Chapter 13 the box girders

13 Box girders 13.1 General The box girder is the most flexible bridge deck form It can cover a range of spans from 25 m up to the largest non-suspended concrete decks built, of the order of 300 m Single box girders may also carry decks up to 30 m wide For the longer span beams, beyond about 50 m, they are practically the only feasible deck section For the shorter spans they are in competition with most of the other deck types discussed in this book The advantages of the box form are principally its high structural efficiency (5.4), which minimises the prestress force required to resist a given bending moment, and its great torsional strength with the capacity this gives to re-centre eccentric live loads, minimising the prestress required to carry them The box form lends itself to many of the highly productive methods of bridge construction that have been progressively refined over the last 50 years, such as precast segmental construction with or without epoxy resin in the joints, balanced cantilever erection either cast in-situ or coupled with precast segmental construction, and incremental launching (Chapter 15) 13.2 Cast-in-situ construction of boxes 13.2.1 General One of the main disadvantages of box decks is that they are difficult to cast in-situ due to the inaccessibility of the bottom slab and the need to extract the internal shutter Either the box has to be designed so that the entire cross section may be cast in one continuous pour, or the cross section has to be cast in stages 13.2.2 Casting the deck cross section in stages The most common method of building box decks in situ is to cast the cross section in stages Either, the bottom slab is cast first with the webs and top slab cast in a second phase, or the webs and bottom slab constitute the first phase, completed by the top slab When the bottom slab is cast first, the construction joint is usually located just above the slab, giving a kicker for the web formwork, position in Figure 13.1 A joint in this location has several disadvantages which are described in 11.7.1 370 Box girders Figure 13.1 Alternative positions of construction joint Alternatively, the joint may be in the bottom slab close to the webs, or at the beginning of the haunches, position The advantages of locating the joint in the bottom slab are that it does not cross prestressing tendons or heavy reinforcement; it is protected from the weather and is also less prominent visually The main disadvantage is that the slab only constitutes a small proportion of the total concrete to be cast, leaving a much larger second pour The joint may be located at the top of the web, just below the top slab, position This retains many of the disadvantages of position 1, namely that the construction joint is crossed by prestressing ducts at a shallow angle, and it is difficult to prepare for the next pour due to the presence of the web reinforcement In addition, most of the difficulty of casting the bottom slab has been re-introduced The advantages are that the joint is less prominent visually and is protected from the weather by the side cantilever, the quantity of concrete in each pour is similar and less of the shutter is trapped inside the box Casting a cross section in phases causes the second phase to crack due to restraint by the hardened concrete of the first phase Although the section may be reinforced to limit the width of the cracks, it is not desirable for a prestressed concrete deck to be cracked under permanent loads Eliminating cracks altogether would require very expensive measures such as cooling the second phase concrete to limit the rise in temperature during setting or adopting crack sealing admixtures 13.2.3 Casting the cross section in one pour There are two approaches to casting a box section in one pour The bottom slab may be cast first with the help of trunking passing through temporary holes left in the soffit form of the top slab This requires access for labourers to spread and vibrate the concrete, and is only generally possible for decks that are at least m deep The casting of the webs must follow on closely, so that cold joints are avoided The fluidity of the concrete needs to be designed such that the concrete will not slump out of the webs This is assisted if there is a strip of top shutter to the bottom slab about 500 mm wide along each web This method puts no restriction on the width of the bottom slab, Figure 13.2 (a) Alternatively the deck cross section may be shaped so that concrete will flow from the webs into the bottom slab, which normally has a complete top shutter, Figure 13.2 (b) This method of construction is most suitable for boxes with relatively narrow bottom flanges The compaction of the bottom slab concrete needs to be effected by external vibrators, which implies the use of steel shutters