5. Assessment of Deck Type Options 5.1 Three corridor options 5.2 Double deck options
5. Assessment of Deck Type Options
5.1 Three corridor options
5.1.1 General
The deck options for the three corridor functional cross section are illustrated in Drawing FRC/C/076/S/101. The stay cables are anchored in the structural zone reserved for the tower legs, in other words in the ‘shadow’ of the tower legs. This means that the stay cables provide less torsional support to the deck than if they were connected in a more traditional manner close to the deck edge.
To compensate for the reduced torsional support a box girder deck is required. This provides the necessary torsional stiffness to achieve aerodynamic stability and prevent unacceptable twisting under eccentric traffic loading.
Bridges with stay cables anchored along the centreline of the bridge are reasonably common. When that is the case, no torsional support is provided by the stays themselves and the torsional behaviour of the deck is governed only by its own torsional strength and stiffness. The Tsurumi Tsubasa Bridge with a centre span of 510m is believed to have the longest cable stay span in the world of this type.
Although the span of the Forth Replacement Crossing will be longer than the Tsurumi Tsubasa Bridge, the stay cables are not anchored exactly on the centreline and studies have been carried out which show that the torsional stiffness of the bridge is provided by both the stays and the deck stiffness in approximately equal measures.
Nevertheless, the torsional behaviour of the bridge is important and the issues which have been considered are:
- Twist of the bridge under out of balance live load (serviceability issue)
- Torsional shear stresses in the deck
- Transfer of torsional shear from steel to concrete (composite option)
- Aerodynamic stability
5.1.2 Orthotropic Deck
(a) Deck structure
The deck is a relatively traditional orthotropic box girder, 4.5m deep at the bridge centre-line. The fatigue sensitive top flange plate of typically 14 mm is stiffened at 300 mm centres by longitudinal trough stiffeners spanning between diaphragms which are required to maintain the shape of the box and provide the transverse framing. The bottom flange plate typically varies between 10 to 12 mm and is governed by transverse flexure under Special Vehicle loading (equivalent to HB 45 loading in BD 37/01).
A braced diaphragm is proposed in preference to a full plate diaphragm. Plated diaphragms typically contribute about 20 % of the weight of the deck structure, although this percentage increases as the box gets deeper. For the 4.5m deep box a braced truss diaphragm will have the advantages of weight saving and better internal access within the deck. It is considered to be more economic, despite the additional support arrangements required during the assembly process.
A continuous internal web is provided at the stay anchorages in order to efficiently transfer the stay forces into the section and also to mobilise intermediate diaphragms between stay locations in transverse bending.
(b) Construction modules
An erection unit length of 22 m is proposed based on a number of issues, one of which is the maximum stay cable spacing achievable within the limit of 127 strands per cable noted in Section 3.3 above. The advantages of maximising the erection unit length are:
- Maximum offsite work in factory controlled environment.
- Maximum work off critical path
- Minimum work at height (Health & Safety benefit)
- Minimum programme
- Maximum speed when overall project is almost at its most cashflow negative
These advantages are believed to justify the additional cost of temporary works and scale of equipment needed in assembly and load-out and erection associated with a larger unit. Gantries and floating plant are available that can handle the envisaged 450 t segment weight.
It is also preferable to maximise the diaphragm spacing, within practical limits, in order to reduce the manual fabrication associated with transverse material. A large part of deck panel fabrication is associated with adding the transverse plating (combs) and this work tends to involve non-automated methods.
Automated Panel Fabrication
Manual Fitting of Transverse ‘Combs’
Typically in UK and Europe, the spacing of diaphragms that provide transverse support to orthotropic steel decks is in the range of 3.5 to 4.5m. In the US, the practice is to extend the span of the orthotropic deck to about 6.1m, which results in a heavier trough and deck plate but significant reduction in workmanship. The reduction in work content can compensate the cost of marginally more material. Two reasonable options are available within the 22 m module, either 4.4 m or 5.5 m. The main concern with greater diaphragm spacings is the fatigue of the orthotropic deck plate and a detailed fatigue assessment will be carried out to determine the preferred diaphragm spacing. The design work to date is based on 4.4 m.
