CT5125: Steel bridges – file <introduction-to-design > 5. Introduction design bridges Dr. A. Romeijn 63 5. Introduction to the Design of Bridges 5.1 General Bridges have been built by man in order to overcome obstacles to travel caused by, for example, straits, rivers, valleys or existing roads. The purpose of a bridge is to carry a service such as a roadway or a railway. Bridges play an outstanding role in structural engineering, deserving the denomination of "ouvrages d'art" in latin languages. The choice between a steel bridge and a concrete bridge (reinforced concrete or prestressed concrete) is a basic decision to be taken at a preliminary design stage. Several factors influence this decision, for example: • spans required • execution processes • local conditions • foundation constraints. The decision should be based on comparisons of: • structural behaviour • economic aspects • aesthetics. In comparing costs, both initial costs and costs associated with maintenance during the life of the structure should be considered. The time required for execution, which in steel bridges is generally shorter than in prestressed concrete bridges, may also influence the decision. In the past, concrete bridges could not compete with steel bridges for medium and long spans due to the lower efficiency (strength/dead load) of concrete solutions. With the development of prestressed concrete, high strength concrete, etc. it is not a straightforward decision to decide between a concrete and a steel solution for medium span (about 40 to 100m) bridges. Even for long spans between 200 and 400m, where cable stayed solutions are generally proposed, the choice between a concrete, steel or composite bridge superstructure is not an easy task. The choice between a steel and a concrete solution is sometimes reconsidered following the contractors' bids to undertake the bridge works. Generally speaking, steel solutions may have the following advantages when compared to concrete solutions: • reduced dead loads • more economic foundations • simpler erection procedures • shorter execution time . A disadvantage of steel when compared to concrete is the maintenance cost for the prevention of corrosion and the fatigue strength of especially the welded and bolted connections. However it is now recognised that concrete bridges also have problems relating to maintenance, i.e. relating to the effects of the corrosion of steel reinforcement on the durability of the structure. Although maintenance costs and aesthetics play a significant role in the design decision, the initial cost of the structure is generally the most decisive parameter for selecting a steel or a concrete bridge solution. Solutions of both types are generally considered, at least at a preliminary design stage. In Fig. 1 the principal components of a bridge structure are shown. The two basic parts are: • the substructure • the superstructure. The former includes the piers, the abutments and the foundations. The latter consists of the deck structure itself, which support the direct loads due to traffic and all the other permanent and variable leads to which the structure is subjected. The connection between the substructure and the superstructure is usually made through bearings. However, rigid connections between the piers (and sometimes the abutments) may be adopted, particularly in frame bridges with tall (flexible) piers. Fig. 1. Basic components of a bridge. Many, if not most bridges, whether road, rail or footbridges, also carry at least some public utility services (electricity, telephone, water, gas, etc.). Provision for carrying these services varies with the type of bridge - for
5.1 GeneralBridges have been built by man in order to overcome obstacles to travel caused by, for example, straits, rivers,valleys or existing roads. The purpose of a bridge is to carry a service such as a roadway or a railway. Bridgesplay an outstanding role in structural engineering, deserving the denomination of "ouvrages d'art" in latinlanguages. The choice between a steel bridge and a concrete bridge (reinforced concrete or prestressed concrete)is a basic decision to be taken at a preliminary design stage. Several factors influence this decision, for example:
• spans required• execution processes• local conditions• foundation constraints.
The decision should be based on comparisons of:• structural behaviour• economic aspects• aesthetics.
In comparing costs, both initial costs and costs associated with maintenance during the life of the structureshould be considered. The time required for execution, which in steel bridges is generally shorter than inprestressed concrete bridges, may also influence the decision.In the past, concrete bridges could not compete with steel bridges for medium and long spans due to the lowerefficiency (strength/dead load) of concrete solutions. With the development of prestressed concrete, high strengthconcrete, etc. it is not a straightforward decision to decide between a concrete and a steel solution for mediumspan (about 40 to 100m) bridges. Even for long spans between 200 and 400m, where cable stayed solutions aregenerally proposed, the choice between a concrete, steel or composite bridge superstructure is not an easy task.The choice between a steel and a concrete solution is sometimes reconsidered following the contractors' bids toundertake the bridge works.Generally speaking, steel solutions may have the following advantages when compared to concrete solutions:
• reduced dead loads• more economic foundations• simpler erection procedures• shorter execution time .
