Unified slenderness limits for structural steel circular hollow sections


  • Leroy Gardner
  • Kwan Ho Lan
  • Craig Buchanan


circular hollow sections, reliability analysis, section classification, slenderness limits, tubular construction


Circular hollow sections (CHS) are widely used in a range of structural engineering applications. The sections may be hot-finished or cold-formed from a variety of metallic materials with a range of yield strengths. The design of these sections is covered by all major design codes, yet there are significant differences in the treatment of local buckling, as considered through cross-section classification. Cross-section classification criteria relate to rotation capacity and strength requirements (attainment of the plastic or elastic moment in bending and the yield load in compression), while the relative performance of structural CHS is governed by susceptibility to local buckling and is influenced by cross-section slenderness, material stiffness and yield strength, forming process (affecting geometry, material homogeneity and residual stresses), material strain hardening characteristics and ovalization. Furthermore, the classification criteria and reliability requirements vary among the different structural design codes. This paper presents a review of 153 test results on CHS in bending, covering structural steel, aluminium, stainless steel and very high strength steel. Based on the available test data, current codified provisions in the European, North American and Australian Standards are reassessed, and following reliability analyses new unified slenderness limits are proposed for structural steel CHS.


DUTTA, D., Structures with Hollow Sections, Wiley VCH, Weinheim, 2002.

EN 1993-1-1 (2005) Eurocode 3: Design of steel structures – Part 1–1: General rules and rules for buildings, CEN, 2005.

BS 5950-1 (2000) Structural use of steelwork in building – Part 1: Code of practice for design – rolled and welded sections, BSI, 2000.

EN 1993-1-4 (2006) Eurocode 3: Design of steel structures – Part 1–4: General rules – supplementary rules for stainless steels, CEN, 2006.

EN 1999-1-1 (2007) Eurocode 9: Design of aluminium structures – Part 1–1: General structural rules, CEN, 2007.

AISC 360 (2005) Load and Resistance Factor Design Specification for Structural Steel Buildings, American Institute of Steel Construction, Chicago, 2005.

AS 4100 (1998) Steel Structures, Standards Australia, Homebush, New South Wales, Australia, 1998.

ZHAO, X. L., Section capacity of very high strength (VHS) circular tubes under compression, Department of Civil Engineering, Monash University, Australia, 2000.

IABSE, Use and application of high-performance steels for steel structures, Structural Engineering Documents, 2005.

ZHAO, X. L. and JIAO, H., Imperfection, residual stress and yield slenderness limit of very high strength (VHS) circular steel tubes, Journal of Constructional Steel Research, 59, 2, pp. 233–249, 2003.

ZHAO, X. L. and JASPART, J. P., Width-to-thickness ratios for classification of tubular sections, Eurosteel 2005, June 8-10, 2005, pp.1.4–183–190, 2005.

SCHILLING, C. G., Buckling strength of circular tubes, Journal of the Structural Division, ASCE, 91, 5, 1965.

KATO, B., Local buckling of steel circular tubes in plastic range, Stability of Structures under Static and Dynamic Loads, ASCE, pp.375–391, 1977.

BRAZIER, L. G., On the Flexure of Thin Cylindrical Shells and other “Thin” Sections, Proceedings of the Royal Society A, 116, 773, pp.104–114, 1927.

ELCHALAKANI, M., ZHAO, X. L. and GRZEBIETA, R. H., Plastic mechanism analysis of circular tubes under pure bending tests to determine slenderness limits for cold-formed circular hollow sections, International Journal of Mechanical Sciences, 44, 6, pp.1117–1143, 2002.

EN 1993-1-6 (2007) Eurocode 3: Design of steel structures – Part 1-6: Strength and Stability of Shell Structures, CEN, 2007.

GARDNER, L. and CHAN, T. M., Cross-section classification of elliptical hollow sections, Steel and Composite Structures, 7, 3, pp.185–200, 2007.

SEDLACEK, G., STRANHÖNER, N., LANGENBERG, P., RONDAL, J. and BOREAEVE, P., Rotation Capacity of Hollow Beam Sections, Final Report-CIDECT Research Project, No 2P, RWTH, Aachen, 1995.

SHERMAN, D. R., Supplemental tests for bending capacity of fabricated pipes, Department of Civil Engineering, University of Wisconsin – Milwaukee, 1984.

JIRSA, J. O., FOOK-HOY, L., WILHOIT, J. C. and MERWIN, J. E., Ovaling of pipelines under pure bending, Paper OTC 1569, 4th Annual Offshore Technology Conf., Houston, Texas, 1972.

SHERMAN, D. R., Tests of circular steel tubes in bending, Journal of the Structural Division, ASCE, 102, 11, 1976.

SHERMAN, D. R., Bending Capacity of Fabricated Tubes, Department of Civil Engineering. University of Wisconsin – Milwaukee, 1983.

KOROL, R. M., Critical buckling strains of round tubes in flexure, Department of Civil Engineering, Mc Master University, Hamilton, Ontario, Canada L8S 4L8, 1978.