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Projeto da Planilha Dados de entrada bw( cm) 30 h(cm) 50 η(%) 80 d=h.η 40 Concreto C80 Aço CA-50 fck 80 fyk 500 Es 210 Solicitação Normal Lista γc 1.4 γs 1.15 Dados calculados em função dos dados de entrada fcd 5.714 αc 0.723 fyd 43.478 εc2 2.516 εyd 2.070 εcu 2.604 εs_lim 4.8351 n 1.402 kx_lim 0.350 λ 0.725 Deformada εc (‰) εs (‰) kx k2 σcd (kN/cm²) σsd (kN/cm²) x (cm) y (cm) z (cm) Rcd (kN) Rsd (kN) Md (kN.m) As cm² As cm² 1 I2 0.000 10 0.000 0.000 0 43.478 0.000 0.000 40.000 0.000 0.000 0.000 0.000 0.000 2 Domínio 2a 0.252 10 0.025 0.137 0.567 43.478 0.982 0.712 39.644 12.106 12.106 4.799 0.278 0.278 3 Domínio 2a 0.503 10 0.048 0.269 1.109 43.478 1.916 1.389 39.305 46.230 46.230 18.171 1.063 1.063 4 Domínio 2a 0.755 10 0.070 0.394 1.625 43.478 2.807 2.035 38.983 99.200 99.200 38.671 2.282 2.282 5 Domínio 2a 1.006 10 0.091 0.511 2.112 43.478 3.657 2.651 38.674 167.957 167.957 64.956 3.863 3.863 6 Domínio 2a 1.258 10 0.112 0.622 2.567 43.478 4.469 3.240 38.380 249.485 249.485 95.752 5.738 5.738 7 Domínio 2a 1.509 10 0.131 0.723 2.986 43.478 5.246 3.803 38.098 340.720 340.720 129.809 7.837 7.837 8 Domínio 2a 1.761 10 0.150 0.815 3.366 43.478 5.989 4.342 37.829 438.398 438.398 165.841 10.083 10.083 9 Domínio 2a 2.012 10 0.168 0.895 3.696 43.478 6.701 4.858 37.571 538.765 538.765 202.418 12.392 12.392 10 Domínio 2a 2.264 10 0.185 0.960 3.965 43.478 7.384 5.354 37.323 636.825 636.825 237.683 14.647 14.647 11 fronteira 2a-2b 2.516 10 0.201 1 4.129 43.478 8.040 5.829 37.086 721.948 721.948 267.738 16.605 16.605 12 Domínio 2b 2.524 10 0.202 1 4.129 43.478 8.062 5.845 37.077 723.962 723.962 268.427 16.651 16.651 13 Domínio 2b 2.533 10 0.202 1 4.129 43.478 8.085 5.861 37.069 725.974 725.974 269.114 16.697 16.697 14 Domínio 2b 2.542 10 0.203 1 4.129 43.478 8.107 5.878 37.061 727.983 727.983 269.799 16.744 16.744 15 Domínio 2b 2.551 10 0.203 1 4.129 43.478 8.129 5.894 37.053 729.990 729.990 270.484 16.790 16.790 16 Domínio 2b 2.560 10 0.204 1 4.129 43.478 8.152 5.910 37.045 731.993 731.993 271.167 16.836 16.836 17 Domínio 2b 2.568 10 0.204 1 4.129 43.478 8.174 5.926 37.037 733.994 733.994 271.849 16.882 16.882 18 Domínio 2b 2.577 10 0.205 1 4.129 43.478 8.196 5.942 37.029 735.992 735.992 272.529 16.928 16.928 19 Domínio 2b 2.586 10 0.205 1 4.129 43.478 8.218 5.958 37.021 737.987 737.987 273.209 16.974 16.974 20 Domínio 2b 2.595 10 0.206 1 4.129 43.478 8.241 5.974 37.013 739.979 739.979 273.887 17.020 17.020 21 fronteira 23 2.604 10 0.207 1 4.129 43.478 8.263 5.991 37.005 741.969 741.969 274.564 17.065 17.065 22 Domínio 3 2.604 9.484 0.215 1 4.129 43.478 8.616 6.247 36.877 773.674 773.674 285.306 17.794 17.794 23 Domínio 3 2.604 8.967 0.225 1 4.129 43.478 9.000 6.525 36.737 808.210 808.210 296.915 18.589 18.589 24 