A disadvantage of steel when compared to concrete is the maintenance cost for the prevention of corrosion andthe fatigue strength of especially the welded and bolted connections. However it is now recognised that concretebridges also have problems relating to maintenance, i.e. relating to the effects of the corrosion of steelreinforcement on the durability of the structure. Although maintenance costs and aesthetics play a significant rolein the design decision, the initial cost of the structure is generally the most decisive parameter for selecting asteel or a concrete bridge solution. Solutions of both types are generally considered, at least at a preliminarydesign stage. In Fig. 1 the principal components of a bridge structure are shown. The two basic parts are:
• the substructure• the superstructure.
The former includes the piers, the abutments and the foundations. The latter consists of the deck structure itself,which support the direct loads due to traffic and all the other permanent and variable leads to which the structureis subjected. The connection between the substructure and the superstructure is usually made through bearings.However, rigid connections between the piers (and sometimes the abutments) may be adopted, particularly inframe bridges with tall (flexible) piers.
Fig. 1. Basic components of a bridge.
Many, if not most bridges, whether road, rail or footbridges, also carry at least some public utility services(electricity, telephone, water, gas, etc.). Provision for carrying these services varies with the type of bridge - for
instance, box girders provide an obvious area for routing them (although care must be taken to provide foraccidents - a flooded box girder arising from a fractured internal water main could be disastrous!) On plate girderbridges it may prove possible to carry the services within the footpath, or hanging from cross-girders if thebridge is of that form of construction.
5.2 The SubstructurePiers may be made of steel or concrete. Even in steel and composite bridges, reinforced concrete piers are veryoften adopted. In some cases, e.g. very tall piers or those made by precast concrete segments, prestressedconcrete may be adopted. Piers are of two basic types:
• columns piers• wall piers.
Concrete column piers may have a solid cross-section, or abox section may be the shape chosen for the cross-section(Fig. 2) for structural and aesthetic reasons.Detailed information is given in the file<bridge-dictionary-piers>
Fig. 2. Pier cross-sections.
Wall piers are generally less economical and less pleasing from an aesthetic point of view. They are very oftenadopted in cases where particular conditions exist, e.g. piers in rivers with significant hydrodynamic actions or inbridges with tall piers where box sections are adopted.Piers may be of constant cross-section or variable cross-section. The former solution is usually adopted in shortor medium piers and the latter in tall piers where at least one of the cross-section dimensions varies along thelength of the pier.The abutments establish the connection between the bridge superstructure and the embankments. They aredesigned to support the loads due to the superstructure which are transmitted through the bearings and to thepressures of the soil contained by the abutment.The abutments must include expansion joints, to accommodate the displacements of the deck, i.e. thelongitudinal shortening and expansion movements of the deck due to temperature.Two basic types of abutments may be considered:
• wall (counterfort) abutments• open abutments.
Counterfort wall abutments (Fig. 3 and 4) are adopted only when the topographic conditions and the shapes ofthe earthfill are such that an open abutment (Fig. 5) cannot be used. They are generally adopted when therequired height of the front wall is above 5,0 to 8,0m (Fig. 4). If the depth is below this order of magnitude,counterfort walls may not be necessary and a simple wall cantilevering from the foundation may be adopted.The connection between the abutments and the earthfill may include a transition slab (Figure 4) which ensures asmooth surface of the pavement even after settlement of the adjacent earthfill.
Fig. 3 Wall abutment.
Fig. 4. Counterfort wall abutment.