(c) Articulation
The deck articulation is as follows:
- Central Tower – monolithic connection
- Flanking Towers – floating system with lateral restraint bearings
- Side Span Piers – guided bearings
- End Piers – guided bearings
The monolithic connection of the central tower provides a maintenance free torsional connection without concerns related to uplift that would be associated with providing bearings. Longitudinal loads due to wind and braking will also be transferred between deck and tower through the monolithic connection. The monolithic connection has to transfer significant loads and will be designed with a combination of prestressing bars and shear connectors as well as local strengthening of the deck. The detailing of this connection needs to allow construction of the tower to proceed above the connection in advance of mobilisation of the deck erection phase of construction. Additional costs would arise if the main span deck erection plant and labour force were to be mobilised for the erection of this segment alone as the remainder of deck erection would not to commence until a number of months after this point. In the event that the units are assembled overseas there would also be either a special delivery of this piece alone or storage costs for the remainder of a full delivery.
At the flanking towers a monolithic connection would result in excessive thermal restraint forces and a floating system has been adopted with no vertical load transfer between deck and tower. Transverse wind loads are transmitted through lateral restraint bearings.
For the guided bearings at the side span piers uplift is a concern when the main span is loaded. This is a common issue for cable stayed bridges with various solutions available. A number of options have been studied:
(i) Monolithic connection
Building the deck into the pier generates significant sway forces in the pier as the ends of the bridge move with thermal expansion and contraction. With conventional reinforced concrete construction the structural demand is excessive. Use of a steel pier which is more flexible is possible, but the additional cost of this solution is unlikely to be justifiable.
(ii) Uplift bearings
Although bearings can be designed to resist both uplift and downward forces, these bearings are both expensive and prone to noise and wear as there is inevitably some free movement between support of upward and downward load. The magnitude of load in this instance is also outside the range of conventional bearings. Uplift bearings are therefore not considered practical for these reasons.
(iii) Non-structural counterweight
It is possible to place non-structural counterweight within the deck such that no uplift would occur. This option is relatively simple but is not the most economical solution.
(iv) Vertical tie down cables
Vertical tie down cables are a practical solution and would utilise the same technology as the stay cables. The cables would be tensioned to ensure that the bearings remained under compression under all serviceability loading conditions. Under ultimate limit state loads lift off of the bearings could occur but the magnitude of the lift off would be limited by the strain in the tie down cables and the lateral guides of the bearings would remain engaged. The height of the piers provides sufficient length for sway of the tie downs under thermal expansion and contraction of the deck. A cost comparison shows the tie-down to be approximately 25% of the cost of the non-structural counterweight.
(v) Composite deck counterweight
The alternative solution is to change the construction material of the last 150 m of the side spans to composite. The additional weight of the concrete slab would ensure that the bearings remained under compression under all serviceability loading conditions. Under ultimate limit state loads lift off of the bearings could occur but the magnitude of the lift off would be limited by separate restraint brackets and the lateral guides of the bearings would remain engaged. Although in isolation this concrete is more expensive than the tie-down option, the saving resulting from the reduced area of orthotropic steel deck would more than compensate for this.
Both vertical tie-down cables and the composite deck counterweight solutions are practical. The composite deck counterweight option is expected to be more economical since it results in a reduction in the overall steel quantities and is therefore the option taken forward.
Movement joints are provisionally located at piers S2 and N2 at the end of the stay cable fan. This minimises the overall length of the cable stayed bridge structure. However, if the approach bridge were to be composite then the movement joint at N2 could be eliminated and the two spans of northern approach could be continuous with the cable stayed bridge structure. The movement joint at S2 could also potentially be eliminated.
(d) Static serviceability
The static serviceability has been assessed to determine the maximum deflections and twists that could occur in the bridge deck due to traffic load. The twist is the change in transverse gradient of the bridge at mid span. Characteristic and frequent values are tabulated below. The quoted return periods are nominal and are for reference only.
Load Condition |
Characteristic Loading |
Frequent Traffic Loading |
|---|---|---|
Maximum Deflection (one span only loaded) |
3,250 mm |
1,300 mm |
Maximum Twist |
2.6% |
1.1% |
The maximum vertical deflection only occurs when one of the main spans is fully loaded and the other is fully unloaded. The chance of this occurring is very low and the maximum deflection of 3,250 mm is expected to have negligible chance of occurring during the design life of the bridge. The maximum twists given are more realistic since commuter traffic could realistically result in one motorway carriageway being fully loaded whilst the other carriageway has little or no load on it.