Domínio 3 2.604 8.451 0.236 1 4.129 43.478 9.421 6.830 36.585 845.973 845.973 309.498 19.457 19.457 25 Domínio 3 2.604 7.934 0.247 1 4.129 43.478 9.883 7.165 36.417 887.438 887.438 323.183 20.411 20.411 26 Domínio 3 2.604 7.418 0.260 1 4.129 43.478 10.392 7.534 36.233 933.177 933.177 338.117 21.463 21.463 27 Domínio 3 2.604 6.901 0.274 1 4.129 43.478 10.957 7.944 36.028 983.887 983.887 354.476 22.629 22.629 28 Domínio 3 2.604 6.385 0.290 1 4.129 43.478 11.586 8.400 35.800 1040.426 1040.426 372.471 23.930 23.930 29 Domínio 3 2.604 5.868 0.307 1 4.129 43.478 12.293 8.912 35.544 1103.858 1103.858 392.354 25.389 25.389 30 Domínio 3 2.604 5.352 0.327 1 4.129 43.478 13.091 9.491 35.255 1175.528 1175.528 414.426 27.037 27.037 31 fronteira LIM 2.604 4.835 0.350 1 4.129 43.478 14.000 10.150 34.925 1257.150 1257.150 439.060 28.914 28.914 32 Domínio 3 2.604 4.559 0.364 1 4.129 43.478 14.540 10.542 34.729 1305.678 1305.678 453.450 30.031 30.031 33 Domínio 3 2.604 4.282 0.378 1 4.129 43.478 15.124 10.965 34.517 1358.103 1358.103 468.783 31.236 31.236 34 Domínio 3 2.604 4.006 0.394 1 4.129 43.478 15.757 11.424 34.288 1414.913 1414.913 485.147 32.543 32.543 35 Domínio 3 2.604 3.729 0.411 1 4.129 43.478 16.445 11.922 34.039 1476.684 1476.684 502.645 33.964 33.964 36 Domínio 3 2.604 3.453 0.430 1 4.129 43.478 17.196 12.467 33.767 1544.095 1544.095 521.389 35.514 35.514 37 Domínio 3 2.604 3.176 0.450 1 4.129 43.478 18.018 13.063 33.468 1617.955 1617.955 541.505 37.213 37.213 38 Domínio 3 2.604 2.900 0.473 1 4.129 43.478 18.923 13.719 33.140 1699.236 1699.236 563.133 39.082 39.082 39 Domínio 3 2.604 2.623 0.498 1 4.129 43.478 19.924 14.445 32.778 1789.115 1789.115 586.427 41.150 41.150 40 Domínio 3 2.604 2.347 0.526 1 4.129 43.478 21.037 15.252 32.374 1889.034 1889.034 611.559 43.448 43.448 41 fronteira 34 2.604 2.070 0.557 1 4.129 43.478 22.281 16.154 31.923 2000.773 2000.773 638.708 46.018 46.018 42 Domínio 4 2.604 1.863 0.583 1 4.129 39.130 23.314 16.903 31.549 2093.509 2093.509 660.475 53.501 53.501 43 Domínio 4 2.604 1.656 0.611 1 4.129 34.783 24.447 17.724 31.138 2195.260 2195.260 683.559 63.114 63.114 44 Domínio 4 2.604 1.449 0.642 1 4.129 30.435 25.696 18.630 30.685 2307.406 2307.406 708.033 75.815 75.815 45 Domínio 4 2.604 1.242 0.677 1 4.129 26.087 27.079 19.633 30.184 2431.628 2431.628 733.956 93.212 93.212 46 Domínio 4 2.604 1.035 0.716 1 4.129 21.739 28.620 20.750 29.625 2569.986 2569.986 761.364 118.219 118.219 47 Domínio 4 2.604 0.828 0.759 1 4.129 17.391 30.347 22.001 28.999 2725.039 2725.039 790.241 156.690 156.690 48 Domínio 4 2.604 0.621 0.807 1 4.129 13.043 32.295 23.414 28.293 2900.002 2900.002 820.496 222.334 222.334 49 Domínio 4 2.604 0.414 0.863 1 4.129 8.696 34.511 25.021 27.490 3098.975 3098.975 851.900 356.382 356.382 50 Domínio 4 2.604 0.207 0.926 1 4.129 