The concrete may be cast down both webs, with inspection holes in the shutter that allow air to be expelled and the complete filling of the bottom slab to be confirmed Alternatively, concrete may be Box girders 371 Figure 13.2 Casting deck in one pour cast down one web first with the second web being cast only when concrete appears at its base, demonstrating that the bottom slab is full The concrete mix design is critical and full-scale trials representing both the geometry of the cross section and density of reinforcement and prestress cables are essential However the section is cast, the core shutter must be dismantled and removed through a hole in the top slab, or made collapsible so it may be withdrawn longitudinally through the pier diaphragm Despite these difficulties, casting the section in one pour is under-used The recent development of self-compacting concrete could revolutionise the construction of decks in this manner This could be particularly important for medium length bridges with spans between 40 m and 55 m Such spans are too long for twin rib type decks, and too short for cast-in-situ balanced cantilever construction of box girders, while a total length of box section deck of less than about 1,000 m does not justify setting up a precast segmental facility Currently, it is this type of bridge that is least favourable for concrete and where steel composite construction is found to be competitive 13.3 Evolution towards the box form Chapters 11 and 12 described how solid slabs evolve into ribbed slabs in order to allow increased spans with greater economy The principal advantage of ribbed slabs is their simplicity and speed of construction However this type of deck suffers from several disadvantages, notably: • • the span is limited to about 45 m; live loads are not efficiently centred, resulting in a concentrated load (such as an HB vehicle) being carried approximately 1.7 times for a deck with two ribs, requiring additional prestress force; 372 • • • Box girders the section has poor efficiency, leading to the requirement for a relatively larger prestress force; the deck cannot be made very shallow; the piers need either multiple columns to carry each rib, or a crosshead that is expensive and visually very significant Box section decks overcome all these disadvantages 13.4 Shape and appearance of boxes 13.4.1 General A box section deck consists of side cantilevers, top and bottom slabs of the box itself and the webs For a good design, there must be a rational balance between the overall width of the deck, and the width of the box Box sections suffer from a certain blandness of appearance; the observer does not know whether the box is made of an assemblage of thin plates, or is solid concrete Also, the large flat surfaces of concrete tend to show up any defects in the finish and any changes in colour The designer should be aware of these problems and what he can within the constraints of the project budget to alleviate them 13.4.2 Side cantilevers Side cantilevers have an important effect on the appearance of the box The thickness of the cantilever root and the shadow cast on the web mask the true depth of the deck If the deck is of variable depth, the perceived variation will be accentuated by these two effects, Figure 13.3 (15.4.2) In general, the cantilever should be made as wide as possible, that is some seven to eight times the depth of the root (9.2) 13.4.3 The box cross section Boxes may be rectangular or trapezoidal, with the bottom flange narrower than the top Rectangular box sections are easier to build, and are virtually essential for the longest spans due to the great depth of the girders However, they have the disadvantages that their appearance is somewhat severe, and that their bottom slabs may be wider than necessary The visual impact of the depth of the box is reduced if it has a trapezoidal cross section This inclination of the web makes it appear darker than a vertical surface, an impression that is heightened if the edge parapet of the deck is vertical The trapezoidal cross section is frequently economical as well as good looking In general, the width of the top of the box is determined by the need to provide points of support to the top slab at suitable intervals The cross section area of the bottom slab is logically determined at mid-span by the need to provide a bottom modulus sufficient to control the range of bending stresses under the variation of live load bending moments For a box of rectangular cross section of span/depth ratio deeper than about 1/20, the area of bottom slab is generally greater than necessary, resulting in redundant weight Choosing a trapezoidal cross section allows the weight of the Box girders 373 Figure 13.3 River Dee Bridge: effect of side cantilever on the appearance of a variable depth deck (Photo: Edmund