Prévia do material em texto
CÁLCULOS DAS RESISTÊNCIAS MÓDULO DE ELASTICIDADE (OBTIDO DO ENSAIO) = 400 kgf/mm2 = 4000 N/mm2 = 4000 MPa = 4 Gpa X CONFIG. Canudos por seção Ix Iy ÁREA [mm2] RESISTÊNCIA À COMPRESSÃO Nres x [kgf] - Flambagem em torno de X COMPRESSÃO [N] - Flambagem em torno de X CONFIG. Canudos por seção TENSÃO RESITENTE PARA FLEXO-COMPRESSÃO COM FLEXÃO EM TORNO DE X [N/mm2 = MPa] Comprimento [cm] Comprimento [cm] Comprimento [cm] 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 13 13.5 14 14.5 15 15.5 16 16.5 17 17.5 18 18.5 19 19.5 20 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 13 13.5 14 14.5 15 15.5 16 16.5 17 17.5 18 18.5 19 19.5 20 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 13 13.5 14 14.5 15 15.5 16 16.5 17 17.5 18 18.5 19 19.5 20 1 1 5.69 5.69 1.9 1.3 1.1 0.9 0.8 0.7 0.6 0.5 0.4 0.4 0.4 0.3 0.3 0.3 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 13 11 9 8 7 6 5 4 4 4 3 3 3 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 6.8 5.6 4.7 4.0 3.5 3.0 2.7 2.3 2.1 1.9 1.7 1.5 1.4 1.3 1.2 1.1 1.0 0.9 0.9 0.8 0.8 0.7 0.7 0.6 0.6 0.6 0.5 0.5 0.5 0.4 0.4 2 2 35.31 11.38 3.8 8.1 6.7 5.6 4.8 4.1 3.6 3.1 2.8 2.5 2.2 2.0 1.8 1.7 1.5 1.4 1.3 1.2 1.1 1.0 1.0 0.9 0.8 0.8 0.7 0.7 0.7 0.6 0.6 0.6 0.5 0.5 81 67 56 48 41 36 31 28 25 22 20 18 17 15 14 13 12 11 10 10 9 8 8 7 7 7 6 6 6 5 5 2 2 21.1 17.4 14.6 12.5 10.7 9.4 8.2 7.3 6.5 5.8 5.3 4.8 4.3 4.0 3.7 3.4 3.1 2.9 2.7 2.5 2.3 2.2 2.1 1.9 1.8 1.7 1.6 1.5 1.5 1.4 1.3 3 3 41.00 41.00 5.7 9.4 7.7 6.5 5.5 4.8 4.2 3.7 3.2 2.9 2.6 2.3 2.1 1.9 1.8 1.6 1.5 1.4 1.3 1.2 1.1 1.0 1.0 0.9 0.9 0.8 0.8 0.7 0.7 0.6 0.6 0.6 94 77 65 55 48 42 37 32 29 26 23 21 19 18 16 15 14 13 12 11 10 10 9 9 8 8 7 7 6 6 6 3 3 16.3 13.5 11.3 9.6 8.3 7.2 6.4 5.6 5.0 4.5 4.1 3.7 3.4 3.1 2.8 2.6 2.4 2.2 2.1 1.9 1.8 1.7 1.6 1.5 1.4 1.3 1.3 1.2 1.1 1.1 1.0 4 4 70.62 70.62 7.7 16.1 13.3 11.2 9.5 8.2 7.2 6.3 5.6 5.0 4.5 4.0 3.7 3.3 3.0 2.8 2.6 2.4 2.2 2.1 1.9 1.8 1.7 1.6 1.5 1.4 1.3 1.2 1.2 1.1 1.1 1.0 161 133 112 95 82 72 63 56 50 45 40 37 33 30 28 26 24 22 21 19 18 17 16 15 14 13 12 12 11 11 10 4 4 21.1 17.4 14.6 12.5 10.7 9.4 8.2 7.3 6.5 5.8 5.3 4.8 4.3 4.0 3.7 3.4 3.1 2.9 2.7 2.5 2.3 2.2 2.1 1.9 1.8 1.7 1.6 1.5 1.5 1.4 1.3 5 5 172.03 76.31 9.6 39.3 32.5 27.3 23.2 20.0 17.5 15.3 13.6 12.1 10.9 9.8 8.9 8.1 7.4 6.8 6.3 5.8 5.4 5.0 4.7 4.4 4.1 3.8 3.6 3.4 3.2 3.0 2.9 2.7 2.6 2.5 393 325 273 232 200 175 153 136 121 109 98 89 81 74 68 63 58 54 50 47 44 41 38 36 34 32 30 29 27 26 25 5 5 41.0 33.9 28.5 24.3 20.9 18.2 16.0 14.2 12.7 11.4 10.3 9.3 8.5 7.8 7.1 6.6 6.1 5.6 5.2 4.9 4.6 4.3 4.0 3.8 3.5 3.3 3.2 3.0 2.8 2.7 2.6 6 1 6 260.62 82.01 11.5 59.5 49.2 41.3 35.2 30.4 26.4 23.2 20.6 18.4 16.5 14.9 13.5 12.3 11.2 10.3 9.5 8.8 8.2 7.6 7.1 6.6 6.2 5.8 5.5 5.1 4.9 4.6 4.3 4.1 3.9 3.7 595 492 413 352 304 264 232 206 184 165 149 135 123 112 103 95 88 82 76 71 66 62 58 55 51 49 46 43 41 39 37 6 1 6 51.8 42.8 36.0 30.6 