035276 2.688552 2.4196970.88 0.0035 0.000477 1 0.035494 2.674408 2.4069670.89 0.0035 0.000433 1 0.035714 2.660783 2.3947050.9 0.0035 0.000389 1 0.035938 2.647664 2.382898
0.91 0.0035 0.000346 1 0.036164 2.635038 2.3715340.92 0.0035 0.000304 1 0.036392 2.622892 2.3606030.93 0.0035 0.000263 1 0.036624 2.611216 2.3500940.94 0.0035 0.000223 1 0.036859 2.599997 2.3399980.95 0.0035 0.000184 1 0.037097 2.589227 2.3303040.96 0.0035 0.000146 1 0.037338 2.578894 2.3210040.97 0.0035 0.000108 1 0.037582 2.568989 2.312090.98 0.0035 7.143E-05 1 0.037829 2.559503 2.3035530.99 0.0035 3.535E-05 1 0.038079 2.550429 2.295386
1 0.0035 0 1 0.038333 2.541757 2.287582
cd
Dimensionamento de seção retangular - Aço CA 50-Afck (MPa)
18 20 21 25 30 35 40 45 50Kc
1850.189 1665.1699 1585.8761 1332.136 1110.1133 951.52568 832.58497 740.07553 666.06798467.8967 421.10705 401.05433 336.88564 280.73803 240.6326 210.55353 187.15869 168.44282210.4858 189.43721 180.41639 151.54977 126.29148 108.24984 94.718607 84.194317 75.774885119.9169 107.92522 102.78593 86.340179 71.950149 61.671556 53.962612 47.966766 43.17008977.78496 70.006464 66.672823 56.005171 46.670976 40.003694 35.003232 31.113984 28.00258654.78866 49.309797 46.961711 39.447837 32.873198 28.177027 24.654898 21.915465 19.72391940.8603 36.774273 35.023117 29.419418 24.516182 21.01387 18.387136 16.344121 14.709709
31.78309 28.604785 27.242652 22.883828 19.069857 16.345591 14.302392 12.713238 11.44191425.53723 22.983504 21.889052 18.386804 15.322336 13.133431 11.491752 10.214891 9.193401821.05615 18.950535 18.048128 15.160428 12.63369 10.828877 9.4752674 8.4224599 7.580213917.73327 15.95994 15.199943 12.767952 10.63996 9.1199657 7.97997 7.0933067 6.38397615.2028 13.68252 13.030972 10.946016 9.1216802 7.818583 6.8412601 6.0811201 5.4730081
13.23352 11.910164 11.343014 9.5281315 7.9401096 6.8058082 5.9550822 5.2934064 4.764065811.67344 10.506096 10.005805 8.4048766 7.0040638 6.0034833 5.2530478 4.6693759 4.202438310.4194 9.3774626 8.9309167 7.5019701 6.2516417 5.35855 4.6887313 4.1677611 3.750985
9.399444 8.4594996 8.0566663 6.7675997 5.6396664 4.8339998 4.2297498 3.7597776 3.38379998.562163 7.7059469 7.3389971 6.1647575 5.137298 4.4033982 3.8529735 3.4248653 3.08237887.867233 7.0805101 6.743343 5.6644081 4.7203401 4.0460058 3.5402551 3.1468934 2.8322047.281582 6.5534235 6.2413557 5.2427388 4.368949 3.7448134 3.2767118 2.9126327 2.62136946.781369 6.1032318 5.8126017 4.8825854 4.0688212 3.487561 3.0516159 2.7125475 2.44129276.34922 5.7142982 5.4421887 4.5714385 3.8095321 3.2653132 2.8571491 2.5396881 2.2857193
5.972174 5.374957 5.1190067 4.2999656 3.5833047 3.071404 2.6874785 2.3888698 2.14998285.640365 5.0763286 4.8345987 4.0610629 3.3842191 2.9007592 2.5381643 2.2561461 2.03053155.346149 4.8115345 4.5824138 3.8492276 3.2076897 2.7494483 2.4057672 2.1384598 1.92461385.083515 4.5751634 4.3572985 3.6601307 3.0501089 2.6143791 2.2875817 2.033406 1.83006544.909816 4.4188348 4.2084141 3.5350679 2.9458899 2.5250485 2.2094174 1.9639266 1.76753394.749173 4.2742558 4.0707198 3.4194046 2.8495039 2.4424319 2.1371279 1.8996692 1.70970234.600188 4.1401696 3.9430186 3.3121357 2.7601131 2.3658112 2.0700848 1.8400754 1.65606784.461659 4.0154929 3.824279 3.2123943 2.6769953 2.2945674 2.0077465 1.7846635 1.60619724.332541 3.899287 3.7136067 3.1194296 2.5995247 2.228164 1.9496435 1.7330164 1.55971484.211927 3.7907341 3.610223 3.0325873 2.5271561 2.1661338 1.8953671 1.6847707 1.51629374.099021 3.689119 3.5134467 2.9512952 2.4594127 2.108068 1.8445595 1.6396084 1.47564763.993125 3.5938129 3.4226789 2.8750503 2.3958753 2.0536074 1.7969064 1.5972502 1.43752523.893624 3.5042612 3.3373916 2.8034089 2.3361741 2.002435 1.7521306 1.5574494 1.40170453.79997 3.4199726 3.2571168 2.7359781 2.2799818 1.9542701 1.7099863 1.5199878 1.3679891
3.711679 3.3405107 3.1814387 2.6724085 2.2270071 1.9088632 1.6702553 1.4846714 1.33620433.628318 3.2654859 3.1099865 2.6123887 2.1769906 1.8659919 1.6327429 1.4513271 1.3061943
3.5495 3.1945499 3.0424285 2.5556399 2.1296999 1.8254571 1.597275 1.4198 1.277823.474878 3.1273902 2.9784669 2.5019122 2.0849268 1.7870801 1.5636951 1.3899512 1.25095613.404139 3.0637255 2.9178338 2.4509804 2.0424837 1.7507003 1.5318627 1.3616558 1.22549023.337002 3.0033019 2.8602875 2.4026415 2.0022013 1.7161725 1.501651 1.3348009 1.20132083.273211 2.9458899 2.8056094 2.3567119 1.9639266 1.6833657 1.4729449 1.3092844 1.1783563.212535 2.8912812 2.7536012 2.313025 1.9275208 1.6521607 1.4456406 1.2850139 1.15651253.154763 2.8392866 2.7040825 2.2714293 1.8928578 1.6224495 1.4196433 1.2619052 1.13571473.099704 2.7897338 2.6568893 2.231787 1.8598225 1.5941336 1.3948669 1.2398817 1.11589353.047184 2.7424653 2.6118717 2.1939722 1.8283102 1.567123 1.3712326 1.2188735 1.09698612.997041 2.6973372 2.5688926 2.1578698 1.7982248 1.5413355 1.3486686 1.1988165 1.0789349