Nuttall) bottom slab to be reduced Close to the piers, the area of bottom slab is determined by the need to limit the maximum bending stress on the bottom fibre and to provide an adequate ultimate moment of resistance If the narrow bottom slab defined by midspan criteria is inadequate, it is simple to thicken it locally For a very wide deck that has a deep span/depth ratio, this logic may give rise to webs that are inclined at a very flat angle The designer should be aware of the difficulties in casting such webs, and make suitable allowances in specifying the concrete and in detailing the reinforcement Also, an important consideration in the design of box section decks is the distortion of the cross section under the effect of eccentric live loads (6.13.4) The effect of this distortion is reduced in a trapezoidal cross section Boxes may have a single cell or multiple cells In Chapter it was explained how important it is for economy to minimise the number of webs Furthermore, it is more 374 Box girders difficult to build multi-cell boxes, and it is worthwhile extending the single-cell box as far as possible before adding internal webs 13.4.4 Variation of depth Once the span of a box section deck exceeds about 45 m, it becomes relevant to consider varying the depth of the beam This is not an automatic decision as it depends on the method of construction For instance, when the deck is to be precast by the countercast method (Chapter 14), if the number of segments is relatively low it is likely to be more economical to keep the depth constant in order to simplify the mould On the other hand, if the deck is to be built by cast-in-situ balanced cantilevering, it is relatively simple to design the mould to incorporate a variable depth, even for a small number of quite short spans Clearly, this decision also has an aesthetic component The depth may be varied continuously along the length of the beam, adopting a circular, parabolic, elliptical or Islamic profile, Figure 13.4 Alternatively, the deck may be haunched The decision on the soffit profile closely links aesthetic and technical criteria Figure 13.4 Variable depth decks Box girders 375 For instance, when the depth varies continuously it is often judged that an elliptical profile is the most beautiful However, this will tend to create a design problem towards the quarter points, as at these locations the beam is shallower than optimal, both for shear resistance and for bending strength As a result, the webs and bottom slab may need to be thickened locally, and the prestress increased However, the economic penalty may be small enough to accept The Islamic form is likely to provide the most flexible method of optimising the depth at all points along the girder, but the cusp at mid-span may give a problem for the profile of the continuity tendons while for long spans the greater weight of the deeper webs either side of mid-span implies a significant cost penalty Also, the appearance may not be suitable for the particular circumstance When the change in the depth of the box is not too great, haunched decks are often chosen for the precast segmental form of construction, as they reduce the number of times the formwork must be adjusted, assisting in keeping to the all-important daily cycle of production However, here again there is a conflict between the technical optimisation of the shape of the beam and aesthetic considerations The beginning of the haunch is potentially a critical design section, both for shear and bending This criticality is relieved if the haunch extends to some 25–30 per cent of the span length However, the appearance of the beam is considerably improved if the haunch length is limited to 20 per cent of the span or less When variation of the depth is combined with a trapezoidal cross section, the bottom slab will become narrower as the deck becomes deeper, Figure 13.5 This has an important aesthetic impact, as well as giving rise to complications in the construction When a deck is built by the cast-in-situ balanced cantilever method, such as the 929 m long Bhairab Bridge [1] in Bangladesh designed by Benaim, Figure 13.6, the formwork Figure 13.5 Variable depth with trapezoidal cross section 376 Box girders Figure 13.6 Bhairab Bridge, Bangladesh (Photo: Roads and Highways Department, Government of Bangladesh and Edmund Nuttall) may be designed to accept this arrangement without excessive additional cost However for a precast deck it is better to avoid this combination, as the modifications to the formwork increase the cost and complexity of the mould and interfere with the casting programme It is easier to cope with a haunched deck than a continuously varying depth, as in the former case the narrowing of the bottom slab is limited to a relatively small proportion of the segments, and the rate at which it narrows is constant