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  • The definition of ‘continuous composite beam’ given in Eurocode 4: Part 1.1[12] is: A beam with three or more supports, in which the steel section is either continuous over internal supports or is jointed by full strength and rigid connections, with connections between the beam and each support such that it can be assumed that the support does not transfer significant bending moment to the beam. At the internal supports the beam may have either effective reinforcement or only nominal reinforcement. Beam-to-column connections in steelwork are classified in Eurocode 3: Part 1.1[11] both by stiffness, as:

    nominally pinned,
    rigid, or
    and by strength, as:
    nominally pinned,
    full-strength, or

    In Eurocode 4: Part 1.1, a ‘composite connection’ is defined as: A connection between a composite member and any other member in which reinforcement is intended to contribute to the resistance of the connection. The system of classification is as for steel connections, except that semi-rigid connections are omitted, because design methods for them are not ye sufficiently developed. A ‘full-strength and rigid’ connection has to be at least as stiff and strong as the beams connected, so a ‘continuous composite beam’ can be analyzed for bending moments as one long member without internal connections, by methods to be explained in Section 4.3. Bridge girders (Volume 2) are usually of this type. The example to be used here is a two-span beam continuous over a wall or supporting beam. In multi-bay plane frames, commonly used in structures for buildings, the beam-to-column connections are often ‘nominally pinned’. The beams are then designed as simply-supported, where full-strength connections are used, the frame should be analysed as a whole, and the beams are not ‘continuous’ as defined above. These beams are referred to here as ‘beams in frames’, as are those with partial-strength connections. In comparison with simple spans, beams in frames have the same advantages and disadvantages as continuous beams. The global analysis is more complex than for continuous beams, because the properties of columns and connections are involved, but the design of hogging moment regions of the beams is the same. In Section 4.3 on global analysis, only continuous beams are considered. For a given floor slab and design load per unit length of beam, the advantages of continuous beams over simple spans are:

    higher span/depth ratios can be used, for given limits to deflections;
    cracking of the top surface of a floor slab near internal columns can be controlled, so that the
    use of brittle finishes (e.g. terrazzo) is feasible;
    the floor structure has a higher fundamental frequency of vibration, and so is less susceptible
    to vibration caused by movements of people;
    the structure is more robust (e.g. in resisting the effects of or explosion).

    The principal disadvantage is that design is more complex. Actions on one span cause action effects in adjacent spans, and the stiffness and bending resistance of a beam very along its length. It is not possible to predict accurately the stresses or deflections in a continuous beam for a given set of actions. Apart from the variation over time caused by the shrinkage and creep of concrete, there are the effects of cracking of concrete. In reinforced concrete beams, these occur at all cross-sections, and so have little influence on distributions of bending moment. In composite beams, significant tension in concrete occurs only in hogging regions. It is influenced by the sequence of construction of the slab, the method of propping used (if any), and by effects of temperature, shrinkage, and longitudinal slip.

    The flexural rigidity of a fully cracked composite section can be as low as quarter of the ‘uncracked’ value, so a wide variation in flexural rigidity can occur along a continuous beam of uniform section. This leads to uncertainty in the distribution of longitudinal moments, and hence in the amount of cracking to be expected. The response to a particular set of actions also depends on whether it precedes or follows another set of actions that causes cracking in a different part of the beam.

    For these reasons, and also for economy, design is based as far as possible on predictions of ultimate strength (which can be checked by testing) rather than on analyses based on elastic theory. Methods have to be developed from simplified models of behaviour. The limits set to be scope of some models seem arbitrary, as they correspond to the range of available research data, rather than to known limitations of the model.

    Almost the whole of Chapter 3, on simply-supported beams and slabs, applies equally to the sagging moment regions of continuous members. The follows of hogging moment regions of beams are treated in Section 4.2, which applies also to cantilevers. Then follows the global analysis of continuous beams, and the calculations of stresses and deflections. Both rolled steel I- or H-sections and small plate or box girders are considered, with or without web encasement and composite slabs. It is always assumed that the concrete slab is above the steel member, because the use of slabs below steel beams with which they are composite is almost unknown in buildings, though it occurs in bridges.

