Section classification

How EN 1993-1-1 Table 5.2 classifies a steel section, why the class depends on the combination, and what the check does with shapes it cannot classify.

Design checks 5 min read

Before a steel cross-section can be checked, EN 1993-1-1 asks which class it is. The class decides whether the resistance is plastic or elastic, and therefore which modulus the check divides the moment by. Getting it wrong in the optimistic direction costs about 10 to 15% for an I-section bent about its strong axis, and up to 50% about its weak axis, where $W_{pl} / W_{e l}$ is about 1.5.

The four classes

Class	Behaviour	Bending resistance uses
1	Forms a plastic hinge with the rotation capacity plastic analysis needs	$W_{pl}$
2	Reaches the plastic moment, but local buckling limits rotation	$W_{pl}$
3	Reaches yield in the extreme fibre; local buckling prevents the plastic moment	$W_{e l}$
4	Local buckling before yield in one or more parts	$W_{e f f}$ — an effective section

Cross-section classes as moment–rotation behaviour (left) and the stress block each class is designed with (right). The class decides which resistance a check may use: plastic for 1 and 2, elastic for 3, an effective section for 4.

Classes 1 and 2 give the same cross-section resistance in this module; the distinction matters for plastic global analysis, which is not in this release. Class 3 gives the elastic resistance. Class 4 is verified on an effective section to EN 1993-1-5 §4.4, for doubly symmetric I and H and rectangular hollow sections.

Where the limits come from

A section is classified by its compressed parts. Each flange outstand and each internal web panel is compared, as a width-to-thickness ratio $c / t$ , against a limit that scales with

ε = \frac{235}{f _{y}}

Higher-strength steel gets a smaller $ε$ and therefore tighter limits: a section that is Class 1 in S235 can be Class 2 or 3 in S460 with no change to its geometry.

$f_{y}$ (MPa)	235	275	355	420	460
$ε$	1.00	0.92	0.81	0.75	0.71

Table 5.2 for doubly symmetric I and H sections

Internal compression parts (the web of an I-section):

Stress distribution	Class 1	Class 2	Class 3
Pure bending	$c / t \leq 72 ε$	$c / t \leq 83 ε$	$c / t \leq 124 ε$
Pure compression	$c / t \leq 33 ε$	$c / t \leq 38 ε$	$c / t \leq 42 ε$
Bending and compression	Between the two, by $α$ (plastic) or $ψ$ (elastic)

Outstand flanges (half the flange width less the root radius and half the web):

Stress distribution	Class 1	Class 2	Class 3
Uniform compression	$c / t \leq 9 ε$	$c / t \leq 10 ε$	$c / t \leq 14 ε$

$c$ is the flat width of the part (for a rolled section, the web depth between the fillets and the flange outstand beyond the fillet) and $t$ its thickness. The section is the class of its worst part.

Worked example

IPE 400 in S355: $h = 400$ , $b = 180$ , $t_{w} = 8.6$ , $t_{f} = 13.5$ , $r = 21$ mm.

ε = 235/355 = 0.814

Web, pure bending:

c c / t_{w} = h - 2 t_{f} - 2 r = 400 - 27 - 42 = 331 mm = 331/8.6 = 38.5 \leq 72 ε = 58.6 \Rightarrow Class 1

Flange:

c c / t_{f} = (b - t_{w}) /2 - r = (180 - 8.6) /2 - 21 = 64.7 mm = 64.7/13.5 = 4.8 \leq 9 ε = 7.3 \Rightarrow Class 1

Class 1 in bending. In pure compression the web's Class 1 limit is $33 ε = 26.9$ , and 38.5 exceeds even the Class 3 limit of $42 ε = 34.2$ . The same section is Class 4 in pure compression, which is one reason columns are usually H-sections, not I-sections.

Classification depends on the combination

The web limits depend on the stress distribution across the web, which depends on the ratio of axial force to moment, and that ratio differs in every load combination. The same member can be Class 1 under a bending-led combination and Class 3 under a compression-led one.

Elementarium classifies at every station, for every combination, and the check reports the worst class encountered. The utilisation at each station uses the class at that station under that combination; the reported class is the summary, not the input. See Steel — EN 1993-1-1.

What the module classifies

Section	How
Doubly symmetric I and H	Table 5.2, from the outline dimensions in the section definition
Rectangular hollow and welded box	Table 5.2, with the flat width $c = b - 3 t$
Solid rectangular and circular	Class 1 by definition — no slender part exists
Everything else	Verified elastically as Class 3, with a message saying so

Channels, angles, tees, circular hollow sections and built-up shapes are not classified in this release. The module uses the elastic resistance instead of guessing: conservative for a section that is really Class 1 or 2, correct for Class 3, unconservative for Class 4, and flagged on the check.

AISC

AISC 360 has its own version of the same idea (compact, noncompact and slender, from Table B4.1), with the same purpose and different limits. The Chapter F flexural strengths in the AISC module depend on it in the same way.

Reading the trace

Every utilisation expands to show the classification it used alongside the other intermediate values. If the class is not what you expected, work the $c / t$ ratios by hand as above. It takes a minute, and a disagreement over one width-to-thickness ratio is a much shorter argument than one over a utilisation.

Steel — EN 1993-1-1 for the checks the class feeds; National annexes for the $γ_{M 0}$ every resistance is divided by.

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