If the bottom slab is maintained at a constant width, the web surfaces will be warped For a deck that has a continuously varying depth, the timber shutters of a cast-in-situ cantilevering falsework can accept this warp, whereas this may not be the case for the steel shutter of a precast segmental casting cell However, for a haunched deck the warp would be introduced suddenly at the beginning of the haunch, which would probably be impossible to build, and would look terrible A successful detail employed on several occasions by the author on precast segmental decks is to adopt a trapezoidal box which runs the full length of the span, and to add a parallel sided haunch Refinements are to define the haunch by a step in from the trapezoidal section and to finish the haunch with a small step rather than fairing it into the soffit; a detail that was adopted on Benaim’s STAR project in Kuala Lumpur, Figure 13.7 and Figure 9.9 If this is not done, the distinction between the inclined web and the vertical haunch will not be clear, leading to visual ambiguity and a lack of crispness in the appearance This detail has the disadvantage that it complicates the web reinforcement A further technical refinement is to keep the centre line of the web approximately straight over its full height by thickening the inside face of the web over the depth of the haunch The web thickening provides additional concrete at the bottom of the section close to the piers, often making it unnecessary to thicken the bottom slab If the thickening is started from a point just above the step, a local reduction in thickness of the web may be avoided, Figure 13.8 An additional advantage Box girders 377 Figure 13.7 Rectangular haunch on STAR (Photo: Robert Benaim) Figure 13.8 Rectangular haunch 378 Box girders of this geometry is that it makes it possible to locate the bearings directly beneath the axis of the webs, greatly simplifying the pier diaphragm 13.5 The number of webs per box One of the principal aims of the bridge designer is to minimise redundant material This is the discipline that is the basis not only for economy, but also for technical innovation and for beauty Economy of materials in the design of box sections is achieved principally by minimising the thickness of the deck members This has the dual benefit of reducing the dead weight bending moments and shear forces, and reducing the cross-sectional area to be prestressed The benchmarks shown in Chapter indicate the target quantities the designer should be aiming for As was explained in 8.2 and 9.5.2, it is much easier to build a few thick webs than several thinner webs; the number of webs should be reduced to a minimum A 200 mm thick top slab haunched to 350 mm is adequate for a clear span of about m 200 mm side cantilevers also haunched to 350 mm are adequate for a span of about 2.8 m Hence, this minimum thickness slab will allow an overall structural box width of about 12.6 m (excluding parapets), once the thickness of the webs is included, Figure 13.9 As the width of the deck increases, the designer has the option of increasing the span and thickness of the slab, or adding a third web Up to a clear span of about m, the more economical option is, without exception, to keep to two webs and thicken the slab up to a maximum of about 300 mm, haunched to 500 mm This haunch thickness will allow side cantilevers of up to m, yielding an overall structural box width of some 18 m These figures are appropriate for UK loading; most other loading codes are lighter, and consequently slabs of a defined thickness will span further Some designers add a third web when it is clearly not essential, presumably in the mistaken belief that the additional cost of the web will be balanced by the reduced cost of the top slab There is no doubt that the economic logic is to maximise the length of the side cantilevers and the span of the top slab in order to keep to two webs for as long as possible Together with the inclination of the webs to reduce the width of the bottom slab, this also gives a good-looking deck For boxes that are still wider, the thickness and weight of a free-spanning solid slab starts to become excessive, and it is necessary either to add a third web, to change to Figure 13.9 Typical width of single cell box designed to UK loading Box girders 379 a ribbed or strutted slab and side cantilever (9.2 and 9.3) or to increase the number of boxes in the cross section The choice will depend on the methods of construction adopted, and on the preferences of designer and builder The author’s preference is, wherever possible, to build single-cell boxes, accepting the resultant complications to the construction procedure, or to increase the number of boxes When three webs are used, it should be noted that the shear force is not evenly distributed, with the centre