Classification of cross-sections

Typical types of cross-section are shown in Fig. 6.1. The classification of cross-sections of composite beams is the established method of taking account in design of local buckling of steel elements in compression. It determines the available methods of global analysis and the basis for resistance to bending, in the same way as for steel members. Unlike the method in EN 1993-1-1, it does not apply to columns.

Clause 5.5 A flow diagram for the provisions of clause 5.5 is given in Fig. 5.6. The clause numbers

given are from EN 1994-1-1, unless noted otherwise.

Clause 5.5.1(1)P Clause 5.5.1(1)P refers to EN 1993-1-1 for definitions of the four classes and the

slendernesses that define the class boundaries. Classes 1 to 4 correspond respectively to the terms ‘plastic’, ‘compact’, ‘ semi-compact’ and ‘slender’ that were formerly used in British codes. The limiting slendernesses are similar to those of BS 5950-3-1.³¹The numbers appear different because the two definitions of flange breadth are different, and the coefficient that takes account of yield strength, ε, is defined as ÷(235/fy) in the Eurocodes, and as ÷(275/fy) in BS 5950.

The scope of EN 1994-1-1 includes members where the cross-section of the steel component has no plane of symmetry parallel to the plane of its web (e.g. a channel section).

Asymmetry of the concrete slab or its reinforcement is also acceptable.

Clause 5.5.1(2) The classifications are done separately for steel flanges in compression and steel webs, but

the methods interact, as described below. The class of the cross-section is the less favourable of the classes so found (clause 5.5.1(2)), with three exceptions. One is where a web is assumed

0

Rigid–plastic Bending

moment

Elastic–perfectly plastic Elasto-plastic

Curvature

Fig. 5.5. Moment–curvature curves for various types of global analysis

to resist shear forces only (clause 5.5.2(12) of EN 1993-1-1). The others are the ‘hole-in-web’

option of clause 5.5.2(3) and the use of web encasement, both discussed later.

Reference is sometimes made to a beam in a certain class. This means that none of its cross-sections is in a less favourable class than the one stated, and may imply a certain distribution of bending moment. Clause 5.5.1(2) warns that the class of a composite section depends on the sign of the bending moment (sagging or hogging), as it does for a steel section that is not symmetrical about its neutral axis for bending.

Designers of structures for buildings normally select beams with steel sections such that the composite sections are in Class 1 or 2, for the following reasons:

• Rigid plastic global analysis is not excluded, provided that the sections at locations of plastic hinges are in Class 1.

Is steel compression flange to Table 5.2 of EN 1993-1-1

Note 1: ‘Flange’ means steel compression flange

Locate the plastic neutral axis, allowing for partial shear connection, if any

From clause 5.5.2(2), classify the web using the plastic stress distribution, to Table 5.2 of EN 1993-1-1

Locate the elastic neutral axis, assuming full shear connection, taking account of sequence of construction, creep, and shrinkage, to clause 5.5.1(4)

Web in Class 3

Class 2 Class 3 Class 4

Web not classified Web is Class 4

Is web encased to clause 5.5.3(2)? elastic stress distribution, to Table 5.2 of EN 1993-1-1

Is the compression flange in Class 1 or 2?

Is the compression flange in Class 3?

Replace web by effective web in Class 2, to clause 5.5.2(3)?

Web is Class 2 Effective web is Class 2

Is the flange in Class 1?

Section is Class 1 Section is Class 2 Web is Class 1

Yes Effective

section is

Class 2 Section is Class 3 Section is Class 4 No

Note 2: Where elastic global analysis will be used, and the web will be assumed to resist shear force only, clause 5.5.4(6) of EN 1993-1-1 permits the section to be designed as Class 2, 3 or 4, depending only on the class of the flange

Yes No

Fig. 5.6. Classification of a cross-section of a composite beam

• Bending resistances of beams can be found using plastic theory. For composite sections, this gives resistances from 20 to 40% above the elastic resistance, whereas the increase for steel sections is about 15%.