26.4 23.0 20.2 17.9 16.0 14.3 12.9 11.7 10.7 9.8 9.0 8.3 7.7 7.1 6.6 6.2 5.8 5.4 5.1 4.8 4.5 4.2 4.0 3.8 3.6 3.4 3.2 6 2 6 225.59 105.94 11.5 51.5 42.6 35.8 30.5 26.3 22.9 20.1 17.8 15.9 14.3 12.9 11.7 10.6 9.7 8.9 8.2 7.6 7.1 6.6 6.1 5.7 5.4 5.0 4.7 4.5 4.2 4.0 3.8 3.6 3.4 3.2 515 426 358 305 263 229 201 178 159 143 129 117 106 97 89 82 76 71 66 61 57 54 50 47 45 42 40 38 36 34 32 6 2 6 44.8 37.1 31.1 26.5 22.9 19.9 17.5 15.5 13.8 12.4 11.2 10.2 9.3 8.5 7.8 7.2 6.6 6.1 5.7 5.3 5.0 4.7 4.4 4.1 3.9 3.7 3.5 3.3 3.1 2.9 2.8 7 7 183.41 183.42 13.4 41.9 34.6 29.1 24.8 21.4 18.6 16.4 14.5 12.9 11.6 10.5 9.5 8.7 7.9 7.3 6.7 6.2 5.7 5.3 5.0 4.7 4.4 4.1 3.8 3.6 3.4 3.2 3.1 2.9 2.8 2.6 419 346 291 248 214 186 164 145 129 116 105 95 87 79 73 67 62 57 53 50 47 44 41 38 36 34 32 31 29 28 26 7 7 31.2 25.8 21.7 18.5 15.9 13.9 12.2 10.8 9.6 8.7 7.8 7.1 6.5 5.9 5.4 5.0 4.6 4.3 4.0 3.7 3.5 3.3 3.1 2.9 2.7 2.6 2.4 2.3 2.2 2.1 2.0 8 1 8 332.69 236.97 15.3 75.9 62.8 52.7 44.9 38.7 33.8 29.7 26.3 23.4 21.0 19.0 17.2 15.7 14.4 13.2 12.2 11.2 10.4 9.7 9.0 8.4 7.9 7.4 7.0 6.6 6.2 5.9 5.5 5.3 5.0 4.7 759 628 527 449 387 338 297 263 234 210 190 172 157 144 132 122 112 104 97 90 84 79 74 70 66 62 59 55 53 50 47 8 1 8 49.6 41.0 34.4 29.3 25.3 22.0 19.4 17.2 15.3 13.7 12.4 11.2 10.2 9.4 8.6 7.9 7.3 6.8 6.3 5.9 5.5 5.2 4.8 4.6 4.3 4.0 3.8 3.6 3.4 3.3 3.1 8 2 8 524.13 141.25 15.3 119.6 98.9 83.1 70.8 61.0 53.2 46.7 41.4 36.9 33.1 29.9 27.1 24.7 22.6 20.8 19.1 17.7 16.4 15.3 14.2 13.3 12.5 11.7 11.0 10.4 9.8 9.2 8.7 8.3 7.9 7.5 1196 989 831 708 610 532 467 414 369 331 299 271 247 226 208 191 177 164 153 142 133 125 117 110 104 98 92 87 83 79 75 8 2 8 78.1 64.6 54.3 46.2 39.9 34.7 30.5 27.0 24.1 21.6 19.5 17.7 16.1 14.8 13.6 12.5 11.6 10.7 10.0 9.3 8.7 8.1 7.6 7.2 6.8 6.4 6.0 5.7 5.4 5.1 4.9 9 1 9 338.38 338.38 17.2 77.2 63.8 53.6 45.7 39.4 34.3 30.2 26.7 23.8 21.4 19.3 17.5 16.0 14.6 13.4 12.4 11.4 10.6 9.9 9.2 8.6 8.0 7.5 7.1 6.7 6.3 6.0 5.6 5.3 5.1 4.8 772 638 536 457 394 343 302 267 238 214 193 175 160 146 134 124 114 106 99 92 86 80 75 71 67 63 60 56 53 51 48 9 1 9 44.8 37.1 31.1 26.5 22.9 19.9 17.5 15.5 13.8 12.4 11.2 10.2 9.3 8.5 7.8 7.2 6.6 6.1 5.7 5.3 5.0 4.7 4.4 4.1 3.9 3.7 3.5 3.3 3.1 2.9 2.8 9 2 9 481.96 194.80 17.2 110.0 90.9 76.4 65.1 56.1 48.9 43.0 38.1 34.0 30.5 27.5 24.9 22.7 20.8 19.1 17.6 16.3 15.1 14.0 13.1 12.2 11.4 10.7 10.1 9.5 9.0 8.5 8.0 7.6 7.2 6.9 1100 909 764 651 561 489 430 381 340 305 275 249 227 208 191 176 163 151 140 131 122 114 107 101 95 90 85 80 76 72 69 9 2 9 63.9 52.8 44.3 37.8 32.6 28.4 24.9 22.1 19.7 17.7 16.0 14.5 13.2 12.1 11.1 10.2 9.4 8.8 8.1 7.6 7.1 6.6 6.2 5.9 5.5 5.2 4.9 4.7 4.4 4.2 4.0 10 1 10 189.11 487.65 19.1 111.3 92.0 77.3 65.9 56.8 49.5 43.5 38.5 34.4 30.8 27.8 25.2 23.0 21.0 19.3 17.8 16.5 15.3 14.2 13.2 12.4 11.6 10.9 10.2 9.6 9.1 8.6 8.1 7.7 7.3 7.0 1113 920 773 659 568 495 435 385 344 308 278 252 230 210 193 178 165 153 142 