2.949131 2.6542176 2.5278263 2.1233741 1.7694784 1.5166958 1.3271088 1.1796523 1.06168712.903317 2.6129855 2.4885576 2.0903884 1.7419903 1.4931346 1.3064927 1.1613269 1.04519422.859477 2.5735294 2.4509804 2.0588235 1.7156863 1.4705882 1.2867647 1.1437908 1.02941182.817496 2.5357468 2.4149969 2.0285974 1.6904979 1.4489982 1.2678734 1.1269986 1.01429872.77727 2.4995429 2.3805171 1.9996344 1.666362 1.4283103 1.2497715 1.110908 0.99981722.7387 2.4648304 2.3474575 1.9718643 1.6432203 1.4084745 1.2324152 1.0954802 0.9859322
2.701698 2.4315282 2.3157411 1.9452225 1.6210188 1.3894447 1.2157641 1.0806792 0.97261132.666179 2.3995612 2.2852964 1.919649 1.5997075 1.3711778 1.1997806 1.0664717 0.95982452.632067 2.3688599 2.2560571 1.8950879 1.5792399 1.3536342 1.18443 1.0528266 0.9475442.599288 2.3393595 2.2279615 1.8714876 1.559573 1.3367769 1.1696798 1.0397153 0.93574382.567778 2.3109998 2.2009522 1.8487999 1.5406666 1.3205713 1.1554999 1.027111 0.92439992.537472 2.2837247 2.1749759 1.8269798 1.5224832 1.3049856 1.1418624 1.0149888 0.91348992.508313 2.2574819 2.1499828 1.8059856 1.504988 1.2899897 1.128741 1.0033253 0.90299282.480247 2.2322226 2.1259263 1.7857781 1.4881484 1.2755558 1.1161113 0.9920989 0.8928892.453223 2.207901 2.1027629 1.7663208 1.471934 1.2616577 1.1039505 0.9812893 0.88316042.427194 2.1844745 2.0804519 1.7475796 1.4563163 1.2482711 1.0922373 0.9708776 0.87378982.402115 2.1619031 2.0589553 1.7295225 1.4412687 1.2353732 1.0809515 0.9608458 0.86476122.377944 2.1401492 2.0382373 1.7121194 1.4267661 1.2229424 1.0700746 0.9511774 0.85605972.354642 2.1191777 2.0182645 1.6953422 1.4127851 1.2109587 1.0595889 0.9418568 0.84767112.332173 2.0989556 1.9990053 1.6791644 1.3993037 1.1994032 1.0494778 0.9328691 0.83958222.310502 2.0794517 1.9804302 1.6635614 1.3863011 1.1882581 1.0397258 0.9242008 0.83178072.289597 2.0606369 1.9625113 1.6485095 1.3737579 1.1775068 1.0303184 0.9158386 0.82425482.269426 2.0424837 1.9452225 1.6339869 1.3616558 1.1671335 1.0212418 0.9077705 0.81699352.249962 2.0249661 1.9285391 1.6199729 1.3499774 1.1571235 1.012483 0.8999849 0.80998642.231178 2.0080598 1.9124379 1.6064478 1.3387065 1.1474627 1.0040299 0.892471 0.80322392.213046 1.9917417 1.8968968 1.5933933 1.3278278 1.1381381 0.9958708 0.8852185 0.79669672.195544 1.97599 1.8818953 1.580792 1.3173267 1.1291372 0.987995 0.8782178 0.7903962.178649 1.9607843 1.8674136 1.5686275 1.3071895 1.1204482 0.9803922 0.8714597 0.78431372.162339 1.9461051 1.8534334 1.5568841 1.2974034 1.1120601 0.9730526 0.8649356 0.7784422.146593 1.9319341 1.8399372 1.5455473 1.2879561 1.1039623 0.965967 0.8586374 0.77277362.131393 1.9182539 1.8269085 1.5346031 1.2788359 1.0961451 0.9591269 0.8525573 0.76730162.11672 1.9050481 1.8143315 1.5240384 1.270032 1.0885989 0.952524 0.846688 0.7620192
2.102557 1.892301 1.8021915 1.5138408 1.261534 1.0813149 0.9461505 0.8410227 0.75692042.088887 1.8799981 1.7904744 1.5039985 1.2533321 1.0742846 0.9399991 0.8355547 0.75199922.075695 1.8681253 1.779167 1.4945002 1.2454169 1.0675002 0.9340626 0.8302779 0.74725012.062966 1.8566694 1.7682565 1.4853355 1.2377796 1.0609539 0.9283347 0.8251864 0.74266772.050686 1.8456178 1.7577312 1.4764942 1.2304118 1.0546387 0.9228089 0.8202746 0.73824712.038843 1.8349586 1.7475796 1.4679669 1.2233057 1.0485478 0.9174793 0.8155371 0.73398342.027423 1.8246805 1.737791 1.4597444 1.2164537 1.0426746 0.9123403 0.8109691 0.72987222.016414 1.8147729 1.7283551 1.4518183 1.2098486 1.0370131 0.9073864 0.8065657 0.72590912.005806 1.8052255 1.7192623 1.4441804 1.2034836 1.0315574 0.9026127 0.8023224 0.72209021.995587 1.7960286 1.7105034 1.4368229 1.1973524 1.0263021 0.8980143 0.7982349 0.71841141.985748 1.7871732 1.7020697 1.4297386 1.1914488 1.0212418 0.8935866 0.7942992 0.71486931.976278 1.7786505 1.6939529 1.4229204 1.185767 1.0163717 0.8893253 0.7905113 0.71146021.967169 1.7704523 1.686145 1.4163618 1.1803015 1.011687 0.8852261 0.7868677 0.70818091.958412 1.7625707 1.6786387 1.4100565 1.1750471 1.0071832 0.8812853 0.7833647 0.70502831.949998 1.7549982 1.6714269 1.4039986 1.1699988 1.0028561 0.8774991 0.7799992 0.70199931.94192 1.747728 1.6645028 1.3981824 1.165152 0.9987017 0.873864 0.776768 0.69909121.93417 1.7407531 1.6578601 1.3926025 1.1605021 0.9947161 0.8703766 0.7736681 0.6963012
1.926742 1.7340674 1.6514928 1.3872539 1.1560449 0.9908957 0.8670337 0.7706966 0.6936271.919628 1.7276648 1.645395 1.3821318 1.1517765 0.987237 0.8638324 0.767851 0.69106591.912822 1.7215395 1.6395614 1.3772316 1.147693 0.9837369 0.8607698 0.7651287 0.68861581.906318 1.7156863 1.6339869 1.372549 1.1437908 0.9803922 0.8578431 0.7625272 0.6862745
