A CRITICAL STUDY ON THE THEODOR HEUSS (NORTH) BRIDGE, DUSSELDORF

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1 Proceedings of Bridge Engineering 2 Conference rd April 2008, University of Bath, Bath, UK I A CRITICAL STUDY ON THE THEODOR HEUSS (NORTH) BRIDGE, DUSSELDORF T. C. F. Tse 1 1 Student of Civil and Architectural Engineering, University of Bath Abstract: This paper aims to provide a general analysis of the Theodor Heuss (TH) Bridge with a particular emphasis on the structural aspects of the bridge. It focuses on other issues concerning the bridge such as aesthetics, design, construction, loading, strength, serviceability and maintenance. The importance of the benefits and drawbacks of the cable-stayed (s-c) system and the ways in which the TH Bridge utilizes these benefits to its best advantage are explored throughout this paper. It looks on to the possible changes which could be made on improving the structural performance of the bridge. Keywords: Concrete pier, Orthotropic deck, Steel box girder, Steel pylon, Suspended cantilever construction Figure 1: General view of the Theodor Heuss Bridge, Ref. [1] 1 Introduction The construction of the North Bridge began in 1953 and completed in 1958 as the first modern, c-s bridge in Germany and second in the world after the first one which was built in Sweden in 1955, the Stromsund Bridge. The original application of a stayed system which had a similar idea to the modern c-s bridge dates back to the 1600 s when a Venetian engineer, named Verantius, built a bridge with a primitive concept of having several diagonal chain stays which partially suspended a bridge, Ref [2]. The TH Bridge crosses the Rhine River between Golzheim and Niederkassel in Dusseldorf, with a central main span of 260.0m. It was the first of the three c-s bridges that were built across the Rhine, known as the Dusseldorf s family of c-s bridges. The other two bridges (Knie Bridge and Oberkassel Bridge) were completed twenty years later. The TH Bridge carries the Bundesstraße 7, a downtown connector to Autobahn 52. The growing traffic in the bridge relaxed in 2002 when the Airport Bridge to the north of this was opened, Ref. [3]. It is currently in use and carries pedestrian and road traffic. The bridge was designed by a German called Theodor Heuss, hence the bridge name, and the consulting engineer was Fritz Leonhardt, whom paid large contributions toward the design. As one of the first modern c-s bridges, the design had relatively few stays, hence the distances created between the elastic supports were large. For this reason, a steel deck was used to provide sufficient stiffness.

2 2 Aesthetics The bridge can be analysed aesthetically with regards to the ten areas stated by Fritz Leonhardt. Some of these areas overlap each other in terms of analysis so it would be discussed in general terms rather than separately. The TH Bridge is a straight-forward c-s bridge that exhibits an obvious function which is simple and clear. The cables show their function of load transfer and the piers are sufficiently sturdy. However, the spans that flank on the outside of the outermost cables do not have supports at spacing equal to that of the cables which could make the number of cables look unnecessary. Figure 2: Sizing of the TH Bridge, Ref. [1] The height of the pylons is of a sensible proportion relative to each of the deck spans. The piers feel like they could have been built higher, almost the same height as the pylons in order to match with the central span of 260.0m. The span to depth ratio for the deck is practical as the deck appears slender and is supported by a series of cables at equal spacing. The cables are of equal diameter and are assembled in a harp arrangement which maintains a good order. This prevents the jumbling of cables, crossing at different angles when seen in an oblique view. The downside of this arrangement is that the cables are working inefficiently in terms of taking vertical load at a shallow angle. Figure 3: Harp arrangement of cables, Ref. [4] There is a minimal amount of repetition within the bridge. The only elements which could be repeated are the cables and piers, and there are relatively few of these. The depth of the deck remains constant and this visual flow is maintained along the deck by having subordinate cable anchorages, which do not break the continuity. However, the piers that are linked to the outermost cables are built enclosing the edge of the deck which then breaks the flow across the deck. This may have been used to indicate that the bridge actually stops there rather than being continuous from then onwards. There would have been a smoother flow if the interconnection between adjacent units along the deck were eliminated by using some form of non-structural covering along the edge. Cable-stays can have a strong visual refinement when a large quantity is used on a long-span c-s bridge, but for the TH Bridge the refinement is just simplicity since no particular part of the bridge is outstanding. The piers and pylons could have been built as a tower rising from the water to the top as a single element to add more continuity to the design, rather than having a separate solid pier beneath the pylons. On the other hand, this could break the visual flow along the deck. The use of a c-s bridge for crossing the Rhine suits well with the environment and is an ideal choice of