Serviceability criteria for twist are rarely given in design standards or even project specific design criteria. The criteria for this project need to be established. However, by making reference to the Messina Bridge design criteria as well as allowable cant values for LRT systems a maximum characteristic twist of 5% is proposed in the draft design criteria for this project. By comparison with this criterion the bridge behaviour is acceptable.
(e) Aerodynamic stability
First Symmetric Vertical Mode 0.290 Hz |
|
First Torsional Mode 0.405 Hz |
|
Orthotropic deck – key dynamic modes
The ratio of the modal frequencies is 1.7 which is significantly higher than the provisional target ratio of 1.2 required to avoid coupled flutter vibrations.
Historic wind tunnel tests carried out for the Setting Forth and Second Severn studies indicate a reduced torsional galloping (flutter) velocity of at least 4.5 for an aerodynamic box-girder section with 3.0m high wind screens. The reduced velocity is a non-dimensional aerodynamic parameter with the following definition:
Where:
UC is the critical wind speed for the onset of torsional galloping (m/s)
b is the width of the deck (m)
f is the fundamental torsional frequency of the deck (Hz)
This non-dimensional parameter would indicate a critical wind speed of at least 90 m/s compared to a target of approximately 60 m/s. Forced displacement discrete vortex method simulations have been carried out to calculate flutter derivatives to study the behaviour of the proposed section which is significantly wider than the referenced wind tunnel tests.
The simulations indicate that the critical wind speed of the proposed cross section should be somewhat higher due to the increased width and the use of the reduced velocity of 4.5 should be safe at this stage and the section is expected to be stable against torsional galloping (flutter). However, sectional model wind tunnel tests are required to confirm this.
Vortex shedding stability cannot readily be studied with numerical simulations and must also be investigated in the wind tunnel. However this low wind speed phenomenon is a serviceability issue not a safety issue and can normally be solved by minor modifications to the section or the addition of guide vanes etc.
ArupDVM discrete vortex method simulations
The corner unit of aerofoil box sections often accounts for a significant proportion of the work content in fabrication and assembly. The outer 2m of the proposed section does not contribute significantly to the structural performance of the section. It does however provide the nosing detail to control the aerodynamic performance of the section. There are arguments therefore to simplify the construction of the box by ‘squaring-off’ the section at the back of footway and creating the nosing in a non-structural material. This would have the advantage of being able to integrate the wind shielding, the nosing and a rail to support an inspection gantry in a single component. This would also reduce the perimeter that needs to be match fitted between box units in the assembly yard, as well as reducing the assembly width.
On the other hand, the additional workmanship associated with the corner units will be less than typical for this particular bridge section as the fabrication complexity associated with the stay cable anchorages is not integrated with the complexity associated with the edge detail. It is intended to consider both options in more detail in the next phase of design. If a non-structural edge unit is to be proposed, a detail that is equally maintainable as the structural option needs to be developed.
Non-Structural Edge Detail, Pont de Normandie
5.1.3 Composite Deck
(a) Deck structure
The deck for the composite option is similar in general principles to that of the orthotropic option, except that the orthotropic deck plate is replaced by a conventional reinforced concrete slab.
The bottom flange plate typically varies between 12 to 14 mm with trough stiffeners at around 900 mm centres spanning between the cross frame diaphragms. A continuous internal web is provided at the stay anchorages in order to efficiently transfer the stay forces into the section and also to mobilise intermediate diaphragms between stay locations. Two further web elements are located at the edges of the deck to form the edge of the concrete slab.
The slab is connected to the webs of the box girder and the flanges of the cross beams by conventional headed shear studs. Transverse prestressing of the slab is proposed to improve the in-service behaviour. This will be anchored on the outer webs.
Three options are being considered for the forming of the slab:
- Cast directly onto the box with folding reusable formwork
- Cast directly onto the box using permanent formwork
- Full depth precast slabs shear connected to the steelwork and stitched together
The advantage of reusable formwork is that given the number of re-uses of the forms, it would ordinarily be expected to be the most economic option. However, for the box girder type deck this will be influenced by the required complexity of the form to withdraw it between the transverse bracing members after the slab has been cast. The further development of the layout of the transverse bracing system should consider how the folding forms might be withdrawn.
Given the anticipated complexity of the forms, the relative economy will also be dependent on the number of forms required to keep pace with erection. The width of the deck and the requirement for it to be a box structure will probably result in the steelwork assembly being on critical path. Depending upon where the boxes are assembled and how much space is available it may be that only a limited number of forms are required to keep pace with the steelwork assembly.