132 124 116 109 102 96 91 86 81 77 73 70 10 1 10 58.1 48.1 40.4 34.4 29.7 25.8 22.7 20.1 17.9 16.1 14.5 13.2 12.0 11.0 10.1 9.3 8.6 8.0 7.4 6.9 6.5 6.1 5.7 5.3 5.0 4.7 4.5 4.2 4.0 3.8 3.6 10 2 10 640.61 296.21 19.1 146.2 120.9 101.6 86.5 74.6 65.0 57.1 50.6 45.1 40.5 36.6 33.2 30.2 27.6 25.4 23.4 21.6 20.1 18.7 17.4 16.2 15.2 14.3 13.4 12.7 11.9 11.3 10.7 10.1 9.6 9.1 1462 1209 1016 865 746 650 571 506 451 405 366 332 302 276 254 234 216 201 187 174 162 152 143 134 127 119 113 107 101 96 91 10 2 10 76.4 63.1 53.0 45.2 39.0 34.0 29.8 26.4 23.6 21.2 19.1 17.3 15.8 14.4 13.3 12.2 11.3 10.5 9.7 9.1 8.5 7.9 7.5 7.0 6.6 6.2 5.9 5.6 5.3 5.0 4.8 11 1 11 732.64 349.76 21.1 167.2 138.2 116.1 99.0 85.3 74.3 65.3 57.9 51.6 46.3 41.8 37.9 34.6 31.6 29.0 26.8 24.7 22.9 21.3 19.9 18.6 17.4 16.3 15.4 14.5 13.7 12.9 12.2 11.6 11.0 10.5 1672 1382 1161 990 853 743 653 579 516 463 418 379 346 316 290 268 247 229 213 199 186 174 163 154 145 137 129 122 116 110 105 11 1 11 79.4 65.6 55.2 47.0 40.5 35.3 31.0 27.5 24.5 22.0 19.9 18.0 16.4 15.0 13.8 12.7 11.7 10.9 10.1 9.4 8.8 8.3 7.8 7.3 6.9 6.5 6.1 5.8 5.5 5.2 5.0 11 2 11 872.78 254.04 21.1 199.2 164.7 138.4 117.9 101.7 88.5 77.8 68.9 61.5 55.2 49.8 45.2 41.2 37.7 34.6 31.9 29.5 27.3 25.4 23.7 22.1 20.7 19.5 18.3 17.2 16.3 15.4 14.6 13.8 13.1 12.5 1992 1647 1384 1179 1017 885 778 689 615 552 498 452 412 377 346 319 295 273 254 237 221 207 195 183 172 163 154 146 138 131 125 11 2 11 94.6 78.2 65.7 56.0 48.3 42.0 37.0 32.7 29.2 26.2 23.7 21.5 19.5 17.9 16.4 15.1 14.0 13.0 12.1 11.2 10.5 9.8 9.2 8.7 8.2 7.7 7.3 6.9 6.6 6.2 5.9 12 1 12 786.19 355.45 23.0 179.5 148.3 124.6 106.2 91.6 79.8 70.1 62.1 55.4 49.7 44.9 40.7 37.1 33.9 31.2 28.7 26.5 24.6 22.9 21.3 19.9 18.7 17.5 16.5 15.5 14.7 13.8 13.1 12.4 11.8 11.2 1795 1483 1246 1062 916 798 701 621 554 497 449 407 371 339 312 287 265 246 229 213 199 187 175 165 155 147 138 131 124 118 112 12 1 12 78.1 64.6 54.3 46.2 39.9 34.7 30.5 27.0 24.1 21.6 19.5 17.7 16.1 14.8 13.6 12.5 11.6 10.7 10.0 9.3 8.7 8.1 7.6 7.2 6.8 6.4 6.0 5.7 5.4 5.1 4.9 122 12 1259.64 331.52 23.0 287.5 237.6 199.7 170.1 146.7 127.8 112.3 99.5 88.7 79.7 71.9 65.2 59.4 54.4 49.9 46.0 42.5 39.4 36.7 34.2 31.9 29.9 28.1 26.4 24.9 23.5 22.2 21.0 19.9 18.9 18.0 2875 2376 1997 1701 1467 1278 1123 995 887 797 719 652 594 544 499 460 425 394 367 342 319 299 281 264 249 235 222 210 199 189 180 12 2 12 125.2 103.4 86.9 74.1 63.9 55.6 48.9 43.3 38.6 34.7 31.3 28.4 25.9 23.7 21.7 20.0 18.5 17.2 16.0 14.9 13.9 13.0 12.2 11.5 10.8 10.2 9.7 9.1 8.7 8.2 7.8 FATORES ENTRE COMPRIMENTOS 1.21 1.19 1.1736111111 1.1597633136 1.1479591837 1.1377777778 1.12890625 1.1211072664 1.1141975309 1.108033241 1.1025 1.0975056689 1.0929752066 1.0888468809 1.0850694444 1.0816 1.0784023669 1.0754458162 1.0727040816 1.0701545779 1.0677777778 1.0655567118 1.0634765625 1.0615243343 1.0596885813 1.0579591837 1.0563271605 1.0547845142 1.0533240997 1.0519395135 