I I

Eurocode 3 Table of design properties for square steel profiles - Square Hollow Sections (SHS)

Description:
Design aid - Table of design properties for square hollow steel sections (SHS) including section dimensions, cross-section properties (area A, second moment of area I, elastic modulus Wel, plastic modulus Wpl), strength properties (elastic moment Mel, plastic moment Mpl, plastic shear Vpl), and buckling properties (section class, buckling curves)
According to:
EN 1993-1-1:2005+AC2:2009 Sections 6.2 & 6.3
Supported National Annexes:
Nationally Defined Parameters (NDPs) automatically filled for supported countries (left blank otherwise)
All Calculations
Input
Steel partial material safety factor for cross-section resistance in accordance with EN1993-1-1 §6.1 and the National Annex for the case of steel buildings, or the relevant parts of EN1993 for other types of structures. It affects the resistance of profiles in axial force, shear, bending.
Notation for Square Hollow Sections (SHS) according to EN1993-1-1
Notation for Square Hollow Sections (SHS) according to EN1993-1-1
Tables
Design properties of hot finished Square Hollow Section (SHS) for S235 steel class (γM0 = 1.00, units = mm)
Profile dimensionsArea propertiesInertia propertiesTorsional propertiesAxial force & shear resistanceBending moment resistanceTorsional resistance
Profile Drawing Side dimension
b
[mm]
Wall thickness
t
[mm]
Outer rounding radius
ro
[mm]
Inner rounding radius
ri
[mm]
Weight
m
[kg/m]
External perimeter
P
[m]
Area
A
[mm2]
Shear area
Av
[mm2]
Second moment of area
I
[×106 mm4]
Radius of gyration
i
[mm]
Elastic section modulus
Wel
[×103 mm3]
Plastic section modulus
Wpl
[×103 mm3]
Torsion constant
IT
[×103 mm4]
Torsion modulus
WT
[×103 mm3]
Design plastic axial force resistance
Npl,Rd
[kN]
Design plastic shear force resistance
Vpl,Rd
[kN]
Design elastic bending moment resistance
Mel,Rd
[kNm]
Design plastic bending moment resistance
Mpl,Rd
[kNm]
Design plastic torsional moment resistance
Tpl,Rd
[kNm]
Buckling curve Section class
SHS 40 / 2.6 dxf 40.0 2.6 3.9 2.6 3.00 0.153 382 191 0.08797 15.2 4.399 5.312 140.3 6.407 89.70 25.89 1.03 1.25 0.87 a 1
SHS 40 / 3.2 dxf 40.0 3.2 4.8 3.2 3.61 0.152 460 230 0.1023 14.9 5.115 6.284 165.4 7.417 108.11 31.21 1.20 1.48 1.01 a 1
SHS 40 / 4 dxf 40.0 4.0 6.0 4.0 4.39 0.150 559 279 0.1183 14.5 5.915 7.439 194.8 8.536 131.33 37.91 1.39 1.75 1.16 a 1
SHS 40 / 5 dxf 40.0 5.0 7.5 5.0 5.28 0.147 673 337 0.1337 14.1 6.684 8.663 225.0 9.602 158.20 45.67 1.57 2.04 1.30 a 1
SHS 50 / 2.6 dxf 50.0 2.6 3.9 2.6 3.81 0.193 486 243 0.1803 19.3 7.212 8.583 284.1 10.55 114.14 32.95 1.69 2.02 1.43 a 1
SHS 50 / 3.2 dxf 50.0 3.2 4.8 3.2 4.62 0.192 588 294 0.2123 19.0 8.491 10.24 338.2 12.37 138.19 39.89 2.00 2.41 1.68 a 1
SHS 50 / 4 dxf 50.0 4.0 6.0 4.0 5.64 0.190 719 359 0.2497 18.6 9.990 12.27 403.9 14.49 168.93 48.76 2.35 2.88 1.97 a 1
SHS 50 / 5 dxf 50.0 5.0 7.5 5.0 6.85 0.187 873 437 0.2888 18.2 11.55 14.53 475.6 16.67 205.20 59.24 2.71 3.41 2.26 a 1
SHS 50 / 6.3 dxf 50.0 6.3 9.4 6.3 8.31 0.184 1059 529 0.3276 17.6 13.10 17.01 551.9 18.82 248.78 71.82 3.08 4.00 2.55 a 1
SHS 60 / 2.6 dxf 60.0 2.6 3.9 2.6 4.63 0.233 590 295 0.3216 23.4 10.72 12.63 502.5 15.74 138.58 40.00 2.52 2.97 2.13 a 1
SHS 60 / 3.2 dxf 60.0 3.2 4.8 3.2 5.62 0.232 716 358 0.3816 23.1 12.72 15.16 601.9 18.60 168.27 48.58 2.99 3.56 2.52 a 1
