I I

Eurocode 3 Table of design properties for steel tubes - Circular Hollow Sections (CHS)

Description:
Design aid - Table of design properties for circular hollow steel sections (CHS) 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 Circular Hollow Sections (CHS) according to EN1993-1-1
Notation for Circular Hollow Sections (CHS) according to EN1993-1-1
Tables
Design properties of hot finished Circular Hollow Section (CHS) for S235 steel class (γM0 = 1.00, units = mm)
Profile dimensionsArea propertiesInertia propertiesTorsional propertiesAxial force & shear resistanceBending moment resistanceTorsional resistance
Profile Drawing Ext. Diameter
D
[mm]
Wall thickness
t
[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 classification
CHS 21.3 / 2.3 dxf 21.3 2.3 1.08 0.067 137 87 0.006286 6.8 0.5902 0.8344 12.57 1.180 32.26 11.86 0.14 0.20 0.16 a 1
CHS 21.3 / 2.6 dxf 21.3 2.6 1.20 0.067 153 97 0.006806 6.7 0.639 0.9151 13.61 1.278 35.89 13.19 0.15 0.22 0.17 a 1
CHS 21.3 / 3.2 dxf 21.3 3.2 1.43 0.067 182 116 0.007684 6.5 0.7215 1.059 15.37 1.443 42.76 15.72 0.17 0.25 0.20 a 1
CHS 26.9 / 2.3 dxf 26.9 2.3 1.40 0.085 178 113 0.01356 8.7 1.008 1.396 27.13 2.017 41.77 15.35 0.24 0.33 0.27 a 1
CHS 26.9 / 2.6 dxf 26.9 2.6 1.56 0.085 198 126 0.01482 8.6 1.102 1.541 29.64 2.203 46.64 17.14 0.26 0.36 0.30 a 1
CHS 26.9 / 3.2 dxf 26.9 3.2 1.87 0.085 238 152 0.01703 8.5 1.266 1.808 34.07 2.533 55.99 20.58 0.30 0.42 0.34 a 1
CHS 33.7 / 2.6 dxf 33.7 2.6 1.99 0.106 254 162 0.03093 11.0 1.835 2.521 61.85 3.671 59.70 21.94 0.43 0.59 0.50 a 1
CHS 33.7 / 3.2 dxf 33.7 3.2 2.41 0.106 307 195 0.03605 10.8 2.139 2.988 72.09 4.279 72.06 26.48 0.50 0.70 0.58 a 1
CHS 33.7 / 4 dxf 33.7 4.0 2.93 0.106 373 238 0.0419 10.6 2.487 3.550 83.80 4.973 87.71 32.24 0.58 0.83 0.67 a 1
CHS 42.4 / 2.6 dxf 42.4 2.6 2.55 0.133 325 207 0.06464 14.1 3.049 4.124 129.3 6.099 76.40 28.08 0.72 0.97 0.83 a 1
CHS 42.4 / 3.2 dxf 42.4 3.2 3.09 0.133 394 251 0.0762 13.9 3.594 4.928 152.4 7.189 92.61 34.04 0.84 1.16 0.98 a 1
CHS 42.4 / 4 dxf 42.4 4.0 3.79 0.133 483 307 0.08991 13.6 4.241 5.920 179.8 8.482 113.40 41.68 1.00 1.39 1.15 a 1
CHS 48.3 / 2.6 dxf 48.3 2.6 2.93 0.152 373 238 0.09777 16.2 4.048 5.436 195.5 8.097 87.72 32.24 0.95 1.28 1.10 a 1
CHS 48.3 / 3.2 dxf 48.3 3.2 3.56 0.152 453 289 0.1159 16.0 4.797 6.520 231.7 9.595 106.55 39.16 1.13 1.53 1.30 a 1
CHS 48.3 / 4 dxf 48.3 4.0 4.37 0.152 557 354 0.1377 15.7 5.701 7.871 275.4 11.40 130.82 48.08 1.34 1.85 1.55 a 1
CHS 48.3 / 5 dxf 48.3 5.0 5.34 0.152 680 433 0.1615 15.4 6.689 9.416 323.1 13.38 159.84 58.75 1.57 2.21 1.81 a 1
CHS 60.3 / 2.6 dxf 60.3 2.6 3.70 0.189 471 300 0.1965 20.4 6.519 8.662 393.1 13.04 110.76 40.71 1.53 2.04 1.77 a 1
CHS 60.3 / 3.2 dxf 60.3 3.2 4.51 0.189 574 365 0.2347 20.2 7.784 10.44 469.4 15.57 134.90 49.58 1.83 2.45 2.11 a 1
CHS 60.3 / 4 dxf 60.3 4.0 5.55 0.189 707 450 0.2817 20.0 9.344 12.70 563.5 18.69 166.26 61.11 2.20 2.98 2.54 a 1
CHS 60.3 / 5 dxf 60.3 5.0 6.82 0.189 869 553 0.3348 19.6 11.10 15.33 669.5 22.21 204.13 75.03 2.61 3.60 3.01 a 1
CHS 76.1 / 2.6 dxf 76.1 2.6 4.71 0.239 600 382 0.4059 26.0 10.67 14.05 811.8 21.34 141.08 51.86 2.51 3.30 2.89 a 1
CHS 76.1 / 3.2 dxf 76.1 3.2 5.75 0.239 733 467 0.4878 25.8 12.82 17.02 975.6 25.64 172.22 63.30 3.01 4.00 3.48 a 1
CHS 76.1 / 4 dxf 76.1 4.0 7.11 0.239 906 577 0.5906 25.5 15.52 20.81 1181 31.04 212.92 78.26 3.65 4.89 4.21 a 1
CHS 76.1 / 5 dxf 76.1 5.0 8.77 0.239 1117 711 0.7092 25.2 18.64 25.32 1418 37.28 262.46 96.47 4.38 5.95 5.06 a 1
CHS 88.9 / 3.2 dxf 88.9 3.2 6.76 0.279 862 548 0.7921 30.3 17.82 23.51 1584 35.64 202.46 74.42 4.19 5.53 4.84 a 1
CHS 88.9 / 4 dxf 88.9 4.0 8.38 0.279 1067 679 0.9634 30.0 21.67 28.85 1927 43.35 250.72 92.15 5.09 6.78 5.88 a 1
CHS 88.9 / 5 dxf 88.9 5.0 10.3 0.279 1318 839 1.164 29.7 26.18 35.24 2327 52.36 309.71 113.83 6.15 8.28 7.10 a 1
CHS 88.9 / 6.3 dxf 88.9 6.3 12.8 0.279 1635 1041 1.402 29.3 31.55 43.07 2805 63.10 384.18 141.21 7.41 10.12 8.56 a 1
CHS 101.6 / 3.2 dxf 101.6 3.2 7.77 0.319 989 630 1.199 34.8 23.59 31.00 2397 47.19 232.47 85.44 5.54 7.28 6.40 a 1
