Class 3 - local buckling prevents attainment of full plastic moment
Class 4 - local buckling prevents attainment of yield moment
Rotation, 0
Fig. 5.6. The four behavioural classes of cross-section defined by Eurocode 3
bending. Class 3 cross-scctions are fully effective in pure compression, but local buckling prevents attainment of the full plastic moment in bending; bending moment resistance is therefore limited to the (elastic) yield moment. For Class 4 cross-sections, local buckling occurs in the elastic range. An effective cross-section is therefore defined based on the width-to-thickness ratios of individual plate elements, and this is used to determine the cross-sectional resistance. In hot-rolled design the majority of standard cross-sections will be Class 1, 2 or 3, where resistances may be based on gross section properties obtained from section tables. Effective width formulations are not contained in Part 1.1 of Eurocode 3, but are instead to be found in Part 1.5; these are discussed later in this section.
For cold-formed cross-sections, which are predominantly of an open nature (e.g. a channel section) and of light-gauge material, design will seldom be based on the gross section properties; the design requirements for cold-formed members are covered in Eurocode 3 - Part 1.3 and in Chapter 14 of this guide.
Each compressed (or partially compressed) element is assessed individually against the limiting width-to-thickness ratios for Class 1. 2 and 3 elements defined in Table 5.2 (see Table 5.1). An element that fails to meet the Class 3 limits should be taken as Class 4. Table 5.2 contains three sheets. Sheet 1 is for internal compression parts, defined as those supported along each edge by an adjoining flange or web. Sheet 2 is for outstand flanges, where one edge of the part is supported by an adjoining flange or web and the other end is free. Sheet 3 deals with angles and tubular (circular hollow) sections.
The limiting width-to-thickness ratios are modified by a factor that is dependent upon the material yield strength. (For circular hollow members the width-to-thickness ratios are modified by r\) s is defined as where/ is the nominal yield strength of the steel as defined in Table 3.1. Clearly, increasing the nominal material yield strength results in stricter classification limits. It is worth noting that the definition of e in Eurocode 3 (equation (D5.2)) utilizes a base value of 235 N/mnr, simply because grade S235 steel is regarded as the normal grade throughout Europe, and is thus expected to be the most widely used. In comparison, BS 5950 and BS 5400 use 275 and 355 N/mm2 as base values, respectively.
The nominal yield strength depends upon the steel grade, the standard to which the steel is produced, and the nominal thickness of the steel element under consideration. Two
Rolled
Welded
Welded
Fig. 5.7. Definition of compression width c for common cases, (a) Outstand flanges, (b) Internal compression parts thickness categories are defined in Table 3.1 of EN 1993-1-1. The first is up to and including 40 mm, and the second greater than 40 mm and less than 80 mm (for hot-rolled structural steel) or less than 65 mm (for structural hollow sections). However, the UK National Annex is likely to specify that material properties are taken from the relevant product standard, as described in Section 3.2 of this guide; essentially this results in a reversion to thickness categories as adopted in BS 5950.
The classification limits provided in Table. 5.2 assume that the cross-section is stressed to Clause 5.5.2(9) yield, though where this is not the case, clauses 5.5.2(9) and 5.5.2(10) may allow some Clause 5.5.2( 10) relaxation of the Class 3 limits. For cross-sectional checks and when buckling resistances are Clause 5.3 determined by means of a second-order analysis, using the member imperfections of clause
5.3, Class 4 cross-sections may be treated as Class 3 if the width-to-thickness ratios are less than the limiting proportions for Class 3 sections when s is increased by a factor to give the definition of equation (D5.3):
\ ^cnm. hd where ¿rcom Kri should be taken as the maximum design compressive stress that occurs in the member.
For conventional member design, whereby buckling resistances are determined using the Clause 6.3 buckling curves defined in clause 6.3, no modification to the basic definition of s (given by equation (D5.2)) is permitted, and the limiting proportions from Table 5.2 should always be applied.
The purpose of this subsection is to provide notes of clarification on Table 5.2 (reproduced here as Table 5.1) and to contrast the approach and slenderness limits with those set out in Section 3.5 of BS 5950: Part 1 (2000).
In general, the Eurocode 3 approach to section classification is more rational than that of BS 5950. but perhaps less practical in some cases. The following points are worth noting:
(1) For sheets 1 and 2 of Table 5.2, all classification limits are compared with cit ratios (compressive width-to-thickness ratios), with the appropriate dimensions for c and t taken from the accompanying diagrams.
(2) The compression widths c defined in sheets 1 and 2 always adopt the dimensions of the flat portions of the cross-sections, i.e. root radii and welds are explicitly excluded from the measurement, as emphasized by Fig. 5.7. This was not the case in the ENV version of Eurocode 3 or BS 5950. where generally more convenient measures were adopted (such as for the width of an outstand flange of an 1 section, taken as half the total flange width).
(3) Implementation of point 2 and re-analysis of test results has enabled Eurocode 3 to offer the same classification limits for both rolled and welded cross-sections.
(4) For rectangular hollow sections where the value of the internal corner radius is not known, it may be assumed that the compression width c can be taken as equal to b - 31.
The factor kr that appears in sheet 2 of Table 5.2 is a buckling factor, which depends on the stress distribution and boundary conditions in the compression element. Calculation of kff is described in Section 6.2.2 of this guide, and should be carried out with reference to Part 1.5 of the code.
Table 5.1 (sheet I of 3). Maximum width-to-thickness ratios for compression parts (Table 5.2 of EN 1993-1-1)
Internal compression parts
Table 5.1 (sheet I of 3). Maximum width-to-thickness ratios for compression parts (Table 5.2 of EN 1993-1-1)
Internal compression parts
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