bridge type. Other bridge types such as a prestressed concrete bridge would require a huge box-section and an enormous amount of prestressing in order to achieve this span, hence it would be impractical. The bridge crosses the river at a low profile which represents the nearby terrain and the choice of cable pattern and tower form reflects on the simplicity of the environment. The deck gives the ordinary surface texture of steel which is smooth and provides subtlety when it is revealed below the walkways. This is emphasised when the fascia overhangs and partially casts a shadow over the steel. The pylons are noticeably darker than the rest of the bridge which is intentional as a way of differentiating the separate parts of the bridge. The break between one material and another is crisp and clear, for instance, between the bridge deck and a pier. This bridge has no particular character since its function is relatively simple and holds the typical form of an early c-s bridge design, thus simplicity would be its character. There are areas where it could have been more complex but have been kept simple, for example if the two cable planes were in a fan configuration then it would lose clarity. It does not have crossbeams in between the pylons so that the view of the sky is kept clear for motorists drive past the pylons and it would generally maintain visual simplicity. The double-plane cable arrangement could be simplified to single-plane as long as the relatively large concentrated cable forces acting on the main deck is permissible with additional stiffening of the deck and that the torsion stiffness of the deck is sufficient. Again, this would be done mainly for aesthetic purposes and possibly for economics, in terms of reducing the number of cables and the associated connections. The structural form of this bridge has no particular integration with nature but the piers appear to merge with the shore of the river and the colour of the deck matches closely with the water. 3 Choice of bridge type The application of a c-s bridge is an ideal choice for serving this purpose. Firstly, it is designed to cross the river and must do so without interrupting much of the river traffic, therefore the minimum temporary and permanent supports should be used. This would imply that bridge types such as masonry or concrete arch are not suitable. The reason is that they are incapable of achieving one clear span across 260.0m without having several intermediate supports, hence they would not be appropriate for this task.

3 Other options can be a steel bow-string arch or cantilever bridge. Both of which may consist of a truss system forming the structural frame of the bridge. The truss should be above the roadway to avoid obstruction to the river traffic. However, these designs would require a deep cross-section in order for a truss system to work efficiently and since the surrounding terrain remains at a relatively low level, it would seem odd to have a big rising structure spanning a river which is not of a great distance compared with the size of a truss which might be used, hence would be out of proportion. Suspension bridges are an alternative for river crossing and have been around for longer than c-s bridges. Conversely, a span of this distance seems impractical to use a suspension bridge since it is generally more difficult and expensive than the c-s design in terms of erection and designing the cables. In most cases, suspension bridges are most suited to long spans and become dominant over other bridge types because the amount of steel used within a bridge becomes a governing factor for exceptionally long bridges and the amount of steel in a suspension bridge does not increase as much as for a c-s or an arch bridge when compared at large distances. As a result, it is more economical and practical for spanning great distances but not so economical for spanning the Rhine River. 4 Design and Construction The design and construction of any structure are always inter-related and it seems best if these are discussed together. The TH Bridge is the second modern c-s bridge built in the world, thus it takes the traditional approach whereby only a few strong concentrated cables were used as a substitute for piers. This inevitably forces the design to adopt a very stiff deck rather than a more flexible one that is often preferred for present c-s bridges. This is because deck has to withstand relatively large bending moments due to few supports, so the deck must be sufficiently stiff in order to withstand these effects. This becomes an issue if the deck was built with deep and heavy concrete units which add masses of dead weight on to the bridge. This makes construction difficult both in terms of cost and feasibility, since large and heavy equipment is needed to erect these hefty units into position. This would also require larger pylons and foundations than otherwise would have needed if the deck was in steel, hence the choice of using a relatively lightweight steel deck was ideal. Initially, the foundations were constructed in order to form a solid base for the piers to rest on. The foundations are assumed to be of reinforced concrete pad footings which were cast in-situ with temporary formwork. This type of foundation should be sufficient since the bridge is not regarded as a particularly large bridge so piles are unnecessary. This is of course assuming