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  • Fire design, based on the 1993 draft Eurocode 4: Part 1.2, ‘Structural fire design’, is introduced in Section 3.3.7, the whole of which is applicable to composite beams, as well as to slabs, except Section
    Beams rarely have insulation or integrity functions, and have then to be designed only for the loadbearing function, R. The fire resistance class is normally the same as that of the slab that acts as the top flange of the beam, so only the structural steel section needs further protection. This may be provided by full encasement in concrete of a lightweight fire-resisting material. A more recent method is to encase only the web in concrete. This can be done before the beam is erected (except near end connections), and gives a cross-section of the type shown in Fig.3.31.
    In a fire, the exposed bottom flange loses its strength, but the protected web and top flange do not.
    For the higher load levels η *(defined in Section and longer periods of fire resistance, minimum areas of longitudinal reinforcement within the encasement, ‘
    sA , are specified, in terms
    of the cross-sectional area f A of the steel bottom flange. The minimum depth a h and breadth f b of the steel I-section are also specified, for each standard fire resistance period.

    The requirements of draft Eurocode 4; Part 1.2 for 60 minutes’ fire exposure (class R60) are shown in Fig.3.28. The minimum dimensions ha and bf increase with η *, as shown by the three lines in Fig.3.28(a). For other values of η *, interpolation may used.
    The minimum ratios f A’ / A are zero for η* = 0.5 (ADE). For η* = 0.7 they are indicated  within the regions where they apply. To ensure that the additional reinforcement maintatins its strength for the period of fire exposure, minimum distances 1 a and 2 a are specified, in terms of Lmin b and the fire class. Those for class R60 are show in Fig.3.28(b).

    The validity of tabulated data of this type is inevitably limited. The principal conditions for its use, given in the Eurocode, are as follows. The notation is as in Fig.3.15.
    (a) The composite beam must be simply-supported with

    (b) If the slab is composite, the voids formed above the steel beam by trapezoidal profiles must be filled with fire-resistant material.
    (c) The web must be encased in normal-density concrete, held in place by stirrups, fabric, or stud connectors that pass through or are welded to the steel web.
    The data given in Fig.3.28 are used for the design example in Section 3.11.4. The Eurocode also gives both simple and advanced calculation models, which are often less conservative than the trbulated data, and have wider applicability. These are outside the scope of this volume.

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  • In composite floors that need checking for vibration, damping is sufficiently low for its influence  on natural frequencies to be neglected. For free elastic vibration of a beam or one-way slab of uniform section, the fundamental natural frequency is

    Values for other end conditions and multi-span members are given by Wyatt. The relevant flexural rigidity is El (pre unit width, for slabs), L is the span, and m the vibrating mass per unit length (beams) or unit area (slabs). Concrete in slabs should normally be assumed to be uncracked, and the dynamic modulus of elasticity should be used for concrete, in both beams and slabs. This modulus, Ecd, is typically about 8 kN/mm2 higher than the static modulus, for normal-density concrete, and 3 to 6 kN/mm2 higher, for lightweight-aggregate concretes of density not less than 1800kg/m3. For composite beams in sagging bending, approximate allowance for these effects can be made by increasing the value of I for variable loading by 10%.
    Unless a more accurate estimate can be made, the mass m is usually taken as the mass of the characteristic permanent load plus 10% of the characteristic variable load. A convenient method of calculating f0 is to find first the midspan deflection, m Ύ say, caused by the weight of the mass m. For simply-supported members this is

    For a single-span layout of the type shown in Fig.3.1, each beam vibrates as if simply-supported, so the length Leff of the vibrating area can be taken as the span, L. The width S of the vibrating area will be several times the beam spacing, s. A cross-section through this area is likely to be as shown in Fig. 3.27, with most spans of the composite slab vibrating as if fixed-ended. It follows from equation (3.95) that:
    for the beam,

    where m is the vibrating mass per unit area, and s is the spacing of the beams, and subscripts b and
    s mean beam and slab, respectively.

