Hollow Section Design Theory - CHS, SHS, RHS (Eurocode 3)

Closed sections and torsion

A closed (hollow) section is enormously stiffer in torsion than an open one of the same size - by orders of magnitude. This makes hollow sections the natural choice wherever torsion or biaxial loading matters, and means lateral-torsional buckling is rarely critical for them.

Compression performance

Square and circular hollow sections have equal (or near-equal) radii of gyration about both axes, so there is no weak axis - buckling resistance is the same in every direction. Combined with their high torsional stiffness, this makes SHS/CHS very efficient columns, and they are widely used architecturally for their clean appearance.

Hot-finished vs cold-formed

Hot-finished hollow sections (EN 10210) have uniform properties and sharper corner geometry; cold-formed (EN 10219) are formed at ambient temperature, with work-hardened, more rounded corners and slightly different design parameters. The tool lists both - check which standard a project specifies.

Combined axial + bending (interaction)

Hollow-section beam-columns are verified by the cross-section interaction (§6.2.9), where axial load $n=N_{Ed}/N_{pl,Rd}$ reduces the moment resistance to $M_{N,Rd}$, and the member stability check (§6.3.3). Both Expressions (6.61) and (6.62) must be satisfied:

Because closed sections are not susceptible to torsional deformation, the Annex B factors take their simpler Table B.1 form ($k_{zy}=0.6\,k_{yy}$), and the $k_{zz}$ form for RHS uses $C_{mz}\,[1+(\bar\lambda_z-0.2)\,n_z]$ rather than the I-section expression. For SHS and CHS there is no lateral-torsional buckling, so $M_{b,Rd}=M_{c,Rd}$ in the equations above. The worked example evaluates the factors and both expressions for a representative section.