that the river has a shallow depth and that the ground is in a good condition, hence allowing relatively cheap and simple construction. The piers would then be cast on top of the footings with reinforcements linking to that of the footing, to form a rigid connection. Again the casting of the piers can be done in a relatively simple manner. The steel pylons were factory-made and then assembled on site. The deck and Mr T. Tse tcft20@bath.ac.uk the cables are assembled simultaneously so that as the deck extends, the next cable is connected to support the deck. The bridge deck consists of two stiffening box girders with an orthotropic deck spanning them. Walkways are made of reinforced concrete which cantilevers from the box girders, giving an overall width of 26.6m for the deck. The deck units, box girders and deck plate were preassembled in roughly 36.0m long sections, which were then floated into position and cranelifted, Ref. [2]. The box girders are continuous along the deck providing the overall strength and stiffness to the bridge, mostly to resist bending. The orthotropic deck comprises a steel bearing plate at the top with stiffening members underneath to increase the bending and torsional stiffness of the bridge and help to distribute the concentrated wheel loads on to the box girders. The advantage of using such deck is that the bridge can achieve the maximum strength for the minimum dead weight applied. The deck has stiffeners applied longitudinally to resist bending and may have transverse stiffeners across the deck to resist torsion in order to take full advantage of the orthotropic system. Three parallel harp stays are attached to either side of each pylon, at third points along its height. The stays are supported on saddles so that they are continuous through the pylons. The saddles for the centre stays are fixed while the upper and lower saddles are supported on bearings, Ref. [2]. The advantage of this system is that the upper and lower saddles allow the pylons to have slight horizontal movements under wind loading and asymmetric loading on the bridge so that the bending moment induced in them can be reduced. The central saddle is fixed to maintain the overall stability of these pylons and to prevent them over-deflecting from their original position. The reason is that over time, this could potentially cause the connection between the pylon and the deck to undergo fatigue, since the deck is much stiffer than the pylons. The benefit of using saddles is that it is no longer necessary to anchor the cables on to the pylons, thus eliminates a set of connections. The pylons are fixed to the stiffening girder at the base and rise through the roadway as a single cantilever (40.0m) supported by cables. The slenderness of the pylons imply that they are not subjected to large bending moments but are experiencing concentrated cable forces at the saddles due to few cables, thus the saddles must be of high quality. Other than being a lightweight bridge, it would be regarded as impractical to build with few concentrated cable stays today since it does not fully exploit the advantages of a c-s design. Given the fact that it was one of the first modern c-s bridges that were built and some of these benefits were only discovered after it has been built, then it is fair to say that bridge was of a good design since it mainly focused on its aesthetic appearance rather than its structural performance. The use of a harp configuration for cable layout proves this point. From a design and manufacture perspective, this configuration allows the cables to be made of the same size in diameter because each cable is assumed to carry roughly the same amount of load due to their same angle of inclination and that they are evenly spaced along the deck. From a construction angle, it allows the cables to act as permanent stays when

4 suspending two cantilevers from either side of the bridge during erection, hence saving the cost of hiring additional kit. The two sides would eventually merge at the centre, closing the deck. This form of suspended cantilever construction proves to be the most economical way of assembling a bridge when compared to assembling on pontoons or trestles. This is especially the case for a c-s bridge because the assembling equipment such as the main tower and guy-ropes are already there as pylons and cable-stays. The c-s bridge also exhibited other benefits such as the ease of fabrication, speed of erection, and its elegant, transparent appearance. 5 Loading Although this bridge is situated in Germany, the assessment of loading on the bridge is done according to the British Standards and assumptions are made where feasible to simplify the analysis process. The bridge is checked against the worst load conditions and combinations in order to ensure that the bridge is safe and serviceable under the Ultimate Limit State (ULS) and the Serviceability Limit State (SLS) theories respectively. Each of the nominal loads below is multiplied by two factors, γ fl and γ f3 in order to obtain the design loading. For a steel bridge, γ f3 = 1.10 at ULS and γ f3 = 1.00 at SLS. These values are used for all the nominal loads throughout. However, γ fl varies with different load combinations as shown below: Table 1 : γ fl for different combinations Load Dead : steel Dead : concrete SD Wind : plus other combination 2 loads Temperature : restraint to