Engineering and Construction

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In buildings and bridges, steel beams often support concrete slabs.Under load each component acts independently with relative movement or slip occurring at the interface. If the components are connected so that slip is eliminated, or considerably reduced, then the slab and steel beam act together as a composite unit (Fig. 21.1).

There is a consequent increase in the strength and stiffness of the composite beam relative to the sum of the components.

Fig. 21.1 Behaviour of composite and non-composite beams

The slab may be solid in situ concrete or the composite deck slab considered later. It may also comprise precast concrete units with an  in situ concrete topping. In buildings, steel beams are usually of standard UB scction, but UC and asymmetric beam sections are sometimes used where there is need to minimize the beam depth.A typical building under construction is shown in Fig. 21.2.Welded fabricated sections are often used for long-span beams in buildings and bridges.

Fig. 21.2 Composite building under construction showing decking and shear-connectors

Design of composite beams in buildings is now covered by BS 5950: Part 3, although guidance was formerly available in an SCI publication.

The design of composite beams incorporating composite slabs is affected by the shape and orientation of the decking, as indicated in Fig. 21.3.

Fig. 21.3 Composite beams incorporating composite deck slabs: (a) deck perpendicular to beam, (b) deck parallel to beam

One of the advantages of composite construction is smaller construction depths.
Services can usually be passed beneath, but there are circumstances where the beam depth is such that services can be passed through the structure, either by forming large openings, or by special design of the structural system.A good example of this is the stub-girder.

The bottom chord is a steel section and the upper chord is the concrete slab. Short steel sections or ‘stubs’ are introduced to transfer the forces between the chords.

Openings through the beam webs can be provided for services. Typically, these can be up to 70% of the beam depth and can be rectangular or circular in shape.

Examples of the above methods of introducing services within the structure are shown in Fig. 21.4.

Fig. 21.4 Different methods of incorporating services within the structural depth

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In situations where a relatively lightly loaded beam is required such as a purlin or sheeting rail spanning between main frames supporting the cladding in a portal frame, it is common practice to use a cold-formed section produced cold from flat steel sheet, typically between about 1mm and 6mm in thickness, in a wide range of shapes of the type shown in Fig. 16.12. A particular feature is that normally each section is formed from a single flat bent into the required shape; thus most available sections are not doubly symmetric but channels, zeds and other singly sym- metric shapes. The forming process does, however, readily permit the use of quite complex cross-sections, incorporating longitudinal stiffening ribs and lips at the edges of flanges. Since the original coils are usually galvanized, the members do not normally require further protective treatment.

Fig. 16.12 Typical cold-formed section beam shapes

The structural design of cold-formed sections is covered by BS 5950: Part 5,which permits three approaches:

(1) design by calculation using the procedures of the code, section 5, for members in bending
(2) design on the basis of testing using the procedures of section 10 to control the testing and section 10.3 for members in bending
(3) for three commonly used types of member (zed purlins, sheeting rails and lattice joists), design using the simplified set of rules given previously.

In practice option (2) is the most frequently used, with all the major suppliers providing design literature, the basis of which is usually extensive testing of their product range, design being often reduced to the selection of a suitable section for a given span, loading and support arrangement using the tables provided.

Most cold-formed section types are the result of considerable development work by their producers. The profiles are therefore highly engineered so as to produce a near optimum performance, a typical example being the ranges of purlins produced by the leading UK suppliers. Because of the combination of the thin material and the comparative freedom provided by the forming process, this means that most sections will contain plate elements having high width-to-thickness ratios. Local buckling effects, due either to overall bending because the profile is non-compact, or to the introduction of localized loads, are of greater importance than is usually the case for design using hot-rolled sections. BS 5950: Part 5 therefore gives rather more attention to the treatment of slender cross-sections than does BS 5950: Part 1. In addition, manufacturers’ design data normally exploit the post-buckling strength observed in their development tests.

The approach used to deal with sections containing slender elements in BS 5950 is the well accepted effective width technique. This is based on the observation that plates, unlike struts, are able to withstand loads significantly in excess of their initial elastic buckling load, provided some measure of support is available to at least one of their longitudinal edges. Buckling then leads to a redistribution of stress, with the regions adjacent to the supported longitudinal  edges attracting higher stresses and the other parts of the plate becoming progressively less effective, as shown in Fig. 16.13. A simple design representation of the condition of  Fig. 16.13 consists of replacing the actual post-buckling stress distribution with the approximation shown in Fig. 16.14. The structural properties of the member (strength and stiffness) are then calculated for this effective cross-section as illus- trated in Fig. 16.15. Tabulated information in BS 5950 for steel of yield strength 280N/mm2 makes the application of this approach simpler in the sense that effective widths may readily be determined, although cross-sectional properties have still to be calculated.The use of manufacturer’s literature removes this requirement. For beams, Part 5 also covers the design of reinforcing lips on the usual basis of ensuring that the free edge of a flange supported by a single web behaves as if
both edges were supported; web crushing under local loads, lateral–torsional buckling and the approximate determination of deflections take into account any loss of plating effectiveness.

Forzed purlins or sheeting rails section 9 of BS 5950: Part 5 provides a set of simple empirically based design rules.Although easy to use, these are likely to lead to heavier members for a given loading, span and support arrangement than either of the other permitted procedures.A particular difference of this material is its use of unfactored loads, with the design conditions being expressed directly in member property requirements.

Fig. 16.13 Loss of plating effectiveness at progressively higher compressive stress

Fig. 16.14 Effective width design approximation

Fig. 16.15 Effective cross-section

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One (or more) of a number of distinct limiting conditions may, in theory, control the design of a particular beam as indicated in Table 16.3, but in any particular practical case only a few of them are likely to require full checks. It is therefore convenient to consider the various possibilities in turn, noting the conditions under which each is likely to be important. For convenience the various phenomena are first considered principally within the context of using standard hot-rolled sections, i.e. UBs, UCs, RSJs and channels.