Fig. 5. Open abutment.Detailed information is given in the file<bridge-dictionary-abutment>
5.3 The SuperstructureIt is common in bridge terminology to distinguish between:
• the longitudinal structural system• the transverse structural system.
It should be understood that bridge structures are basically three-dimensional systems which are only split intothese two basic systems for the sake of understanding their behaviour and simplifying structural analysis. Thelongitudinal structural system of a bridge may be one of the following types which are illustrated in Figure 6:
The types of girder incorporated in all these types of bridges may either be continuous i.e. rolled sections, plategirders or box girders, or discontinuous i.e. trusses.
Beam bridges are the most common and thesimplest type of bridge (Figure 6a), whetherthey use statically determinate beams(simply supported or Gerber beams) orcontinuous beams. Simply supported beamsare usually adopted only for very small spans(up to 25m). Continuous beams are one ofthe most common types of bridge. Spansmay vary from small (10 - 20m) to medium(20 - 50m) or large spans (> 100m). Inmedium and large spans continuous beamswith variable depth section are very oftenadopted for reasons of structural behaviour,economy and aesthetics (Fig. 1).
Frame bridges are one of the possiblealternatives to continuous beams (Fig. 6b).Avoiding bearings and providing a goodstructural system to support horizontallongitudinal actions, e.g. earthquakes, frameshave been adopted in modern bridgetechnology in prestressed concrete bridges orin steel and composite bridges. Frames maybe adopted with vertical piers (the mostcommon type) or with inclined struts (Fig.6b).
Fig. 6. Longitudional structural systems ofbridges.
Arches have played an important role in the history of bridges. Several outstanding examples have been builtranging from masonry arches built by the Romans to modern prestressed concrete or steel arches with spansreaching the order of 300m.The arch may work from below the deck, from above the deck or be intermediate to the deck level (fig. 6c). Themost convenient solution is basically dependent on the topography of the bridge site. In rocky gorges and goodgeotechnical conditions for the springings, an arch bridge of the type represented in fig. 6(c) is usually anappropriate solution both from the structural and aesthetic point of view.Arches work basically as a structure under compressive stress. The shape is chosen in order to minimise bendingmoments under permanent loads. The resultant force of the normal stresses at each cross-section, must remainwithin the central core of the cross-section in order to avoid tensile stresses in the arch. Arches are idealstructures to build in materials which are strong in compression but weak in tension, e.g. concrete.The ideal "inverted arch" in its simplest form is a cable. Cables are adopted as principal structural elements insuspension bridges where the main cable supports permanent and imposed loads on the deck (fig. 6(e)).Good support conditions are required to resist the anchorage forces of the cable. For the last approx. 50 years, asimpler form of cable bridges has been used - the cable stayed bridge.
Cable stayed bridges (Figure 6(d)) have been used for a range of spans, generally between 100m and 500m,where the suspension bridge is not an economical solution. The range of spans for cable stayed bridges is quitedifferent from the usual range of spans for suspension bridges - from 500m to 1500m. Cable stayed bridges maybe used with a deck made in concrete or in steel. Generally, cable stayed bridges are designed with very slenderdecks which are "continuously" supported by the stays which are made of a number of strands of high strengthsteel.Three main types of transverse structural system may be considered:
• slab• beam-slab (slab with cross-girders)• box girders for longitudinal structural system which contribute to the transverse structural system.
Slab cross-sections are only adopted for small spans, generally below 25m, or where multiple girders are used forthe longitudinal structural system, at spacings of 3 - 4,5m. Beam-slab cross-sections (Figure 1) are generallyadopted for medium spans below 80m where only two longitudinal girders are provided. For large spans (>100m), and also for some medium spans (40 - 80m), box girder sections are very convenient solutions leading togood structural behaviour and aesthetically pleasing bridge structures. Box girders are used in prestressedconcrete or in steel or composite bridges.
Three basic types of structural elements are adopted for steel bridge superstructures:• Beam and Plate Girders• Truss Girders• Box Girders.
