Table 2.
Maximum stress average values (KPa) produced by orthodontic forces in tooth structure and dentine.
| Resorption (mm) | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | ||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Intrusion | Structure | a | 73.51 | 100.14 | 126.77 | 153.40 | 180.03 | 200.70 | 221.36 | 242.03 | 262.72 |
| 0.6 N/60 gf | m | 73.51 | 100.14 | 126.77 | 153.40 | 180.03 | 200.70 | 221.36 | 242.03 | 262.72 | |
| c | 109.41 | 135.97 | 162.52 | 189.08 | 215.63 | 227.40 | 239.18 | 250.95 | 262.72 | ||
| C | 145.20 | 162.81 | 180.42 | 198.02 | 215.63 | 227.40 | 239.18 | 250.95 | 262.72 | ||
| Dentine | a | 44.18 | 74.76 | 105.34 | 135.92 | 166.50 | 187.15 | 207.81 | 228.46 | 249.11 | |
| m | 44.18 | 74.76 | 105.34 | 135.92 | 166.50 | 187.15 | 207.81 | 228.46 | 249.11 | ||
| c | 107.50 | 130.48 | 153.45 | 176.43 | 199.40 | 211.83 | 224.26 | 236.68 | 249.11 | ||
| C | 54.28 | 57.66 | 61.04 | 64.41 | 67.79 | 69.88 | 71.97 | 74.06 | 76.15 | ||
| 1.2 N/120 gf | Structure | a | 147.02 | 200.28 | 253.54 | 306.80 | 360.05 | 401.39 | 442.72 | 484.05 | 525.44 |
| m | 147.02 | 200.28 | 253.54 | 306.80 | 360.05 | 401.39 | 442.72 | 484.05 | 525.44 | ||
| c | 218.82 | 271.93 | 325.04 | 378.15 | 431.25 | 454.80 | 478.35 | 501.90 | 525.44 | ||
| C | 290.40 | 325.62 | 360.83 | 396.05 | 431.25 | 454.80 | 478.35 | 501.90 | 525.44 | ||
| Dentine | a | 88.35 | 149.52 | 210.68 | 271.84 | 333.00 | 374.31 | 415.61 | 456.92 | 498.22 | |
| m | 88.35 | 149.52 | 210.68 | 271.84 | 333.00 | 374.31 | 415.61 | 456.92 | 498.22 | ||
| c | 215.00 | 260.95 | 306.90 | 352.85 | 398.80 | 423.66 | 448.51 | 473.37 | 498.22 | ||
| C | 108.56 | 115.32 | 122.07 | 128.83 | 135.57 | 139.76 | 143.94 | 148.12 | 152.30 | ||
| Extrusion | Structure | a | 73.51 | 100.14 | 126.77 | 153.40 | 180.03 | 200.70 | 221.36 | 242.03 | 262.72 |
| 0.6 N/60 gf | m | 73.51 | 100.14 | 126.77 | 153.40 | 180.03 | 200.70 | 221.36 | 242.03 | 262.72 | |
| c | 109.41 | 135.97 | 162.52 | 189.08 | 215.63 | 227.40 | 239.18 | 250.95 | 262.72 | ||
| C | 145.20 | 162.81 | 180.42 | 198.02 | 215.63 | 227.40 | 239.18 | 250.95 | 262.72 | ||
| Dentine | a | 44.18 | 74.76 | 105.34 | 135.92 | 166.50 | 187.15 | 207.81 | 228.46 | 249.11 | |
| m | 44.18 | 74.76 | 105.34 | 135.92 | 166.50 | 187.15 | 207.81 | 228.46 | 249.11 | ||
| c | 107.50 | 130.48 | 153.45 | 176.43 | 199.40 | 211.83 | 224.26 | 236.68 | 249.11 | ||
| C | 54.28 | 57.66 | 61.04 | 64.41 | 67.79 | 69.88 | 71.97 | 74.06 | 76.15 | ||
| 1.2 N/120 gf | Structure | a | 147.02 | 200.28 | 253.54 | 306.80 | 360.05 | 401.39 | 442.72 | 484.05 | 525.44 |
| m | 147.02 | 200.28 | 253.54 | 306.80 | 360.05 | 401.39 | 442.72 | 484.05 | 525.44 | ||