movement HA alone HA with HB or HB alone Limit γfl for combination: state 1 2 ULS SLS ULS SLS ULS SLS ULS SLS ULS SLS ULS SLS ULS SLS The superimposed dead (SD) load is in most cases insignificant compared to the dead load of the bridge. For the TH Bridge with a central main span of 260m, the dead, wind and temperature loads will be the governing factors. The primary and secondary live loads are of less importance in this case since these loads tend to dominate short to medium-span bridges. Therefore, the following Mr T. Tse tcft20@bath.ac.uk two load combinations which focus on wind and temperature will be considered: 1) Dead + SD + Primary Live + Wind + (Erection Load) 2) Dead + SD + Primary Live + Temperature + (Erection Load) 5.1 Dead and SD Load Assuming the orthotropic deck and the box girders are made of 15.0mm thick steel. The volume of steel and reinforced concrete estimates to be 1.92m 3 and 12.7m 3 per metre length along the bridge respectively. The total factored dead load at ULS is given as load per metre length along the bridge: 286.0kN/m kN/m / The SD load mainly comprises asphalt, with other insignificant elements such as: parapets, lampposts and services. These elements are neglected since they are relatively weightless. The asphalt layer is assumed to be 60.0mm thick, which gives the total factored SD load at ULS as follows: 20.7 / / As mentioned before, the SD load is significantly smaller than the dead load, nonetheless it increases the adverse effect in structural analysis 5.2 Primary Live Loads These are the vertical static loads due to the weight of traffic acting directly on the bridge. These are the HA and HB loading, which are applied separately within the notional lanes of a carriageway. The notional lanes can be defined in the British Standards, Ref. [5]. The TH Bridge has a 15.0m wide carriageway which roughly equates to four notional lanes, each of 3.3m wide with two in each direction and a 1.8m wide central reserve. The carriageway is flanked by a 3.3m wide walkway on either side. The steel piers are approximately 1.8m wide, located in between the carriageway and walkway HA Loading The HA loading consists of a uniformly-distributed load (UDL) plus a knife-edge load (KEL) acting over a notional lane. By assuming the deck has constant rigidity and cross-section along the entire length of the bridge and applying the appropriate load case, then the maximum sagging moment can be achieved within the central span of 44.0m in between the longest cables. All other spans are of 36.0m.

5 loaded by HA and HB. This is to represent pedestrian loading, especially on the walkways for this bridge. The HA loading condition on the notional lanes is shown below. Figure 4: Load Combination 1 for maximum sagging moment Given that the loaded length is 116.0m, the nominal HA UDL is taken as 22.4 kn/m acting along each notional lane. This UDL value is given in the British Standards, Ref. [5]. The KEL is taken as kn per notional lane. Although the whole bridge may be analysed with factored loads acting on every other span from either side of the central span in order to produce the maximum sagging moment in the central span, it seems sensible to simplify the case and only consider the central part as shown above in figure 3 since the concept is more important than the actual value. Similarly, the maximum hogging moment can be achieved by loading two adjacent spans on either side of a support and on every other span from either side of this loaded span, as shown in figure 5 below. Figure 6: HA Loading on notional lanes HB Loading Due to the fact that the HA loading is relatively large, it has already been checked that even a full HB loading of 45 units does not produce a load case that could be more adverse than the HA loading in both the hogging and sagging cases. Therefore, for future loading analyses, only HA loading is necessarily checked, thus the HB loading need not be defined in this case. 5.3 Wind Load For wind load analysis, the maximum wind gust, v c is taken as: Figure 5: Load Combination 1 for maximum hogging moment Since the bridge is symmetrical down the middle of the central span, the same maximum hogging moment occurs either on the left or the right support of the central span depending on which side is loaded. The HA UDL is factored to give the design loading per metre length per notional lane and the factored KEL is given as a line load across each notional lane as: 22.4 / / The HA load case would give the maximum bending effect in between supports when the KEL is placed at mid-span, and the maximum torsion effect due to the full HA loading acting on two notional lanes whilst only a third acts on the other two notional lanes together with the existing KEL at mid-span. Similarly the maximum shear within the deck is obtained when the KEL is placed close to a line of support. Together with HA and HB loading, a nominal load intensity of 5.0 kn/m 2 is placed elsewhere which is not (1) Assuming the bridge is 10.0m above ground and the minimum horizontal loaded length is 116.0m, then K 1 is taken as 1.39, S 1 is taken as 1.0, S 2 is taken as 1.0 for the gust factor, Ref. [6] and v is taken as 30.0m/s as the mean hourly wind speed. This gives the maximum wind gust as: / this gives the dynamic pressure head, q: / This is substituted into Eq. (2) shown below, to give the horizontal wind load, P t, which acts in the transverse direction against the deck, where: A 1 = 116.0m * [3.2m (deck) m (parapet)] = 516.2m 2 C D = 1.3 (for a b/d ratio of 26.6/3.8), Ref. [5] (2)