CHS 101.6 / 4 dxf 101.6 4.0 9.63 0.319 1226 781 1.463 34.5 28.80 38.12 2926 57.59 288.22 105.94 6.77 8.96 7.81 a 1
CHS 101.6 / 5 dxf 101.6 5.0 11.9 0.319 1517 966 1.775 34.2 34.93 46.70 3549 69.87 356.59 131.06 8.21 10.97 9.48 a 1
CHS 101.6 / 6.3 dxf 101.6 6.3 14.8 0.319 1886 1201 2.151 33.8 42.34 57.30 4301 84.67 443.25 162.92 9.95 13.47 11.49 a 1
CHS 101.6 / 8 dxf 101.6 8.0 18.5 0.319 2352 1498 2.595 33.2 51.08 70.26 5190 102.2 552.82 203.19 12.00 16.51 13.86 a 1
CHS 101.6 / 10 dxf 101.6 10.0 22.6 0.319 2878 1832 3.054 32.6 60.12 84.24 6108 120.2 676.26 248.56 14.13 19.80 16.31 a 1
CHS 114.3 / 3.2 dxf 114.3 3.2 8.77 0.359 1117 711 1.725 39.3 30.18 39.51 3449 60.36 262.47 96.47 7.09 9.28 8.19 a 1
CHS 114.3 / 4 dxf 114.3 4.0 10.9 0.359 1386 882 2.111 39.0 36.93 48.69 4221 73.86 325.73 119.72 8.68 11.44 10.02 a 1
CHS 114.3 / 5 dxf 114.3 5.0 13.5 0.359 1717 1093 2.569 38.7 44.96 59.77 5138 89.91 403.47 148.30 10.56 14.05 12.20 a 1
CHS 114.3 / 6.3 dxf 114.3 6.3 16.8 0.359 2138 1361 3.127 38.2 54.72 73.57 6254 109.4 502.32 184.63 12.86 17.29 14.85 a 1
CHS 114.3 / 8 dxf 114.3 8.0 21.0 0.359 2672 1701 3.795 37.7 66.40 90.57 7590 132.8 627.83 230.76 15.60 21.28 18.02 a 1
CHS 114.3 / 10 dxf 114.3 10.0 25.7 0.359 3277 2086 4.497 37.0 78.68 109.1 8993 157.4 770.02 283.02 18.49 25.64 21.35 a 1
CHS 139.7 / 4 dxf 139.7 4.0 13.4 0.439 1705 1086 3.929 48.0 56.24 73.68 7857 112.5 400.74 147.29 13.22 17.31 15.26 a 1
CHS 139.7 / 5 dxf 139.7 5.0 16.6 0.439 2116 1347 4.805 47.7 68.80 90.76 9611 137.6 497.23 182.76 16.17 21.33 18.67 a 1
CHS 139.7 / 6.3 dxf 139.7 6.3 20.7 0.439 2640 1681 5.886 47.2 84.27 112.2 11770 168.5 620.46 228.05 19.80 26.37 22.87 a 1
CHS 139.7 / 8 dxf 139.7 8.0 26.0 0.439 3310 2107 7.203 46.6 103.1 138.9 14410 206.2 777.85 285.90 24.23 32.65 27.98 a 1
CHS 139.7 / 10 dxf 139.7 10.0 32.0 0.439 4075 2594 8.619 46.0 123.4 168.6 17240 246.8 957.54 351.95 29.00 39.61 33.48 a 1
CHS 139.7 / 12.5 dxf 139.7 12.5 39.2 0.439 4995 3180 10.20 45.2 146.0 202.9 20400 292.1 1173.86 431.45 34.32 47.68 39.63 a 1
CHS 168.3 / 4 dxf 168.3 4.0 16.2 0.529 2065 1314 6.971 58.1 82.84 108.0 13940 165.7 485.19 178.33 19.47 25.38 22.48 a 1
CHS 168.3 / 5 dxf 168.3 5.0 20.1 0.529 2565 1633 8.558 57.8 101.7 133.4 17120 203.4 602.80 221.56 23.90 31.34 27.60 a 1
CHS 168.3 / 6.3 dxf 168.3 6.3 25.2 0.529 3206 2041 10.53 57.3 125.2 165.4 21070 250.4 753.48 276.94 29.42 38.87 33.97 a 1
CHS 168.3 / 8 dxf 168.3 8.0 31.6 0.529 4029 2565 12.97 56.7 154.2 205.7 25950 308.3 946.76 347.99 36.23 48.35 41.83 a 1
CHS 168.3 / 10 dxf 168.3 10.0 39.0 0.529 4973 3166 15.64 56.1 185.9 250.9 31280 371.7 1168.69 429.55 43.68 58.97 50.43 a 1
CHS 168.3 / 12.5 dxf 168.3 12.5 48.0 0.529 6118 3895 18.68 55.3 222.0 304.1 37370 444.1 1437.79 528.46 52.18 71.46 60.25 a 1
CHS 177.8 / 5 dxf 177.8 5.0 21.3 0.559 2714 1728 10.14 61.1 114.1 149.3 20280 228.1 637.87 234.45 26.80 35.10 30.95 a 1
CHS 177.8 / 6.3 dxf 177.8 6.3 26.6 0.559 3394 2161 12.50 60.7 140.6 185.4 24990 281.1 797.67 293.19 33.03 43.56 38.14 a 1
CHS 177.8 / 8 dxf 177.8 8.0 33.5 0.559 4268 2717 15.41 60.1 173.4 230.8 30830 346.8 1002.87 368.61 40.75 54.24 47.05 a 1
CHS 177.8 / 10 dxf 177.8 10.0 41.4 0.559 5272 3356 18.62 59.4 209.4 281.9 37240 418.9 1238.82 455.33 49.22 66.25 56.83 a 1
CHS 177.8 / 12.5 dxf 177.8 12.5 51.0 0.559 6491 4132 22.30 58.6 250.8 342.2 44600 501.6 1525.46 560.69 58.94 80.42 68.06 a 1
CHS 193.7 / 5 dxf 193.7 5.0 23.3 0.609 2964 1887 13.20 66.7 136.3 178.1 26400 272.6 696.56 256.02 32.03 41.85 36.99 a 1
CHS 193.7 / 6.3 dxf 193.7 6.3 29.1 0.609 3709 2361 16.30 66.3 168.3 221.3 32600 336.6 871.62 320.37 39.55 52.01 45.67 a 1
CHS 193.7 / 8 dxf 193.7 8.0 36.6 0.609 4667 2971 20.16 65.7 208.1 276.0 40310 416.2 1096.78 403.12 48.91 64.87 56.47 a 1
CHS 193.7 / 10 dxf 193.7 10.0 45.3 0.609 5771 3674 24.42 65.0 252.1 337.8 48830 504.2 1356.21 498.48 59.24 79.38 68.41 a 1
CHS 193.7 / 12.5 dxf 193.7 12.5 55.9 0.609 7116 4530 29.34 64.2 303.0 411.1 58690 605.9 1672.19 614.62 71.20 96.60 82.21 a 1
CHS 193.7 / 14.2 dxf 193.7 14.2 62.9 0.609 8008 5098 32.45 63.7 335.1 458.5 64910 670.2 1881.79 691.66 78.74 107.74 90.93 a 1
