Joint displacements — ULS3a
translations in mm, rotations in rad
| Joint | uX | uY | uZ | θX | θY | θZ |
|---|---|---|---|---|---|---|
| 1 | 0.0000 | 0.0000 | 0.0000 | 4.056e-5 | 4.488e-3 | 9.891e-5 |
| 2 | 0.0067 | 0.2676 | -12.3358 | -2.135e-4 | 3.094e-3 | 3.104e-5 |
| 3 | 0.8379 | 0.2217 | -17.1533 | 1.685e-4 | 5.265e-9 | -3.447e-7 |
| 4 | 1.6692 | 0.2663 | -12.3358 | -2.122e-4 | -3.094e-3 | -3.114e-5 |
| 5 | 1.6758 | 0.0000 | 0.0000 | 4.392e-5 | -4.488e-3 | -9.863e-5 |
| 6 | 2.3364 | -0.1438 | -1.1306 | -1.386e-4 | 4.411e-3 | 4.745e-4 |
| 7 | 1.6992 | 0.7297 | -13.1609 | -2.473e-4 | 2.983e-3 | -1.774e-4 |
| 8 | 0.8380 | -0.4148 | -17.7149 | 1.261e-4 | 8.426e-9 | -7.090e-7 |
| 9 | -0.0233 | 0.7254 | -13.1610 | -2.461e-4 | -2.983e-3 | 1.760e-4 |
| 10 | -0.6605 | -0.1524 | -1.1306 | -1.355e-4 | -4.411e-3 | -4.760e-4 |
| 11 | 0.0000 | 0.0005 | 0.0000 | 1.005e-4 | 4.498e-3 | 1.007e-4 |
| 12 | 0.0068 | 0.2680 | -12.3558 | -1.513e-4 | 3.093e-3 | 2.711e-5 |
| 13 | 0.8396 | 0.2221 | -17.1590 | 2.092e-4 | -8.449e-9 | -3.484e-7 |
| 14 | 1.6723 | 0.2668 | -12.3558 | -1.499e-4 | -3.093e-3 | -2.721e-5 |
| 15 | 1.6792 | 0.0005 | 0.0000 | 1.037e-4 | -4.498e-3 | -1.005e-4 |
| 16 | 2.3418 | -0.1387 | -1.1309 | 9.867e-5 | 4.413e-3 | 4.712e-4 |
| 17 | 1.6997 | 0.7458 | -13.1817 | -7.896e-5 | 2.983e-3 | -1.752e-4 |
| 18 | 0.8395 | -0.3930 | -17.7177 | 3.174e-4 | -1.045e-8 | -7.084e-7 |
| 19 | -0.0207 | 0.7416 | -13.1816 | -7.808e-5 | -2.983e-3 | 1.737e-4 |
| 20 | -0.6628 | -0.1473 | -1.1309 | 1.020e-4 | -4.413e-3 | -4.726e-4 |
Support reactions — ULS3a
kN and kNm
| Joint | FX | FY | FZ | MX | MY | MZ |
|---|---|---|---|---|---|---|
| 1 | -0.0145 | -0.0024 | 175.6762 | -4.99e-18 | 6.19e-16 | -6.07e-18 |
| 11 | 0.0145 | 1.08e-17 | 175.6826 | -4.88e-17 | -1.86e-14 | 9.95e-17 |
| 5 | -6.71e-14 | 0.0024 | 175.6826 | 2.34e-17 | 7.37e-15 | -1.45e-17 |
| 15 | -1.06e-14 | 3.92e-16 | 175.6762 | 7.59e-18 | -4.36e-14 | 6.29e-16 |
Equilibrium residuals (case D): ΣFX 1.72e-13, ΣFY 6.44e-15, ΣFZ -1.93e-12
Member end forces — ULS3a
internal actions in local axes; N positive = tension