| c | 218.82 | 271.93 | 325.04 | 378.15 | 431.25 | 454.80 | 478.35 | 501.90 | 525.44 | ||
| C | 290.40 | 325.62 | 360.83 | 396.05 | 431.25 | 454.80 | 478.35 | 501.90 | 525.44 | ||
| Dentine | a | 88.35 | 149.52 | 210.68 | 271.84 | 333.00 | 374.31 | 415.61 | 456.92 | 498.22 | |
| m | 88.35 | 149.52 | 210.68 | 271.84 | 333.00 | 374.31 | 415.61 | 456.92 | 498.22 | ||
| c | 215.00 | 260.95 | 306.90 | 352.85 | 398.80 | 423.66 | 448.51 | 473.37 | 498.22 | ||
| C | 108.56 | 115.32 | 122.07 | 128.83 | 135.57 | 139.76 | 143.94 | 148.12 | 152.30 | ||
| Translation | Structure | a | 67.94 | 82.78 | 97.63 | 112.47 | 127.31 | 236.39 | 345.46 | 454.54 | 563.61 |
| 0.6 N/60 gf | m | 67.94 | 156.66 | 245.38 | 334.10 | 465.02 | 536.60 | 608.19 | 679.77 | 751.35 | |
| c | 202.41 | 257.51 | 312.62 | 367.72 | 422.82 | 458.02 | 493.22 | 528.41 | 563.61 | ||
| C | 202.42 | 236.42 | 270.41 | 304.41 | 338.40 | 363.43 | 388.47 | 413.50 | 438.53 | ||
| Dentine | a | 67.94 | 78.67 | 89.40 | 100.12 | 110.85 | 208.50 | 306.16 | 403.81 | 501.46 | |
| m | 67.94 | 160.53 | 253.13 | 345.72 | 438.31 | 516.57 | 594.83 | 673.09 | 751.35 | ||
| c | 200.11 | 250.38 | 300.65 | 350.91 | 401.18 | 441.88 | 482.57 | 523.27 | 563.96 | ||
| C | 67.94 | 69.55 | 71.16 | 72.77 | 74.38 | 87.45 | 100.51 | 113.58 | 126.64 | ||
| 1.2 N/120 gf | Structure | a | 135.88 | 165.57 | 195.25 | 224.94 | 254.61 | 472.77 | 690.92 | 909.07 | 1127.22 |
| m | 135.88 | 313.32 | 490.76 | 668.20 | 930.05 | 1073.21 | 1216.37 | 1359.54 | 1502.69 | ||
| c | 404.82 | 515.03 | 625.23 | 735.44 | 845.63 | 916.04 | 986.43 | 1056.83 | 1127.22 | ||
| C | 404.83 | 472.83 | 540.82 | 608.81 | 676.80 | 726.87 | 776.93 | 827.00 | 877.05 | ||
| Dentine | a | 135.88 | 157.34 | 178.79 | 200.25 | 221.69 | 417.01 | 612.31 | 807.62 | 1002.92 | |
| m | 135.88 | 321.07 | 506.25 | 691.44 | 876.62 | 1033.14 | 1189.66 | 1346.18 | 1502.69 | ||
| c | 400.21 | 500.76 | 601.29 | 701.83 | 802.36 | 883.75 | 965.14 | 1046.53 | 1127.93 | ||
| C | 135.88 | 139.10 | 142.32 | 145.54 | 148.76 | 174.89 | 201.02 | 227.15 | 253.28 | ||
| Rotation | Structure | a | 90.50 | 158.53 | 226.55 | 294.58 | 362.60 | 427.48 | 492.76 | 558.04 | 623.72 |
| 0.6 N/60 gf | m | 90.50 | 181.11 | 271.72 | 362.32 | 452.93 | 540.10 | 627.27 | 714.44 | 801.61 | |
| c | 179.20 | 292.80 | 406.40 | 520.00 | 633.60 | 653.38 | 673.17 | 692.95 | 712.73 | ||
| C | 356.62 | 358.12 | 359.61 | 361.11 | 362.60 | 383.41 | 404.22 | 425.03 | 445.84 | ||
| Dentine | a | 71.84 | 136.25 | 200.66 | 265.07 | 329.48 | 376.99 | 424.50 | 472.01 | 519.52 | |
| m | 71.84 | 159.55 | 247.27 | 334.99 | 422.70 | 489.96 | 557.21 | 624.47 | 691.72 | ||