6 A horizontal wind load also acts on the piers which cause them to bend. Since they have a different drag coefficient then this load is taken as another value, P p which acts on the piers only. The piers are assumed to have a continuous, square hollow section. The section tapers from the base to the top, therefore an average breath of 1.6m is estimated and C D is taken as 1.85 for an h/b ratio of 40.0/1.6 and a t/b ratio of 1, Ref. [5]: Upward/Downward Vertical Wind Load The effect caused by wind uplift or downward vertical force can enhance the overall adverse condition caused by other loads which act on the bridge. This load is placed as shown in Figure 4 and 5 in order to obtain the maximum sagging and hogging moment respectively. This nominal force can be calculated using the equation below. C L is taken from Ref. [5]. (3) / This UDL is acting per metre length along the bridge, which can be converted into an intensity of 0.42 kn/m 2. This seems rather low compared to other live loads that are acting on the bridge, nonetheless it is accounted for in the calculations. 5.4 Temperature Load The TH Bridge has an overall length of 476.0m, of which the deck is entirely steel. This makes the bridge liable of taking up a substantial temperature load due to the vast range of maximum and minimum effective bridge temperatures that exist for a steel bridge, thus a significant factor to be considered. The bridge is assumed to have no movement joints or any functions of relieving the compressive or tensile stresses which build up during the lengthening or shortening of the bridge, so that the significance of these stresses can be analysed. For the purpose of analysing this temperature load, the maximum and minimum air temperatures in Dusseldorf are taken as 28.0 o C and -5.0 o C respectively. This bridge adopts type 1 construction (steel deck on steel box girders), and the maximum and minimum effective bridge temperatures are given as 42.0 o C and -7.0 o C respectively, Ref. [5]. The datum temperature is taken as 12.0 o C, at which the deck becomes effectively restrained, therefore the maximum change in effective temperature is 30.0 o C. Although this bridge contains a large amount of stainless steel, the coefficient of thermal expansion, α is still taken as 12.0*10-6 / o C as if it was ordinary steel, so that it can be treated together with the concrete parts as one structure which effectively has a constant thermal behaviour throughout. This is done for simplifying the calculations. Mr T. Tse tcft20@bath.ac.uk The longitudinal expansion of the deck can be estimated using Eq. (3) below: (3) This equates to a 0.04% expansion of the deck which is not huge but may still be a problem if this extension had nowhere to go. This is crucial when the piers are stiff and are fixed or pinned to the deck since they would have to withstand shear and bending stresses within them. Assuming that there are no movement joints within the bridge and the Young s Modulus of Steel, E s is 200,000 N/mm 2. The compressive stress which builds up due to the increase in temperature is estimated to be: (4) ,000. / This would impose a large horizontal force on the piers which in turn imposes large bending moments in the foundations. This can be eliminated by either having the deck supported on rollers above the piers or have flexible piers which are capable of withstanding horizontal deflections of this magnitude. This compressive stress can also buckle the slender elements within the deck if both ends of the bridge are restrained from horizontal movements. In this case, the deck plate would be liable to buckling. The problem could be solved by introducing bearings into at least one of the end supports of the bridge to allow horizontal movements due to longitudinal expansion of the deck, and rotation due to the bending of the deck. The shape at which the deck bends is most likely in a longitudinal hogging profile due to the top surface of the deck being heated more than the underside. 5.5 Other loads Creep deformation does not affect this bridge due to its structural elements being steel. There are concrete parts such as the walkways which may undergo creep deformation but is not considered as significant in this case since they are not primary structural elements. Earthquake loading is crucial for bridges which carry little flexibility for example, beam-and-slab bridges, pedestrian bridges over motorways or masonry and concrete arch bridges. These types of bridges are vulnerable to earthquakes and can lead to potential damage or failure. However, suspension and c-s bridges are relatively flexible, hence are considered as safe against this effect. Differential settlement should not be a problem for the TH Bridge due to its relatively long spans with few intermediate pier supports. This means that if one of the piers settles by a few centimetres, then it would be negligible across the deck since it is over a large span. Its flexibility allows the cables to gradually adjust and adapt to the induced internal stresses, keeping the deck and pylons at their relative positions. Bridges that carry exceptional stiffness such as a masonry arch bridge with multiple spans would be susceptible to cracks due to differential settlement.