5.4 Deck systemsThere are two basic solutions for the deck - a reinforced concrete or partially prestressed concrete slab and anorthotropic steel plate (fig. 7). In the former the slab may act independently of the girders (a very uneconomic
solution for medium and large spans) or it may worktogether with the girders (composite bridge deck). Thecomposite action requires the shear flow between theslab and the girders to be taken by shear connectors.
Fig. 7. Reinforced concrete and orthotropic platedecks.
Concrete decks are usually more economic than orthotropic steel plates. The latter are only adopted when deckweight is an important component of loading, i.e. for long span and moveable bridges.The orthotropic plate deck, acting as the top flange of the main girders, gives a very efficient section in bending.The deck is basically a steel plate overlain with a wearing surface which may be concrete or mastic asphalt. Thesteel plate is longitudinally stiffened by ribs which may be of open or closed section. Transversally, the ribs areconnected through the transverse beams (fig. 7) yielding a complex grillage system where the main girders, thesteel plate, the ribs and the floor beams act together.
Fig. 9. Composite box girder bridge.
Top flanges of box girders, e.g. in Niteroi bridge (Figure 10) with a 300m span (the largest in the world for a boxgirder bridge) or in the deck of cable stayed bridges (Figure 11) or suspension bridges like the Humber bridge(Figure 12) with a lightweight wearing surface give a deck of very low dead load which makes this type ofsolution very suitable for long spans. The biggest disadvantage of orthotropic steel plate decks is their initial costand the maintenance required when compared to a simple concrete slab. However, for box girders themaintenance cost may be lower than for an open orthotropic deck.
The deck must be strong enough to distribute the local loads to the main girders. For multi-girder structures thereis little conceptual choice for a designer - it has been found by experience that a reinforced concentre slabbetween about 200 and 300mm thick, supported at about 3 - 3,5m centres is suitable for most purposes. For largespan structures, twin girder solutions become more attractive and either a thicker deck, probably with varyingdepth, is required or cross girders have to be introduced. Only in bridges where weight is at a real premium (e.g.long span bridges, or moving bridges) is it normally necessary to think further than this. One possibility forreducing the deck weight is the use of lightweight concrete (an example is the 174m main span Friarton Bridgein UK where the deck has been constructed as a lightweight reinforced concrete slab). However, a more normalalternative to an RC slab is an orthotropically stiffened steel plate deck. Many layouts have been tried, some ofwhich have suffered from premature fatigue from the repeated stresses from traffic. There now seems to begeneral agreement within Europe that the cross-section shown in fig. 7 is the "state of the art" solution for a steeldeck in 1992. Finally, it must be emphasised that in modern designs the deck, whether of reinforced concrete orstiffened steel plating, will invariably be connected to the girders below it so that it acts compositely with them incarrying the bending moments imposed on them. In the case of concrete decks this connection will be madeusing shear connectors (see fig. 9) and in the case of steel decks by a direct connection (normally welding or highstrength friction grip bolting).Other possibilities for reducing the deck weight are the use of aluminium and fibre reinforce plastics.
5.5 Beam and Plate girder bridgesPlate girder bridges can provide a very competitive solution for short and medium span bridges. They are almostalways designed to act compositely with the concrete slab. The plate girders are fabricated with two flangeswelded to a thin web which usually has transverse stiffening and may have longitudinal stiffening. Three types ofbridge cross-section may be used. For shorter spans, upto 60m, multiple girders at spacings of 3 to 4,5 m enablea simple reinforced concrete slab to be used, as shown.Plate girder bridges with only two girders, even for verywide decks (fig. 15), are very often preferred for the sake
of simplicity. However, in bridge construction, aclassical solution consists in adopting several I beams(hot rolled sections for small spans - up to 25m) with3,0 to 4,5m spacing. Diaphragms may be providedbetween the beams (transverse beams) to contribute totransverse load distribution and also to lateral bracing.The top flanges of the beams have continuous lateralsupport against buckling provided by the deck.