As
unid
ades
de
Ks
e K
c es
tão
em K
N e
cm
Dimensionamento de seção retangular - Aço CA 60-B60
fyk (MPa) = 6000.44
fck (MPa)Módulo de elasticidade (MPa) = 210000 13.5 15
Domínio Kx Ks Kc
0.01 2
0.01 0.000101 0.01 0.062068 0.019244 2466.918 2220.2270.02 0.000204 0.01 0.123213 0.019321 623.8623 561.47610.03 0.000309 0.01 0.183335 0.019399 280.6477 252.5830.04 0.000417 0.01 0.242332 0.019478 159.8892 143.90030.05 0.000526 0.01 0.300092 0.019558 103.7133 93.341950.06 0.000638 0.01 0.356496 0.019638 73.05155 65.74640.07 0.000753 0.01 0.411416 0.019719 54.4804 49.032360.08 0.00087 0.01 0.464713 0.0198 42.37746 38.139710.09 0.000989 0.01 0.516242 0.019882 34.04964 30.644670.1 0.001111 0.01 0.565844 0.019965 28.07487 25.26738
0.11 0.001236 0.01 0.613348 0.020049 23.64436 21.279920.12 0.001364 0.01 0.658574 0.020133 20.2704 18.243360.13 0.001494 0.01 0.701326 0.020218 17.64469 15.880220.14 0.001628 0.01 0.741392 0.020304 15.56459 14.008130.15 0.001765 0.01 0.778547 0.02039 13.89254 12.503280.16 0.001905 0.01 0.812547 0.020477 12.53259 11.279330.17 0.002048 0.01 0.843137 0.020565 11.41622 10.27460.18 0.002195 0.01 0.87037 0.020654 10.48964 9.440680.19 0.002346 0.01 0.894737 0.020743 9.708776 8.7378980.2 0.0025 0.01 0.916667 0.020833 9.041825 8.137642
0.21 0.002658 0.01 0.936508 0.020924 8.465627 7.6190640.22 0.002821 0.01 0.954545 0.021016 7.962899 7.1666090.23 0.002987 0.01 0.971014 0.021109 7.520487 6.7684380.24 0.003158 0.01 0.986111 0.021202 7.128199 6.4153790.25 0.003333 0.01 1 0.021296 6.77802 6.1002180.26 0.003514 0.01 1 0.021391 6.546422 5.89178
0.0035 3
0.27 0.0035 0.009463 1 0.021487 6.332231 5.6990080.28 0.0035 0.009 1 0.021584 6.133585 5.5202260.29 0.0035 0.008569 1 0.021682 5.948878 5.3539910.3 0.0035 0.008167 1 0.02178 5.776721 5.199049
0.31 0.0035 0.00779 1 0.02188 5.615902 5.0543120.32 0.0035 0.007437 1 0.02198 5.465361 4.9188250.33 0.0035 0.007106 1 0.022081 5.324167 4.7917510.34 0.0035 0.006794 1 0.022184 5.191498 4.6723480.35 0.0035 0.0065 1 0.022287 5.066626 4.5599640.36 0.0035 0.006222 1 0.022391 4.948905 4.4540140.37 0.0035 0.005959 1 0.022496 4.837757 4.3539810.38 0.0035 0.005711 1 0.022602 4.732667 4.25940.39 0.0035 0.005474 1 0.022709 4.633171 4.1698540.4 0.0035 0.00525 1 0.022817 4.538853 4.084967
0.41 0.0035 0.005037 1 0.022927 4.449336 4.0044030.42 0.0035 0.004833 1 0.023037 4.364281 3.9278530.43 0.0035 0.00464 1 0.023148 4.28338 3.8550420.44 0.0035 0.004455 1 0.023261 4.206351 3.785716
0.0035 4
0.45 0.0035 0.004278 1 0.021252 4.132939 3.7196450.46 0.0035 0.004109 1 0.021474 4.062912 3.656620.47 0.0035 0.003947 1 0.021695 3.996055 3.59645
cd
sd
cd
(Kx)lim
sd
f yk (KNcm2)=
0.0035 4
0.48 0.0035 0.003792 1 0.021917 3.932174 3.5389570.49 0.0035 0.003643 1 0.022139 3.87109 3.4839810.5 0.0035 0.0035 1 0.022362 3.812636 3.431373
0.51 0.0035 0.003363 1 0.022585 3.756662 3.3809960.52 0.0035 0.003231 1 0.022808 3.703027 3.3327240.53 0.0035 0.003104 1 0.023033 3.651601 3.2864410.54 0.0035 0.002981 1 0.023258 3.602264 3.2420380.55 0.0035 0.002864 1 0.023483 3.554906 3.1994150.56 0.0035 0.00275 1 0.02371 3.509422 3.158480.57 0.0035 0.00264 1 0.023937 3.465718 3.1191460.58 0.0035 0.002534 1 0.024166 3.423703 3.0813330.59 0.0035 0.002432 1 0.024395 3.383296 3.0449660.6 0.0035 0.002333 1 0.024626 3.344418 3.009976
0.61 0.0035 0.002238 1 0.024858 3.306996 2.9762970.62 0.0035 0.002145 1 0.025091 3.270964 2.9438680.63 0.0035 0.002056 1 0.025325 3.236259 2.9126330.64 0.0035 0.001969 1 0.025561 3.202819 2.8825370.65 0.0035 0.001885 1 0.025798 3.170591 2.8535320.66 0.0035 0.001803 1 0.026036 3.139523 2.825570.67 0.0035 0.001724 1 0.026276 3.109564 2.7986070.68 0.0035 0.001647 1 0.026328 3.080669 2.7726020.69 0.0035 0.001572 1 0.026473 3.052795 2.7475160.7 0.0035 0.0015 1 0.02662 3.025902 2.723312
0.71 0.0035 0.00143 1 0.026769 2.99995 2.6999550.72 0.0035 0.001361 1 0.026919 2.974903 2.6774130.73 0.0035 0.001295 1 0.027072 2.950728 2.6556560.74 0.0035 0.00123 1 0.027225 2.927393 2.6346530.75 0.0035 0.001167 1 0.027381 2.904866 2.6143790.76 0.0035 0.001105 1 0.027538 2.883119 2.5948070.77 0.0035 0.001045 1 0.027697 2.862125 2.5759120.78 0.0035 0.000987 1 0.027859 2.841858 2.5576720.79 0.0035 0.00093 1 0.028021 2.822293 2.5400640.8 0.0035 0.000875 1 0.028186 2.803409 2.523068
0.81 0.0035 0.000821 1 0.028353 2.785182 2.5066640.82 0.0035 0.000768 1 0.028522 2.767593 2.4908340.83 0.0035 0.000717 1 0.028693 2.750621 2.4755590.84 0.0035 0.000667 1 0.028865 2.734249 2.4608240.85 0.0035 0.000618 1 0.02904 2.718457 2.4466110.86 0.0035 0.00057 1 0.029217 2.70323 2.4329070.87 0.0035 0.000523 1 0.029397 2.688552 2.4196970.88 0.0035 0.000477 1 0.029578 2.674408 2.4069670.89 0.0035 0.000433 1 0.029762 2.660783 2.3947050.9 0.0035 0.000389 1 0.029948 2.647664 2.382898