4.348 37.053 26.864 26.568 3327.262 3327.262 883.992 765.270 765.270 51 F4 2.604 0 1.000 1 4.129 0.000 40.000 29.000 25.500 3591.857 3591.857 915.924 ERROR:#DIV/0! ERROR:#DIV/0! kx -Md 0 2.45384816118463E-2 4.7901532352872381E-2 7.01716341280883E-2 9.1423728039252306E-2 0.11172605688908398 0.13114089719871888 0.14972519728105652 0.16753113514124429 0.18460660771575055 0.20099566111047948 0.20155657707818617 0.20211670605140827 0.20267604968527636 0.20323460963028311 0.20379238753229939 0.20434938503259065 0.20490560376783271 0.20546104537012808 0.20601571146702172 0.20656960368151703 0.2153965799166874 0.22501160585527746 0.2355251450183288 0.24706931823265688 0.25980348481230553 0.27392164348476966 0.2896623850557129 0.30732248583073779 0.32727579646029614 0.35 0.36351051827437547 0.37810596855379403 0.39392250206176521 0.41112004593332668 0.4298877 3008248005 0.45045087159409547 0.47308006435517558 0.49810315340694827 0.52592122175915013 0.55703025106860904 0.58284868461761474 0.61117681952844982 0.64239928622897535 0.67698354311906306 0.71550344084363471 0.75867131666818 0.80738245273406151 0.86277783628778382 0.92633465943223914 1 0 4.7994194279772433 18.170996790750877 38.670654697980751 64.956095802040679 95.752153517552344 129.80894285501756 165.84133015221661 202.41840501728254 237.68338293898935 267.73836887573094 268.4266609440503 269.11366026461894 269.79937024353103 270.48379427541175 271.16693574346408 271.84879801951553 272.52938446406432 273.20869842632584 273.88674324427836 274.5635222447093 285.30572927233368 296.91462102841075 309.49813344184577 323.18257736266156 338.11661866534104 354.47629645378527 372.47138651519572 392.35350983394164 414.42649722698485 439.05963750000001 453.45013391121813 468.78257690162104 485.14724092755489 502.64507407624939 521.38891928699877 541.50472066517125 563.13257469578309 586.42736671504611 611.55852160274731 638.70801993643033 660.47481638475404 683.55860183609536 708.03252734840817 733.9562926529411 761.36353811906679 790.24130219335495 820.49636610744051 851.89951981340812 883.99181089170668 915.92357142857145 kx Md (kN.m) kx x As As cm² 0 2.45384816118463E-2 4.7901532352872381E-2 7.01716341280883E-2 9.1423728039252306E-2 0.11172605688908398 0.13114089719871888 0.14972519728105652 0.16753113514124429 0.18460660771575055 0.20099566111047948 0.20155657707818617 0.20211670605140827 0.202676049685276360.20323460963028311 0.20379238753229939 0.20434938503259065 0.20490560376783271 0.20546104537012808 0.20601571146702172 0.20656960368151703 0.2153965799166874 0.22501160585527746 0.2355251450183288 0.24706931823265688 0.25980348481230553 0.27392164348476966 0.2896623850557129 0.30732248583073779 0.32727579646029614 0.35 0.36351051 827437547 0.37810596855379403 0.39392250206176521 0.41112004593332668 