SHS 60 / 4 dxf 60.0 4.0 6.0 4.0 6.90 0.230 879 439 0.4539 22.7 15.13 18.31 725.1 22.03 206.53 59.62 3.56 4.30 2.99 a 1
SHS 60 / 5 dxf 60.0 5.0 7.5 5.0 8.42 0.227 1073 537 0.5326 22.3 17.75 21.89 864.0 25.72 252.20 72.80 4.17 5.15 3.49 a 1
SHS 60 / 6.3 dxf 60.0 6.3 9.4 6.3 10.3 0.224 1311 655 0.6165 21.7 20.55 26.00 1020 29.62 308.00 88.91 4.83 6.11 4.02 a 1
SHS 60 / 8 dxf 60.0 8.0 12.0 8.0 12.5 0.219 1595 798 0.6973 20.9 23.24 30.44 1182 33.35 374.90 108.22 5.46 7.15 4.53 a 1
SHS 70 / 3.2 dxf 70.0 3.2 4.8 3.2 6.63 0.272 844 422 0.6231 27.2 17.80 21.04 975.8 26.11 198.35 57.26 4.18 4.94 3.54 a 1
SHS 70 / 4 dxf 70.0 4.0 6.0 4.0 8.15 0.270 1039 519 0.7469 26.8 21.34 25.54 1182 31.16 244.13 70.47 5.01 6.00 4.23 a 1
SHS 70 / 5 dxf 70.0 5.0 7.5 5.0 9.99 0.267 1273 637 0.885 26.4 25.29 30.76 1420 36.76 299.20 86.37 5.94 7.23 4.99 a 1
SHS 70 / 6.3 dxf 70.0 6.3 9.4 6.3 12.3 0.264 1563 781 1.038 25.8 29.67 36.88 1695 42.92 367.22 106.01 6.97 8.67 5.82 a 1
SHS 70 / 8 dxf 70.0 8.0 12.0 8.0 15.0 0.259 1915 958 1.198 25.0 34.22 43.77 1997 49.24 450.10 129.93 8.04 10.29 6.68 a 1
SHS 80 / 3.2 dxf 80.0 3.2 4.8 3.2 7.63 0.312 972 486 0.9495 31.3 23.74 27.88 1479 34.90 228.43 65.94 5.58 6.55 4.73 a 1
SHS 80 / 4 dxf 80.0 4.0 6.0 4.0 9.41 0.310 1199 599 1.145 30.9 28.61 33.98 1800 41.90 281.73 81.33 6.72 7.98 5.68 a 1
SHS 80 / 5 dxf 80.0 5.0 7.5 5.0 11.6 0.307 1473 737 1.366 30.5 34.15 41.13 2174 49.79 346.20 99.94 8.03 9.66 6.75 a 1
SHS 80 / 6.3 dxf 80.0 6.3 9.4 6.3 14.2 0.304 1815 907 1.619 29.9 40.47 49.65 2615 58.71 426.44 123.10 9.51 11.67 7.97 a 1
SHS 80 / 8 dxf 80.0 8.0 12.0 8.0 17.5 0.299 2235 1118 1.893 29.1 47.32 59.51 3117 68.29 525.30 151.64 11.12 13.99 9.27 a 1
SHS 90 / 4 dxf 90.0 4.0 6.0 4.0 10.7 0.350 1359 679 1.663 35.0 36.95 43.61 2601 54.23 319.33 92.18 8.68 10.25 7.36 a 1
SHS 90 / 5 dxf 90.0 5.0 7.5 5.0 13.1 0.347 1673 837 1.996 34.5 44.35 52.99 3155 64.81 393.20 113.51 10.42 12.45 8.79 a 1
SHS 90 / 6.3 dxf 90.0 6.3 9.4 6.3 16.2 0.344 2067 1033 2.383 34.0 52.95 64.31 3818 77.01 485.66 140.20 12.44 15.11 10.45 a 1
SHS 90 / 8 dxf 90.0 8.0 12.0 8.0 20.1 0.339 2555 1278 2.815 33.2 62.55 77.65 4590 90.50 600.50 173.35 14.70 18.25 12.28 a 1
SHS 100 / 4 dxf 100.0 4.0 6.0 4.0 11.9 0.390 1519 759 2.318 39.1 46.36 54.44 3611 68.15 356.93 103.04 10.90 12.79 9.25 a 1
SHS 100 / 5 dxf 100.0 5.0 7.5 5.0 14.7 0.387 1873 937 2.794 38.6 55.89 66.36 4394 81.83 440.20 127.07 13.13 15.59 11.10 a 1
SHS 100 / 6.3 dxf 100.0 6.3 9.4 6.3 18.2 0.384 2319 1159 3.356 38.0 67.11 80.86 5342 97.82 544.88 157.29 15.77 19.00 13.27 a 1
SHS 100 / 8 dxf 100.0 8.0 12.0 8.0 22.6 0.379 2875 1438 3.996 37.3 79.92 98.18 6462 115.9 675.70 195.06 18.78 23.07 15.72 a 1
SHS 100 / 10 dxf 100.0 10.0 15.0 10.0 27.4 0.374 3493 1746 4.621 36.4 92.42 116.2 7610 133.4 820.78 236.94 21.72 27.31 18.10 a 1
SHS 120 / 5 dxf 120.0 5.0 7.5 5.0 17.8 0.467 2273 1137 4.977 46.8 82.95 97.59 7765 121.9 534.20 154.21 19.49 22.93 16.53 a 1
SHS 120 / 6.3 dxf 120.0 6.3 9.4 6.3 22.2 0.464 2823 1411 6.029 46.2 100.5 119.6 9502 147.0 663.32 191.48 23.61 28.11 19.94 a 1
SHS 120 / 8 dxf 120.0 8.0 12.0 8.0 27.6 0.459 3515 1758 7.263 45.5 121.1 146.5 11600 176.2 826.10 238.48 28.45 34.42 23.91 a 1
SHS 120 / 10 dxf 120.0 10.0 15.0 10.0 33.7 0.454 4293 2146 8.521 44.6 142.0 175.2 13820 205.8 1008.78 291.21 33.38 41.16 27.92 a 1