Rion Antirion Deck Assembly Lines
Considering the complexity of the re-usable forms, permanent formwork has been considered as an alternative. This has the advantage of minimum initial plant cost. However, there would also be additional costs associated with this formwork which are believed to be likely to outweigh the savings in initial plant costs. Furthermore there would be a weight penalty associated with increased slab thickness required for either precast plank systems such as Omnia or GRP formwork. The knock on costs associated with this would further reduce the economy of the system.
The full depth precast slab option is attractive as installation of the slabs would be faster than the in-situ options and would avoid the cost of the folding forms. This appears to be a valid alternative to re-usable formwork for this deck type worthy of further investigation.
(b) Construction modules
As for the orthotropic deck, the maximum segment length that can be achieved within the 127 strand limit for the stay cables is proposed (refer Section 3.3). However, the deck will be heavier than the orthotropic option and current studies indicate that the cable stay spacing should be limited to 14 m centres. This leads to typical units which weigh approximately 600 t including both the steel and the concrete. Consideration of the possibility of erecting double length units is discussed in Section 9.1.4 (e).
For the transverse system, the same arguments apply as for the orthotropic deck and a braced diaphragm is proposed, in preference to a full plate diaphragm, for overall economy and better internal access. In addition, a plated diaphragm would prevent the use of folding forms for casting the deck as it would obstruct their extraction after casting. It is preferable to maximise the diaphragm spacing, within practical limits for the maximum span of the concrete deck slab achievable with the minimum thickness required for constructability.
Study work carried out to date indicates that the optimum spacing would be 4.0 m which is attainable with a 265 mm slab if considered independent of the erection unit length. However, the number of diaphragms and the diaphragm position in each 14 m unit should be ideally the same so that the stay anchorage is located at the same point in each unit. This allows common formwork to be used in each unit and any strong points for lifting or attachment of gantries will be in the same position in each unit. Consequently 4 diaphragms at 3.5 m spacing is the optimum regular pattern for the 14 m segment length. For this spacing the concrete slab thickness can be reduced to 250 mm. With the diaphragm spacing below 4.0 m potentially the erection unit length could be slightly increased by further reducing the thickness of the slab outside of the trafficked areas in order to reduce the dead load. This will be studied but the benefit is likely to be marginal.
An alternating pattern is also feasible with diaphragms at 4.0 m centres, with each alternate unit having 3 or 4 diaphragms respectively. The box projection beyond the diaphragm at the end of each unit would be adjusted to create the 14 m length and the stay cable anchorages would fall either at the diaphragm or mid-way between diaphragms alternately. The anchorage detailing would have to accommodate this. This option will be studied as an alternative to the 3.5 m spacing.
(c) Articulation
The requirements for articulation for the composite deck are similar to those presented for the orthotropic deck, and the same arrangements are adopted.
To solve the uplift at the side span piers it is unlikely that adding counterweight, either as non-structural weight, or an increase to the deck slab thickness, will be economically viable for the composite option as there will not be a consequential saving in the deck slab cost. Vertical tie-down cables are, therefore, the current preferred option for the composite deck scheme.
Movement joints are provisionally located at piers S2 and N2 at the end of the stay cable fan which minimises the overall length of the cable stayed bridge structure. However, if the approach bridge were to be composite then the movement joint at N2 would be eliminated and the two spans of northern approach would be continuous with the cable stayed bridge structure. The movement joint at S2 would also probably be eliminated.
(d) Static serviceability
The static serviceability has been assessed to determine the maximum deflections and twists that could occur in the bridge deck due to traffic load. Characteristic and frequent values are tabulated below. The quoted return periods are nominal and are for reference only.
Load Condition |
Characteristic Loading |
Frequent Traffic Loading |
Maximum Deflection (one span only loaded) |
2,200 mm |
880 mm |
Maximum Twist |
2.2% |
0.9% |
The vertical deflections are approximately 30% less than for the orthotropic deck and the twists are approximately 15% less. The increased stiffness is due to the greater dead to live load ratio for the deck which results in increased stay cable quantities and therefore a stiffer stay system.
(e) Aerodynamic stability
The behaviour of the composite decks is similar to that of the orthotropic deck (see discussion in previous section). The natural frequencies are, of course, altered by the differing mass / stiffness of the systems. The comparable frequencies are as follows:
First Symmetric Vertical Mode 0.263 Hz |
|
First Torsional Mode 0.369 Hz |
|
Composite deck – key dynamic modes
The ratio of the modal frequencies is 1.4 which is higher than the target ratio of 1.2 required to avoid coupled flutter vibrations.