| Mbr | N i | Vy i | Vz i | T i | My i | Mz i | N j | Vy j | Vz j | T j | My j | Mz j |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 2.0319 | 0.0493 | -3.6043 | -0.0006 | 1.5499 | 0.0394 | 2.0319 | 0.0493 | -2.2847 | -0.0006 | -7.2837 | -0.1084 |
| 2 | 253.2619 | -0.0623 | -1.1999 | 0.0008 | -5.9554 | -0.1095 | 253.2619 | -0.0623 | 0.1197 | 0.0008 | -7.5757 | 0.0776 |
| 3 | 253.2562 | 0.0623 | -0.1197 | -0.0008 | -7.5758 | 0.0778 | 253.2562 | 0.0623 | 1.1999 | -0.0008 | -5.9554 | -0.1091 |
| 4 | 2.0182 | -0.0486 | 2.2848 | 0.0006 | -7.2837 | -0.1072 | 2.0182 | -0.0486 | 3.6043 | 0.0006 | 1.5499 | 0.0386 |
| 5 | -250.2094 | 0.5819 | -4.6519 | -0.0004 | 1.7967 | 0.2080 | -250.2094 | 0.5819 | -2.9512 | -0.0004 | -9.6080 | -1.5378 |
| 6 | -338.1799 | -1.1931 | -1.1723 | 0.0015 | -8.1401 | -1.6094 | -338.1799 | -1.1931 | 0.5285 | 0.0015 | -9.1058 | 1.9699 |
| 7 | -338.1873 | 1.1931 | -0.5285 | -0.0015 | -9.1059 | 1.9699 | -338.1873 | 1.1931 | 1.1723 | -0.0015 | -8.1401 | -1.6094 |
| 8 | -250.2112 | -0.5819 | 2.9511 | 0.0004 | -9.6080 | -1.5379 | -250.2112 | -0.5819 | 4.6519 | 0.0004 | 1.7965 | 0.2079 |
| 9 | -171.9340 | -0.1031 | 2.0573 | 0.0005 | -1.5499 | -0.0614 | -171.7694 | -0.1031 | 2.0573 | 0.0005 | 1.5361 | 0.0932 |
| 10 | -125.5075 | 0.0552 | 1.3589 | -0.0003 | -1.0291 | 0.0444 | -125.3429 | 0.0552 | 1.3589 | -0.0003 | 1.0093 | -0.0384 |
| 11 | -85.4404 | -0.1971 | -2.10e-5 | -4.39e-7 | 1.60e-5 | -0.1440 | -85.2758 | -0.1971 | -2.10e-5 | -4.39e-7 | -1.55e-5 | 0.1516 |
| 12 | -125.5107 | 0.0547 | -1.3590 | 0.0002 | 1.0291 | 0.0440 | -125.3461 | 0.0547 | -1.3590 | 0.0002 | -1.0094 | -0.0380 |
| 13 | -171.9390 | -0.1049 | -2.0574 | -0.0005 | 1.5499 | -0.0627 | -171.7744 | -0.1049 | -2.0574 | -0.0005 | -1.5362 | 0.0946 |
| 14 | 279.3947 | -0.0046 | -0.0345 | 0.0001 | -0.3597 | -0.0302 | 279.1637 | -0.0046 | 0.4275 | 0.0001 | 0.2992 | -0.0147 |
| 15 | 96.9614 | -0.0102 | -0.0959 | 0.0003 | -0.4585 | 0.0010 | 96.7304 | -0.0102 | 0.3661 | 0.0003 | -0.0054 | 0.0350 |
| 16 | 279.4029 | 0.0045 | -0.0345 | -0.0001 | -0.3597 | 0.0302 | 279.1719 | 0.0045 | 0.4275 | -0.0001 | 0.2992 | 0.0150 |
| 17 | 96.9676 | 0.0101 | -0.0959 | -0.0003 | -0.4585 | -0.0009 | 96.7366 | 0.0101 | 0.3661 | -0.0003 | -0.0053 | -0.0349 |