web taking more than one-third The prestress should be distributed between the webs in proportion to the shear they carry 13.6 Number of boxes in the deck cross section 13.6.1 General Once it has been decided that it is appropriate to adopt a box section for the bridge deck, the designer must decide how many boxes should be used across the width of the deck This decision governs not only the material content of the deck, but also the arrangement and cost of the substructure, and the type and scale of the temporary works that need to be mobilised It is intimately linked to the other basic decision that must be made, whether to cast in-situ or to precast There are many factors that influence these linked decisions Some of the most important are the following: • • • the scale of the project and subdivision of the scale; many short bridges; several longer bridges; one very long bridge (Chapter 16); complication of the project; change of crossfall; variable width of the deck; bifurcations of the bridge deck; presence of a family of bridge decks; presence of slip roads etc; criteria for sub-structure and foundations (Chapter 7) 13.6.2 Constant-width decks Consider a 15 m wide deck carried by a single-cell box This would typically have 3.25 m long side cantilevers, and an overall box width of 8.5 m If the span were 50 m and the depth of the box 2.8 m, the thickness of the webs at the piers would be 625 mm (9.5.2), while at mid-span the webs could be reduced to 350 mm or 400 mm, Figure 13.10 (a) The top slab would be 250 mm thick with 450 mm haunches If two boxes were to be used, the side cantilevers would typically be 1.25 m, the overall width of each box 4.25 m, and the slab between boxes m, Figure 13.10 (b) For the same span and depth, the webs would be 350 mm thick at the piers, and this thickness would be maintained at mid-span The top slab would be 200 mm thick with 350 mm haunches This is not a very economical scheme as there is too much web material at mid-span, and the 200 mm top slab will be under-used Furthermore, the side cantilever length is somewhat short for the appearance of the deck and the 3.55 m internal width of the box is too small for economical striking and handling of the shutter for precast segmental construction One bonus is that the webs may be of constant thickness, simplifying construction 380 Box girders The substructure will be more expensive due to the increased dead weight of the deck Also, if the pier consists of one central column a crosshead will be necessary to carry the two boxes If the pier consists of one column beneath each box, the cost of the foundation to carrying a live load that consists of a single heavy vehicle (such as the British HB Vehicle) is increased as it is carried twice If the deck is made of precast segments a 15 m wide segment, 3.5 m long is likely to weigh of the order of 80 tons, while the narrower segments will weigh about 30 tons, and may more easily be transported by road The casting cells for the smaller boxes would be smaller and cheaper, the lifting equipment lighter, and the precasting run doubled The practical maximum width of deck that may be carried by these two small boxes without thickening the top slab is defined by 2.8 m long side cantilevers and a span between boxes of m, giving an overall width of 20.1 m, Figure 13.10 (c) The webs would need to be increased in width to about 450 mm at the piers A single box could still be used for this width, with typically a box that is 10 m wide at the top Figure 13.10 Strategies for wide decks Box girders 381 and side cantilevers that are 4.5 m long However, the thicker top slab required for the British code of practice erodes the weight advantage, and the two box scheme becomes more competitive A ribbed or strutted cantilever or top slab may regain the weight advantage for the single box, at the expense of a more complicated construction process, Figure 9.6 (c) For lighter loading codes, the single box with solid slabs remains economical over greater widths, as demonstrated by the Benaim project for the approach spans of the Storabaelt crossing, where a 23.7 m wide deck was carried by a single box with solid slabs The overall box width was 14.2 m, with 4.75 m long cantilevers, 500 mm thick at the root, Figure 9.12 (e) As the deck becomes wider still, two of the 8.5 m wide boxes, with 3.6 m side cantilevers and a 7.5 m span, 250 mm thick slab between boxes give rise to a 31.7 m wide deck, Figure 13.10 (d) This is clearly not the limiting width for a two-box deck, as the top slab may be thickened to 300 mm with 500 mm haunches, leading to a box that was 10 m wide, m side cantilevers and a m slab between boxes, yielding a 37 m wide deck Even wider decks may be achieved by adopting a ribbed slab However, the option remains to adopt more small boxes 13.6.3 Variable-width decks