refers to the additional deflection caused by slip at the interface between steel and concrete Its three conditions all apply Condition (b) relates to the minimum value

of the degree of shear connection, η, given as 0.4 in clause 6.6.1.2(1), and gives a higher limit, 0.5.

For use where the design is such that 0.4 £ η < 0.5, ENV 1994-1-149_{gave the following}

equation for the additional deflection due to partial interaction:

δ = δc+ α(δa– δc)(1 – η) (D7.1)

where α = 0.5 for propped construction and 0.3 for unpropped construction, δa is the

deflection of the steel beam acting alone, and δcis the deflection for the composite beam with

complete interaction; both δaand δcare calculated for the design loading for the composite

member. The method comes from a summary of pre-1975 research on this subject,94_which

also gives results of relevant tests and parametric studies. Other methods are also available.95

Cracking in global analysis

Clause 7.3.1(5)

Apart from the different loading, global analysis for serviceability differs little from that for an ultimate limit state. Clause 5.4.1.1(2) requires ‘appropriate corrections’ for cracking of concrete, and clause 7.3.1(5) says that clause 5.4.2.3 applies. Clause 5.4.2.3(2) permits the use of the same distribution of beam stiffnesses at SLS as for ULS. Clauses 5.4.2.3(3) to

5.4.2.3(5) also apply, including the reference in clause 5.4.2.3(4) to a method given in Section 6 for the effect of cracking on the stiffness of composite columns.

Clause 7.3.1(6)

In the absence of cracking, continuous beams in buildings can often be assumed to be of uniform section within each span, which simplifies global analysis. Cracking reduces bending moments at internal supports to an extent that can be estimated by the method of clause

7.3.1(6), based on Stark and van Hove.95_{The maximum deflection of a given span normally}

occurs when no imposed load acts on adjacent spans. The conditions for the use of curve A in

Fig. 7.1 are then not satisfied, and the method consists simply of reducing all ‘uncracked’

moments at internal supports by 40%.

Using the new end moments, Mh1and Mh2, say, the maximum deflection can be found

either by elastic theory for the span, of uncracked flexural stiffness EaI1, or by an approximate

method given in BS 5950-3-1.31_{This consists of multiplying the deflection for the simply-}

supported span by the factor

1 – 0.6(Mh1+ Mh2)/M0 (D7.2)

where M0is the maximum sagging moment in the beam when it is simply supported.

Yielding of steel Clause 7.3.1(7)

In continuous beams built unpropped, with steel beams in Class 1 or 2, it is possible that serviceability loading may cause yielding at internal supports. This is permitted for beams in buildings, but it causes additional deflection, which should be allowed for. Clause 7.3.1(7) provides a method. The bending moments at internal supports are found by elastic analysis, with allowance for effects of cracking. The two values given in the clause for factors f2

correspond to different checks. The first is for dead load only: wet concrete on a steel beam. According to the UK’s draft National Annex to EN 1990,96_{the load combination to be}

used for the second check depends on the functioning of the structure. It may be the characteristic, frequent or quasi-permanent combination, with the load additional to that for the first check acting on the composite beam. For each analysis, appropriate assumptions are needed for the adjacent spans, on their loading and on the state of construction.

Local buckling

This does not influence stiffnesses for elastic analysis except for Class 4 sections. For these,

clause 5.4.1.1(6) refers to clause 2.2 in EN 1993-1-5, which gives a design rule. Shrinkage

Clause 7.3.1(8) In principle, shrinkage effects appear in all load combinations. For SLS, clause 5.4.2.2(7)refers to Section 7, where clause 7.3.1(8) enables effects of shrinkage on deflections of beams to be ignored for span/depth ratios up to 20. In more slender beams, shrinkage deflections are significantly reduced by provision of continuity at supports.

Temperature

Clause 5.4.2.5(2), on neglect of temperature effects, does not apply. For buildings, neither ψ0

nor ψ1is given as zero in clause A1.2.2 of EN 1990 (nor in the UK’s draft National Annex to

BS EN 199096_{), so if temperature effects are relevant at ULS, they should be included in all}

SLS combinations except quasi-permanent.

Welded mesh

Clause 5.5.1(6) gives conditions for the inclusion of welded mesh in the effective section,

within the rules for classification of sections.

7.3.2. Vibration

Clause 7.3.2(1)

Limits to vibration in buildings are material-independent, and vibration is in clause A1.4.4 of EN 1990, not in EN 1994. Composite floor systems are lighter and have less inherent damping than their equivalents in reinforced concrete. During their design, dynamic behaviour should be checked against the criteria in EN 1990 referred to from clause 7.3.2(1). These are general, and advise that the lowest natural frequency of vibration of the structure or member should be kept above a value to be agreed with the client and/or the relevant authority. No values are given for either limiting frequencies or damping coefficients.

More specific guidance can be found in EN 1991-1-1 and the extensive literature on this subject.97,98 _{These sources refer to several criteria that are likely to be specific to the}

individual project, and, with other aspects, should be agreed with the client. A note to clause 7.2.3 of EN 1993-1-1 says that limits to vibration of floors may be specified in a National Annex.

7.4. Cracking of concrete

7.4.1. General

In the early 1980s it was found44,99 _{that for composite beams in hogging bending, the}

long-established British methods for control of crack width were unreliable for initial cracks, which were wider than predicted. Before this, it had been found for reinforced concrete that the appropriate theoretical model for cracking caused by restraint of imposed deformation was different from that for cracking caused by applied loading. This has led to the presentation of design rules for control of cracking as two distinct procedures:

• for minimum reinforcement, in clause 7.4.2, for all cross-sections that could be subjected to significant tension by imposed deformations (e.g. by effects of shrinkage, which cause higher stresses than in reinforced concrete, because of restraint from the steel beam) • for reinforcement to control cracking due to direct loading (clause 7.4.3).

The rules given in EN 1994-1-1 are based on an extensive and quite complex theory, supported by testing on hogging regions of composite beams.99,100 _{Much of the original}

literature is in German, so a detailed account of the theory has recently been published in English,101 _{with comparisons with results of tests on composite beams, additional to}

those used originally. The paper includes derivations of the equations given in clause 7.4, comments on their scope and underlying assumptions, and procedures for estimating the mean width and spacing of cracks. These are tedious, and so are not in EN 1994-1-1. Its methods are simple: Tables 7.1 and 7.2 give maximum diameters and spacings of reinforcing bars for three design crack widths: 0.2, 0.3 and 0.4 mm.

Tables 7.1 and 7.2 are for ‘high-bond’ bars only. This means ribbed bars with properties as

in clause 3.2.2(2)P of EN 1992-1-1. The use of reinforcement other than ribbed is outside the scope of the Eurocodes.

Clause 7.4.1(1)

The references to EN 1992-1-1 in clause 7.4.1(1) give the surface crack-width limits required for design. Concrete in tension in a composite beam or slab for a building will usually be in exposure class XC3, for which the recommended limit is 0.3 mm; however, for spaces with low or very low air humidity, Tables 4.1 and 7.1N of EN 1992-1-1 recommend a limit of 0.4 mm. The limits are more severe for prestressed members, which are not discussed further. The severe environment for a floor of a multistorey car park is discussed in Chapter 4. All these limits may be modified in a National Annex.

Clause 7.4.1(2)

Clause 7.4.1(2) refers to ‘estimation’ of crack width, using EN 1992-1-1. This rather long