A critical wind speed of at least 80 m/s is predicted, compared to a target of approximately 60 m/s.
(f) Edge Detail
The issues relating to the edge detail discussed for the orthotropic steel deck in Section 5.1.2(f) apply equally to this composite option. There is an additional consideration that a vertical web plate is proposed for the composite deck to form the edge of the slab and be an end plate for the transverse prestressing in the slab. This tends to favour the use of a non-structural edge detail.
Orthotropic Deck |
Composite Deck |
|---|---|
√ Better aerodynamic performance √ Lower stay cable material and construction costs √ Lower tower construction costs / programme √ Potentially lower foundation construction costs / programme Χ Increased inspection requirements for fatigue critical welds |
√ Better performance for static serviceability √ Lower deck fabrication costs √ Potentially lower cantilever construction cycle time Χ Increased number of cantilever construction cycles Χ Increased inspection requirements for stay cables (due to increased numbers of cables) |
Each deck type – orthotropic and composite – has both advantages and disadvantages. In terms of construction cost and schedule it is difficult to differentiate between the two decks, particularly when future commodity price fluctuations could occur. Whilst the composite deck is cheaper to fabricate it requires additional stay and tower quantities to support it. Similarly, whilst the cycle time for each cantilever construction stage could potentially be reduced for the composite deck, the number of cycles is higher due to the need for a reduced stay spacing to limit the stay size.
The most significant technical difference between the two decks lies in the serviceability performance. The heavier weight of the composite deck results in increased stay cable quantities which gives a stiffer structural system. This stiffness reduces the deflections of the deck under traffic loads. However, the increased mass of the deck results in a lower torsional frequency which increases the risk of aerodynamic instability of the composite deck.
Despite these differences, investigations to date indicate that the serviceability performance of both deck types is likely to be adequate. It is recommended that both types be progressed with a view to allowing each tendering contractor to select the deck type for which they can provide the most competitive price.
5.2 Double deck options
5.2.1 General
Accommodating the multi-modal corridor on a separate level underneath the roadway enables a narrower deck to be used than for the three corridor layout. This enables the legs of the towers to straddle the deck without the proportions of the tower becoming too wide compared to the height. The stay cables can then be anchored close to the edges of the deck in a traditional manner.
The deck required for this layout is relatively deep, providing sufficient bending stiffness to the overall structure to deal with the issues arising from asymmetric live loading as described in Section 3.1 and Appendix D which arises due to three tower arrangement.
Both orthotropic steel decks and concrete decks were considered. A steel deck is lighter which would result in reduced stay and tower quantities. However, steel orthotropic decks are best utilised in box girder construction so as to enclose the exposed surface of the deck stiffeners which would otherwise be difficult to maintain. This is not readily achievable with truss option and therefore a composite deck option is preferred.
(a) Truss Arrangement
Three forms of truss arrangement have been considered which generate differing bending moment demands on the chord and bracing members. The options under consideration, which are illustrated in Drawings FRC/C/076/D/111 to 113 are:
- 2 Plane Warren Truss
- 4 Plane Warren Truss
- 2 Plane Vierendeel Truss
Both the two-plane Warren truss and the Vierendeel truss require deep cross beams for the transverse bending effects whereas the four plane Warren truss is partially triangulated transversely.
The longitudinal pitch of the truss is related to the pitch of the stay cable anchorages. The maximum pitch achievable within the 127 strand stay limit has been adopted in order to maximise the size of the erection unit.
The demand on the stays increases considerably towards the mid span of the bridge. Whilst for the Warren truss options varying the pitch of the truss to match the varying stay cable demand would be visually unacceptable this is not the case for the Vierendeel truss where the pitch can be adjusted, or the width of the "posts" varied to suit the demands on the girder, creating an interesting visual appearance with the structural form reflecting its behaviour. Thus the pitch or "transparency" of the structure can be increased away from the high demand mid span regions.
(b) Chord Options
Tubular and fabricated box chord options have been considered for the trusses.
There is availability of large diameter tube within the UK although this is somewhat dependent on the wall thickness required. There are also periods of time when the oil business tends to absorb the majority of large diameter tube supply when demand in that industry is high. The advantages of tubular chord members is that they are easier to paint than box sections and the fabrication cost of the basic member tends to be lower.