CHS 193.7 / 16 dxf 193.7 16.0 70.1 0.609 8932 5686 35.54 63.1 367.0 506.6 71090 734.0 2099.06 771.52 86.24 119.05 99.58 a 1
CHS 219.1 / 5 dxf 219.1 5.0 26.4 0.688 3363 2141 19.28 75.7 176.0 229.2 38560 352.0 790.32 290.49 41.36 53.87 47.76 a 1
CHS 219.1 / 6.3 dxf 219.1 6.3 33.1 0.688 4212 2681 23.86 75.3 217.8 285.4 47720 435.6 989.76 363.79 51.19 67.06 59.10 a 1
CHS 219.1 / 8 dxf 219.1 8.0 41.6 0.688 5306 3378 29.60 74.7 270.2 356.7 59190 540.3 1246.80 458.26 63.49 83.82 73.31 a 1
CHS 219.1 / 10 dxf 219.1 10.0 51.6 0.688 6569 4182 35.98 74.0 328.5 437.6 71970 656.9 1543.73 567.40 77.19 102.83 89.13 a 1
CHS 219.1 / 12.5 dxf 219.1 12.5 63.7 0.688 8113 5165 43.45 73.2 396.6 534.2 86890 793.2 1906.59 700.77 93.20 125.54 107.61 a 1
CHS 219.1 / 14.2 dxf 219.1 14.2 71.8 0.688 9141 5819 48.20 72.6 440.0 597.1 96400 880.0 2148.07 789.53 103.40 140.32 119.39 a 1
CHS 219.1 / 16 dxf 219.1 16.0 80.1 0.688 10209 6499 52.97 72.0 483.5 661.4 105900 967.0 2399.10 881.79 113.62 155.42 131.20 a 1
CHS 219.1 / 20 dxf 219.1 20.0 98.2 0.688 12510 7964 62.61 70.7 571.5 795.5 125200 1143 2939.81 1080.53 134.31 186.94 155.09 a 1
CHS 244.5 / 5 dxf 244.5 5.0 29.5 0.768 3762 2395 26.99 84.7 220.7 286.8 53970 441.5 884.08 324.95 51.87 67.41 59.90 a 1
CHS 244.5 / 6.3 dxf 244.5 6.3 37.0 0.768 4714 3001 33.46 84.2 273.7 357.5 66920 547.4 1107.90 407.21 64.32 84.02 74.27 a 1
CHS 244.5 / 8 dxf 244.5 8.0 46.7 0.768 5944 3784 41.60 83.7 340.3 447.6 83210 680.6 1396.81 513.40 79.98 105.19 92.35 a 1
CHS 244.5 / 10 dxf 244.5 10.0 57.8 0.768 7367 4690 50.73 83.0 415.0 550.2 101500 830.0 1731.25 636.33 97.52 129.31 112.61 a 1
CHS 244.5 / 12.5 dxf 244.5 12.5 71.5 0.768 9111 5800 61.47 82.1 502.9 673.5 122900 1006 2141.00 786.93 118.17 158.26 136.45 a 1
CHS 244.5 / 14.2 dxf 244.5 14.2 80.6 0.768 10274 6541 68.37 81.6 559.3 754.1 136700 1119 2414.35 887.40 131.43 177.21 151.76 a 1
CHS 244.5 / 16 dxf 244.5 16.0 90.2 0.768 11486 7312 75.33 81.0 616.2 836.8 150700 1232 2699.13 992.07 144.80 196.64 167.21 a 1
CHS 244.5 / 20 dxf 244.5 20.0 110.7 0.768 14106 8980 89.57 79.7 732.7 1011 179100 1465 3314.85 1218.38 172.18 237.51 198.82 a 1
CHS 244.5 / 25 dxf 244.5 25.0 135.3 0.768 17239 10975 105.2 78.1 860.3 1210 210300 1721 4051.28 1489.06 202.17 284.28 233.45 a 1
CHS 273 / 5 dxf 273.0 5.0 33.0 0.858 4210 2680 37.81 94.8 277.0 359.2 75620 554.0 989.29 363.62 65.09 84.40 75.16 a 2
CHS 273 / 6.3 dxf 273.0 6.3 41.4 0.858 5279 3360 46.96 94.3 344.0 448.2 93920 688.0 1240.46 455.93 80.84 105.33 93.35 a 1
CHS 273 / 8 dxf 273.0 8.0 52.3 0.858 6660 4240 58.52 93.7 428.7 562.0 117000 857.4 1565.14 575.27 100.74 132.06 116.33 a 1
CHS 273 / 10 dxf 273.0 10.0 64.9 0.858 8262 5260 71.54 93.1 524.1 692.0 143100 1048 1941.66 713.66 123.17 162.63 142.22 a 1
CHS 273 / 12.5 dxf 273.0 12.5 80.3 0.858 10230 6512 86.97 92.2 637.2 848.9 173900 1274 2404.01 883.60 149.74 199.49 172.90 a 1
CHS 273 / 14.2 dxf 273.0 14.2 90.6 0.858 11545 7350 96.95 91.6 710.3 952.0 193900 1421 2713.13 997.22 166.91 223.73 192.73 a 1
CHS 273 / 16 dxf 273.0 16.0 101.4 0.858 12918 8224 107.1 91.0 784.4 1058 214100 1569 3035.78 1115.81 184.33 248.67 212.85 a 1
CHS 273 / 20 dxf 273.0 20.0 124.8 0.858 15896 10120 128.0 89.7 937.6 1283 256000 1875 3735.67 1373.05 220.34 301.47 254.43 a 1
CHS 273 / 25 dxf 273.0 25.0 152.9 0.858 19478 12400 151.3 88.1 1108 1543 302500 2216 4577.30 1682.40 260.42 362.56 300.71 a 1
CHS 323.9 / 5 dxf 323.9 5.0 39.3 1.018 5009 3189 63.69 112.8 393.3 508.5 127400 786.6 1177.18 432.67 92.42 119.50 106.72 a 2
CHS 323.9 / 6.3 dxf 323.9 6.3 49.3 1.018 6286 4002 79.29 112.3 489.6 635.6 158600 979.2 1477.20 542.95 115.05 149.36 132.85 a 2
CHS 323.9 / 8 dxf 323.9 8.0 62.3 1.018 7939 5054 99.10 111.7 611.9 798.5 198200 1224 1865.77 685.77 143.80 187.65 166.05 a 1
CHS 323.9 / 10 dxf 323.9 10.0 77.4 1.018 9861 6278 121.6 111.0 750.7 985.7 243200 1501 2317.44 851.78 176.43 231.63 203.72 a 1
CHS 323.9 / 12.5 dxf 323.9 12.5 96.0 1.018 12229 7785 148.5 110.2 916.7 1213 296900 1833 2873.73 1056.25 215.43 285.00 248.76 a 1
