References
3.1 Mid-line theory
When calculating the section properties of light steel sections, it is standard practice to measure all dimensions along the mid-lines of the individual elements. Initially, corner radii are ignored resulting in an idealised section consisting of a series of thin rectangular elements. In calculating the lengths of the individual elements, an allowance is made for the intersection between adjacent elements, to avoid double-counting the over-lapping corner regions. Using the mid-line theory, this is simply achieved by measuring each element length between the points of intersection of the mid-lines. This results in a reduction in the element length below its nominal value of either t/2 or t, depending on the number of corners.
3.2 Corner radii
The use of mid-line theory results in an idealised section that is easy to analyse. However, without modification, the impact of the rounded corners on the section properties, which could be significant, is ignored.
3.3 Influence of rounded corners
The influence of rounded corners should always be taken into account when calculating cross section stiffness properties (EN 1993‑1‑3 (§5.1(3)).
Where the influence of rounded corners needs to be accounted for, this is achieved by first calculating the section properties assuming sharp corners (i.e. ignoring the corner radii) and then applying reduction factors as follows:
| For area, | Ag ≈ Ag,sh ( 1 - δ ) |
| For second moment of area, | Ig ≈ Ig,sh ( 1 - 2δ ) |
| For warping, | Iw ≈ Iw,sh ( 1 - 4δ ) |
In these expressions, the subscript 'sh' denotes the section property based on sharp corners and δ is a reduction factor given by:
where:
| rj | is the internal radius of curved element j |
| n | is the number of curved elements (number of corners) |
| øj | is the angle between two plane elements |
| bp,i | is the notional flat width of plane element i |
| m | is the number of plane elements. |
The same reduction factors may also be applied to the effective section properties (Aeff, Iy,eff, Iz,eff and Iw,eff) provided that the notional flat widths of the plane elements are measured to the points of intersection of their midlines.
3.4 Gross cross-section properties
Gross section properties for thin-walled cross-sections are determined using Annex C of EN 1993-1-3.
3.5 Effective section properties
The approach used in light steel design is that there is an implied assumption that the section is class 4 (although this term is not used in EN 1993-1-3). Having made this assumption, the design process focuses on the calculation of effective section properties, following the same procedures for design resistance as for class 4 sections to EN 1993-1-1. The use of effective section properties stems from the need to simplify the complex stress distributions associated with local buckling, in order to minimise the required computational effort, without being over conservative in terms of the cross-section resistance.