10.4615384615 Y CONFIG. Canudos por seção Ix Iy ÁREA [mm2] RESISTÊNCIA À COMPRESSÃO Nres y [kgf] - Flambagem em torno de Y COMPRESSÃO [N] - Flambagem em torno de Y CONFIG. Canudos por seção TENSÃO RESITENTE PARA FLEXO-COMPRESSÃO COM FLEXÃO EM TORNO DE Y [N/mm2 = MPa] Comprimento [cm] Comprimento [cm] Comprimento [cm] 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 13 13.5 14 14.5 15 15.5 16 16.5 17 17.5 18 18.5 19 19.5 20 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 13 13.5 14 14.5 15 15.5 16 16.5 17 17.5 18 18.5 19 19.5 20 5 6 7 8 10 12 14 15 20 hx hy wx wy 1 1 5.69 5.69 1.9 1.3 1.1 0.9 0.8 0.7 0.6 0.5 0.4 0.4 0.4 0.3 0.3 0.3 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 13 11 9 8 7 6 5 4 4 4 3 3 3 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 6.8 5.6 4.7 4.0 3.5 3.0 2.7 2.3 2.1 5 5 2.28 2.28 2 2 35.31 11.38 3.8 2.6 2.1 1.8 1.5 1.3 1.2 1.0 0.9 0.8 0.7 0.6 0.6 0.5 0.5 0.5 0.4 0.4 0.4 0.3 0.3 0.3 0.3 0.3 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 26 21 18 15 13 12 10 9 8 7 6 6 5 5 5 4 4 4 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 6.8 5.6 4.7 4.0 3.5 3.0 2.7 2.3 2.1 10 5 7.06 4.55 3 3 41.00 41.00 5.7 9.4 7.7 6.5 5.5 4.8 4.2 3.7 3.2 2.9 2.6 2.3 2.1 1.9 1.8 1.6 1.5 1.4 1.3 1.2 1.1 1.0 1.0 0.9 0.9 0.8 0.8 0.7 0.7 0.6 0.6 0.6 94 77 65 55 48 42 37 32 29 26 23 21 19 18 16 15 14 13 12 11 10 10 9 9 8 8 7 7 6 6 6 3 3 16.3 13.5 11.3 9.6 8.3 7.2 6.4 5.6 5.0 9.33 10 8.79 8.20 4 4 70.62 70.62 7.7 16.1 13.3 11.2 9.5 8.2 7.2 6.3 5.6 5.0 4.5 4.0 3.7 3.3 3.0 2.8 2.6 2.4 2.2 2.1 1.9 1.8 1.7 1.6 1.5 1.4 1.3 1.2 1.2 1.1 1.1 1.0 161 133 112 95 82 72 63 56 50 45 40 37 33 30 28 26 24 22 21 19 18 17 16 15 14 13 12 12 11 11 10 4 4 21.1 17.4 14.6 12.5 10.7 9.4 8.2 7.3 6.5 10 10 14.12 14.12 5 5 172.03 76.31 9.6 17.4 14.4 12.1 10.3 8.9 7.7 6.8 6.0 5.4 4.8 4.4 4.0 3.6 3.3 3.0 2.8 2.6 2.4 2.2 2.1 1.9 1.8 1.7 1.6 1.5 1.4 1.3 1.3 1.2 1.1 1.1 174 144 121 103 89 77 68 60 54 48 44 40 36 33 30 28 26 24 22 21 19 18 17 16 15 14 13 13 12 11 11 5 5 18.2 15.0 12.6 10.8 9.3 8.1 7.1 6.3 5.6 14.55 10 23.65 15.26 6 1 6 260.62 82.01 11.5 18.7 15.5 13.0 11.1 9.6 8.3 7.3 6.5 5.8 5.2 4.7 4.2 3.9 3.5 3.3 3.0 2.8 2.6 2.4 2.2 2.1 1.9 1.8 1.7 1.6 1.5 1.4 1.4 1.3 1.2 1.2 187 155 130 111 96 83 73 65 58 52 47 42 39 35 33 30 28 26 24 22 21 19 18 17 16 15 14 14 13 12 12 6 1 6 16.3 13.5 11.3 9.6 8.3 7.2 6.4 5.6 5.0 18.66 10 27.93 16.40 6 2 6 225.59 105.94 11.5 24.2 20.0 16.8 14.3 12.3 10.7 9.4 8.4 7.5 6.7 6.0 5.5 5.0 4.6 4.2 3.9 3.6 3.3 3.1 2.9 2.7 2.5 2.4 2.2 2.1 2.0 1.9 1.8 1.7 1.6 1.5 242 200 168 143 123 107 94 84 75 67 60 55 50 46 42 39 36 33 31 29 27 25 24 22 21 20 19 18 17 16 15 6 2 6 21.1 17.4 14.6 12.5 10.7 9.4 8.2 7.3 6.5 15 10 30.08 21.19 7 7 183.41 183.42 13.4 41.9 34.6 29.1 24.8 21.4 18.6 16.4 14.5 12.9 11.6 10.5 9.5 8.7 7.9 7.3 6.7 6.2 5.7 5.3 5.0 4.7 4.4 4.1 3.8 3.6 3.4 3.2 3.1 2.9 2.8 2.6 419 346 291 248 214 186 164 145 129 116 105 95 