CHS 323.9 / 14.2 dxf 323.9 14.2 108.5 1.018 13816 8795 166.0 109.6 1025 1363 332000 2050 3246.74 1193.35 240.86 320.29 278.13 a 1
CHS 323.9 / 16 dxf 323.9 16.0 121.5 1.018 15477 9853 183.9 109.0 1136 1518 367800 2271 3637.03 1336.80 266.85 356.78 308.13 a 1
CHS 323.9 / 20 dxf 323.9 20.0 149.9 1.018 19095 12156 221.4 107.7 1367 1850 442800 2734 4487.23 1649.29 321.25 434.70 370.95 a 1
CHS 323.9 / 25 dxf 323.9 25.0 184.3 1.018 23476 14945 264.0 106.0 1630 2239 528000 3260 5516.75 2027.70 383.08 526.10 442.35 a 1
CHS 355.6 / 6.3 dxf 355.6 6.3 54.3 1.117 6913 4401 105.5 123.5 593.2 768.7 210900 1186 1624.64 597.14 139.40 180.66 160.97 a 2
CHS 355.6 / 8 dxf 355.6 8.0 68.6 1.117 8736 5562 132.0 122.9 742.5 966.8 264000 1485 2052.99 754.58 174.48 227.19 201.48 a 1
CHS 355.6 / 10 dxf 355.6 10.0 85.2 1.117 10857 6912 162.2 122.2 912.5 1195 324500 1825 2551.48 937.80 214.43 280.76 247.60 a 1
CHS 355.6 / 12.5 dxf 355.6 12.5 105.8 1.117 13474 8578 198.5 121.4 1117 1472 397000 2233 3166.27 1163.77 262.39 345.95 302.98 a 1
CHS 355.6 / 14.2 dxf 355.6 14.2 119.6 1.117 15230 9696 222.3 120.8 1250 1656 444500 2500 3579.07 1315.49 293.78 389.16 339.23 a 1
CHS 355.6 / 16 dxf 355.6 16.0 134.0 1.117 17070 10867 246.6 120.2 1387 1847 493300 2774 4011.49 1474.43 325.97 433.95 376.40 a 1
CHS 355.6 / 20 dxf 355.6 20.0 165.5 1.117 21086 13424 297.9 118.9 1676 2255 595800 3351 4955.30 1821.33 393.76 529.98 454.67 a 1
CHS 355.6 / 25 dxf 355.6 25.0 203.8 1.117 25965 16530 356.8 117.2 2007 2738 713500 4013 6101.84 2242.75 471.54 643.34 544.49 a 1
CHS 406.4 / 6.3 dxf 406.4 6.3 62.2 1.277 7919 5041 158.5 141.5 780.0 1009 317000 1560 1860.92 683.98 183.30 237.02 211.65 a 2
CHS 406.4 / 8 dxf 406.4 8.0 78.6 1.277 10013 6374 198.7 140.9 978.0 1270 397500 1956 2353.03 864.86 229.84 298.44 265.40 a 2
CHS 406.4 / 10 dxf 406.4 10.0 97.8 1.277 12453 7928 244.8 140.2 1205 1572 489500 2409 2926.52 1075.65 283.06 369.34 326.85 a 1
CHS 406.4 / 12.5 dxf 406.4 12.5 121.4 1.277 15468 9848 300.3 139.3 1478 1940 600600 2956 3635.08 1336.08 347.30 455.93 401.03 a 1
CHS 406.4 / 14.2 dxf 406.4 14.2 137.3 1.277 17496 11138 336.9 138.8 1658 2185 673700 3315 4111.63 1511.24 389.57 513.52 449.84 a 1
CHS 406.4 / 16 dxf 406.4 16.0 154.0 1.277 19624 12493 374.5 138.1 1843 2440 749000 3686 4611.56 1694.99 433.09 573.39 500.09 a 1
CHS 406.4 / 20 dxf 406.4 20.0 190.6 1.277 24278 15456 454.3 136.8 2236 2989 908600 4472 5705.38 2097.03 525.42 702.36 606.70 a 1
CHS 406.4 / 25 dxf 406.4 25.0 235.1 1.277 29955 19070 547.0 135.1 2692 3642 1094000 5384 7039.45 2587.37 632.63 855.84 730.50 a 1
CHS 406.4 / 30 dxf 406.4 30.0 278.5 1.277 35475 22584 632.2 133.5 3111 4259 1264000 6223 8336.59 3064.14 731.18 1000.94 844.29 a 1
CHS 406.4 / 40 dxf 406.4 40.0 361.4 1.277 46043 29312 781.9 130.3 3848 5391 1564000 7696 10820.15 3976.97 904.22 1266.95 1044.11 a 1
CHS 457 / 6.3 dxf 457.0 6.3 70.0 1.436 8920 5679 226.5 159.4 991.4 1280 453100 1983 2096.26 770.49 232.99 300.75 269.03 a 3
CHS 457 / 8 dxf 457.0 8.0 88.6 1.436 11285 7184 284.5 158.8 1245 1613 568900 2490 2651.88 974.71 292.56 379.05 337.81 a 2
CHS 457 / 10 dxf 457.0 10.0 110.2 1.436 14043 8940 350.9 158.1 1536 1998 701800 3071 3300.09 1212.96 360.90 469.63 416.73 a 1
CHS 457 / 12.5 dxf 457.0 12.5 137.0 1.436 17455 11112 431.4 157.2 1888 2470 862900 3776 4102.04 1507.71 443.72 580.54 512.37 a 1
CHS 457 / 14.2 dxf 457.0 14.2 155.1 1.436 19754 12576 484.6 156.6 2121 2785 969300 4242 4642.09 1706.21 498.42 654.52 575.53 a 1
CHS 457 / 16 dxf 457.0 16.0 174.0 1.436 22167 14112 539.6 156.0 2361 3113 1079000 4723 5209.26 1914.68 554.94 731.57 640.79 a 1
CHS 457 / 20 dxf 457.0 20.0 215.5 1.436 27458 17480 656.8 154.7 2874 3822 1314000 5749 6452.52 2371.64 675.50 898.18 780.00 a 1
CHS 457 / 25 dxf 457.0 25.0 266.3 1.436 33929 21600 794.2 153.0 3475 4671 1588000 6951 7973.36 2930.63 816.74 1097.64 943.09 a 1
CHS 457 / 30 dxf 457.0 30.0 315.9 1.436 40244 25620 921.7 151.3 4034 5479 1843000 8068 9457.29 3476.05 947.95 1287.53 1094.60 a 1
CHS 457 / 40 dxf 457.0 40.0 411.4 1.436 52402 33360 1149 148.1 5031 6977 2299000 10060 12314.41 4526.20 1182.19 1639.57 1365.08 a 1