0.91 0.0035 0.000346 1 0.030136 2.635038 2.3715340.92 0.0035 0.000304 1 0.030327 2.622892 2.3606030.93 0.0035 0.000263 1 0.03052 2.611216 2.3500940.94 0.0035 0.000223 1 0.030716 2.599997 2.3399980.95 0.0035 0.000184 1 0.030914 2.589227 2.3303040.96 0.0035 0.000146 1 0.031115 2.578894 2.3210040.97 0.0035 0.000108 1 0.031318 2.568989 2.312090.98 0.0035 7.143E-05 1 0.031524 2.559503 2.3035530.99 0.0035 3.535E-05 1 0.031733 2.550429 2.295386
1 0.0035 0 1 0.031944 2.541757 2.287582
cd
Equação para determinação da tensãoa = 0b = -0.029 Tensão
c = 0.31239 65.9903
0.31937 65.62990.32607 65.2796
0.3325 64.93880.33868 64.6070.34462 64.28370.35033 63.96870.35583 63.66140.36114 63.36160.36625 63.06890.37118 62.78290.37595 62.50350.38055 62.2303
0.385 61.9630.3893 61.7015
0.39347 61.44540.3975 61.1946
0.40141 60.94890.40519 60.70790.40886 60.47170.41243 60.23990.41588 60.01250.41924 59.7892
Valor da defeomação no início do trecho parabólico0.0017391
Dimensionamento de seção retangular - Aço CA 60-Bfck (MPa)
18 20 21 25 30 35 40 45 18Kc
1850.189 1665.17 1585.876 1332.136 1110.113 951.5257 832.585 740.0755 1850.189467.8967 421.1071 401.0543 336.8856 280.738 240.6326 210.5535 187.1587 467.8967210.4858 189.4372 180.4164 151.5498 126.2915 108.2498 94.71861 84.19432 210.4858119.9169 107.9252 102.7859 86.34018 71.95015 61.67156 53.96261 47.96677 119.916977.78496 70.00646 66.67282 56.00517 46.67098 40.00369 35.00323 31.11398 77.7849654.78866 49.3098 46.96171 39.44784 32.8732 28.17703 24.6549 21.91547 54.7886640.8603 36.77427 35.02312 29.41942 24.51618 21.01387 18.38714 16.34412 40.8603
31.78309 28.60478 27.24265 22.88383 19.06986 16.34559 14.30239 12.71324 31.7830925.53723 22.9835 21.88905 18.3868 15.32234 13.13343 11.49175 10.21489 25.5372321.05615 18.95053 18.04813 15.16043 12.63369 10.82888 9.475267 8.42246 21.0561517.73327 15.95994 15.19994 12.76795 10.63996 9.119966 7.97997 7.093307 17.7332715.2028 13.68252 13.03097 10.94602 9.12168 7.818583 6.84126 6.08112 15.2028
13.23352 11.91016 11.34301 9.528132 7.94011 6.805808 5.955082 5.293406 13.2335211.67344 10.5061 10.00581 8.404877 7.004064 6.003483 5.253048 4.669376 11.6734410.4194 9.377463 8.930917 7.50197 6.251642 5.35855 4.688731 4.167761 10.4194
9.399444 8.4595 8.056666 6.7676 5.639666 4.834 4.22975 3.759778 9.3994448.562163 7.705947 7.338997 6.164758 5.137298 4.403398 3.852973 3.424865 8.5621637.867233 7.08051 6.743343 5.664408 4.72034 4.046006 3.540255 3.146893 7.8672337.281582 6.553424 6.241356 5.242739 4.368949 3.744813 3.276712 2.912633 7.2815826.781369 6.103232 5.812602 4.882585 4.068821 3.487561 3.051616 2.712547 6.7813696.34922 5.714298 5.442189 4.571439 3.809532 3.265313 2.857149 2.539688 6.34922
5.972174 5.374957 5.119007 4.299966 3.583305 3.071404 2.687479 2.38887 5.9721745.640365 5.076329 4.834599 4.061063 3.384219 2.900759 2.538164 2.256146 5.6403655.346149 4.811534 4.582414 3.849228 3.20769 2.749448 2.405767 2.13846 5.3461495.083515 4.575163 4.357298 3.660131 3.050109 2.614379 2.287582 2.033406 5.0835154.909816 4.418835 4.208414 3.535068 2.94589 2.525048 2.209417 1.963927 4.9098164.749173 4.274256 4.07072 3.419405 2.849504 2.442432 2.137128 1.899669 4.7491734.600188 4.14017 3.943019 3.312136 2.760113 2.365811 2.070085 1.840075 4.6001884.461659 4.015493 3.824279 3.212394 2.676995 2.294567 2.007746 1.784664 4.4616594.332541 3.899287 3.713607 3.11943 2.599525 2.228164 1.949643 1.733016 4.3325414.211927 3.790734 3.610223 3.032587 2.527156 2.166134 1.895367 1.684771 4.2119274.099021 3.689119 3.513447 2.951295 2.459413 2.108068 1.844559 1.639608 4.0990213.993125 3.593813 3.422679 2.87505 2.395875 2.053607 1.796906 1.59725 3.9931253.893624 3.504261 3.337392 2.803409 2.336174 2.002435 1.752131 1.557449 3.8936243.79997 3.419973 3.257117 2.735978 2.279982 1.95427 1.709986 1.519988 3.79997
3.711679 3.340511 3.181439 2.672409 2.227007 1.908863 1.670255 1.484671 3.7116793.628318 3.265486 3.109987 2.612389 2.176991 1.865992 1.632743 1.451327 3.628318
3.5495 3.19455 3.042428 2.55564 2.1297 1.825457 1.597275 1.4198 3.54953.474878 3.12739 2.978467 2.501912 2.084927 1.78708 1.563695 1.389951 3.4748783.404139 3.063725 2.917834 2.45098 2.042484 1.7507 1.531863 1.361656 3.4041393.337002 3.003302 2.860288 2.402642 2.002201 1.716173 1.501651 1.334801 3.3370023.273211 2.94589 2.805609 2.356712 1.963927 1.683366 1.472945 1.309284 3.2732113.212535 2.891281 2.753601 2.313025 1.927521 1.652161 1.445641 1.285014 3.2125353.154763 2.839287 2.704083 2.271429 1.892858 1.62245 1.419643 1.261905 3.1547633.099704 2.789734 2.656889 2.231787 1.859823 1.594134 1.394867 1.239882 3.0997043.047184 2.742465 2.611872 2.193972 1.82831 1.567123 1.371233 1.218873 3.0471842.997041 2.697337 2.568893 2.15787 1.798225 1.541336 1.348669 1.198817 2.997041