SHS 120 / 12.5 dxf 120.0 12.5 18.8 12.5 40.9 0.448 5207 2604 9.818 43.4 163.6 206.8 16230 235.9 1223.73 353.26 38.45 48.60 32.01 a 1
SHS 140 / 5 dxf 140.0 5.0 7.5 5.0 21.0 0.547 2673 1337 8.075 55.0 115.4 134.8 12530 169.9 628.20 181.34 27.11 31.68 23.05 a 1
SHS 140 / 6.3 dxf 140.0 6.3 9.4 6.3 26.1 0.544 3327 1663 9.839 54.4 140.6 166.0 15400 206.2 781.76 225.68 33.03 39.00 27.98 a 1
SHS 140 / 8 dxf 140.0 8.0 12.0 8.0 32.6 0.539 4155 2078 11.95 53.6 170.7 204.3 18920 249.3 976.50 281.89 40.12 48.02 33.83 a 1
SHS 140 / 10 dxf 140.0 10.0 15.0 10.0 40.0 0.534 5093 2546 14.16 52.7 202.3 246.1 22720 294.1 1196.78 345.48 47.54 57.83 39.90 a 1
SHS 140 / 12.5 dxf 140.0 12.5 18.8 12.5 48.7 0.528 6207 3104 16.53 51.6 236.1 293.3 26960 341.6 1458.73 421.10 55.49 68.92 46.35 a 1
SHS 150 / 5 dxf 150.0 5.0 7.5 5.0 22.6 0.587 2873 1437 10.02 59.0 133.6 155.7 15500 196.9 675.20 194.91 31.38 36.59 26.71 a 1
SHS 150 / 6.3 dxf 150.0 6.3 9.4 6.3 28.1 0.584 3579 1789 12.23 58.5 163.1 192.0 19090 239.6 840.98 242.77 38.33 45.11 32.51 a 1
SHS 150 / 8 dxf 150.0 8.0 12.0 8.0 35.1 0.579 4475 2238 14.91 57.7 198.7 236.9 23510 290.6 1051.70 303.60 46.71 55.66 39.43 a 1
SHS 150 / 10 dxf 150.0 10.0 15.0 10.0 43.1 0.574 5493 2746 17.73 56.8 236.4 286.0 28320 344.2 1290.78 372.62 55.56 67.22 46.70 a 1
SHS 150 / 12.5 dxf 150.0 12.5 18.8 12.5 52.7 0.568 6707 3354 20.80 55.7 277.4 342.1 33750 401.9 1576.23 455.02 65.19 80.40 54.53 a 1
SHS 150 / 14.2 dxf 150.0 14.2 21.3 14.2 58.9 0.563 7497 3749 22.62 54.9 301.5 376.9 37070 435.7 1761.81 508.59 70.86 88.56 59.11 a 1
SHS 150 / 16 dxf 150.0 16.0 24.0 16.0 65.2 0.559 8301 4151 24.30 54.1 324.0 410.7 40260 467.0 1950.81 563.15 76.14 96.52 63.36 a 1
SHS 160 / 5 dxf 160.0 5.0 7.5 5.0 24.1 0.627 3073 1537 12.25 63.1 153.1 178.1 18920 225.9 722.20 208.48 35.97 41.84 30.65 a 1
SHS 160 / 6.3 dxf 160.0 6.3 9.4 6.3 30.1 0.624 3831 1915 14.99 62.6 187.4 219.9 23330 275.5 900.20 259.87 44.03 51.67 37.38 a 1
SHS 160 / 8 dxf 160.0 8.0 12.0 8.0 37.6 0.619 4795 2398 18.31 61.8 228.9 271.8 28800 335.2 1126.90 325.31 53.79 63.87 45.48 a 1
SHS 160 / 10 dxf 160.0 10.0 15.0 10.0 46.3 0.614 5893 2946 21.86 60.9 273.2 329.0 34780 398.3 1384.78 399.75 64.21 77.32 54.04 a 1
SHS 160 / 12.5 dxf 160.0 12.5 18.8 12.5 56.6 0.608 7207 3604 25.76 59.8 322.0 394.7 41580 467.1 1693.73 488.94 75.66 92.76 63.38 a 1
SHS 160 / 14.2 dxf 160.0 14.2 21.3 14.2 63.3 0.603 8065 4033 28.09 59.0 351.1 435.8 45790 508.0 1895.29 547.12 82.51 102.40 68.92 a 1
SHS 160 / 16 dxf 160.0 16.0 24.0 16.0 70.2 0.599 8941 4471 30.28 58.2 378.5 476.1 49880 546.3 2101.21 606.57 88.96 111.88 74.12 a 1
SHS 180 / 5 dxf 180.0 5.0 7.5 5.0 27.3 0.707 3473 1737 17.65 71.3 196.1 227.3 27180 289.9 816.20 235.62 46.10 53.41 39.33 a 1
SHS 180 / 6.3 dxf 180.0 6.3 9.4 6.3 34.0 0.704 4335 2167 21.68 70.7 240.9 281.3 33610 354.9 1018.64 294.06 56.61 66.11 48.15 a 1
SHS 180 / 8 dxf 180.0 8.0 12.0 8.0 42.7 0.699 5435 2718 26.61 70.0 295.6 348.9 41620 433.8 1277.30 368.73 69.48 81.99 58.86 a 1
SHS 180 / 10 dxf 180.0 10.0 15.0 10.0 52.5 0.694 6693 3346 31.93 69.1 354.8 423.9 50480 518.5 1572.78 454.02 83.38 99.63 70.35 a 1
SHS 180 / 12.5 dxf 180.0 12.5 18.8 12.5 64.4 0.688 8207 4104 37.90 68.0 421.1 511.2 60700 612.6 1928.73 556.78 98.97 120.12 83.11 a 1
SHS 180 / 14.2 dxf 180.0 14.2 21.3 14.2 72.2 0.683 9201 4601 41.54 67.2 461.6 566.3 67110 669.5 2162.25 624.19 108.47 133.09 90.84 a 1
