Round Steel Tube (CHS) Section Properties
Mass, area, second moment and section modulus of 12 standard round steel tubes.
Round tube, called a circular hollow section (CHS), is the stiffest shape for its weight in torsion and in bending in every direction, which makes it a favorite for frames, handrails, roll cages, posts and columns. The outside diameters in this table are the standard pipe sizes (33.7, 42.4, 48.3, 60.3 mm and so on), shown with a common wall thickness for each.
All the properties are exact geometry, computed from the outside diameter and wall.
The table
| Outside diameter D (mm) | Wall t (mm) | Mass (kg/m) | Area (cm2) | I (cm4) | Elastic modulus W (cm3) | Radius of gyration i (cm) | Torsion constant section modulus Wt (cm3) |
|---|---|---|---|---|---|---|---|
| 33.7 | 3.2 | 2.41 | 3.07 | 3.6 | 2.14 | 1.08 | 4.28 |
| 42.4 | 3.2 | 3.09 | 3.94 | 7.62 | 3.59 | 1.39 | 7.19 |
| 48.3 | 3.2 | 3.56 | 4.53 | 11.59 | 4.8 | 1.6 | 9.59 |
| 60.3 | 3.6 | 5.03 | 6.41 | 25.87 | 8.58 | 2.01 | 17.16 |
| 76.1 | 3.6 | 6.44 | 8.2 | 54.01 | 14.19 | 2.57 | 28.39 |
| 88.9 | 4 | 8.38 | 10.67 | 96.34 | 21.67 | 3 | 43.35 |
| 114.3 | 4.5 | 12.19 | 15.52 | 234.32 | 41 | 3.89 | 82 |
| 139.7 | 5 | 16.61 | 21.16 | 480.54 | 68.8 | 4.77 | 137.59 |
| 168.3 | 5 | 20.14 | 25.65 | 855.85 | 101.7 | 5.78 | 203.41 |
| 219.1 | 6.3 | 33.06 | 42.12 | 2386.14 | 217.81 | 7.53 | 435.63 |
| 273 | 6.3 | 41.44 | 52.79 | 4695.82 | 344.02 | 9.43 | 688.03 |
| 323.9 | 8 | 62.32 | 79.39 | 9910.08 | 611.92 | 11.17 | 1223.84 |
Source and notes: Circular hollow sections of the standard pipe outside diameters (EN 10210, EN 10219; see ISO 4200). Everything is exact geometry: A = pi/4 (D2 - d2), I = pi/64 (D4 - d4), W = I / (D/2), Wt = 2W, mass at 7 850 kg/m3.
How to use this table
- Find the outside diameter and wall.
- Bending stress = moment ÷ section modulus W; deflection uses the second moment I.
- The radius of gyration i is the same in every direction, so a tube column has no weak axis.
- For a twisting load the stress is moment ÷ torsion modulus Wt (twice W for a thin tube).
Worked example: a 1 m cantilever tube with 500 N at the end
- The tube is 60.3 mm × 3.6 mm: mass 5.03 kg/m, W = 8.58 cm³, I = 25.87 cm⁴.
- Bending moment at the wall = 500 N × 1 m = 500 N·m.
- Bending stress = M ÷ W = 500 000 N·mm ÷ 8 580 mm³ = 58.3 MPa, well below the yield of S355 steel (355 MPa).
- Tip deflection = F L³ ÷ (3 E I) = 500 × 1 000³ ÷ (3 × 210 000 × 258 700) = 3.1 mm.
Notes and cautions
- Seamless pipe, welded structural tube (EN 10219) and cold-finished tube are made in these diameters with several wall thicknesses; the table lists one common wall for each size.
- Thin-walled tubes can buckle locally when D ÷ t is large (more than about 50 for common steels), which limits the usable bending moment.
- The mass is for steel at 7 850 kg/m³; aluminum tube is about 0.34 times as heavy.
Related tools and guides
- Beam Calculator with Diagrams and Section Properties
- Square Hollow Section (SHS) Properties
- Steel Pipe Sizes (NPS and DN, Schedule 40 and 80)
- Columns and Buckling (guide)
- All reference tables
FAQ
Why is tube better than solid bar for bending?
Material near the surface carries most of the bending stress, so a tube gives a much higher section modulus for the same mass than a solid round bar.
What is the section modulus of a round tube?
W = π (D⁴ − d⁴) ÷ (32 D), where D is the outside and d the inside diameter. It equals I ÷ (D/2).
Sources
- EN 10210 and EN 10219 (hot finished and cold formed structural hollow sections); EN 10220 and ISO 4200 (standard plain-end pipe diameters and walls).
- Circular hollow sections of the standard pipe outside diameters (EN 10210, EN 10219; see ISO 4200). Everything is exact geometry: A = pi/4 (D2 – d2), I = pi/64 (D4 – d4), W = I / (D/2), Wt = 2W, mass at 7 850 kg/m3.