2.949131 2.654218 2.527826 2.123374 1.769478 1.516696 1.327109 1.179652 2.9491312.903317 2.612985 2.488558 2.090388 1.74199 1.493135 1.306493 1.161327 2.9033172.859477 2.573529 2.45098 2.058824 1.715686 1.470588 1.286765 1.143791 2.8594772.817496 2.535747 2.414997 2.028597 1.690498 1.448998 1.267873 1.126999 2.8174962.77727 2.499543 2.380517 1.999634 1.666362 1.42831 1.249771 1.110908 2.777272.7387 2.46483 2.347458 1.971864 1.64322 1.408475 1.232415 1.09548 2.7387
2.701698 2.431528 2.315741 1.945223 1.621019 1.389445 1.215764 1.080679 2.7016982.666179 2.399561 2.285296 1.919649 1.599707 1.371178 1.199781 1.066472 2.6661792.632067 2.36886 2.256057 1.895088 1.57924 1.353634 1.18443 1.052827 2.6320672.599288 2.33936 2.227961 1.871488 1.559573 1.336777 1.16968 1.039715 2.5992882.567778 2.311 2.200952 1.8488 1.540667 1.320571 1.1555 1.027111 2.5677782.537472 2.283725 2.174976 1.82698 1.522483 1.304986 1.141862 1.014989 2.5374722.508313 2.257482 2.149983 1.805986 1.504988 1.28999 1.128741 1.003325 2.5083132.480247 2.232223 2.125926 1.785778 1.488148 1.275556 1.116111 0.992099 2.4802472.453223 2.207901 2.102763 1.766321 1.471934 1.261658 1.103951 0.981289 2.4532232.427194 2.184475 2.080452 1.74758 1.456316 1.248271 1.092237 0.970878 2.4271942.402115 2.161903 2.058955 1.729522 1.441269 1.235373 1.080952 0.960846 2.4021152.377944 2.140149 2.038237 1.712119 1.426766 1.222942 1.070075 0.951177 2.3779442.354642 2.119178 2.018264 1.695342 1.412785 1.210959 1.059589 0.941857 2.3546422.332173 2.098956 1.999005 1.679164 1.399304 1.199403 1.049478 0.932869 2.3321732.310502 2.079452 1.98043 1.663561 1.386301 1.188258 1.039726 0.924201 2.3105022.289597 2.060637 1.962511 1.64851 1.373758 1.177507 1.030318 0.915839 2.2895972.269426 2.042484 1.945223 1.633987 1.361656 1.167134 1.021242 0.907771 2.2694262.249962 2.024966 1.928539 1.619973 1.349977 1.157123 1.012483 0.899985 2.2499622.231178 2.00806 1.912438 1.606448 1.338707 1.147463 1.00403 0.892471 2.2311782.213046 1.991742 1.896897 1.593393 1.327828 1.138138 0.995871 0.885219 2.2130462.195544 1.97599 1.881895 1.580792 1.317327 1.129137 0.987995 0.878218 2.1955442.178649 1.960784 1.867414 1.568627 1.30719 1.120448 0.980392 0.87146 2.1786492.162339 1.946105 1.853433 1.556884 1.297403 1.11206 0.973053 0.864936 2.1623392.146593 1.931934 1.839937 1.545547 1.287956 1.103962 0.965967 0.858637 2.1465932.131393 1.918254 1.826908 1.534603 1.278836 1.096145 0.959127 0.852557 2.1313932.11672 1.905048 1.814331 1.524038 1.270032 1.088599 0.952524 0.846688 2.11672
2.102557 1.892301 1.802191 1.513841 1.261534 1.081315 0.946151 0.841023 2.1025572.088887 1.879998 1.790474 1.503998 1.253332 1.074285 0.939999 0.835555 2.0888872.075695 1.868125 1.779167 1.4945 1.245417 1.0675 0.934063 0.830278 2.0756952.062966 1.856669 1.768257 1.485335 1.23778 1.060954 0.928335 0.825186 2.0629662.050686 1.845618 1.757731 1.476494 1.230412 1.054639 0.922809 0.820275 2.0506862.038843 1.834959 1.74758 1.467967 1.223306 1.048548 0.917479 0.815537 2.0388432.027423 1.824681 1.737791 1.459744 1.216454 1.042675 0.91234 0.810969 2.0274232.016414 1.814773 1.728355 1.451818 1.209849 1.037013 0.907386 0.806566 2.0164142.005806 1.805225 1.719262 1.44418 1.203484 1.031557 0.902613 0.802322 2.0058061.995587 1.796029 1.710503 1.436823 1.197352 1.026302 0.898014 0.798235 1.9955871.985748 1.787173 1.70207 1.429739 1.191449 1.021242 0.893587 0.794299 1.9857481.976278 1.778651 1.693953 1.42292 1.185767 1.016372 0.889325 0.790511 1.9762781.967169 1.770452 1.686145 1.416362 1.180302 1.011687 0.885226 0.786868 1.9671691.958412 1.762571 1.678639 1.410057 1.175047 1.007183 0.881285 0.783365 1.9584121.949998 1.754998 1.671427 1.403999 1.169999 1.002856 0.877499 0.779999 1.9499981.94192 1.747728 1.664503 1.398182 1.165152 0.998702 0.873864 0.776768 1.941921.93417 1.740753 1.65786 1.392602 1.160502 0.994716 0.870377 0.773668 1.93417
1.926742 1.734067 1.651493 1.387254 1.156045 0.990896 0.867034 0.770697 1.9267421.919628 1.727665 1.645395 1.382132 1.151777 0.987237 0.863832 0.767851 1.9196281.912822 1.72154 1.639561 1.377232 1.147693 0.983737 0.86077 0.765129 1.9128221.906318 1.715686 1.633987 1.372549 1.143791 0.980392 0.857843 0.762527 1.906318
As
unid
ades
de
Ks
e K
c es
tão
em K
N e
cm
As
unid
ades
de
Ks
e K
c es
tão
em K
N e
cm
Programa para o cálculo da área de aço em vigas de Concreto Armado
Dados de entrada
bw (cm) = 15 18 3599
Escolha o Aço
Para seus dados tem-se dmin (cm) = 24.158
Adote um valor para Kx 0.518
Você está trabalhando no Domínio 3.