SHS 180 / 16 dxf 180.0 16.0 24.0 16.0 80.2 0.679 10221 5111 45.04 66.4 500.4 621.2 73430 724.0 2402.01 693.40 117.60 145.98 98.23 a 1
SHS 200 / 5 dxf 200.0 5.0 7.5 5.0 30.4 0.787 3873 1937 24.45 79.5 244.5 282.5 37560 361.9 910.20 262.75 57.47 66.39 49.10 a 2
SHS 200 / 6.3 dxf 200.0 6.3 9.4 6.3 38.0 0.784 4839 2419 30.11 78.9 301.1 350.3 46530 444.3 1137.08 328.25 70.76 82.33 60.28 a 1
SHS 200 / 8 dxf 200.0 8.0 12.0 8.0 47.7 0.779 6075 3038 37.09 78.1 370.9 435.6 57780 545.2 1427.70 412.14 87.16 102.35 73.98 a 1
SHS 200 / 10 dxf 200.0 10.0 15.0 10.0 58.8 0.774 7493 3746 44.71 77.2 447.1 530.9 70310 654.6 1760.78 508.29 105.07 124.75 88.82 a 1
SHS 200 / 12.5 dxf 200.0 12.5 18.8 12.5 72.3 0.768 9207 4604 53.36 76.1 533.6 642.6 84910 777.9 2163.73 624.61 125.41 151.01 105.55 a 1
SHS 200 / 14.2 dxf 200.0 14.2 21.3 14.2 81.1 0.763 10337 5169 58.72 75.4 587.2 714.0 94170 853.7 2429.21 701.25 137.99 167.78 115.83 a 1
SHS 200 / 16 dxf 200.0 16.0 24.0 16.0 90.3 0.759 11501 5751 63.94 74.6 639.4 785.5 103400 927.1 2702.81 780.23 150.25 184.59 125.79 a 1
SHS 220 / 6.3 dxf 220.0 6.3 9.4 6.3 41.9 0.864 5343 2671 40.49 87.1 368.1 426.9 62400 543.8 1255.52 362.44 86.50 100.32 73.78 a 1
SHS 220 / 8 dxf 220.0 8.0 12.0 8.0 52.7 0.859 6715 3358 50.02 86.3 454.7 531.8 77650 669.4 1578.10 455.56 106.85 124.98 90.83 a 1
SHS 220 / 10 dxf 220.0 10.0 15.0 10.0 65.1 0.854 8293 4146 60.50 85.4 550.0 649.8 94730 806.8 1948.78 562.57 129.26 152.70 109.46 a 1
SHS 220 / 12.5 dxf 220.0 12.5 18.8 12.5 80.1 0.848 10207 5104 72.54 84.3 659.5 789.1 114800 963.2 2398.73 692.45 154.98 185.43 130.69 a 1
SHS 220 / 14.2 dxf 220.0 14.2 21.3 14.2 90.1 0.843 11473 5737 80.07 83.5 727.9 878.6 127700 1060 2696.17 778.32 171.07 206.47 143.88 a 1
SHS 220 / 16 dxf 220.0 16.0 24.0 16.0 100.3 0.839 12781 6391 87.49 82.7 795.3 969.0 140500 1156 3003.61 867.07 186.91 227.71 156.81 a 1
SHS 250 / 6.3 dxf 250.0 6.3 9.4 6.3 47.9 0.984 6099 3049 60.14 99.3 481.1 555.9 92380 712.0 1433.18 413.72 113.06 130.64 96.60 a 2
SHS 250 / 8 dxf 250.0 8.0 12.0 8.0 60.3 0.979 7675 3838 74.55 98.6 596.4 694.2 115300 879.8 1803.70 520.68 140.15 163.14 119.36 a 1
SHS 250 / 10 dxf 250.0 10.0 15.0 10.0 74.5 0.974 9493 4746 90.55 97.7 724.4 850.7 141100 1065 2230.78 643.97 170.24 199.91 144.48 a 1
SHS 250 / 12.5 dxf 250.0 12.5 18.8 12.5 91.9 0.968 11707 5854 109.2 96.6 873.2 1037 171600 1279 2751.23 794.21 205.21 243.66 173.47 a 1
SHS 250 / 14.2 dxf 250.0 14.2 21.3 14.2 103.4 0.963 13177 6589 120.9 95.8 967.5 1158 191400 1413 3096.61 893.92 227.36 272.02 191.72 a 1
SHS 250 / 16 dxf 250.0 16.0 24.0 16.0 115.4 0.959 14701 7351 132.7 95.0 1061 1280 211400 1546 3454.81 997.32 249.41 300.85 209.81 a 1
SHS 260 / 6.3 dxf 260.0 6.3 9.4 6.3 49.9 1.024 6351 3175 67.88 103.4 522.2 602.7 104200 773.0 1492.40 430.82 122.71 141.64 104.89 a 2
SHS 260 / 8 dxf 260.0 8.0 12.0 8.0 62.8 1.019 7995 3998 84.23 102.6 647.9 753.2 130100 956.3 1878.90 542.39 152.25 177.00 129.74 a 1
SHS 260 / 10 dxf 260.0 10.0 15.0 10.0 77.7 1.014 9893 4946 102.4 101.8 787.9 923.6 159300 1159 2324.78 671.11 185.15 217.06 157.24 a 1
SHS 260 / 12.5 dxf 260.0 12.5 18.8 12.5 95.8 1.008 12207 6104 123.6 100.6 951.1 1127 194100 1394 2868.73 828.13 223.52 264.83 189.09 a 1
SHS 260 / 14.2 dxf 260.0 14.2 21.3 14.2 107.9 1.003 13745 6873 137.1 99.9 1055 1259 216600 1542 3230.09 932.45 247.90 295.88 209.21 a 1