87 79 73 67 62 57 53 50 47 44 41 38 36 34 32 31 29 28 26 7 7 31.2 25.8 21.7 18.5 15.9 13.9 12.2 10.8 9.6 13.66 15 26.85 24.46 8 1 8 332.69 236.97 15.3 54.1 44.7 37.6 32.0 27.6 24.0 21.1 18.7 16.7 15.0 13.5 12.3 11.2 10.2 9.4 8.7 8.0 7.4 6.9 6.4 6.0 5.6 5.3 5.0 4.7 4.4 4.2 4.0 3.7 3.6 3.4 541 447 376 320 276 240 211 187 167 150 135 123 112 102 94 87 80 74 69 64 60 56 53 50 47 44 42 40 37 36 34 8 1 8 35.3 29.2 24.5 20.9 18.0 15.7 13.8 12.2 10.9 20 15 33.27 31.60 8 2 8 524.13 141.25 15.3 32.2 26.6 22.4 19.1 16.5 14.3 12.6 11.2 10.0 8.9 8.1 7.3 6.7 6.1 5.6 5.2 4.8 4.4 4.1 3.8 3.6 3.4 3.1 3.0 2.8 2.6 2.5 2.4 2.2 2.1 2.0 322 266 224 191 165 143 126 112 100 89 81 73 67 61 56 52 48 44 41 38 36 34 31 30 28 26 25 24 22 21 20 8 2 8 21.1 17.4 14.6 12.5 10.7 9.4 8.2 7.3 6.5 20 10 52.41 28.25 9 1 9 338.38 338.38 17.2 77.2 63.8 53.6 45.7 39.4 34.3 30.2 26.7 23.8 21.4 19.3 17.5 16.0 14.6 13.4 12.4 11.4 10.6 9.9 9.2 8.6 8.0 7.5 7.1 6.7 6.3 6.0 5.6 5.3 5.1 4.8 772 638 536 457 394 343 302 267 238 214 193 175 160 146 134 124 114 106 99 92 86 80 75 71 67 63 60 56 53 51 48 9 1 9 44.8 37.1 31.1 26.5 22.9 19.9 17.5 15.5 13.8 15 15 45.12 45.12 9 2 9 481.96 194.80 17.2 44.5 36.8 30.9 26.3 22.7 19.8 17.4 15.4 13.7 12.3 11.1 10.1 9.2 8.4 7.7 7.1 6.6 6.1 5.7 5.3 4.9 4.6 4.3 4.1 3.8 3.6 3.4 3.2 3.1 2.9 2.8 445 368 309 263 227 198 174 154 137 123 111 101 92 84 77 71 66 61 57 53 49 46 43 41 38 36 34 32 31 29 28 9 2 9 25.8 21.3 17.9 15.3 13.2 11.5 10.1 8.9 8.0 22.32 15 43.19 25.97 10 1 10 189.11 487.65 19.1 43.2 35.7 30.0 25.5 22.0 19.2 16.9 14.9 13.3 12.0 10.8 9.8 8.9 8.2 7.5 6.9 6.4 5.9 5.5 5.1 4.8 4.5 4.2 4.0 3.7 3.5 3.3 3.2 3.0 2.8 2.7 432 357 300 255 220 192 169 149 133 120 108 98 89 82 75 69 64 59 55 51 48 45 42 40 37 35 33 32 30 28 27 10 1 10 22.5 18.6 15.7 13.3 11.5 10.0 8.8 7.8 7.0 13.66 20 27.69 48.77 10 2 10 640.61 296.21 19.1 67.6 55.9 47.0 40.0 34.5 30.1 26.4 23.4 20.9 18.7 16.9 15.3 14.0 12.8 11.7 10.8 10.0 9.3 8.6 8.0 7.5 7.0 6.6 6.2 5.8 5.5 5.2 4.9 4.7 4.4 4.2 676 559 470 400 345 301 264 234 209 187 169 153 140 128 117 108 100 93 86 80 75 70 66 62 58 55 52 49 47 44 42 10 2 10 35.3 29.2 24.5 20.9 18.0 15.7 13.8 12.2 10.9 18.66 15 68.66 39.49 11 1 11 732.64 349.76 21.1 79.8 66.0 55.4 47.2 40.7 35.5 31.2 27.6 24.6 22.1 20.0 18.1 16.5 15.1 13.9 12.8 11.8 11.0 10.2 9.5 8.9 8.3 7.8 7.3 6.9 6.5 6.2 5.8 5.5 5.2 5.0 798 660 554 472 407 355 312 276 246 221 200 181 165 151 139 128 118 110 102 95 89 83 78 73 69 65 62 58 55 52 50 11 1 11 37.9 31.3 26.3 22.4 19.3 16.9 14.8 13.1 11.7 25 15 58.61 46.63 11 2 11 872.78 254.04 21.1 58.0 47.9 40.3 34.3 29.6 25.8 22.7 20.1 17.9 16.1 14.5 13.2 12.0 11.0 10.1 9.3 8.6 8.0 7.4 6.9 6.4 6.0 5.7 5.3 5.0 4.7 4.5 4.2 4.0 3.8 3.6 580 479 403 343 296 258 227 201 179 161 145 132 120 110 101 93 86 80 74 69 64 60 57 53 50 47 45 42 40 38 36 11 2 11 27.5 22.8 19.1 16.3 14.1 12.2 10.8 9.5 8.5 23.66 15 73.78 33.87 12 1 12 786.19 355.45 23.0 81.1 67.1 56.3 