Resultados: O valor para a deformação no CONCRETO é igual a 0.3500%
Cálculo de Psi. = 1 O valor para a deformação no AÇO é igual a 0.3257%
Cálculo de Kc. Kc = 2.78518Cálculo de Ks. Ks = 0.02901
Espaçamentos mínimos exigidosCálculo de d. d = 25.8507 cm
Cálculo de As. As = 4.039 cm² Vertical Horizontal
Bitolas usuais Dimensão máxima dos grãos - dmáx (mm)Bitola usual
Caso seu dmáx (mm) não esteja entre os dados, digite-o aqui:
Sua seção contará com 6
barras de aço submetidas ao esforço de tração. 2 2
Totalizando: 4.712 cm² de área. 1 1
0.95 2.28
Armadura mínima de tração - NB-1
0.582 2 cm 2.28 cm
Bitola usual Seriam 2 barras.
Colocação das barras na seção
Entre com o valor da cobertura 'C' em cm: 3 Qual o diâmetro do estribo utilizado (mm): 8
Cálculo da altura (h) da viga
Número de barras na fileira inferior 2Número de fileiras com o número máximo de barras = 3Número de barras que completam o total de barras tracionadas 0 7.300Número total de fileiras na horizontal 3
Sua viga deve ter no mínimo 33.15 centímetros de altura.
Criado por Walter Luiz (2001)
Sua seção contará com 3 fileiras de 2 barras dispostas na base da nervura, separadas 5.4 centímetros uma da outra na horizontal. Estas estarão separadas de 2 centímetros na vertical.
Distância (cm) do centróide da armadura de aço à base da viga.
CA 25 - A CA 50 - A CA 60 - B
ASmin =
eh ≥ ¿ {2 cm ¿ {φ ¿ ¿¿eV ≥ ¿ {2 cm ¿ {φ ¿¿¿eV = eh =
d
bw
As
Ch
M d ( kN . cm)=f ck ( MPa ) =
Programa para o cálculo da área de aço em vigas de Concreto Armado
Dados geométricos da seção
bw (cm) = 15d' (cm) = 4
Tabela ao lado
Escolha o Aço
Dados Mecânicos
500
Área de aço da armadura de tração - As =
Observação: Cuidado com as unidades!!! Área de aço da armadura de Compressão-As' =
O valor de Kc para seus dados é igual a 60.75 Bitolas usuais
Escolha a bitola para As (mm)
0.628 Sua seção contará com 3
Totalizando: 2.356 cm² de área.
Espaçamentos mínimos exigidos
VerticalDimensão máxima dos grãos - dmáx (mm)
Caso seu dmáx (mm) não esteja entre os dados, digite-o aqui:
Armadura mínima de tração - NB-1 2
1.013 1
0.95
Bitola usual Seriam 2 barras. 2 cm
Colocação das barras na seção
Entre com o valor da cobertura 'c' em cm: 2.5 Qual o diâmetro do estribo utilizado (mm):
Com este valor de Kc (para o fck desejado), vá até a tabela ao lado e colha o valor de Kx mais próximo e
digite-o no espaço abaixo.
barras de aço submetidas ao esforço de tração.
CA 25 - A CA 50 - A
ASmin = eV ≥ ¿ {2 cm ¿ {φ ¿¿¿
eV =
d
bwd'
As
As'Ch
M d ( kN . cm)= f ck ( MPa ) =
σ ' sd (kN /cm2 )=
Cálculo da altura (h) da viga
Número de barras na fileira inferior 3
Número de fileiras com o número máximo de barras 1
Número de barras que completam o total de barras tracionadas 0
Número total de fileiras na horizontal 1
Sua viga deve ter no mínimo 48.50 centímetros de altura.
Sua seção contará com 1 fileira de 3 barras dispostas na base da nervura, separadas 3 centímetros uma da outra na horizontal.
Programa para o cálculo da área de aço em vigas de Concreto Armado
Dados geométricos da seção
d (cm) = 45 Valores de
43.5 Tabela ao lado Relação d'/d CA 50 A CA 50 B
Escolha o Aço 0.05
43.5
40.5
0.1 39.10.15 37.50.2 35.5
Dados MecânicosKx Kc
18 dmin (cm) 9.004 0.01 1850.189
0.02 467.8967
Área de aço da armadura de tração - As = 1.799 cm² 0.03 210.4858
Área de aço da armadura de Compressão-As' = 0 cm² 0.04 119.9169
0.05 77.78496
Bitolas usuais 0.06 54.788660.07 40.8603
Escolha a bitola para As' (mm) 0.08 31.78309
0.09 25.53723
0.1 21.05615
Sua seção contará com 0 0.11 17.73327
0.12 15.2028
Totalizando: 0.000 cm² de área. 0.13 13.23352
0.14 11.67344
Espaçamentos mínimos exigidos 0.15 10.4194
Horizontal 0.16 9.399444
Dimensão máxima dos grãos - dmáx (mm) 0.17 8.562163
Caso seu dmáx (mm) não esteja entre os dados, digite-o aqui: 0.18 7.867233
0.19 7.281582
2 0.2 6.781369
1 0.21 6.34922
2.28 0.22 5.972174
0.23 5.640365
2.28 cm 0.24 5.346149
0.25 5.0835150.26 4.909816
Colocação das barras na seção 0.27 4.749173
0.28 4.600188
Qual o diâmetro do estribo utilizado (mm): 5 0.29 4.461659
0.3 4.332541
Criado por Walter Luiz (2001)
barras de aço submetidas ao esforço de compressão.