| 18 | 2.0847 | 0.0514 | -3.6228 | -0.0006 | 1.5520 | 0.0396 | 2.0847 | 0.0514 | -2.3032 | -0.0006 | -7.3370 | -0.1145 |
| 19 | 253.6984 | -0.0583 | -1.1599 | 0.0008 | -6.0134 | -0.1015 | 253.6984 | -0.0583 | 0.1597 | 0.0008 | -7.5137 | 0.0735 |
| 20 | 253.7041 | 0.0583 | -0.1597 | -0.0008 | -7.5137 | 0.0738 | 253.7041 | 0.0583 | 1.1599 | -0.0008 | -6.0133 | -0.1011 |
| 21 | 2.0983 | -0.0507 | 2.3032 | 0.0006 | -7.3369 | -0.1134 | 2.0983 | -0.0507 | 3.6228 | 0.0006 | 1.5520 | 0.0388 |
| 22 | -252.1126 | 0.5991 | -4.7206 | -0.0007 | 1.8931 | 0.2395 | -252.1126 | 0.5991 | -3.0199 | -0.0007 | -9.7176 | -1.5580 |
| 23 | -337.7795 | -1.1900 | -1.0993 | 0.0016 | -8.2499 | -1.6070 | -337.7795 | -1.1900 | 0.6015 | 0.0016 | -8.9966 | 1.9629 |
| 24 | -337.7795 | 1.1900 | -0.6014 | -0.0016 | -8.9966 | 1.9629 | -337.7795 | 1.1900 | 1.0993 | -0.0016 | -8.2499 | -1.6071 |
| 25 | -252.1052 | -0.5991 | 3.0198 | 0.0007 | -9.7174 | -1.5580 | -252.1052 | -0.5991 | 4.7205 | 0.0007 | 1.8930 | 0.2394 |
| 26 | -171.9783 | 0.0048 | 2.0592 | 0.0004 | -1.5520 | 0.0038 | -171.8137 | 0.0048 | 2.0592 | 0.0004 | 1.5368 | -0.0035 |
| 27 | -125.6111 | 0.1447 | 1.3585 | -0.0002 | -1.0287 | 0.1021 | -125.4465 | 0.1447 | 1.3585 | -0.0002 | 1.0091 | -0.1150 |
| 28 | -85.0129 | -0.1044 | 1.64e-5 | -4.34e-7 | -1.25e-5 | -0.0879 | -84.8483 | -0.1044 | 1.64e-5 | -4.34e-7 | 1.21e-5 | 0.0687 |
| 29 | -125.6079 | 0.1441 | -1.3585 | 0.0002 | 1.0286 | 0.1017 | -125.4433 | 0.1441 | -1.3585 | 0.0002 | -1.0091 | -0.1144 |
| 30 | -171.9733 | 0.0031 | -2.0592 | -0.0004 | 1.5520 | 0.0025 | -171.8087 | 0.0031 | -2.0592 | -0.0004 | -1.5368 | -0.0022 |
| 31 | 279.7993 | -0.0168 | -0.0368 | -2.50e-5 | -0.3562 | -0.0547 | 279.5683 | -0.0168 | 0.4252 | -2.50e-5 | 0.2950 | 0.0016 |
| 32 | 96.4113 | -0.0200 | -0.0941 | 0.0002 | -0.4616 | -0.0186 | 96.1803 | -0.0200 | 0.3679 | 0.0002 | -0.0023 | 0.0484 |
| 33 | 279.7911 | 0.0167 | -0.0368 | 2.62e-5 | -0.3562 | 0.0547 | 279.5601 | 0.0167 | 0.4252 | 2.62e-5 | 0.2950 | -0.0013 |
| 34 | 96.4051 | 0.0199 | -0.0941 | -0.0002 | -0.4616 | 0.0186 | 96.1741 | 0.0199 | 0.3679 | -0.0002 | -0.0023 | -0.0483 |