  • In the fairly dry environment of a building, an unrestrained concrete slab could be expected to shrink by 0.03% of its length (3 mm in 10 m) or more. In a composite beam, the slab is restrained by the steel member, which exerts a tensile force on it, through the shear connectors near the free ends of the beam, so it apparent shrinkage is less than the ‘free’ shrinkage. The forces on the shear connectors act in the opposite direction to those due to the loads, and so can be neglected in design.
    The stresses due to shrinkage develop slowly, and to are reduced by creep of the concrete, but the increase they cause in the deflection of a composite beam may be significant. An approximate and usually conservative rule of thumb for estimating this deflection in a simply supported beam is to take it as equal to the long-term deflection due to the weight of the concrete slab acting on the composite member.
    In the beam studied in Section 3.11, this rule gives an additional deflection of 9 mm, whereas the calculated long-term deflection due to a shrinkage of 0.03% (with a modular ration n=22) is 10mm.
    In beams for buildings, it can usually be assumed that tabulated span/depth rations are sufficiently conservative to allow for shrinkage deflections; but the designer should be alert for situations where the problem may be unusually severe (e.g. thick slabs on small steel beams, electrically heated floors, and concrete mixes with high ‘free shrinkage’).
    Composite beams also deflect when the slab is colder than the steel member. Such differential temperatures rarely occur in buildings, but are important in beams for bridges. Methods of calculation for shrinkage and temperature effects are given in Volume 2.

  • In British Standard 6472, ‘Evaluation of human exposure to vibration in buildings (1 Hz to 80 Hz)’, the performance of a floor structure is considered to be satisfactory when the probability of annoyance to users of the floor, or of complaints from then about interference with activities, is low. There can be no simple specification of the dynamic properties that would make a floor structure ‘serviceable’ in this space concerned, and the psychology of its users are all relevant.
    An excellent guide to this complex subject is available. It and BS 6472 provided much of the basis for the following introduction to vibration design, which is limited to the situation in the design example a typical floor of an office building, shown if Fig.3.1.
    Sources of vibration excitation
    Vibration from external sources, such as highway or rail traffic, is rarely severe enough to influence design. If it is, the building should be isolated at foundation level.
    Vibration from machinery in the building, such as lifts and traveling cranes, should be isolated at or near its source. In the design of a floor structure, it should be necessary to consider only sources of vibration on or near that floor. Near gymnasia or dance floors, the effects of rhythmic movement of groups of people can be troublesome; but in most buildings only two situations need be considered;

    People waling across a floor with a pace frequency between 1.4 Hz and 2.5Hz; and an impulse, such as the effect of the fall of a heavy object.
    Typical reactions on floors from people walking have been analysed by Fourier series. The basic fundamental component has an amplitude of about 240N. The second and third harmonics are smaller, but are relevant to design. Fundamental natural frequencies of floor structures (4.2Hz to 7.5 Hz). The number of cycles of this harmonic, as a person walks across the span of a floor, can be sufficient for the amplitude of forced vibration to approach is steady=state value. This situation will be considered in more detail later.
    Pedestrian movement causes little vibration of floor structures with f0 exceeding about 7 Hz, but these should be checked for the effect of an impulsive load. The consequences that most influence human reactions are the peak vertical velocity of the floor, which is proportional to the impulse, and the time for the vibration to decay, which increases with reduction in the damping ratio of the floor structure. Design guidance is available for this situation, which is not further discussed here.
    Human reaction to vibration
    Models for human response to continuous vibration are given in BS 6472. For vibration of a floor that supports people who are standing or sitting, rather than lying down, the model consist of a base curve of root-mean-square (r.m.s) acceleration against fundamental natural frequency of the floor, and higher curves of similar shape. These are shown in the double logarithmic plot of Fig.3.26. Each curve represents an approximately uniform level of human response. The base curve denoted by R=1, where R is the response factor, corresponds to a ‘minimal level of adverse comment from occupants’ of sensitive locations such as hospital operating theatres and precision laboratories.

    Curves for other values of R are obtained by multiplying the ordinates of the base curve of R. Those for R=4, 8 and 16 are shown. The appropriate value for R for use in design depends on the environment. The British Standard gives:
    R=4 for offices
    R=8 for workshops
    with the comment that use of double those values ‘may result in adverse comment’, which ‘may increase significantly’ if the magnitudes of vibration are quadrupled.
    Some relaxation is possible if the vibration is not continuous. Wyatt recommends that a floor subject to a person walking at resonant frequency once a minute could reasonably be permitted a response double the value acceptable for continuous oscillation.

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