CHS 508 / 6.3 dxf 508.0 6.3 77.9 1.596 9930 6321 312.5 177.4 1230 1586 624900 2460 2333.47 857.67 289.09 372.67 333.81 a 3
CHS 508 / 8 dxf 508.0 8.0 98.6 1.596 12566 8000 392.8 176.8 1546 2000 785600 3093 2953.10 1085.42 363.42 470.04 419.64 a 2
CHS 508 / 10 dxf 508.0 10.0 122.8 1.596 15645 9960 485.2 176.1 1910 2480 970400 3820 3676.61 1351.35 448.91 582.89 518.35 a 2
CHS 508 / 12.5 dxf 508.0 12.5 152.7 1.596 19458 12388 597.6 175.2 2353 3070 1195000 4705 4572.69 1680.70 552.86 721.37 638.38 a 1
CHS 508 / 14.2 dxf 508.0 14.2 172.9 1.596 22029 14024 672.0 174.7 2646 3463 1344000 5291 5176.75 1902.73 621.72 813.91 717.90 a 1
CHS 508 / 16 dxf 508.0 16.0 194.1 1.596 24731 15744 749.1 174.0 2949 3874 1498000 5898 5811.70 2136.10 693.06 910.48 800.27 a 1
CHS 508 / 20 dxf 508.0 20.0 240.7 1.596 30662 19520 914.3 172.7 3600 4766 1829000 7199 7205.56 2648.42 845.89 1119.90 976.75 a 1
CHS 508 / 25 dxf 508.0 25.0 297.8 1.596 37935 24150 1109 171.0 4367 5837 2218000 8734 8914.66 3276.61 1026.21 1371.80 1184.97 a 1
CHS 508 / 30 dxf 508.0 30.0 353.6 1.596 45050 28680 1292 169.3 5086 6864 2583000 10170 10586.85 3891.23 1195.11 1612.93 1379.99 a 1
CHS 508 / 40 dxf 508.0 40.0 461.7 1.596 58811 37440 1622 166.1 6385 8782 3244000 12770 13820.49 5079.76 1500.56 2063.84 1732.69 a 1
CHS 508 / 50 dxf 508.0 50.0 564.7 1.596 71942 45800 1909 162.9 7515 10530 3818000 15030 16906.48 6214.02 1766.06 2474.52 2039.27 a 1
CHS 610 / 6.3 dxf 610.0 6.3 93.8 1.916 11948 7607 544.4 213.5 1785 2296 1089000 3570 2807.89 1032.05 419.45 539.59 484.34 a EN 1993-1-6
CHS 610 / 8 dxf 610.0 8.0 118.8 1.916 15130 9632 685.5 212.9 2248 2899 1371000 4495 3555.53 1306.84 528.18 681.36 609.89 a 3
CHS 610 / 10 dxf 610.0 10.0 148.0 1.916 18850 12000 848.5 212.2 2782 3600 1697000 5564 4429.65 1628.13 653.74 846.08 754.87 a 2
CHS 610 / 12.5 dxf 610.0 12.5 184.2 1.916 23464 14938 1048 211.3 3435 4463 2095000 6869 5513.99 2026.68 807.13 1048.86 931.99 a 1
CHS 610 / 14.2 dxf 610.0 14.2 208.6 1.916 26579 16921 1180 210.7 3869 5042 2360000 7738 6246.07 2295.76 909.21 1184.78 1049.87 a 1
CHS 610 / 16 dxf 610.0 16.0 234.4 1.916 29858 19008 1318 210.1 4321 5647 2636000 8641 7016.56 2578.95 1015.37 1326.98 1172.44 a 1
CHS 610 / 20 dxf 610.0 20.0 291.0 1.916 37071 23600 1615 208.7 5295 6965 3230000 10590 8711.64 3201.98 1244.26 1636.70 1436.75 a 1
CHS 610 / 25 dxf 610.0 25.0 360.7 1.916 45946 29250 1969 207.0 6456 8561 3938000 12910 10797.26 3968.56 1517.15 2011.80 1751.85 a 1
CHS 610 / 30 dxf 610.0 30.0 429.1 1.916 54664 34800 2305 205.3 7557 10100 4610000 15110 12845.97 4721.57 1775.80 2373.74 2050.51 a 1
CHS 610 / 40 dxf 610.0 40.0 562.3 1.916 71628 45600 2923 202.0 9585 13020 5847000 19170 16832.65 6186.89 2252.40 3059.07 2600.85 a 1
CHS 610 / 50 dxf 610.0 50.0 690.5 1.916 87965 56000 3476 198.8 11400 15720 6951000 22790 20671.68 7597.93 2678.00 3694.59 3092.29 a 1
CHS 711 / 6.3 dxf 711.0 6.3 109.5 2.234 13947 8879 865.9 249.2 2436 3129 1732000 4871 3277.65 1204.71 572.37 735.24 660.91 a EN 1993-1-6
CHS 711 / 8 dxf 711.0 8.0 138.7 2.234 17668 11248 1092 248.6 3071 3954 2183000 6141 4152.05 1526.10 721.61 929.15 833.24 a 3
CHS 711 / 10 dxf 711.0 10.0 172.9 2.234 22023 14020 1353 247.9 3806 4914 2706000 7612 5175.30 1902.20 894.40 1154.87 1032.76 a 3
CHS 711 / 12.5 dxf 711.0 12.5 215.3 2.234 27430 17462 1673 247.0 4707 6099 3347000 9415 6446.06 2369.27 1106.21 1433.37 1277.34 a 2
CHS 711 / 14.2 dxf 711.0 14.2 244.0 2.234 31085 19789 1887 246.4 5309 6895 3775000 10620 7304.90 2684.93 1247.62 1620.44 1440.62 a 2
CHS 711 / 16 dxf 711.0 16.0 274.2 2.234 34935 22240 2110 245.8 5936 7730 4221000 11870 8209.61 3017.46 1395.06 1816.49 1610.88 a 1
CHS 711 / 20 dxf 711.0 20.0 340.8 2.234 43417 27640 2594 244.4 7295 9552 5187000 14590 10202.95 3750.12 1714.41 2244.79 1979.64 a 1
CHS 711 / 25 dxf 711.0 25.0 422.9 2.234 53878 34300 3174 242.7 8927 11770 6347000 17850 12661.40 4653.73 2097.86 2765.98 2422.40 a 1
CHS 711 / 30 dxf 711.0 30.0 503.8 2.234 64183 40860 3728 241.0 10490 13920 7456000 20970 15082.94 5543.78 2464.30 3271.63 2845.52 a 1