The advantages of the box chord option are; the ratio of vertical and plan bending capacities can be matched to the bending demand of the section; jointing of box sections is simpler most particularly with regard to bolted erection splices; it is easier to use thick plates in areas of high structural demand; and, it is easier to form the joints onto the other sections.
The box chord option has been taken forward on the balance of the above views.
(c) Slab Options
Similar considerations discussed above for the single level deck apply to the truss options. The open nature of the truss section will allow relatively conventional formwork to be used for the slab. The forms will be able to be re-used without complex folding form arrangements. The advantages of permanent formwork are minimal as a result and would not warrant the extra cost.
Truss assembly will be relatively simple as there are no full length longitudinal connections to create. If may therefore be possible, with sufficient assembly beds to assemble at the same rate as erection. The slab construction may therefore be on the critical path and hence the speed of full depth precast slab erection may be of more advantage for this option.
Both a conventionally formed and a full depth precast slab option will be considered in the next phase of design.
(d) Construction Unit Size
Again the desire has been to maximise the unit size for erection to limit the work at the erection front. A 16 m stay spacing, truss pitch and erection unit size would be ideal but the weight of the structure would result in excessive stay sizes. As a result the typical stay spacing has been reduced to 12 m. The combined steel and concrete weight of a 12m length of deck including the concrete slabs is approximately 450 t. This is easily manageable as an erection unit but will involve relatively frequent erection splices.
The section depth will permit greater lengths of cantilever and erection of double length units is considered favourable as discussed in Section 9.1.4(e).
5.2.2 Two Plane Warren Truss
(a) Deck Structure
The two-plane Warren truss is fully triangulated longitudinally. This results in longitudinal bending and axial effects only generating small secondary bending effects in the chord and bracing members. In the transverse direction there the structure is not triangulated so that distortional loads on the deck and the bending of the upper and lower deck crossbeams generates transverse bending in the bracing members. The initial design has shown these bending moments to be manageable. There will be a cost penalty associated with the required framing around the joints to deal with this bending but this will be compensated for with the halving of the number of bracing members and associated connections in comparison with the four plane option.
Both the upper and lower decks are traditional ladder type composite construction consisting of a reinforced concrete deck slab supported on transverse spanning cross girders. However, in order to minimise maintenance the cross girders will be fabricated hollow sections rather than traditional open I-girders.
The ability to erect the deck in double length units leads to a higher priority for optimising the cross girder spacing than for the box girder solutions where the erection unit length must first be optimised and the diaphragm spacing must follow. Study work carried out to date indicates that a spacing of 4.0 m would be attainable with a 250 mm slab although local thickening may be required in the region of the towers. The reduction in slab thickness compared to the composite box girder option for the same transverse structure spacing is achievable because of the flange width and torsional stiffness of the crossbeam,
The deck structure is based on a 12 m truss and stay module which is the maximum multiple of 4.0 m spaces that can be accommodated within the limit of 127 strands per stay. It is anticipated that decks will be erected in either 12 m or 24 m long modules.
Future studies will investigate whether a 14 m truss and stay module could be achieved.
The deck articulation for all of the truss options is as follows:
- Central tower – floating system with longitudinal and transverse restraint
- Flanking Towers – floating system with transverse restraint
- Side Span Piers –guided bearings
- End Piers –guided bearings
Where transverse restraint is provided at the towers it is envisaged that bearings will be provided to permit the requisite sliding and rotational movement.
The main bridge will be made structurally continuous with the approach spans. Expansion joints will be provided at the abutments only.
Longitudinal restraint is provided to the deck by the stay cables. However, this delivers loads due to longitudinal wind and braking forces direct to the top of the tower which is already significantly loaded in longitudinal bending due to the double main span cable system. It is likely therefore that additional longitudinal restraint will be required and the most practical way to provide this is in the form of buffers.
Two options are available with the first being hydraulically linked buffers at one of the towers which would completely restrain longitudinal movement but would allow plan rotation to avoid an undesirable plan moment connection between tower and deck. The most obvious location for this would be at the central tower but it is possible that providing the restraint at the south tower could be more favourable in reducing the design moments in the critical central tower.
The alternative option would be to provide hydraulically independent buffers at one or both of the abutments which would only restrain short term displacements due to the braking and the dynamic component of wind load. Long term displacements due to sustained wind and thermal expansion / contraction would be unrestrained and the stay cable system would act to transfer sustained wind to the towers and keep the bridge centralised under thermal strains. Locating the buffers at the abutments is advantageous in terms of ease of access for maintenance.