SHS 260 / 16 dxf 260.0 16.0 24.0 16.0 120.4 0.999 15341 7671 150.6 99.1 1159 1394 239400 1689 3605.21 1040.73 272.25 327.48 229.21 a 1
SHS 300 / 6.3 dxf 300.0 6.3 9.4 6.3 57.8 1.184 7359 3679 105.5 119.7 703.1 808.8 161400 1043 1729.28 499.20 165.23 190.07 141.46 a 4
SHS 300 / 8 dxf 300.0 8.0 12.0 8.0 72.8 1.179 9275 4638 131.3 119.0 875.2 1013 201900 1294 2179.70 629.23 205.67 238.04 175.60 a 2
SHS 300 / 10 dxf 300.0 10.0 15.0 10.0 90.2 1.174 11493 5746 160.3 118.1 1068 1246 248100 1575 2700.78 779.65 251.08 292.69 213.71 a 1
SHS 300 / 12.5 dxf 300.0 12.5 18.8 12.5 111.5 1.168 14207 7104 194.4 117.0 1296 1525 303300 1904 3338.73 963.81 304.59 358.34 258.33 a 1
SHS 300 / 14.2 dxf 300.0 14.2 21.3 14.2 125.7 1.163 16017 8009 216.4 116.2 1442 1708 339400 2114 3764.01 1086.58 338.97 401.30 286.85 a 1
SHS 300 / 16 dxf 300.0 16.0 24.0 16.0 140.5 1.159 17901 8951 238.5 115.4 1590 1895 376200 2325 4206.81 1214.40 373.64 445.31 315.47 a 1
SHS 350 / 8 dxf 350.0 8.0 12.0 8.0 85.4 1.379 10875 5438 211.3 139.4 1207 1392 323800 1789 2555.70 737.77 283.73 327.03 242.68 a 3
SHS 350 / 10 dxf 350.0 10.0 15.0 10.0 105.9 1.374 13493 6746 258.8 138.5 1479 1715 398900 2185 3170.78 915.33 347.58 403.10 296.49 a 1
SHS 350 / 12.5 dxf 350.0 12.5 18.8 12.5 131.2 1.368 16707 8354 315.4 137.4 1802 2107 489300 2654 3926.23 1133.40 423.56 495.05 360.14 a 1
SHS 350 / 14.2 dxf 350.0 14.2 21.3 14.2 148.0 1.363 18857 9429 352.1 136.6 2012 2364 548800 2957 4431.41 1279.24 472.83 555.60 401.21 a 1
SHS 350 / 16 dxf 350.0 16.0 24.0 16.0 165.6 1.359 21101 10551 389.4 135.8 2225 2630 609900 3264 4958.81 1431.48 522.94 617.97 442.80 a 1
SHS 400 / 10 dxf 400.0 10.0 15.0 10.0 121.6 1.574 15493 7746 391.3 158.9 1956 2260 600900 2895 3640.78 1051.00 459.75 531.13 392.83 a 2
SHS 400 / 12.5 dxf 400.0 12.5 18.8 12.5 150.8 1.568 19207 9604 478.4 157.8 2392 2782 739100 3530 4513.73 1303.00 562.10 653.79 478.89 a 1
SHS 400 / 14.2 dxf 400.0 14.2 21.3 14.2 170.3 1.563 21697 10849 535.3 157.1 2676 3127 830300 3942 5098.81 1471.90 628.94 734.92 534.81 a 1
SHS 400 / 16 dxf 400.0 16.0 24.0 16.0 190.8 1.559 24301 12151 593.4 156.3 2967 3484 924400 4362 5710.81 1648.57 697.29 818.83 591.81 a 1
SHS 400 / 20 dxf 400.0 20.0 30.0 20.0 235.3 1.548 29971 14985 715.3 154.5 3577 4247 1125000 5237 7043.14 2033.18 840.53 998.03 710.55 a 1
Notes
  1. The design resistances of the profiles correspond to cross-section resistances reduced by the partial material factor γM0 in accordance with EN1993-1-1 §6.2.3(2), §6.2.4(2), §6.2.5(2), §6.2.6(2). The aforementioned design resistances do not take into account a) flexural buckling, b) local shell buckling, c) interaction effects of axial force, shear force, bending moment, and d) interaction effects of biaxial bending. Therefore the presented cross-section resistances are indicative values applicable for special cases. In general the overall element resistance is smaller and must be verified according to the relevant clauses of EN1993-1-1 Section 6.
  2. The outer rounding radius ro and the inner rounding radius ri are nominal values to be used in calculations and they are specified in the design standards EN 10210-2 §A.3 for hot finished structural hollow sections and EN 10219-2 §B.3 for cold formed structural hollow sections. The actual rounding radii may vary within the tolerances allowed by the aforementioned standards and the sectional properties still remain valid.
Details