48.0 41.4 36.1 31.7 28.1 25.0 22.5 20.3 18.4 16.8 15.3 14.1 13.0 12.0 11.1 10.3 9.6 9.0 8.4 7.9 7.5 7.0 6.6 6.3 5.9 5.6 5.3 5.1 811 671 563 480 414 361 317 281 250 225 203 184 168 153 141 130 120 111 103 96 90 84 79 75 70 66 63 59 56 53 51 12 1 12 35.3 29.2 24.5 20.9 18.0 15.7 13.8 12.2 10.9 20 15 78.62 47.39 12 2 12 1259.64 331.52 23.0 75.7 62.5 52.6 44.8 38.6 33.6 29.6 26.2 23.4 21.0 18.9 17.2 15.6 14.3 13.1 12.1 11.2 10.4 9.7 9.0 8.4 7.9 7.4 6.9 6.5 6.2 5.8 5.5 5.2 5.0 4.7 757 625 526 448 386 336 296 262 234 210 189 172 156 143 131 121 112 104 97 90 84 79 74 69 65 62 58 55 52 50 47 12 2 12 32.9 27.2 22.9 19.5 16.8 14.6 12.9 11.4 10.2 23.66 15 106.48 44.20 Canudos por seção TRAÇÃO [kgf] TRAÇÃO [N] TENSÃO RESITENTE DE TRAÇÃO [kgf/mm2] TENSÃO RESITENTE DE TRAÇÃO [N/mm2] 1 6.8 68 3.55 35.52 2 13.6 136 3.55 35.52 3 20.4 204 3.55 35.52 4 27.2 272 3.55 35.52 5 34 340 3.55 35.52 6 40.8 408 3.55 35.52 7 47.6 476 3.55 35.52 8 54.4 544 3.55 35.52 9 61.2 612 3.55 35.52 10 68 680 3.55 35.52 11 74.8 720 3.55 35.52 12 81.6 816 3.55 35.52 PROPRIEDADES GEOMÉTRICAS 1 CANUDO D[mm] e [mm] d [mm] A [mm2] 5 0.125 4.75 1.91 res y [kgf] res x [kgf] Config. Canudos Ix Iy rel Ix rel Iy 0.9 0.9 1 5.7 5.7 6.205 2.000 1.8 5.6 2 35.3 11.4 1.161 3.602 6.5 6.5 3 41.0 41.0 1.722 1.722 11.2 11.2 4 70.6 70.6 2.436 1.081 12.1 27.3 5 172.0 76.3 1.515 1.075 VALOR DO ENSAIO 13.0 41.3 6 1 260.6 82.0 0.866 1.292 16.8 35.8 6 2 225.6 105.9 0.813 1.731 29.1 29.1 7 183.4 183.4 1.814 1.292 37.6 52.7 8 1 332.7 237.0 1.575 0.596 22.4 83.1 8 2 524.1 141.2 0.646 2.396 53.6 53.6 9 1 338.4 338.4 1.424 0.576 30.9 76.4 9 2 482.0 194.8 1.012 0.971 30.0 77.3 10 1 487.7 189.1 1.314 1.566 47.0 101.6 10 2 640.6 296.2 1.144 1.181 55.4 116.1 11 1 732.6 349.8 1.191 0.726 40.3 138.4 11 2 872.8 254.0 0.901 1.399 56.3 124.6 12 1 786.2 355.5 1.602 0.933 52.6 199.7 12 2 1259.6 331.5 RESUMO RESISTÊNCIAS E EXEMPLO MÓDULO DE ELASTICIDADE (OBTIDO DO ENSAIO) E = 400 kgf/mm2 = 4000 N/mm2 = 4000 MPa = 4 Gpa COEFICIENTE DE POISON n = 0,33 CÉCULAS COLORIDAS SÃO OS VALORES USADOS NO EXEMPLO ABAIXO CONFIG. Canudos por seção Nres = FORÇA NORMAL RESISTENTE À COMPRESSÃO [N] (menor valor entre Nres x e Nres y) Comprimento [cm] 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 13 13.5 14 14.5 15 15.5 16 16.5 17 17.5 18 18.5 19 19.5 20 1 1 13 11 9 8 7 6 5 4 4 4 3 3 3 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 2 2 26 21 18 15 13 12 10 9 8 7 6 6 5 5 5 4 4 4 3 3 3 3 3 2 2 2 2 2 2 2 2 3 3 94 77 65 55 48 42 37 32 29 26 23 21 19 18 16 15 14 13 12 11 10 10 9 9 8 8 7 7 6 6 6 4 4 161 133 112 95 82 72 63 56 50 45 40 37 33 30 28 26 24 22 21 19 18 17 16 15 14 13 12 12 11 11 10 5 5 174 144 121 103 89 77 68 60 54 48 44 40 36 33 30 28 26 24 22 21 19 18 17 16 15 14 13 13 12 11 11 6 1 6 187 155 130 111 96 83 73 65 58 52 47 42 39 35 33 30 28 26 24 22 21 19 18 17 16 15 14 14 13 12 12 6 2 6 242 200 168 143 123 107 94 84 75 67 60 55 50 