Section properties
Circular hollow section (tube): A, I, Z, r
- where
- inside diameter (mm)
- outside diameter (mm)
- wall thickness (mm)
- area (cm²)
- second moment of area (cm⁴)
- elastic section modulus (cm³)
- radius of gyration (cm)
Explain this equation
Works out section properties of a circular tube, which are the same about any axis.
The tube is a solid circle of diameter D with a circle of diameter d removed. Area is π/4 times the difference of the squares; second moment is π/64 times the difference of the fourth powers. Z is I divided by the outer radius in cm, D/20. r is √(I/A). The powers of ten convert mm to cm.
Solid-circle formulas, outer minus inner.
Sense check: 168.3 × 6.3 CHS gives about 32 cm², 1053 cm⁴ and 125 cm³, the same as the published tables.
Watch out: tubes are efficient in compression and torsion because their stiffness is equal in every direction.
Properties of round tube from outside diameter and wall thickness. A tube has the same properties about every axis through its centre.
Enter your values to see the result.
Good to know
These are exact for a perfect tube and agree with the Blue Book tables for CHS. Radius of gyration r is used for strut (column) buckling checks: the slenderness is the effective length divided by r.
Common mistake
Using the solid-bar formula πD⁴/64 without subtracting the bore, or entering the nominal pipe bore instead of the outside diameter.
Limits
Elastic properties only. Very thin tubes (D/t over about 90 for S275) are slender and need a local buckling check.
Sources
- SCI / Steel for Life Blue Book: Steel building design – design data (section property formulas and tables for UKB, UKC, hot-finished and cold-formed hollow sections)
- BS EN 10210-2:2019 Hot finished steel structural hollow sections – Part 2: Tolerances, dimensions and sectional properties (density 7.85 kg/dm³)
Results are calculations from the published methods and figures shown, and depend on the data you enter. Follow the welding procedure specification (WPS), BS EN ISO 15614/9606, BS EN 1090, BS EN 1993 and manufacturers’ data. Structural welds need qualified welders and engineered designs.