Fig. 15. Plate girder bridge with two main plate girders.
Fig. 17. Typical cross section for a railwaybridge.
Fig. 16. Typical cross secions for highway bridges.
Figure 16, in particular, identifies three types of cross-section for highway bridges, all of which have been usedsuccessfully.
Fig. 17. Plate girder bridge, Hagenstein, The Netherlands.
The complexity of fabrication of the plate girder is primarily controlled by the web slenderness (depth/thicknessratio). For short spans a low slenderness is feasible with a web that is unstiffened except at cross bearingpositions and supports. For medium spans the web will usually need to be of intermediate slenderness andrequire vertical (transverse) stiffening. For larger spans the web is likely to require both transverse andlongitudinal stiffening, as shown in fig. 17. The distance between transverse stiffeners is of the order ofmagnitude of the depth of the girder. Where they are required, 1 to 3 longitudinal stiffeners are usually provided.In sections at supports, it is essential to adopt vertical stiffeners to resist the high reaction forces. One of the basicrequirements when designing plate girder bridges is the bracing system which is required for all but the simpleststructures. The bracing:
• provides lateral stability to the girders, particularly during erection• supports the horizontal shear forces due to horizontal actions (wind, earthquakes)• works as a transverse load distribution system.• takes part in the shear flows due to torsion from eccentric loading or plan curvature.
The bracing system generally includes:• horizontal lateral bracing• intermediate cross frames - diaphragms.
The former (fig. 18) consists of a set of crossing diagonal members and is located near the bottom or near the topand the bottom flanges; the bridge deck may act as a horizontal bracing. The latter are a set of bracings (trusses)normal to the bridge axis – fig. 19 which provide resistance to the deformation of the overall cross-sections of thebridge.
Fig. 18. Brace system in curved bridge. Fig. 19. Plate girders for composite bridges.
5.6 Truss girder bridgesA truss girder may be adopted in some cases as an alternative to a plate girder. Although less commonly used inmodern construction because of their high fabrication content, they may still be an economic solution for largespans, say between 100 and 200 metres. A plane truss girder may be considered as a deep beam where theflanges are the compression and tension chords of the truss and the web of the beam is replaced by an opentriangular system which resists the shear forces.
Several types of truss girders are used in bridge design. Some typical examples are shown in fig. 20. Trussgirders may be adopted in simply supported (fig. 20) or continuous spans (fig. 21 and 22).
Fig. 20. Types of trusses.
Fig. 21. Bridge over the river Fulda (Germany).
Fig. 22. Warren truss girder for a railway bridge.
Bracing systems are required in truss girder bridges, sincetruss girders can only resist forces in their planes. Trussgirders working from above the deck have been extensivelyused in railway bridges, even for medium spans of the order of40 to 100 metres. From an aesthetic point of view, it isimportant to reduce as far as possible the number of barelements in the truss girder. If possible the simplest triangularsystem (Warren type) yields the best appearance when the
bridge is viewed from skew angles. Truss chords and diagonals are made using hot rolled sections generally ofan open shape for simplicity of connections. However, tubular cross-sections may be adopted, for example, forthe chords. An example is shown in Figure 22, which represents the bridge over the river Fulda in Germany, nearKassel. In this bridge, a Warren type truss was used with a maximum span/depth ratio of 23,8. The deck is anorthotropic plate giving a reduced dead weight for the superstructure. A Dutch example of a railway bridge usingtubular members only is shown in fig. 23. Because of the fatigue criteria, casted nodes are used instead of weldedconnections
Fig. 23. Railway bridge, Oosterbeek, The Netherlands.
Fig. 24. Some examples of truss girder bridges.Hollandsch Diep High Speed Rail bridge in construction,
on the left the railroad bridge picture taken from the north.