| c | 169.46 | 267.67 | 365.89 | 464.10 | 562.31 | 565.96 | 569.62 | 573.27 | 576.92 | ||
| C | 169.43 | 174.34 | 179.24 | 184.15 | 189.65 | 186.04 | 182.42 | 178.81 | 175.19 | ||
| 1.2 N/120 gf | Structure | a | 181.00 | 317.05 | 453.10 | 589.15 | 725.20 | 854.96 | 985.52 | 1116.08 | 1247.45 |
| m | 181.00 | 362.22 | 543.43 | 724.65 | 905.86 | 1080.20 | 1254.54 | 1428.88 | 1603.23 | ||
| c | 358.40 | 585.60 | 812.80 | 1040.00 | 1267.20 | 1306.77 | 1346.33 | 1385.90 | 1425.46 | ||
| C | 713.24 | 716.23 | 719.22 | 722.21 | 725.20 | 766.82 | 808.44 | 850.06 | 891.67 | ||
| Dentine | a | 143.67 | 272.50 | 401.32 | 530.14 | 658.95 | 753.98 | 849.00 | 944.02 | 1039.04 | |
| m | 143.67 | 319.10 | 494.54 | 669.97 | 845.40 | 979.91 | 1114.42 | 1248.93 | 1383.44 | ||
| c | 338.91 | 535.35 | 731.77 | 928.20 | 1124.63 | 1131.93 | 1139.23 | 1146.54 | 1153.84 | ||
| C | 338.86 | 348.67 | 358.48 | 368.29 | 379.30 | 372.07 | 364.84 | 357.61 | 350.37 | ||
| Tipping | Structure | a | 61.67 | 90.71 | 119.74 | 148.78 | 177.81 | 232.79 | 287.76 | 342.74 | 397.71 |
| 0.6 N/60 gf | m | 61.67 | 101.79 | 141.91 | 182.03 | 222.15 | 299.15 | 376.14 | 453.14 | 530.13 | |
| c | 122.61 | 169.65 | 216.68 | 263.72 | 310.75 | 332.49 | 354.23 | 375.97 | 397.71 | ||
| C | 183.65 | 204.34 | 225.03 | 245.72 | 266.41 | 299.24 | 332.06 | 364.89 | 397.71 | ||
| Dentine | a | 60.01 | 89.00 | 118.00 | 147.00 | 176.00 | 228.50 | 281.00 | 333.50 | 386.00 | |
| m | 60.01 | 99.92 | 139.84 | 179.75 | 219.66 | 280.48 | 341.29 | 402.11 | 462.92 | ||
| c | 118.61 | 154.76 | 190.91 | 227.06 | 263.21 | 293.91 | 324.61 | 355.30 | 386.00 | ||
| C | 60.01 | 61.76 | 63.51 | 65.26 | 67.01 | 69.85 | 72.70 | 75.54 | 78.38 | ||
| 1.2 N/120 gf | Structure | a | 123.33 | 181.41 | 239.48 | 297.55 | 355.62 | 465.57 | 575.52 | 685.47 | 795.43 |
| m | 123.33 | 203.58 | 283.82 | 364.06 | 444.30 | 598.29 | 752.28 | 906.27 | 1060.26 | ||
| c | 245.23 | 339.29 | 433.36 | 527.43 | 621.50 | 664.98 | 708.46 | 751.94 | 795.43 | ||
| C | 367.30 | 408.68 | 450.06 | 491.44 | 532.81 | 598.47 | 664.12 | 729.77 | 795.43 | ||
| Dentine | a | 120.03 | 178.00 | 236.00 | 294.00 | 352.00 | 457.00 | 562.00 | 667.00 | 772.00 | |
| m | 120.03 | 199.85 | 279.67 | 359.50 | 439.33 | 560.95 | 682.58 | 804.21 | 925.83 | ||
| c | 237.21 | 309.52 | 381.82 | 454.12 | 526.42 | 587.82 | 649.21 | 710.61 | 772.00 | ||
| C | 120.03 | 123.52 | 127.02 | 130.52 | 134.02 | 139.71 | 145.39 | 151.08 | 156.77 |
Structure—stress displayed by the entire tooth structure. Dentine—stress displayed by the dentine component. a—root apical third, m—root middle third, c—root cervical third, C—crown.