CHS 711 / 40 dxf 711.0 40.0 661.9 2.234 84320 53680 4762 237.7 13400 18030 9525000 26790 19815.28 7283.16 3148.16 4237.28 3635.18 a 1
CHS 711 / 50 dxf 711.0 50.0 815.1 2.234 103830 66100 5703 234.4 16040 21890 11410000 32090 24399.96 8968.27 3769.99 5143.61 4353.21 a 1
CHS 711 / 60 dxf 711.0 60.0 963.3 2.234 122711 78120 6556 231.1 18440 25500 13110000 36880 28836.99 10599.11 4333.67 5992.51 5004.09 a 1
CHS 762 / 6.3 dxf 762.0 6.3 117.4 2.394 14957 9522 1068 267.2 2803 3598 2136000 5605 3514.86 1291.89 658.60 845.51 760.49 a EN 1993-1-6
CHS 762 / 8 dxf 762.0 8.0 148.8 2.394 18950 12064 1347 266.6 3535 4548 2694000 7070 4453.27 1636.81 830.72 1068.85 959.24 a EN 1993-1-6
CHS 762 / 10 dxf 762.0 10.0 185.5 2.394 23625 15040 1670 265.9 4384 5655 3341000 8768 5551.82 2040.59 1030.23 1329.01 1189.60 a 3
CHS 762 / 12.5 dxf 762.0 12.5 231.0 2.394 29433 18738 2067 265.0 5426 7023 4135000 10850 6916.71 2542.25 1275.11 1650.29 1472.37 a 2
CHS 762 / 14.2 dxf 762.0 14.2 261.9 2.394 33360 21238 2333 264.4 6123 7942 4665000 12250 7839.56 2881.45 1438.81 1866.29 1661.40 a 2
CHS 762 / 16 dxf 762.0 16.0 294.4 2.394 37498 23872 2610 263.8 6850 8906 5219000 13700 8812.04 3238.89 1609.68 2092.82 1858.70 a 1
CHS 762 / 20 dxf 762.0 20.0 366.0 2.394 46621 29680 3211 262.4 8427 11010 6422000 16850 10955.99 4026.90 1980.43 2588.28 2286.81 a 1
CHS 762 / 25 dxf 762.0 25.0 454.4 2.394 57884 36850 3935 260.7 10330 13580 7869000 20650 13602.70 4999.71 2426.86 3192.34 2802.30 a 1
CHS 762 / 30 dxf 762.0 30.0 541.6 2.394 68989 43920 4629 259.0 12150 16080 9257000 24300 16212.50 5958.95 2854.87 3779.67 3296.52 a 1
CHS 762 / 40 dxf 762.0 40.0 712.2 2.394 90729 57760 5930 255.7 15560 20870 11860000 31130 21321.36 7836.72 3657.68 4905.08 4223.52 a 1
CHS 762 / 50 dxf 762.0 50.0 877.9 2.394 111841 71200 7122 252.3 18690 25390 14240000 37390 26282.56 9660.22 4392.88 5966.38 5072.46 a 1
CHS 813 / 8 dxf 813.0 8.0 158.8 2.554 20232 12880 1639 284.6 4032 5184 3278000 8064 4754.49 1747.52 947.52 1218.33 1094.10 a EN 1993-1-6
CHS 813 / 10 dxf 813.0 10.0 198.0 2.554 25227 16060 2034 283.9 5003 6448 4067000 10010 5928.34 2178.98 1175.66 1515.38 1357.53 a 3
CHS 813 / 12.5 dxf 813.0 12.5 246.8 2.554 31436 20012 2519 283.1 6196 8011 5037000 12390 7387.36 2715.24 1456.02 1882.50 1681.27 a 2
CHS 813 / 14.2 dxf 813.0 14.2 279.7 2.554 35635 22686 2843 282.5 6994 9062 5686000 13990 8374.22 3077.96 1643.64 2129.50 1897.91 a 2
CHS 813 / 16 dxf 813.0 16.0 314.5 2.554 40062 25504 3182 281.8 7828 10160 6364000 15660 9414.47 3460.31 1839.66 2388.71 2124.25 a 2
CHS 813 / 20 dxf 813.0 20.0 391.1 2.554 49826 31720 3919 280.5 9641 12580 7838000 19280 11709.03 4303.68 2265.65 2956.22 2616.15 a 1
CHS 813 / 25 dxf 813.0 25.0 485.8 2.554 61889 39400 4809 278.7 11830 15530 9617000 23660 14544.00 5345.69 2779.86 3649.27 3209.90 a 1
CHS 813 / 30 dxf 813.0 30.0 579.3 2.554 73796 46980 5664 277.0 13930 18400 11330000 27870 17342.06 6374.12 3274.24 4324.39 3780.77 a 1
CHS 914 / 8 dxf 914.0 8.0 178.7 2.871 22770 14496 2337 320.3 5113 6567 4673000 10230 5351.01 1966.78 1201.49 1543.21 1387.36 a EN 1993-1-6
CHS 914 / 10 dxf 914.0 10.0 222.9 2.871 28400 18080 2901 319.6 6349 8172 5803000 12700 6674.00 2453.05 1492.00 1920.54 1722.82 a EN 1993-1-6
CHS 914 / 12.5 dxf 914.0 12.5 277.9 2.871 35402 22538 3597 318.8 7871 10160 7194000 15740 8319.43 3057.83 1849.70 2387.47 2135.85 a 3
CHS 914 / 14.2 dxf 914.0 14.2 315.1 2.871 40141 25554 4063 318.2 8892 11500 8127000 17780 9433.05 3467.14 2089.52 2701.99 2412.77 a 2
CHS 914 / 16 dxf 914.0 16.0 354.3 2.871 45138 28736 4551 317.5 9959 12900 9103000 19920 10607.52 3898.82 2340.44 3032.40 2702.51 a 2
CHS 914 / 20 dxf 914.0 20.0 440.9 2.871 56172 35760 5615 316.2 12290 15990 11230000 24570 13200.34 4851.82 2887.16 3757.04 3333.81 a 1
CHS 914 / 25 dxf 914.0 25.0 548.1 2.871 69822 44450 6903 314.4 15110 19760 13810000 30210 16408.15 6030.86 3549.77 4644.36 4098.92 a 1
CHS 914 / 30 dxf 914.0 30.0 654.0 2.871 83315 53040 8148 312.7 17830 23450 16300000 35660 19579.03 7196.32 4189.76 5511.38 4837.92 a 1