CA 50 - A CA 60 - B
σ ' sd (KN /cm2)
eh ≥ ¿ {2 cm ¿ {φ ¿ ¿¿eh =
f ck ( MPa ) =
σ ' sd (kN /cm2 )=
0.31 4.211927
0.32 4.099021
0.33 3.993125
0.34 3.893624
Cálculo da altura (h) da viga 0.35 3.79997
0.36 3.711679
0.37 3.628318
0.38 3.5495
0.39 3.474878
3.500 0.4 3.404139
0.41 3.337002
0.42 3.273211
centímetros de altura. 0.43 3.212535
0.44 3.1547630.45 3.0997040.46 3.0471840.47 2.9970410.48 2.9491310.49 2.9033170.5 2.859477
0.51 2.8174960.52 2.777270.53 2.73870.54 2.7016980.55 2.6661790.56 2.6320670.57 2.5992880.58 2.5677780.59 2.5374720.6 2.508313
0.61 2.4802470.62 2.4532230.63 2.4271940.64 2.4021150.65 2.3779440.66 2.3546420.67 2.3321730.68 2.3105020.69 2.2895970.7 2.269426
0.71 2.2499620.72 2.2311780.73 2.2130460.74 2.1955440.75 2.178649
Sua seção contará com 1 fileira de 3 barras dispostas na base da nervura, separadas 3 centímetros uma da outra na horizontal.
Distância (cm) do centróide da armadura de aço à base da viga.
0.76 2.1623390.77 2.1465930.78 2.1313930.79 2.116720.8 2.102557
0.81 2.0888870.82 2.0756950.83 2.0629660.84 2.0506860.85 2.0388430.86 2.0274230.87 2.0164140.88 2.0058060.89 1.9955870.9 1.985748
0.91 1.9762780.92 1.9671690.93 1.9584120.94 1.9499980.95 1.941920.96 1.934170.97 1.9267420.98 1.9196280.99 1.912822
1 1.906318
2 50
Md,c = 12488.06 Aço Kx (lim)CA 25 A 0.77
Valores de Delta Md = -11988.06 CA 50 A 0.63
CA 60 B 0.44
CA 60
46.9
44.942.439 Kc do problema
60.75
Kx adotado para o problema0.628
Kc para os cálculos
2.432322
Ks limite
0.030716
Cálculo da distribuição das barras
3.44 3
Espaçamento horizontal real
3.00 3
Número de fileiras horizontais completas
1
Barras que sobram
0
Número de fileiras horizontais no total
1
1 fileira de
σ ' sd (KN /cm2)
Sua seção contará com 3 barras dispostas na base da nervura, separadas
Kc (lim) Kc(lim)2.14659344 2.432322 Bitolas usuais (mm)As As' As min Aço utiliz
2.43232239 0.628 10 1 1 2 10
3.15476293 Aço usado 12.5
A 16
2022.225.4
Kc do problema
1 1 1.252.290572 0 0.825059
Kx adotado para o problema 3 0 1
Dimensão dos agregados
Kc para os cálculos Ks2 9.5 3 1.9 1
0.023 15
19Ks limite Ks' 25
0.022989 38
50
Cálculo da distribuição das barras
Espaçamento horizontal real
Número de fileiras horizontais completas
Número de fileiras horizontais no total
barras dispostas na base da nervura, separadas 3.00 centímetros uma da outra na horizontal.
Aço utiliz 2
10
Programa para o cálculo do momento máximo em vigas de Concreto Armado
Dados de entrad
18 h (cm) = 30
Qual o tipo de AÇO utilizado?
Qual o tipo de armação da viga?
Quantas barras foram utilizadas na armadura de tração?
Quantas barras foram utilizadas na armadura de compressão?
Qual a bitola do AÇO submetido a tração? Qual a bitola do AÇO submetido a compressão?
Qual o valor do cobrimento de concreto 'C' (cm)? 2 Qual o valor da espessura do estribo (mm)?
Qual o tamanho do agregado utilizado (mm)? Caso seu dmáx (mm) não esteja entre os dados, digite-o aqui:
Informações sobre a colocação das armaduras de aço na viga
Armadura de tração - Cálculo de d
Qual o número de barras da fileira inferior? 2Para seus dados d vale
Quantas vezes esta mesma fileira se repete? 0
centímetros.Quantas barras sobram isoladas sobre estas fileiras? 1
Número total de fileiras na horizontal 2
Armadura de compressão - Cálculo de d'
Qual o número de barras da fileira superior? 2Para seus dados d' vale
Quantas vezes esta mesma fileira se repete? 0
centímetros.Quantas barras sobram isoladas sobre estas fileiras? 0
CA 25 - A CA 50 - A
d
bwd'
As
As'Ch
f ck ( MPa ) =
Número total de fileiras na horizontal 1
d'/d
Relação d'/d ### 0.05
0.1
Na tabela ao lado pegue o valor de 0.15
43.5 0.2
O momento máximo suportado pela viga é de 4115.6 kN.cm4.12 tf.m
σ ' sd (kN /cm2 )=
Programa para o cálculo do momento máximo em vigas de Concreto Armado
bw (cm) = 15
Qual o tipo de AÇO utilizado?
Qual o tipo de armação da viga?
Quantas barras foram utilizadas na armadura de tração? 3
Quantas barras foram utilizadas na armadura de compressão? 2
Qual a bitola do AÇO submetido a compressão?
Qual o valor da espessura do estribo (mm)? 5
Caso seu dmáx (mm) não esteja entre os dados, digite-o aqui:
Informações sobre a colocação das armaduras de aço na viga
Armadura de tração - Cálculo de d
Para seus dados d vale
25.833centímetros.