46 42 39 36 33 31 29 27 25 24 22 21 20 19 18 17 16 15 7 7 419 346 291 248 214 186 164 145 129 116 105 95 87 79 73 67 62 57 53 50 47 44 41 38 36 34 32 31 29 28 26 8 1 8 541 447 376 320 276 240 211 187 167 150 135 123 112 102 94 87 80 74 69 64 60 56 53 50 47 44 42 40 37 36 34 8 2 8 322 266 224 191 165 143 126 112 100 89 81 73 67 61 56 52 48 44 41 38 36 34 31 30 28 26 25 24 22 21 20 9 1 9 772 638 536 457 394 343 302 267 238 214 193 175 160 146 134 124 114 106 99 92 86 80 75 71 67 63 60 56 53 51 48 9 2 9 445 368 309 263 227 198 174 154 137 123 111 101 92 84 77 71 66 61 57 53 49 46 43 41 38 36 34 32 31 29 28 10 1 10 432 357 300 255 220 192 169 149 133 120 108 98 89 82 75 69 64 59 55 51 48 45 42 40 37 35 33 32 30 28 27 10 2 10 676 559 470 400 345 301 264 234 209 187 169 153 140 128 117 108 100 93 86 80 75 70 66 62 58 55 52 49 47 44 42 11 1 11 798 660 554 472 407 355 312 276 246 221 200 181 165 151 139 128 118 110 102 95 89 83 78 73 69 65 62 58 55 52 50 11 2 11 580 479 403 343 296 258 227 201 179 161 145 132 120 110 101 93 86 80 74 69 64 60 57 53 50 47 45 42 40 38 36 12 1 12 811 671 563 480 414 361 317 281 250 225 203 184 168 153 141 130 120 111 103 96 90 84 79 75 70 66 63 59 56 53 51 12 2 12 757 625 526 448 386 336 296 262 234 210 189 172 156 143 131 121 112 104 97 90 84 79 74 69 65 62 58 55 52 50 47 CONFIG. Canudos por seção wx wy Mres = MOMENTO FLETOR RESISTENTE EM TORNO DE X [N.mm] Comprimento [cm] 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 13 13.5 14 14.5 15 15.5 16 16.5 17 17.5 18 18.5 19 19.5 20 1 1 2.28 2.28 15 13 11 9 8 7 6 5 5 4 4 4 3 3 3 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 2 2 7.06 4.55 149 123 103 88 76 66 58 51 46 41 37 34 31 28 26 24 22 20 19 18 17 15 15 14 13 12 11 11 10 10 9 3 3 8.79 8.20 143 118 99 85 73 64 56 50 44 40 36 32 30 27 25 23 21 20 18 17 16 15 14 13 12 12 11 10 10 9 9 4 4 14.12 14.12 297 246 207 176 152 132 116 103 92 82 74 67 61 56 52 48 44 41 38 35 33 31 29 27 26 24 23 22 21 20 19 5 5 23.65 15.26 970 802 674 574 495 431 379 336 299 269 243 220 200 183 168 155 144 133 124 115 108 101 95 89 84 79 75 71 67 64 61 6 1 6 27.93 16.40 1447 1196 1005 856 738 643 565 501 447 401 362 328 299 274 251 231 214 198 185 172 161 151 141 133 125 118 112 106 100 95 90 6 2 6 30.08 21.19 1348 1114 936 798 688 599 527 467 416 374 337 306 279 255 234 216 199 185 172 160 150 140 132 124 117 110 104 99 93 89 84 7 7 26.85 24.46 839 693 583 496 428 373 328 290 259 232 210 190 173 159 146 134 124 115 107 100 93 87 82 77 73 68 65 61 58 55 52 8 1 8 33.27 31.60 1650 1363 1146 976 842 733 644 571 509 457 412 374 341 312 286 264 244 226 210 196 183 172 161 151 143 135 127 121 114 108 103 8 2 8 52.41 28.25 4095 3384 2843 2423 2089 1820 1599 1417 1264 1134 1024 928 846 774 711 655 606 562 522 487 455 426 400 376 354 334 316 299 284 269 256 9 1 9 45.12 45.12 2023 1672 1405 1197 1032 899 790 700 624 560 506 459 418 382 351 324 299 277 