7 6 Structural Analysis Initially, the analysis begins as shown previously in Figure 4 and 5 to ensure that the cross-section can withstand the ultimate bending moments induced by the factored design loading. Longitudinal bending for this bridge would be the governing factor rather than the shear forces at the supports because there are relatively few cables along the deck, hence the spans are large. For the purpose of this analysis, only half of the deck s cross section is analysed since the bridge is symmetrical about its longitudinal central axis, thus only half the load is taken. This simplifies the calculations especially when checking the cable and pier sizes by analysing one plane of cables which is supporting half the deck. First of all, load combination 1 was used to find the maximum sagging and hogging moments within the central span as shown in Figures 4 and 5 respectively. The predicted bending moment diagrams are shown below. For Figure 8, the predicted bending moment diagram is asymmetrical down the centre since the central right span is slightly longer than the central left span, therefore increases all the other hogging and sagging moments to the right. The same formulae were used in order to estimate the values for these bending moments and they were 77.4 MNm, 38.7 MNm, and 62.2 MNm for the central hogging, maximum sagging, and the sagging moments in the end-span respectively. The bending moment diagram was predicted incorrectly for this load case because the maximum sagging moment should be at the right end-span rather than the one shown in Figure 8. This can be confirmed since both central spans are loaded in the middle in order to produce the maximum hogging moment, which means that the maximum sagging moment does not occur directly adjacent to this but at the end span where there is free rotation allowed at the end support. The bending capacity of the deck is then estimated and checked to ensure that it is capable of taking the maximum bending moment as calculated above to be 77.4 MNm. The deck is treated as comprising two steel box sections in parallel supporting a steel plate on top as shown below. Figure 7: Predicted maximum sagging moment Figure 9: Assumption of the deck section The bending moment is assumed to be taken by one of these steel box sections only, since the bending moments were calculated for half of the bridge loading. The moment capacity of the deck is estimated using Eq. (5): Figure 8: Predicted maximum hogging moment In Figure 7, the values for the maximum sagging, maximum hogging, and sagging moments at the end-span were calculated to be 40.5 MNm, 64.0 MNm, and 71.4 MNm respectively. These values are not the correct values since they were estimated using standard beam bending formulae which do not account for the bending moment carried forward from one end to the other at every other span due to the different loading on each span, hence the clash between the estimated values and the predicted moment diagram. The bending moment in the end span came out to be considerably higher than the central sagging moment because the static check assumes that the end span is a propped cantilever which should carry a greater sagging moment than a fixed end beam (the central span). In reality, these two values should be about the same and one of which must be greater than any of the hogging moments along that deck. The formulae used were wl 2 /24, wl 2 /12 and wl 2 /10 for the central sagging, hogging, and sagging moments at end spans respectively. / (5) The I xx and y values are estimated according to Figure 9 above and σ y is assumed to be N/mm 2. The bending moment capacity of the deck comes out as: /1700. This is more than six times the estimated applied bending moment which is within expectation because the applied moments were underestimated using the bending formulae alone, so they may have been closer to this moment capacity. Furthermore, the conversion of the existing deck section into a simplified section must have significantly altered this value of capacity due to a big change from the real I xx value. The erection loads are somewhat difficult to predict due to the unknown equipment and the actual method which was used to build the bridge. This should not be a problem because at every stage during the erection process, these loads are designed to be lower than the ultimate design loads if not the serviceability load, hence the worst case loading does not include the erection load in this case. But for constructing a cantilever bridge, the erection load is often more important.