CHS 1016 / 8 dxf 1016.0 8.0 198.9 3.192 25334 16128 3218 356.4 6334 8129 6436000 12670 5953.44 2188.20 1488.55 1910.24 1718.83 a EN 1993-1-6
CHS 1016 / 10 dxf 1016.0 10.0 248.1 3.192 31604 20120 3998 355.7 7871 10120 7997000 15740 7427.04 2729.83 1849.70 2378.36 2135.85 a EN 1993-1-6
CHS 1016 / 12.5 dxf 1016.0 12.5 309.3 3.192 39407 25088 4961 354.8 9766 12590 9922000 19530 9260.73 3403.80 2295.06 2958.25 2650.10 a 3
CHS 1016 / 14.2 dxf 1016.0 14.2 350.8 3.192 44691 28451 5608 354.2 11040 14250 11220000 22080 10502.36 3860.17 2594.08 3349.25 2995.38 a 3
CHS 1016 / 16 dxf 1016.0 16.0 394.6 3.192 50265 32000 6285 353.6 12370 16000 12570000 24740 11812.39 4341.67 2907.34 3760.32 3357.10 a 2
CHS 1016 / 20 dxf 1016.0 20.0 491.3 3.192 62581 39840 7763 352.2 15280 19840 15530000 30560 14706.42 5405.38 3591.26 4663.10 4146.83 a 2
CHS 1016 / 25 dxf 1016.0 25.0 611.0 3.192 77833 49550 9561 350.5 18820 24560 19120000 37640 18290.75 6722.81 4422.84 5770.95 5107.06 a 1
CHS 1016 / 30 dxf 1016.0 30.0 729.5 3.192 92928 59160 11300 348.8 22250 29170 22610000 44500 21838.15 8026.67 5228.99 6856.10 6037.92 a 1
CHS 1067 / 10 dxf 1067.0 10.0 260.7 3.352 33207 21140 4638 373.7 8693 11170 9276000 17390 7803.56 2868.22 2042.95 2625.61 2358.99 a EN 1993-1-6
CHS 1067 / 12.5 dxf 1067.0 12.5 325.1 3.352 41410 26362 5757 372.8 10790 13900 11510000 21580 9731.38 3576.79 2535.74 3266.57 2928.02 a 3
CHS 1067 / 14.2 dxf 1067.0 14.2 368.7 3.352 46966 29900 6508 372.3 12200 15740 13020000 24400 11037.02 4056.69 2866.81 3698.91 3310.30 a 3
CHS 1067 / 16 dxf 1067.0 16.0 414.7 3.352 52829 33632 7296 371.6 13680 17670 14590000 27350 12414.82 4563.10 3213.82 4153.62 3711.00 a 2
CHS 1067 / 20 dxf 1067.0 20.0 516.4 3.352 65785 41880 9018 370.2 16900 21930 18040000 33810 15459.46 5682.17 3972.11 5152.81 4586.60 a 2
CHS 1067 / 25 dxf 1067.0 25.0 642.4 3.352 81838 52100 11110 368.5 20830 27150 22230000 41660 19232.04 7068.79 4895.38 6380.09 5652.70 a 1
CHS 1067 / 30 dxf 1067.0 30.0 767.2 3.352 97735 62220 13150 366.8 24650 32270 26300000 49290 22967.71 8441.84 5791.81 7583.47 6687.80 a 1
CHS 1168 / 10 dxf 1168.0 10.0 285.6 3.669 36380 23160 6098 409.4 10440 13410 12200000 20890 8549.22 3142.29 2453.99 3151.34 2833.62 a EN 1993-1-6
CHS 1168 / 12.5 dxf 1168.0 12.5 356.2 3.669 45376 28888 7574 408.6 12970 16690 15150000 25940 10663.45 3919.38 3047.79 3922.24 3519.29 a EN 1993-1-6
CHS 1168 / 14.2 dxf 1168.0 14.2 404.1 3.669 51472 32768 8567 408.0 14670 18900 17130000 29340 12095.86 4445.86 3447.15 4442.62 3980.43 a 3
CHS 1168 / 16 dxf 1168.0 16.0 454.6 3.669 57906 36864 9608 407.3 16450 21240 19220000 32900 13607.87 5001.61 3866.13 4990.23 4464.22 a 3
CHS 1168 / 20 dxf 1168.0 20.0 566.2 3.669 72131 45920 11890 405.9 20350 26360 23770000 40710 16950.78 6230.30 4783.02 6194.78 5522.96 a 2
CHS 1168 / 25 dxf 1168.0 25.0 704.7 3.669 89771 57150 14670 404.2 25120 32670 29330000 50230 21096.19 7753.96 5902.03 7676.61 6815.08 a 1
CHS 1219 / 10 dxf 1219.0 10.0 298.2 3.830 37982 24180 6940 427.5 11390 14620 13880000 22770 8925.74 3280.68 2675.86 3435.03 3089.81 a EN 1993-1-6
CHS 1219 / 12.5 dxf 1219.0 12.5 371.9 3.830 47379 30162 8622 426.6 14150 18200 17240000 28290 11134.10 4092.37 3324.24 4276.10 3838.50 a EN 1993-1-6
CHS 1219 / 14.2 dxf 1219.0 14.2 421.9 3.830 53747 34216 9753 426.0 16000 20610 19510000 32000 12630.51 4642.38 3760.52 4844.02 4342.27 a 3
CHS 1219 / 16 dxf 1219.0 16.0 474.7 3.830 60469 38496 10940 425.4 17950 23160 21880000 35900 14210.30 5223.03 4218.40 5441.83 4870.99 a 3
CHS 1219 / 20 dxf 1219.0 20.0 591.4 3.830 75335 47960 13540 424.0 22220 28750 27080000 44430 17703.82 6507.08 5221.10 6757.35 6028.81 a 2
CHS 1219 / 25 dxf 1219.0 25.0 736.1 3.830 93777 59700 16720 422.2 27430 35650 33440000 54860 22037.49 8099.94 6446.11 8376.84 7443.32 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. For the case of circular hollow sections that cannot be classified as Class 3 their strength and stability verifications should be based on EN 1993-1-6: Strength and Stability of Shell Structures
Details