Design properties for rectangular hollow steel sections (RHS) and square hollow steel sections (SHS) according to EN1993-1-1

Differences between Rectangular Hollow Sections (RHS) and Square Hollow Sections (SHS)

In general the procedure for calculating the properties of Square Hollow Sections (SHS) is the same as for Rectangular Hollow Sections (RHS). The equations for Rectangular Hollow Sections (RHS) may also be used for Square Hollow Sections (SHS) by substituting h = b. The rest of the text covers the more general case of Rectangular Hollow Sections (RHS).

Definition of the cross-section

For typical Rectangular Hollow Sections (RHS) the geometric properties of the cross-section are defined in the following standards:

  • EN 10210-2: Hot finished structural hollow sections of non-alloy and fine grain steels

  • EN 10219-2: Cold formed welded structural hollow sections of non-alloy and fine grain steels

The geometric properties that define the cross-section are: height h, width b and wall thickness t. In addition the rounding of the corners is defined by the outer rounding radius ro and the inner rounding radius ri. The notation is defined in EN1993-1-1 §1.7 which is reproduced in the figure above.

The outer rounding radius ro and the inner rounding radius ri are specified as nominal values to be used in calculations in the standards and they are specified in the design standards EN 10210-2 §A.3 for hot finished structural hollow sections and EN 10219-2 §B.3 for cold formed structural hollow sections:

  • EN 10210-2 (Hot finished):

    • For any thickness: ro = 1.5t and ri = 1.0t

  • EN 10219-2 (Cold formed):

    • For thickness t ≤ 6 mm: ro = 2.0t and ri = 1.0t

    • For thickness 6 mm > t ≤ 10 mm: ro = 2.5t and ri = 1.5t

    • For thickness t > 10 mm: ro = 3.0t and ri = 2.0t

The actual rounding radii may vary within the tolerances allowed by the aforementioned standards and the sectional properties still remain valid.