8 In most cases, the erection loads may form a basis for determining the suitable method of erection so that these loads are ensured to be the non-governing factors. 6.1 Cables In order to understand how much the loading is affecting the cables, it is crucial in determining the tension under ultimate design loading, thus Load Combination 2 is used (which was stated before Table 1 earlier). It accounts for the temperature load which causes the deck to expand and induce additional tensile stresses into the cables along with the factored dead, SD, HA and wind loading. Clearly, the stresses within the cables are also largely affected by aerodynamic effects due to certain wind speeds hitting the bridge and the cables themselves, hence would be computationally anaylised in practice but has been neglected for simplifying this calculation. Initially, calculate the vertical loading from the deck on the cables and add to this the horizontal temperature load. This is assuming that the deck is a continuous beam and is free to expand at the end supports, so that each cable can be assumed to take a finite vertical load and a maximum temperature load, hence cable 1 supports the greatest load as shown below. section, therefore the load is assumed to be taken evenly by each cable. In this case, there are 12 cables to be considered, hence the horizontal temperature load acting on each cable is 5.8 MN. Finally, the tension within the cable is found by trigonometry, which comes out as 83.5 MN, as a result of a large vertical component and a relatively small horizontal component of force. From this design load, the required diameter of the cable can be estimated by dividing the tensile force (83.5 MN) by the ultimate tensile strength of a cable, which is taken as N/mm 2. This is assuming that the cables were not pre-tensioned beforehand: / Again, the enormous size of this cable is justified by the overestimated loading as well as assuming that the cable is a circular solid member. In reality the required diameter would be less than half of 258.0mm due to the locking of cables and various other stay technologies which would improve the cables performance. 6.2 Deck, Pylons and Piers The compression in the deck is at its greatest just beneath the pylons. Assuming that the tension in each cable is 83.5 MN and ignoring the compression due to restraining the horizontal movement of the deck from temperature increase, then the maximum compression from the cables alone is estimated as: Figure 10: Loading on cables Using the loadings defined in section 5, the maximum vertical load acting on cable 1: 5.0 / This is a gigantic load for a single cable due to the overestimated dead load, and the spans being relatively large in between cables. The horizontal load due to a temperature increase can be estimated using the compressive stress, σ c which was calculated to be 72.0 N/mm 2 in Eq. (4), multiplied by the cross-sectional area of the deck: Clearly, the magnitude of this load is much greater than expected, especially when it is compared with the vertical load of 26.2 MN. Bearing in mind that the deck is steel and it is assumed to have no resistance against its expansion so that none of this horizontal load is taken by the piers or the end-supports, then it would be a larger value than expected. Also, this load is not taken by a single cable, since it is the load for half of the deck s This is a huge number as expected since all the previous values were overestimated. The deck is certainly not designed to take this substantial load so the actual value in this case is irrelevant, but it gives an idea of the proportion of tension that gets transferred from the cables to the deck as compression. This is especially high for a harp configuration of cables since they are all inclined at a small angle from the horizontal, hence an inefficient use of cables. This level of compression is more than adequate for increasing its bending stiffness to withstand vibrations caused by other types of loading such as pedestrians and wind. The highest compression within the pylons occurs at its base. This force is treated as the entire vertical load that acts on a quarter of the bridge since there are 4 pylons, plus the self-weight of the bridge and cables. The total axial load per pylon is: This value can be checked against the compressive strength of the pylons to ensure that they are capable of taking this load before failure, but for simplification, they are assumed to be sufficiently strong. The horizontal wind load is assumed to have little effect on the deflection of the pylons because their slenderness gets rid of the wind.