258 241 225 210 198 186 175 165 156 148 140 133 126 9 2 9 43.19 25.97 2758 2279 1915 1632 1407 1226 1077 954 851 764 689 625 570 521 479 441 408 378 352 328 306 287 269 253 239 225 213 201 191 181 172 10 1 10 27.69 48.77 1610 1331 1118 953 821 716 629 557 497 446 402 365 333 304 280 258 238 221 205 191 179 168 157 148 139 131 124 118 111 106 101 10 2 10 68.66 39.49 5245 4335 3642 3104 2676 2331 2049 1815 1619 1453 1311 1189 1084 991 911 839 776 719 669 624 583 546 512 482 454 428 405 383 363 345 328 11 1 11 58.61 46.63 4655 3847 3233 2754 2375 2069 1818 1611 1437 1289 1164 1056 962 880 808 745 689 639 594 553 517 484 455 427 403 380 359 340 322 306 291 11 2 11 73.78 33.87 6980 5769 4847 4130 3561 3102 2727 2415 2154 1934 1745 1583 1442 1319 1212 1117 1033 957 890 830 776 726 682 641 604 570 539 510 483 459 436 12 1 12 78.62 47.39 6142 5076 4265 3634 3134 2730 2399 2125 1896 1701 1535 1393 1269 1161 1066 983 909 843 783 730 682 639 600 564 531 501 474 449 425 404 384 12 2 12 106.48 44.20 13328 11015 9255 7886 6800 5923 5206 4612 4113 3692 3332 3022 2754 2519 2314 2132 1972 1828 1700 1585 1481 1387 1302 1224 1153 1088 1028 974 923 876 833 Canudos por seção FORÇA NORMAL RESISTENTE À TRAÇÃ [N] 1 68 2 136 3 204 4 272 5 340 6 408 7 476 8 544 9 612 10 680 11 720 12 816 EXEMPLO: (ESTRUTURA DO FTOOL, ESFORÇOS SOLICITANTES E ABAIXO PLANILHA COM OS DIMENSIONAMENTOS) CARGA = 10 N CARGA = 10 N CARGA = 12 N BARRA Configuração L [cm] Nat [N] Mat [N.mm] Nres [N] Mres [N.mm] Nat / Nres + Mat / Mres SITUAÇÃO: | Nat / Nres + Mat / Mres | ≤ 1? BARRA Configuração L [cm] Nat Mat Nres Mres Nat / Nres + Mat / Mres SITUAÇÃO: Nat / Nres + Mat / Mres ≤1? BARRA No. Canudos L [cm] Nat Mat Nres Mres Nat / Nres + Mat / Mres SITUAÇÃO: Nat / Nres + Mat / Mres ≤1? 1 1 8.5 -7.03 -0.72 4 5 -1.70 NÃO OK 1 2 8.5 -7.06 -2.00 9 51 -0.82 OK 1 2 8.5 -8.47 -2.40 9 51 -0.99 OK 2 1 6 4.97 1.46 68 11 0.21 OK 2 1 6 5.01 1.1 68 11 0.18 OK 2 1 6 6.02 1.32 68 11 0.21 OK 3 1 6 0.06 3.10 68 11 0.29 OK 3 1 6 0.05 2.96 68 11 0.28 OK 3 1 6 0.06 3.55 68 11 0.33 OK 4 1 6 -9.82 -4.61 9 11 -1.52 NÃO OK 4 2 6 -9.62 -18.24 18 103 -0.71 OK 4 2 6 -11.55 -21.89 18 103 -0.85 OK 5 1 8.5 6.74 1.89 68 11 0.28 OK 5 1 8.5 6.39 0.9 68 11 0.18 OK 5 1 8.5 7.67 1.08 68 11 0.21 OK 6 1 6 5.07 4.27 38 11 0.53 OK 6 1 6 5.11 3.41 68 11 0.39 OK 6 1 6 6.13 4.09 68 11 0.47 OK 7 1 6 0.23 0 68 11 0.00 OK 7 1 6 0.79 0 68 11 0.01 OK 7 1 6 0.95 0 68 11 0.01 OK 1 2 3 4 5 6 7 MODELOS DE CÁLCULO (DOIS CASOS DE CARGAS 10 E 12 N): RESULTADOS - ESFORÇOS SOLICITANTES TODAS AS BARRAS COM 1 CANUDO E 10 N: RESULTADOS - ESFORÇOS SOLICITANTES BARRAS 1 E 4 COM 2 CANUDOS E RESTANTE COM 1 E 10 N: RESULTADOS - ESFORÇOS SOLICITANTES BARRAS 1 E 4 COM 2 CANUDOS E RESTANTE COM 1 E 12 N: FORÇAS NORMAIS [N]: MOMENTOS FLETORES [N.mm]: FORÇAS NORMAIS [N]: MOMENTOS FLETORES [N.mm]: FORÇAS NORMAIS [N]: MOMENTOS FLETORES [N.mm]: CONFIGURAÇÕES DE SEÇÕES INTRUÇÕES