Geometric properties

The basic geometric properties of the cross-section are calculated by using the fundamental relations of mechanics. Due to symmetry the centroid of the cross-section (center of mass) as well as the shear center are located at the center. The geometric quantities include the total area of the cross section A and the second moments of the area Iy and Iz about the major axis y-y and about the minor axis z-z respectively. They are calculated by adding the contribution of the external boundary and then subtracting the contribution of the internal void where the rounding of the corners is properly taken into account:

A = 2t⋅(b + h - 2t) - (4 - π)⋅(ro2 - ri2)

Iy = bh3 / 12 - (b - 2⋅t)⋅(h - 2t)3 / 12 - 4(Ig + Aghg,y2) + 4(Iξξ + Aξξhξ,y2)

Iz = hb3 / 12 - (h - 2⋅t)⋅(b - 2t)3 / 12 - 4(Ig + Aghg,z2) + 4(Iξξ + Aξξhξ,z2)

where the following auxiliary quantities are defined in EN 10210-2 §A.3 and EN 10219-2 §B.3:

Ag = (1 - π / 4)⋅ro2

Aξξ = (1 - π / 4)⋅ri2

hg,y = h / 2 - ro ⋅ (10 - 3π) / (12 - 3π) and hg,z = b / 2 - ro ⋅ (10 - 3π) / (12 - 3π)

hξ,y = (h - 2t) / 2 - ri ⋅ (10 - 3π) / (12 - 3π) and hξ,z = (b - 2t) / 2 - ri ⋅ (10 - 3π) / (12 - 3π)

Ig = [1/3 - π/16 - 1 / (3⋅(12 - 3π))]⋅ro4

Iξξ = [1/3 - π/16 - 1 / (3⋅(12 - 3π))]⋅ri4

Shear area

The shear areas Av,z and Av,y for the case of rectangular hollow sections are specified in EN1993-1-1 §6.2.6(3) as:

Load parallel to depth: Av,z = Ah / (b + h)

Load parallel to width: Av,y = Ab / (b + h)

Elastic section modulus

The elastic section modulii Wel,y and Wel,z about the major axis y-y and the minor axis z-z respectively are calculated by dividing the second moment of the area Iy and Iz with the corresponding distance from the centroid to the most distant edge:

Wel,y = Iy / (h / 2)

Wel,z = Iz / (b / 2)

Plastic section modulus

The plastic section modulii Wpl,y and Wpl,z about the major axis y-y and the minor axis z-z respectively correspond to the maximum plastic bending moment when the axial force of the cross-section is zero and the stress profile is fully plastic. Due to symmetry when the full plastic bending stress profile is reached with zero axial force the section is divided into two parts separated by the axis of symmetry. The plastic section modulus corresponds to the sum of first moments of the area of the two halves about the major axis y-y and the minor axis z-z respectively.

Wpl,y = bh2 / 4 - (b - 2t)⋅(h - 2t)2 / 4 - 4⋅Aghg,y + 4⋅Aξξhξ,y

Wpl,z = hb2 / 4 - (h - 2t)⋅(b - 2t)2 / 4 - 4⋅Aghg,z + 4⋅Aξξhξ,z

Torsional properties

The torsional constant IT and the torsional modulus WT are defined in EN 10210-2 §A.3 and EN 10219-2 §B.3. The specified values are good approximations for the case of thin walled rectangular hollow sections with rounded corners. In the following equations the quantity h in EN 10210 and EN 10219 is denoted as h0:

IT = t3h0 / 3 + 2⋅KAh

WT = IT / (t + K / t)

where the following auxiliary quantities are defined in EN 10210-2 §A.3 and EN 10219-2 §B.3:

Rc = (ro + ri) / 2

Ah = (b - t)⋅(h - t) - Rc2⋅(4 - π)

h0 = 2⋅[(b - t) + (h - t)] - 2⋅Rc⋅(4 - π)

K = 2⋅Aht / h0

Design cross-section resistance

The design resistance of the cross-section for axial force, shear force, and bending moment are calculated in accordance with EN1993-1-1 §6.2. They correspond to the gross cross-section resistance reduced by the steel partial material safety factor for cross-section resistance γM0 that is specified in EN1993-1-1 §6.1 for buildings, or the relevant parts of EN1993 for other type of structures, and the National Annex.

The aforementioned design resistances do not take into account a) flexural buckling, b) lateral torsional buckling, c) interaction effects of axial force, shear force, bending moment, and d) interaction effects of biaxial bending. Therefore the presented cross-section resistances are indicative values applicable for special cases. In general the overall element resistance is smaller and must be verified according to the relevant clauses of EN1993-1-1 Section 6.