• The limits to redistribution of moments are more favourable than for Classes 3 and 4.

• Where composite floor slabs are used, it may be difficult to provide full shear connection. Clause 6.6.1.1(14) permits partial connection, but only where all beam cross-sections are in Class 1 or 2.

Clause 5.5.1(3) Simply-supported composite beams in buildings are almost always in Class 1 or 2, because

the depth of web in compression (if any) is small, and the connection to the concrete slab prevents local buckling of the adjacent steel flange. Clause 5.5.1(3) refers to this, and clause 5.5.2(1) refers to the more useful clause 6.6.5.5, which limits the spacing of the shear connectors required.

Clause 5.5.1(4) Since the class of a web depends on the level of the neutral axis, and this is different for

elastic and plastic bending, it is not obvious which stress distribution should be used for a section near the boundary between Classes 2 and 3. Clause 5.5.1(4) provides the answer, the plastic distribution. This is because the use of the elastic distribution could place a section in Class 2, for which the bending resistance would be based on the plastic distribution, which in turn could place the section in Class 3.

Clause 5.5.1(5)

Clause 5.5.1(6) Clause 5.5.1(5), on the minimum area of reinforcement for a concrete flange, appears

here, rather than in Section 6, because it gives a further condition for a cross-section to be placed in Class 1 or 2. The reason is that these sections must maintain their bending resistance, without fracture of the reinforcement, while subjected to higher rotation than those in Class 3 or 4. This is ensured by disallowing the use of bars in ductility Class A (the lowest), and by requiring a minimum cross-sectional area, which depends on the tensile force in the slab just before it cracks.⁴⁰Clause 5.5.1(6), on welded mesh, has the same objective.

Clause 5.5.1(7) Clause 5.5.1(7) draws attention to the use of unpropped construction, during which both

the top flange and the web of a steel beam may be in a lower class until the member becomes composite.

The hole-in-web method

Clause 5.5.2(3) This useful device first appeared in BS 5930-3-1.³¹It is now in clause 6.2.2.4 of EN 1993-1-1,

which is referred to from clause 5.5.2(3).

In beams subjected to hogging bending, it often happens that the bottom flange is in Class 1 or 2, and the web is in Class 3. The initial effect of local buckling of the web would be a small reduction in the bending resistance of the section. The assumption that a defined depth of web, the ‘hole’, is not effective in bending enables the reduced section to be upgraded from Class 3 to Class 2, with the advantages for design that are listed above. The method is analogous to the use of effective areas for Class 4 sections, to allow for local buckling.

There is a limitation to its scope that is not evident from the wording in EN 1993-1-1:

The proportion of the web in compression should be replaced by a part of 20εt_wadjacent to the compression flange, with another part of 20εtwadjacent to the plastic neutral axis of the effective cross-section.

It follows that for a design yield strength fydthe compressive force in the web is limited to 40εtwfyd. For a composite beam in hogging bending, the tensile force in the longitudinal reinforcement in the slab can exceed this value, especially where fydis reduced to allow for vertical shear. The method is then not applicable, because the second ‘part of 20εtw’ is not adjacent to the plastic neutral axis, which lies within the top flange. The method, and this limitation, are illustrated in Examples 6.1 and 6.2.

Partially encased cross-sections

Partially encased sections are defined in clause 6.1.1(1)P. Those illustrated there also have concrete flanges. The web encasement improves the resistance of both the web and the other

Clause 5.5.3(1) flange to local buckling. A concrete flange is not essential, as shown in clause 5.5.3(1), which gives the increased slenderness ratios for compression flanges in Classes 2 and 3. The limit for Class 1 is unaltered.

The rest of clause 5.5.3 specifies the encasement that enables a Class 3 web to be treated as Class 2, without loss of cross-section. Conditions under which the encasement contributes to the bending and shear resistance of the member are given in Section 6, where relevant comments will be found.

CHAPTER 6