It is possible that these options could be combined with buffers at the tower and at the abutments to minimise the loads on the tower.
Current design work has been based on hydraulically linked buffers at the central tower providing complete longitudinal restraint at this location. The alternatives described above will be studied at the next stage.
As for all of the deck options, uplift is experienced at the side span piers. In common with all options which include concrete deck slabs for the main span, tie down cables are expected to be the most economical way to resist uplift.
(d) Static Serviceability
The static serviceability has been assessed to determine the maximum deflections and twists that could occur in the bridge deck due to traffic load. Characteristic and frequent values are tabulated below. The quoted return periods are nominal and are for reference only.
Load Condition |
Characteristic Loading |
Frequent Traffic Loading |
|---|---|---|
Maximum Deflection (one span only loaded) |
2,250 mm |
900 mm |
Maximum Twist |
0.6 % |
0.2 % |
The vertical deck deflections are similar to those found for the composite box girder deck type. Since the dead to live load ratio is similar for those two structural options this indicates that the stiff truss girder provides equivalent global stiffness to the crossing stays adopted for the slender box girder.
As would be expected, the maximum twist of the deck is very much less than for the box girder solutions since the overall deck width is less and the stay cables are anchored close to the deck edge.
Divergent aerodynamic instability (flutter and galloping) is not expected to be a problem for any of the truss options in view of the flow of air between the decks and the high bending stiffness of the deck. Nevertheless, this will need to be demonstrated through wind tunnel testing. Wind tunnel testing will also be required to verify non-divergent vortex shedding behaviour of the trusses.
Similarly wind tunnel testing of the towers will be required to verify their aerodynamic stability and their sensitivity to wake buffeting effects, both in service and during erection when they are in a free-standing condition.
5.2.3 Four Plane Warren Truss
(a) Deck Structure
The four plane truss is triangulated longitudinally and partially triangulated transversely. This solution involves the minimum bending at the connection nodes. Each bracing connection will therefore be simpler than those in the other truss options. There are twice as many bracing members and top chord members and the lower chord node is formed with four intersecting bracing members, although these have been separated into two planes for simplicity of detailing. The cost comparison will assess the relative benefit of increased structural efficiency compared with increased numbers of members and connections.
Because of the support provided by the inner plane of the truss and inner top chords, the top deck crossbeams are 3-span beams and are therefore lighter and shallower than in the Two Plane Warren Truss. This has a small effect on overall girder depth and vertical alignment.
As for the Two Plane option the deck structure is of traditional ladder type composite construction with a reinforced concrete deck slab supported on transverse spanning fabricated hollow box section cross girders.
(b) Construction Modules
The construction modules are the same as for the Two Plane Warren Truss. Refer to Section 5.2.2(b).
(c) Articulation
The proposed articulation arrangements are the same as for the Two Plane Warren Truss. Refer to Section 5.2.2(c)
(d) Static Serviceability
The static serviceability has been assessed to determine the maximum deflections and twists that could occur in the bridge deck due to traffic load. Characteristic and frequent values are tabulated below. The quoted return periods are nominal and are for reference only.
Load Condition |
Characteristic Loading |
Frequent Traffic Loading |
|---|---|---|
Maximum Deflection (one span only loaded) |
2,200 mm |
880 mm |
Maximum Twist |
0.8 % |
0.3 % |
The vertical deflection is similar to the Two Plane Warren Truss whereas the twist is slightly higher as one would expect.
(e) Aerodynamic Stability
The aerodynamic performance is similar to the Two Plane Warren Truss. Refer to Section 5.2.2(e)
5.2.4 Vierendeel Truss
(a) Deck Structure
In the longitudinal direction the structural system comprises two planar Vierendeel trusses inclined outwards. The truss comprises an upper and lower chord with vertical bracing members which appear tapered when viewed in elevation. While this is an interesting and unique solution, with some advantages from an aesthetic and originality point of view, the design development has revealed some disadvantages, as discussed below.
The upper and lower chords are required to span longitudinally between web members. However, unlike the fully triangulated Warren truss options, the upper and lower chords of the Vierendeel truss must also carry global shear forces, resulting in significant additional flexural bending effects within the chords. As a consequence the upper and lower decks require significantly heavier truss chords when compared to the Warren Truss option.