5.7 Box girder bridgesFor long spans (say, in excess of 100m) box girders are, in general, the most common and efficient type of bridgesuperstructure. Built with an orthotropic plate deck to reduce the dead weight of the bridge, or with a concreteslab to obtain a composite cross-section, box girders have many structural advantages when compared to plategirders and truss girders. Some of the advantages are:
• high torsional rigidities• wide top and bottom flanges to carry longitudinal forces• large internal space to accommodate services• simple maintenance due to easy access to the interior of the superstructure• better appearance due to high slenderness and smooth bottom surfaces.
Due to the high torsional rigidity of this type of cross-section, box girders are a very convenient solution forbridges curved in plan. For large spans, the depth of continuous box girder bridges may vary along the spangiving improved structural efficiency to accommodate the large bending moment at the supports. The cross-section may consist of a single cell box, with vertical or inclined webs, or of a multiple cell box (fig. 25, left),
other possibilitiesconsist of using,for example, asingle cell withinclined struts tosupport largeoverhangs (fig. 25right).
Fig. 25. Single cell and multiple cell box girders.
For medium spans, a type of box girder deck very common in bridge construction, e.g. in North America, is thecomposite box girder deck made of several parallel boxes interconnected by a reinforced concrete slab deck(Figure25). Composite action between the box girders and the reinforced concrete slab is obtained through shear
connectors.
Fig. 26. Composite multiple box girder bridge.
The two flanges associated with each web in composite box girder bridges may be quite narrow because theyonly need to transfer the load to the web and to accommodate the shear connectors. A minimum flange widthmay therefore be defined by edge distances and clearances for automatic welding of shear connectors. Loadbearing diaphragms are necessary at supports to transfer the reaction forces. In addition, even in small boxgirders, it is good practice to adopt intermediate cross frames (say, at 10m to 15m apart) to avoid distortion of the
cross-section under eccentric loading (fig. 26). It should benoted that during construction some "box" girders have opensections and so will be subjected to distortion under eccentricloading. A top bracing between the top flanges and/or a crossdiagonal bracing between the webs is generally convenient toovercome the distortion effects during execution. The diagonalbracing may consist of small size angles welded to platestiffeners.
Fig. 27. Intermediate cross frames to avoid distortion in box girders.
The use of composite box girders in wide bridgeswith long spans is possible with single cell boxes.Internal cross trusses may be used, not only tomaintain the shape of the cross-section (avoidingdistortion) but also to support longitudinal stringersfor the reinforced concrete slab. A solution of thistype is shown in fig. 28.
Fig. 28.Wuppertal bridge (Germany).
For long spans an orthotropic plate deck is preferredto reduce the dead load of box girder bridges. Asolution with a rectangular box girder bridge with amain span of 200m is given in fig. 29 which showsthe "Europe Bridge" in Austria.
The use of box girders is not restricted to beambridges. Slender box girders in cable stayed bridgeshave been used with orthotropic plate decks.Although, in the last few years, concrete box girderdecks have been shown to be an economic solutionfor some cable stayed bridges, steel box girders arethe most convenient solution for long spans.Compared to open sections, box girder decks incable stayed bridges present a significant advantagein respect of aerodynamic stability. The advantage isassociated with a higher natural frequency oftorsional vibration of the deck avoiding aninteraction with the fundamental modecorresponding to vertical vibrations (flexure mode).The risk of flutter instabilities is thus eliminated. Forreasons similar to those given for cable stayedbridges, slender steel box girders with orthotropicplate decks have been adopted in modern suspensionbridges.