Armadura de compressão - Cálculo de d'
Para seus dados d' vale
centímetros.
Criado por Walter Luiz (2001)
CA 60 - B
CA 50 CA 60
43.5
46.9
44.9
42.4
39
ou
2 50 Escolhidos
Aço Kx (lim) Kc (lim) Kx (lim) Kc(lim)
CA 25 A 0.77 2.1465934 0.628 2.432322 Aço utiliz
CA 50 A 0.63 2.4323224 10 4CA 60 B 0.44 3.1547629 Aço usado 12.5 2
A 1620
22.225.4
Ks limite 0.0307158 As9.424777961
Ks2 0.023
Ks' 0.0229885 Dimensão dos agregados
9.5 2Delta Md = 0 15
Md,c = 4115.5797 19
#VALUE! 25
38
50
Bitolas usuais (mm)
Escolhida
Aço utiliz 2 1 Armadura Simples 1
1 2 Armadura Dupla1
Armadura de Tração
n= 2 Cálculo da distância do centróide inferior ao estribo inferiorAs' N= 0
1.5707963 n'= 1 1.666667n''= 2
Dimensão dos agregados Espaçamento vertical Armadura de Compressão
1.5 22 n= 2 Cálculo da distância do centróide superior ao estribo inferior
0.75 N= 0
2 n'= 0 0
n''= 1 1
Armadura de Tração
Cálculo da distância do centróide inferior ao estribo inferior
Cálculo da distância do centróide superior ao estribo inferior
Programa para o cálculo da armadura transversal em vigas de Concreto Armado
h (cm) d (cm)
15 18 50 25.85068 3599
15 18 50 70 51 456 144.2
90 Graus Verificação das bielas de compressão
0.18806 kN/cm² 0.321429 kN/cm²
Cálculo das armaduras transversais
Taxa geométrica
Quantas barras chegam ao apoio? 2
Qual a bitola destas barras?
Criado por Walter Luiz (2001)
Onde (com qual planilha) foi determinada a armação da viga?
Digite, nas células de cor cinza, os dados que faltam. Cuidado com as unidades!!!
bw (cm) Fck (MPa)
Aço (kN/cm²)
Md (kN.cm) Vd1 (kN)
No apoio seguinte (Vd2) =
a =
twd = twu =
Área de aço que chega na face do apoio, tem que ser no
mínimo:
sAs' e As
b
h
h/2
b/2
Vão da viga - L
1.5708 cm²
0.0332 kN/cm² 0.1867 kN/cm² 0.1816
Verificação
Cálculo dos estribos Verificações
0.06264 cm²/cm 0.14%
Espaçamentos
S = 9.95 cm
Determinação do ponto a partir do qual se pode colocar a armadura mínima
62.46 kN Este valor de cortante é aplicado a uma distância de
centímetros do centro do apoio.
A partir deste ponto, podemos colocar a armadura mínima de estribo, ou seja, a cadaaté o ponto simétrico a este.
Ancoragem em apoios centrais
Qual a bitola das barras de ancoragem? Região?
71.12 cm 61.04 cm
Ancoragem em apoios externos
0.85 0.50 75.6 kN
39.36 cm Verificação:
OK!!!
As1 = r1 =
tc = twd = td =
O valor, para pw, encontrado é MAIOR que o mínimo da norma, por isso está OK!.
Asw/S = bw seno(a) =
Bitola do estribo - F (mm)
Vd (mínimo) =
Lb1 = Lb =
h = al/d= Vd =
Lbapoio =
lb ≥ ¿ {10 cm ¿ {10 φ ¿¿¿
lb ≥ ¿ {10 cm ¿ {10 φ ¿¿¿
Programa para o cálculo da armadura transversal em vigas de Concreto Armado 1
Arm. Simples
Arm. Dupla
Nenhuma
4.712 4.039
-144.2 3.6815 3.16
Dados complementares sobre a viga.
L (cm) = 10000 b (cm) = 23
Cortantes importantes.
144.2 kN
-144.2 kN
Na face do apoio = 143.8683 kN
À distância h/2 = 142.8589 kN
Verificação das bielas de compressão
Resultado
Twu > Twd OK!!!
Cálculo das armaduras transversais
1.227 cm²
Criado por Walter Luiz (2001)
Onde (com qual planilha) foi determinada a armação da viga?
Digite, nas células de cor cinza, os dados que faltam. Cuidado com as unidades!!!
Vd2 (kN) As exist (cm²)
As calc (cm²)
No apoio (Vd1) =
No apoio seguinte (Vd2) =
Área de aço que chega na face do apoio, tem que ser no
mínimo:
AS 1 ≥13
AS
0.150% 0.24744
kN/cm² 0.00418
0.0210 cm²/cm
25.5 cm
Determinação do ponto a partir do qual se pode colocar a armadura mínima
Este valor de cortante é aplicado a uma distância de 2834.17centímetros do centro do apoio.
A partir deste ponto, podemos colocar a armadura mínima de estribo, ou seja, a cada 25.50 centímetrosaté o ponto simétrico a este.
Ancoragem em apoios centrais
15.28 kgf/cm²
Ancoragem em apoios externos
0.87 cm²
10 cm23.71 cm
y1 =
rw =
O valor, para pw, encontrado é MAIOR que o mínimo da norma, por isso está OK!.
É menor OK!!!
tbu =
As,cal =
S ≤ ¿ {30 cm ¿¿¿
lb ≥ ¿ {10 cm ¿ {10 φ ¿¿¿
lb ≥ ¿ {10 cm ¿ {10 φ ¿¿¿
Valores utilizados Vd1 144.2 Bitolas de estribo
Arm. Simples bw 15 h 70 5
Arm. Dupla fck 18 Vd2 -144.2 6.3
Nenhuma aço 50 Md 456 8
d 51 As 3.6815 10
d' 0 As calc 3.16 12.516
coeficiente para twu 1 20
condição 1
Condição de espaçamentopw adotado 0.00417583 25.5
Bitolas de barras Relação de distâncias para cortantes
10 1 5000
12.5 10 116 Região20 2
22.2 1.525
Escolhido
2 Estribo máximo
6.3 mm 12.5
0.63 cm
Área do estribo limites para 10
0.3117245 cm² 23.705185 1023.705185
Asw/S = 0.0626374
Condição de espaçamento
Barras de ancoragem
Relação de distâncias para cortantes 10 1
12.5 10 1
16Boa aderência 20Má aderência 22.2
25