These local moments are at their peak at the joints between the members. The result of this is that there is highest structural demand in the areas that are most complicated to fabricate. Several options for the connection details were developed. However, these resulted in either excessively thick plate or large numbers of butt welds in thick plate. It was concluded that these moment connections will inevitably have a very high fabrication content and thus be disproportionally expensive.
Furthermore, the material demand in the chords changes more frequently than would be economic to actually reflect in the structure by changing plate thicknesses. As a consequence of this the Vierendeel truss tends to be relatively inefficient in terms of material quantities when compared to the Warren truss options.
The result of the above is that the steelwork tonnage is greater than for the other options and there will be additional fabrication cost per tonne associated with the increased complexity. The lack of direct load path for the compressive load to the lower deck structure may also dictate a complex phased construction sequence to allow the upper deck to compress without generating secondary moments in the bracings.
As for the Two Plane option the deck structure is of traditional ladder type composite construction with a reinforced concrete deck slab supported on transverse spanning fabricated hollow box section cross girders.
(b) Construction Modules
As for the Warren truss options, the cross girder spacing typically at 4.0 m centres with a 250 mm slab. However, the deck structure and stay spacing is based on a combination of 12 m and 16 m modules to keep the stay size within the limit of 127 strands. This results in an opening up of the structure towards the towers where the longer 16 m module can be adopted due to the reduced demand on the stays.
(c) Articulation
The proposed articulation arrangements are the same as for the Two Plane Warren Truss. Refer to Section 5.2.2(c)
(d) Static Serviceability
The static serviceability has been assessed to determine the maximum deflections and twists that could occur in the bridge deck due to traffic load. Characteristic and frequent values are tabulated below. The quoted return periods are nominal and are for reference only.
Load Condition |
Characteristic Loading |
Frequent Traffic Loading |
|---|---|---|
Maximum Deflection (one span only loaded) |
4,600 mm |
1,850 mm |
Maximum Twist |
0.6 % |
0.2 % |
Static vertical deflection of the Vierendeel Truss is more than double that of the Warren Truss options. This greater flexibility is attributable to flexural bending effects in the upper and lower decks as they are subjected to global shear effects. The Vierendeel Truss is also 40% more flexible than the Orthotropic Deck making it the most flexible of all the solutions considered.
The maximum vertical deflection only occurs when one of the main spans is fully loaded and the other is fully unloaded. Although the chance of this occurring is very low and the maximum deflection of 4,600 mm is expected to have negligible chance of occurring during the design life of the bridge the poor static serviceability performance under more common load patches is a cause for concern and would require careful study before this deck type could be adopted.
The large vertical deflections of the Vierendeel Truss could be reduced by adopting crossing stay cables as proposed for the box girder decks. However, this poses some additional fabrication complexities for a truss type deck and requires additional deck width.
(e) Aerodynamic Stability
The aerodynamic performance is similar to the Two Plane Warren Truss. Refer to Section 5.2.2(e)
5.2.5 Comparison
The technical and aesthetic differences between the different truss options are too significant to consider offering multiple options to the tendering contractor. It is recommended that only one of the truss options is eventually carried forward.
However, at this stage it is too early to select between the Two Plane and Four Plane Warren Truss options. Both of them provide interesting aesthetic possibilities. Whilst the number of members is of course less for the two plane option, provided that the member size can be kept sufficiently slim the four plane option may provide a very interesting and transparent structure. The reduction in distortional effects as well as the load share for longitudinal effects should allow this transparency and may result in a more structurally efficient deck overall. Further design development is required to provide sufficient quantities for detailed cost comparison and to provide confidence in member sizes for aesthetic comparison. Once the structures are defined in more detail in this way an informed selection can take place.
On the other hand, sufficient investigation has been carried out to indicate that the Vierendeel Truss is currently the least favourable option from the point of view of structural performance and construction economy. This option was worthy of consideration since it offered a unique structural form which potentially could have been very clean visually and relatively easy to maintain with the minimum number of surfaces for repainting. However, the structural demands have led to heavy vertical members which have to a large extent negated the initial aesthetic benefits of this option. The steel quantities are estimated to be approximately double the other truss options and the fabrication complexity will be high with significant structural demand on the connections. Furthermore the structure will be significantly more flexible than any of the other options considered which raises question marks over whether it would perform adequately in-service.
Considering all of these points it is recommended that the Vierendeel truss is not progressed further.