5.8 Guidance on initial designEach form of bridge is suited to a particular range of spans, see Figure 33, which also records the longest spanfor each type of construction.Suspension or cable stayed bridges are the only forms capable of achieving the longest spans. They are clearlyless suitable for road or rail bridges of short or medium span. However, they can be appropriate for shorter spanfootbridges, partly because they do not have any concentrated loading that requires an expensive stiffening girderand partly for aesthetic considerations. (It should be noted that the same special consideration which is neededfor long spans, such as aerodynamic stability, needs to be applied to steel footbridges). Suspension bridges arestill used for the longest spans where intermediate piers are not feasible. The cables are subjected to very hightension and are tied to the ground, usually by gravity foundations sometimes combined with rock anchors. Thusground conditions with rock at or close to the surface of the ground are essential. Cable stayed bridges are ofsuspension form with normally straight cables which are directly connected to the deck. The structure is selfanchoring and, therefore, less dependant on good ground conditions. However, the deck must be designed for thesignificant axial forces from the horizontal component of the cable force. The construction process is quickerthan for a suspension bridge because the cables and the deck are erected at the same time.Bridge types, such as arches or portals, may be suitable for special locations. For example, an arch is the logicalsolution for a medium span across a steep-sided ravine. A tied arch is a suitable solution for a single span whereconstruction depth is limited and the presence of curved highway geometry or some other obstruction conflictswith the back stays of a cable stayed bridge.Portal frame bridges are usually suitable for short or medium spans. In a three span form with sloping legs, theycan provide an economic solution by reducing the main span; they also have an attractive appearance. The risk ofshipping collision must be considered if sloping legs are used over navigable rivers.Cantilever trusses were used during the early evolution of steel bridges. They are rarely adopted for modernconstruction.
Haunched girders are frequently used for continuous structures where the main span exceeds 50m. They aremore attractive in appearance and the greater efficiency of the varying depth of construction usually more thanoffsets the extra fabrication costs.Flat girders, i.e. girders of constant depth, are used for all shorter span bridges of both simple spans andcontinuous construction up to spans of around 30m. Rolled sections are feasible and usually offer greatereconomy. Above this span fabricated sections will be required. Both haunched and flat girders can be either plategirders or box girders. Development in the semi-automatic manufacture of plate girders has markedly improvedtheir relative economy. This form of construction is likely to be the preferred solution for spans up to 60m or so,if depth of construction is not unduly limited. Above 60m span, and significantly below that figure if either depthof construction is limited or there is plan curvature, the box girder is likely to give greater economy.
For major crossings, the governing span is likely to be controlled by the local topography. Even for minorcrossings the physical size of the obstacle to be crossed will be the biggest determinant of span.However, for multispan viaducts a range of spans is possible and the engineer should seek to make the mosteconomic choice. The table below summarises the factors which influence this choice.
Factor ReasonsLocation of obstacles Pier positions are often dictated by rivers, railway
tracks and buried services.
Construction depth Span length may be limited by the maximum availableconstruction depth.
Feasibility of constructing intermediate piers in rivercrossings
(a) Tidal or fast-flowing rivers may precludeintermediate piers(b) For navigable waterways, accidental shipimpact may preclude mid-river piers.
Height of deck above ground Where the height exceeds about 15m, costs of piers aresignificant, encouraging longer spans
Loading Heavier loadings such as railways encourage shorterspans
Table 1. Factors which influence choice of span for viaducts.
For long viaducts it is worthwhile to carry out initial costed designs for different spans to determine the mosteconomical combination of superstructure and substructure costs. The outcome of a typical study is shown inFigure 32. Typical optimum spans are shown below.
Conditions Highway RailwaySimple foundations(spread footing or short piles)
25-45 20-30
Difficult foundations (piles 20mlong)
35-55 25-40
Piers 15m high 45-65 30-45Table 2 Typical optimum span ranges for viaducts.
Fig. 32. Results of typical cost study todetermine optimum span for a viaduct.
Fig. 33 Basic structural systems for some typical layouts.
It must not be thought that flexure is immaterial in structures as shown in fig. 33a and 33b. Certainly, in mostsuspension bridges, flexure of the stiffening girder (seefig. 33c) is not a primary loading in that overstress isunlikely to cause overall failure; however, in cablestayed bridges (particularly if the stays are widelyspaced) flexure of the girder is a primary loading.Similarly, in arch bridges, non-uniform loading of the ribcan cause primary bending moments to be developed init and may well govern the arch design.