1 Moment capacity, Mc
The most basic design requirement for a beam is the provision of adequate in-plane bending strength. This is provided by ensuring that Mc for the selected section exceeds the maximum moment produced by the factored loading.Determination of Mc, which is linked to section classification.

For a statically determinate structural arrangement, simple considerations of statics provide the moment levels produced by the applied loads against which Mc must be checked. For indeterminate arrangements, a suitable method of elastic analysis such as moment distribution or slope deflection is required. The justification for using an elastically obtained distribution of moments with, in the case of compact or plastic cross-sections, a plastic cross-sectional resistance has been fully discussed by Johnson and Buckby.

2 Effect of shear
Only in cases of high coincident shear and moment, found for example at the internal supports of continuous beams, is the effect of shear likely to have a significant influence on the design of beams.

Shear capacity Pv is normally calculated as the product of a shear strength pv, often taken for convenience as 0.6py which is close to the yield stress of steel in shear of 1/÷3 of the uniaxial tensile yield stress, and an appropriate shear area Av.

The process approximates the actual distribution of shear stress in a beam web as well as assuming some degree of plasticity.While suitable for rolled sections, it may not therefore be applicable to plate girders.An alternative design approach, more suited to webs containing large holes or having variations in thickness, is to work from first principles and to limit the maximum shear stress to a suitable value; BS 5950: Part 1 uses 0.7py. In cases where d/t > 63, shear buckling limits the effectiveness of the web and reference to Chapter 17 should be made for methods of determining the reduced capacity.

In principle the presence of shear in a section reduces its moment capacity. In practice the reduction may be regarded as negligibly small up to quite large fractions of the shear capacity Pv. For example, BS 5950: Part 1 requires a reduction in Mc for plastic or compact sections only when the applied shear exceeds 0.6Pv, and permits the full value of Mc to be used for all cases of semi-compact or slender  sections.

Figure 16.2 illustrates the application of the BS 5950: Part 1 rule for plastic or compact sections to a typical UB and UC having approximately equal values of plastic section modulus Sx. Evaluation of the formula in cases where Fv/Pv > 0.6 first requires that the value of Sv, the plastic modulus of the shear area Av (equal to tD in this case), be determined. This is readily obtained from the tabulated values of S for rectangles given in Reference 2 corresponding to a linear reduction from Sx to (Sx - Sv).

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Beams are possibly the most fundamental type of member present  in a civil engineering structure. Their principal function is the transmission  of vertical load by means of flexural (bending) action into, for example, the columns  in a rectangular building frame or the abutments in a bridge which support them.

Table 16.1 provides some idea of the different structural forms suitable for use  as beams in a steel structure; several of these are illustrated in Fig. 16.1. For modest spans, including the majority of those found in buildings, the use of standard  hot-rolled sections (normally UBs but possibly UCs if minimizing floor depth is a prime consideration or channels if only light loads need to be  supported) will  be sufficient. Lightly loaded members such as the purlins supporting the roof  of a portal-frame building are frequently selected from the range of proprietary cold-formed sections produced from steel sheet only a few millimetres thick, nor- mally already protected against corrosion by galvanizing, in a variety of highly efficient shapes, advantage being taken of the roll-forming process to produce sections with properties carefully selected for the task they are required to perform. For spans in excess of those that can be achieved sensibly using ready-made sections some form of built-up member is required. Castellated beams, formed by profile cutting of the web and welding to produce a deeper section, typically 50% deeper using the standard UK geometry, are visually attractive but cannot withstand high shear loads unless certain of the castellations are filled in with plate. The range of spans for which UBs may be used can be extended if cover plates are welded to both flanges.

Fig. 16.1 Types of beam cross-section

Alternatively a beam fabricated entirely by welding plates together may be employed allowing variations in properties by changes in depth, for example, flange thickness, or, in certain cases where the use of very thin webs is required, stiffening to prevent premature buckling failure is necessary.A full treatment of the specialist aspects of plate-girder design is provided later. If spans are so large that a single member cannot economically be provided, then a truss may be a suitable alternative. In addition to the deep truss fabricated from open hot-rolled sections, SHS or both, used to provide long clear spans in sports halls and supermarkets, smaller prefabricated arrangements using RHS or CHS provide an attractive alter- native to the use of standard sections for more modest spans.


Since the principal requirement of a beam is adequate resistance to vertical bending, a very useful indication of the size of section likely to prove suitable may be obtained through the concept of the span to depth ratio.This is simply the value of the clear span divided by the overall depth. An average figure for a properly designed steel beam is between 15 and 20, perhaps more if a particularly slender form of construction is employed or possibly less if very heavy loadings are present.

When designing beams, attention must be given to a series of issues, in addition to simple vertical bending, that may have some bearing upon the problem.Torsional loading may often be eliminated by careful detailing or its effects reasonably regarded as of negligible importance by a correct appreciation of how the structure actually behaves; in certain instances it should, however, be considered. Section classification (allowance for possible local buckling effects) is more involved than is the case for struts since different elements in the cross-section are subject to different patterns of stress; the flanges in an I-beam in the elastic range will be in approximately uniform tension or compression while the web will contain a stress gradient.

The possibility of members being designed for an elastic or a plastic state, including the use of a full plastic design for the complete structure, also affects section classification.Various forms of instability of the beam as a whole or of parts subject to locally high stresses, such as the web over a support, also require attention. Finally certain forms of construction may lend themselves to the appearance of unacceptable vibrations; although this is likely to be affected by the choice of beams, its coverage later on floors.