When the width of a deck varies along its length, considerable care must be taken to design a scheme that is practical to build In general, it is not good practice to change the width of the box itself, as this involves substantial modification to complex formwork The variation in width should be taken out in the side cantilevers and the slab spanning between boxes, initially by reducing the width of the constant-thickness sections, and then if necessary cutting short the haunches For instance, the 15 m wide deck shown in Figure 13.10 (a) could be simply reduced to a 12.2 m width by cutting off the 200 mm side cantilever, and then further reduced to 8.5 m, with some complications to the edge parapet that would have to suit the haunch thickness If the width was to increase locally up to 16.5 m, the side cantilevers could be stretched to m (span/depth of 9) with heavier reinforcement For still greater width, the top slab could be thickened upwards locally by 50 mm to allow side cantilevers of 4.5 m, or the 450 mm thick side cantilevers could be prestressed to permit the greater span Although these are expensive solutions, they may be better than adopting a less economical option over the majority of the length of the bridge However, if the width were to start at 10 m, and increase linearly to 21 m, the two small boxes could initially be cut down, and then stretched slightly by reinforcing the slab more heavily at the widest point This maximum width may be further increased by thickening the top slab and increasing the side cantilevers and the span between boxes If the width varied from 10 m to 30 m, it would be necessary to adopt the small box scheme, and to introduce a third box once the width became greater than 21 m The choice of the method of adapting to a variable width of deck can have a very significant impact on the appearance of the deck, particularly if the width of the side cantilever is changed Where possible, the side cantilever should remain constant, or should vary only slightly, and gradually However, often this is not possible, and the various methods of widening the deck must be evaluated for both economy and appearance This is illustrated by the Dagenham Dock Viaduct on the A13 highway in London, Figures 13.11 and 13.12, designed by Benaim This bridge was 1,700 m long and, Figure 13.11 Dagenham Dock Viaduct: widening at the West Abutment 384 Box girders Figure 13.12 Dagenham Dock Viaduct: introduction of third box (Photo: Benaim) over most of its length, was 30.57 m wide However at each end it widened, to a maximum of 46.52 m at the West Abutment It was made up of two trapezoidal precast boxes that were m wide across the box As the deck widened, the side cantilever was kept constant, while the slab between boxes was widened When this slab reached its maximum span a third box was introduced, which initially required the inner cantilevers of the external boxes as well as both cantilevers of the new box to be cropped short On this bridge the additional box was introduced at the point of inflexion of a span Alternatively, additional boxes may be introduced at an expansion joint Figure 13.13 is based loosely on the project for the approach viaducts to the Ting Kau Bridge in Hong Kong, designed for tender by the Benaim–Rendell Joint Venture The decks were to be made by the precast segmental technique The slip roads adopted a narrower box than the main line Where the main line was locally too wide for two boxes, the castin-situ intermediate slab was carried by post-tensioned beams, also cast in-situ The beneficial effect of the sagging parasitic moment due to the beam prestress made it possible to connect these beams directly to the webs of the boxes These examples demonstrate the type of options open to the designer The decisions taken will depend on many factors, among which the most important is how much of the deck is wider or narrower than the average If most of the deck is of constant width, with a local widening at one end, for instance, the designer should opt for a scheme that gives maximum economy over the greater length, even if the widened portion is locally uneconomical Box girders 385 Figure 13.13 Typical detail for bifurcation of multiple box section deck ... may be avoided, Figure 13. 8 An additional advantage Box girders 377 Figure 13. 7 Rectangular haunch on STAR (Photo: Robert Benaim) Figure 13. 8 Rectangular haunch 378 Box girders of this geometry... A13 highway in London, Figures 13. 11 and 13. 12, designed by Benaim This bridge was 1,700 m long and, Figure 13. 11 Dagenham Dock Viaduct: widening at the West Abutment 384 Box girders Figure 13. 12... significant Box section decks overcome all these disadvantages 13. 4 Shape and appearance of boxes 13. 4.1 General A box section deck consists of side cantilevers, top and bottom slabs of the box itself