0.42988773008248005 0.45045087159409547 0.47308006435517558 0.49810315340694827 0.52592122175915013 0.55703025106860904 0.58284868461761474 0.61117681952844982 0.64239928622897535 0.67698354311906306 0.71550344084363471 0.75867131666818 0.80738245273406151 0.86277783628778382 0.92633465943223914 0 0.27844342696447533 1.0632957069367825 2.2816002055163156 3.8629995691000047 5.738147804942983 7.8365527674797546 10.083142938829331 12.391600648000209 14.646968089992065 16.604797123988295 16.651135914566741 16.697409689394689 16.743618585206971 16.789762738355254 16.835842284809409 16.88185736015 8826 16.927808099613742 16.97369463800657 17.019517109793213 17.065275649054403 17.794496114777317 18.588819505491792 19.457371512500618 20.411066995920702 21.463071061231908 22.629410469880565 23.929795855926166 25.388744715510214 27.037141865604028 28.914450000000002 30.030590586052899 31.236360349857854 32.543007113542302 33.963742891819649 35.514192220238186 37.212969154753978 39.082428190841448 41.149653497221529 43.447779629982449 46.017780980030693 53.50079094902155 63.113719962194239 75.814783843687337 93.212413373042807 118.21936265772132 156.68974180168755 222.33351962339415 356.38209440644727 765.27020552629961 kx As (cm²) AUXILIAR-LISTAS 1 2 3 4 5 6 7 8 Concreto fck (M Pa) αc εc2 (‰) εcu (‰) n kx_lim εs_lim (‰) Concreto C20 20 0.85 2 3.5 2 0.45 4.278 C20 C25 25 0.85 2 3.5 2 0.45 4.278 C25 C30 30 0.85 2 3.5 2 0.45 4.278 C30 C35 35 0.85 2 3.5 2 0.45 4.278 C35 C40 40 0.85 2 3.5 2 0.45 4.278 C40 C45 45 0.85 2 3.5 2 0.45 4.278 C45 C50 50 0.85 2 3.5 2 0.45 4.278 C50 C55 55 0.829 2.199 3.125 1.751 0.35 5.804 C55 C60 60 0.808 2.288 2.884 1.590 0.35 5.355 C60 C65 65 0.786 2.357 2.737 1.491 0.35 5.082 C65 C70 70 0.765 2.416 2.656 1.437 0.35 4.933 C70 C75 75 0.744 2.468 2.618 1.412 0.35 4.861 C75 C80 80 0.723 2.516 2.604 1.402 0.35 4.835 C80 C85 85 0.701 2.559 2.600 1.400 0.35 4.829 C85 C90 90 0.680 2.600 2.600 1.400 0.35 4.829 C90 Concreto fck αc εc2 (‰) εcu (‰) n kx_lim εs_lim (‰) Concreto 1 2 3 4 5 6 7 8 1 2 3 Aço fyk (M Pa) Es (G Pa) CA-25 250 210 CA-50 500 210 CA-60 600 210 1 2 3 1 2 3 Solicitações γc γs Normais 1.4 1.15 Especiais ou de Construção 1.2 1.15 Excepcionais 1.2 1 1 2 3 Domínios de Deformação - Teoria Deformada εc (‰) εs (‰) 1 2 I2 0 10 aço no limite Domínio 2a 0 < εc < εc2 10 aço no limite 11 fronteira 2a-2b εc2 10 aço no limite Domínio 2b εc2 < εc < εcu 10 aço no limite 21 fronteira 23 εcu 10 aço no limite 3 Domínio 3 εcu εs_lim < εs < 10 escoamento do aço 31 fronteira LIM εcu εs_lim escoamento do aço Domínio 3 εcu εyd < εs < εs_lim escoamento do aço 41 fronteira 34 εcu εyd início do escoamento do aço 4 Domínio 4 εcu 0 < εs < εyd antes do escoamento (Lei de Hooke) 51 F4 εcu 0 antes do escoamento (Lei de Hooke)
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