Design axial force resistance

The design plastic resistance of the cross-section in uniform tension is specified in EN1993-1-1 §6.2.3(2). The design plastic resistance of the cross-section in uniform compression for cross-section class 1, 2, 3 is specified in EN1993-1-1 §6.2.4(2). The aforementioned axial force resistances correspond to the gross cross-sectional area A and the steel yield stress fy:

Npl,Rd = Afy / γM0

Design shear force resistance

The design plastic shear resistance of the cross-section is specified in EN1993-1-1 §6.2.6(2). It corresponds to the relevant shear area Av,z or Av,y, for shear force along the axis z-z and y-y respectively, multiplied by the steel yield stress in pure shear fy / √3 corresponding to the yield criterion in EN1993-1-1 §6.2.1(5)::

Vpl,Rd,z = Av,z ⋅ ( fy / √3 ) / γM0

Vpl,Rd,y = Av,y ⋅ ( fy / √3 ) / γM0

Design torsional moment resistance

The design torsional moment resistance of the cross-section for the case of St. Venant torsion is specified in EN1993-1-1 §6.2.7. The shear stress due to St. Venant torsion is derived from the theory of elasticity as specified above. For elastic verification the yield criterion in EN1993-1-1 §6.2.1(5) is applied, i.e. the shear stress τ is limited the steel yield stress in pure shear fy / √3:

TRd = WT ⋅ ( fy / √3 ) / γM0

Design elastic bending moment resistance

The design elastic bending moment resistance of the cross-section is specified in EN1993-1-1 §6.2.5(2). It corresponds to the relevant elastic section modulus Wel,y or Wel,z, for bending about the major axis y-y or about the minor axis z-z respectively, multiplied by the steel yield stress fy:

Mpl,Rd,y = Wel,yfy / γM0

Mpl,Rd,z = Wel,zfy / γM0

The elastic bending moment resistance is applicable for class 3 cross-sections. For class 4 cross-sections the effective cross-section properties must be defined that take into account the reduced effective widths of the compression parts of the cross-section as specified in EN1993-1-1 §6.2.2.5.

Design plastic bending moment resistance

The design plastic bending moment resistance of the cross-section is specified in EN1993-1-1 §6.2.5(2). It corresponds to the relevant plastic section modulus Wpl,y or Wpl,z, for bending about the major axis y-y or about the minor axis z-z respectively, multiplied by the steel yield stress fy:

Mpl,Rd,y = Wpl,yfy / γM0

Mpl,Rd,z = Wpl,zfy / γM0

The plastic bending moment resistance is applicable for class 1 or 2 cross-sections.

Cross-section class

The classification of cross-sections is specified in EN1993-1-1 §5.5. The role of the classification is to identify the extent to which the resistance and rotation capacity of the cross-section are limited by local buckling of its parts.

Four section classes are identified:

  • Class 1: Plastic bending moment resistance develops and plastic hinge develops with rotation capacity adequate for plastic analysis.

  • Class 2: Plastic bending moment resistance develops but the rotation capacity is limited by local buckling.

  • Class 3: Elastic bending moment resistance develops but local buckling prevents the development of plastic resistance.

  • Class 4: Elastic bending moment resistance cannot develop because local buckling occurs before the yield stress is reached at the extreme fiber. Effective widths are used to account for the effects of local buckling of compression parts.

The classification of the cross-section parts (web parallel to depth, web parallel to width) is specified in EN1993-1-1 Table 5.2. The class of the compression part depends on its width c to thickness t ratio, adjusted by the factor ε that takes into account the value of the steel yield stress fy:

ε = (235 MPa / fy)0.5

In general the class of the compression part is more unfavorable when it is subjected to uniform compression, as compared to pure bending. Indicative classification of the webs of the steel profiles is presented for the characteristic cases of pure uniform compression and pure bending moment. In general the class may have an intermediate value if the stress profile of the compression part occurs from a combination of compressive axial force and bending moment. The classification of the total cross-section is determined by the class of its most unfavorable compression part.

The examined width to thickness limits c / t for cross-section classification according to EN1993-1-1 Table 5.2 are presented below:

Width to thickness limits for cross-section classification according to EN1993-1-1 Table 5.2
Class Web in pure compression Web in pure bending
Class 1 c / t ≤ 33ε c / t ≤ 72ε
Class 2 c / t ≤ 38ε c / t ≤ 83ε
Class 3 c / t ≤ 42ε c / t ≤ 124ε

For the classification of the web parallel to depth: c = h - 2t - 2ri.

For the classification of the web parallel to width: c = b - 2t - 2ri

Buckling curves

The appropriate buckling curve for rectangular hollow sections and square hollow sections is specified in EN1993-1-1 Table 6.2 depending on the steel yield stress fy, and whether the section is hot finished or cold formed as described in the following table:

Buckling curve of rectangular hollow sections and square hollow sections according to EN1993-1-1 Table 6.2
Type Steel Class Buckling Curve
Hot finished S235, S275, S355, S420 a
Hot finished S460 a0
Cold formed S235, S275, S355, S420 c
Cold formed S460 c