Plate girder behaviour and design part 1
To introduce basic aspects of the behaviour and design of plate girders. To explain how the typical proportions employed influence the types of behaviour that must be addressed in design, and to identify the various buckling considerations involved as preparation for the subsequent consideration of the design approaches of Eurocode 3 .
Modern plate girders are introduced by explaining typical usage, types, and the reasons for their inherent slender proportions. Their behaviour is described with particular emphasis on the different forms of buckling that can occur. The general basis of plate girder design is discussed in a simplified way as a prelude to a more detailed presentation in Plate girder behaviour and design part 2 and Plate girder design - special topics. Post-buckling and tension field action are introduced and the roles of the main components in a plate girder are identified.
Modern plate girders are fabricated by welding together two flanges and a web plate, as shown in Figure 1. Such girders are capable of carrying greater loads over longer spans than is generally possible using standard rolled sections or compound girders. Plate girders are typically used as long-span floor girders in buildings, as bridge girders, and as crane girders in industrial structures.
Plate girders are at their most impressive in modern bridge construction where main spans of well over 200m are feasible with corresponding cross-section depths haunched over the supports in the range of 5-10m. Because plate girders are fabricated separately, each may be designed individually to resist the applied actions using proportions that ensure low self-weight and high load resistance.
For efficient design, it is usual to choose a relatively deep girder, thus minimising the required area of flanges for a given applied moment, MEd. This obviously entails a deep web whose area will be minimised by reducing its thickness to the minimum required to carry the applied shear, VEd. Such a web may be quite slender (i.e. a high d/tw ratio) and may be prone to local buckling (see Local buckling) and shear buckling (see below). Such buckling problems have to be given careful consideration in plate girder design and during erection. One way of improving the load carrying resistance of a slender plate is to employ stiffeners (see Introduction to plate behaviour and design); the selection of appropriate forms of stiffening is an important aspect of plate girder design.
There are several forms of plate girder. Figure 2 illustrates three different types - unstiffened, transversely stiffened, and transversely and longitudinally stiffened. The three girders shown have bisymmetric I-profile cross-sections, although flanges of different size are sometimes used, as shown in Figure 1. Other types of cross-section (see Figure 3) are monosymmetric I-profiles, which are popular in composite construction with the smaller flange on top, or as crane girders with the larger flange on top. Figure 3 also shows two other (less common) variations - the 'delta girder' and the tubular-top-flange girder - both being possible solutions in cases of long laterally-unsupported top compression flanges prone to lateral-torsional buckling.
There is also considerable scope for variation of cross-section in the longitudinal direction. A designer may choose to reduce the flange thickness (or breadth) in a zone of low applied moment, especially when a field-splice facilitates the change. Equally, in a zone of high shear, the designer might choose to thicken the web plate (see Figure 4). Alternatively, higher grade S460 steel might be employed for zones of high applied moment and shear, while the more standard grade S355 would be used elsewhere. So-called 'hybrid' girders with different strength material in the flanges and the web offer another possible means of more closely matching resistance to requirements.
In order to ease the design and calculation process, an online tool has been developed to pre-calculate hybrid girders' load bearing capacity depending on the steel grade combination. It is available at https://constructalia.arcelormittal.com/en/tools/orange_book.
More unusual variations are adopted in special circumstances, such as bridgework, e.g. tapered girders, cranked girders, haunched girders (see Figure 5), and of course, plate girders with web holes to accommodate services (see Figure 6).
Since the designer, in principle, is quite free to choose all the dimensions of a plate girder, some indication of the more usual proportions is now given (see also Figure 7):
Depth: Overall girder depth, h, will usually be in the range Lo/12 ≤ h ≤ Lo/8, where Lo is the length between points of zero moment. However, for plate girder bridges the range will extend to approximately Lo/20 for road bridges and Lo/15 for railway bridges.
Flange breadth: The breadth, b, will usually be in the range h/5 ≤ b ≤ h/3, b being in multiples of 25mm.
Flange thickness: The flange thickness, tf, will usually at least satisfy the requirements of Eurocode 3  (EN 1993-1-1/Table 5.2) for Class 3 (semi-compact) sections, i.e. c/tf ≤ 14ε. The thickness will usually be chosen from the standard plate thicknesses.
Web thickness: Web thickness, tw, will determine the exact basis for web design, depending on whether the web is classified with regard to shear buckling as 'thick' or 'thin' (see below). Thin webs will often require stiffening; this may take the form of transverse stiffeners, longitudinal stiffeners, or a combination (see Figure 2). Longitudinally stiffened girders are more likely to be found in large bridge construction where high d/tw ratios are appropriate, e.g. 200 ≤ d/tw ≤ 500, due to the need to minimise self-weight.
Clearly, depending on the particular loading pattern, and on depth and breadth restrictions, one can expect wide variations within all of the above limits, which should be regarded as indicative only.Read more