| 35 | 0.5775 | -0.1903 | -0.1018 | 2.03e-6 | 0.0128 | -0.1905 | 0.5775 | -0.1903 | 0.1176 | 2.03e-6 | 0.0287 | 0.1901 |
| 36 | 1.8404 | 0.0705 | -0.0486 | 7.38e-8 | -0.0358 | 0.0706 | 1.8404 | 0.0705 | 0.1709 | 7.38e-8 | 0.0865 | -0.0703 |
| 37 | 2.4844 | -1.71e-5 | -0.1990 | -1.71e-8 | 0.1131 | -1.70e-5 | 2.4844 | -1.71e-5 | 0.0204 | -1.71e-8 | -0.0655 | 1.71e-5 |
| 38 | 1.8399 | -0.0705 | -0.0490 | -9.38e-8 | -0.0354 | -0.0706 | 1.8399 | -0.0705 | 0.1705 | -9.38e-8 | 0.0861 | 0.0703 |
| 39 | 0.5793 | 0.1903 | -0.1031 | -2.01e-6 | 0.0141 | 0.1905 | 0.5793 | 0.1903 | 0.1164 | -2.01e-6 | 0.0274 | -0.1900 |
| 40 | 0.0562 | -0.0400 | -0.1380 | 9.28e-6 | 0.0608 | -0.0398 | 0.0562 | -0.0400 | 0.0815 | 9.28e-6 | 0.0043 | 0.0401 |
| 41 | 0.0518 | -0.0117 | -0.0407 | -8.15e-7 | -0.0366 | -0.0119 | 0.0518 | -0.0117 | 0.1787 | -8.15e-7 | 0.1014 | 0.0114 |
| 42 | 0.0521 | -0.0002 | -0.1864 | -1.24e-8 | 0.1106 | -0.0002 | 0.0521 | -0.0002 | 0.0330 | -1.24e-8 | -0.0428 | 0.0002 |
| 43 | 0.0517 | 0.0111 | -0.0413 | 8.14e-7 | -0.0360 | 0.0113 | 0.0517 | 0.0111 | 0.1782 | 8.14e-7 | 0.1009 | -0.0108 |
| 44 | 0.0538 | 0.0392 | -0.1393 | -9.27e-6 | 0.0621 | 0.0390 | 0.0538 | 0.0392 | 0.0802 | -9.27e-6 | 0.0030 | -0.0393 |
| 45 | -2.2961 | 0.0189 | -0.2232 | -0.0004 | 0.1194 | 0.0101 | -2.2961 | 0.0189 | 0.1724 | -0.0004 | 0.0279 | -0.0581 |
| 46 | -4.6301 | -0.0385 | -0.1974 | 0.0009 | 0.0305 | -0.0758 | -4.6301 | -0.0385 | 0.1982 | 0.0009 | 0.0320 | 0.0629 |
| 47 | -4.6213 | 0.0385 | -0.1974 | -0.0009 | 0.0306 | 0.0758 | -4.6213 | 0.0385 | 0.1982 | -0.0009 | 0.0319 | -0.0629 |
| 48 | -2.3028 | -0.0189 | -0.2233 | 0.0004 | 0.1197 | -0.0101 | -2.3028 | -0.0189 | 0.1723 | 0.0004 | 0.0278 | 0.0581 |
Diagrams — member 6 (W200x46)
L = 3.000 m · local UDL w = (0.000, 0.000, -0.567) kN/m
N(x) axialmax 338.180 kN
Vy(x) shear local ymax 1.193 kN
Vz(x) shear local zmax 1.172 kN
T(x) torsionmax 0.002 kNm
My(x) bending about local ymax 9.352 kNm
Mz(x) bending about local zmax 1.970 kNm
| Action | x = 0 | x = L | x* (m) | value at x* | Governing |
|---|---|---|---|---|---|
| My | -8.1401 | -9.1058 | 2.0678 | -9.35214 | -9.35214 |
| Mz | -1.6094 | 1.9699 | — | — | 1.96985 |