Design properties for circular hollow steel sections (CHS) according to EN1993-1-1

Definition of the cross-section

For typical Circular Hollow Sections (CHS) 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 fully define the cross-section are: external diameter D and wall thickness t. The notation is defined in EN1993-1-1 §1.7 which is reproduced in the figure above.

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 I, which is constant for any axis of bending due to symmetry. They are calculated by adding the contribution of the external boundary and then subtracting the contribution of the internal void.

A = π⋅D2 / 4 - π⋅(D-2⋅t)2 / 4

I = π⋅D4 / 64 - π⋅(D-2⋅t)4 / 64

Shear area

The shear area Av for the case of circular hollow sections is specified in EN1993-1-1 §6.2.6(3) as:

Av = 2⋅A / π

Due to symmetry the shear area is constant for shear load along any axis.

Elastic section modulus

The elastic section modulus Wel is calculated by dividing the second moment of the area I with the corresponding distance from the centroid to the most distant edge:

Wel = I / (D / 2)

Plastic section modulus

The plastic section modulus Wpl corresponds 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 a bending axis passing through the centroid.

The plastic section modulus Wpl is calculated by adding the contribution of the external boundary and then subtracting the contribution of the internal void. The centroid of a semi-circular segment is located 2D / 3π from the center of the arc. The following result is obtained:

Wpl = 2⋅(π⋅D2 / 4 / 2)⋅(2⋅D / 3⋅π) - 2⋅(π⋅(D-2⋅t)2 / 4 / 2)⋅(2⋅(D-2⋅t) / 3⋅π) ⇒
Wpl = [D3 - (D-2⋅t)3] / 6

Torsional properties

For circular cross-sections and tubular cross sections the torsional constant IT is equal to the polar moment of inertia of the area IP that is given by the following relation:

IT = IP = 2⋅I

For circular cross-sections and tubular cross sections the maximum shear stress due to St. Venant torsion τ is related to the maximum torque T by the following relation:

T = τIP / (D / 2)

Therefore the torsional modulus WT is obtained as:

WT = T / τ = 2⋅Wel

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 applicable 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) 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.

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 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 = Av ⋅ ( 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 multiplied by the steel yield stress fy:

Mpl,Rd = Welfy / γM0

The elastic bending moment resistance is applicable for class 3 cross-sections. For the case of circular hollow sections that cannot be classified as Class 3 their strength and stability verifications should be based on EN 1993-1-6: Strength and Stability of Shell Structures.

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 multiplied by the steel yield stress fy:

Mpl,Rd = Wplfy / 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 circular hollow sections (tubular sections) is specified in EN1993-1-1 Table 5.2. The class of the cross-section in bending and/or compression depends on the ratio of its diameter D to the wall thickness t, adjusted by the factor ε that takes into account the value of the steel yield stress fy:

ε = (235 MPa / fy)0.5

The diameter to wall thickness limits D / t for cross-section classification according to EN1993-1-1 Table 5.2 are presented below:

Classification of tubular sections according to EN1993-1-1 Table 5.2
Ratio D / t Section Class
D / t ≤ 50ε2 Class 1
D / t ≤ 70ε2 Class 2
D / t ≤ 90ε2 Class 3
D / t > 90ε2 See EN1993-1-6

For the case of circular hollow sections (tubular sections) that cannot be classified as Class 3 their strength and stability verifications should be based on EN 1993-1-6: Strength and Stability of Shell Structures.

Buckling curves

The appropriate buckling curve for circular 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 circular 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