9 The pylons are stiff under high axial compression, together with its natural bending stiffness provides their serviceability under these negligible deflections. The concrete piers are there to provide a sturdy base upon which the pylons rest, therefore it is crucial that these members remain serviceable at all times. The major damage which they are prone to experience is the impact load from a small to medium-sized vessel. By inspection, the piers are situated at its best orientation where the longer side is placed parallel to the flow of the river, e.g. parallel to the motion of the undercrossing vessels therefore provides the maximum resistance against the impact from a colliding vessel. The piers are assumed to be safe in this case because the vessels that travel up and down this river are not expected to be large, mostly boats, and the traffic is relatively quiet, thus the chance of a boat collision is highly unlikely. 6.3 Vibration Although this bridge is primarily designed for road traffic, there are walkways provided for pedestrians, so the serviceability requirements must be satisfied. Firstly, the fundamental natural frequency of the bridge, f o must be checked so that it is greater than 5Hz for the unloaded bridge in the vertical direction in order for the bridge to be serviceable against vibrations. The following equation is used: 2 where E is the same as in Eq. (4), I is the same as in Eq. (5), M is the unfactored dead weight per metre length of the bridge, l is the length of the main span, g is taken as 9.81 m/s 2 and C is the configuration factor taken from Ref. [5] Since this bridge is symmetrical, a simplified method can be taken to determine the maximum vertical acceleration, α within the deck which is given as Eq. (7) below. It must be ensured that this vertical acceleration does not exceed 0.5*(f o ) 0.5, Ref. [6]. 4 Ψ (7) where y s is calculated to be 1.1*10-4 m as the static deflection at mid-span under a point load of 0.7 kn, and K and ψ are factors taken from Ref. [5] / / / 7 Maintenance The benefit of steel bridges is generally noted as being more durable than concrete bridges since they do not suffer from weaknesses such as crack formation, deterioration and creep deformation. However, the major drawback of steel is usually corrosion and there are precautions such as to paint or coat the steel elements with a non-corrosive layer in order to prevent this. This applies to the deck, pylons, and cables. In particular, the cable-stays are the most exposed structural elements and must therefore be protected against aggressive influences from the environment in general. There are ways of achieving this such as coating the individual wires in grease or wax, or encase the cables with plastic ducts. The TH Bridge had bare wires which appear to have been coated with an anticorrosion resin. This method allows the coating to be replaced without affecting the cables themselves, and as much as possible, without affecting the traffic. Other protective measures should be made against accidents such as vehicle impact, explosion and vandalism. Areas which are liable of taking this damage are the base of the pylons and the region from the anchorages and above. The TH Bridge has rubber collars enclosing the vital zones of the anchorages in order to absorb the impact load from a collision. The protection of these anchorages appears to be strong enough to take vehicle impact without failure. Alternatively, the base of the cable can be fitted with a steel tube, 3.0m or 4.0m up from the anchorage in order to remain serviceable during a fire or when experiencing vandalism. 8 Improvements Suggestions have been mentioned in previous sections on improving the bridge design but a more structural-based analysis is given here with some Figures to clarify the ideas. The three fundamental load-bearing elements of a c-s bridge are cables, deck and pylons. All of which play an important role in the structural behaviour of the bridge. Firstly, the harp configuration of cables which is used in the TH Bridge is considered to be less efficient than a fan configuration simply because the cables are all at the same shallow angle to the deck. Furthermore, there are insufficient cables to allow for a flexible deck design, hence a stiff deck was required. The stiffness could either have come from a deep concrete deck or in this case a material which is naturally stiff, steel. A possible solution is given below: Figure 21: Left: current design, Right: improved design At first glance, it seems that the mass from the deck has been directly transferred to the pylons without gaining

10 much structural benefit, but when considering the whole bridge then it becomes obvious that a lot of material could be saved in the deck from having a stiff pylon with plenty of cables to support a slim and more flexible deck, hence the cost for materials and the total weight of the bridge are reduced. A slender deck reduces the horizontal wind load that acts upon it and also makes transport and erection of the deck a lot easier. Most importantly, this change in design means that the longitudinal moments caused by live loads are now taken by the pylons rather than the deck, due to the many cables which transfer this load efficiently by a fan pattern. This pattern can reduce the total weight of cables used to that of a harp pattern and reduce the excess compression in the deck which is induced by a harp pattern. The slim deck design is now governed by transverse bending which is less of an issue for a deck width of 26.6m since it is relatively narrow compared to modern designs with a high traffic capacity which require decks to be as wide as 40.0m. When a flexible deck is adopted, it increases its vulnerability to wind effects. The slender deck option would help to reduce its solid projected area but the actual deck section has a strong impact on a bridge s performance under aerodynamic effects such as vortex shedding. A possible sketch improvement is shown below, which is not of the same scale as the existing section. Figure 12: Current section Figure 13: Improved section The improved design is a more streamlined section comprises a twin triangular edge box girder with stiffening elements to increase its bending and torsional strength. This section is similar to a trapezoidal box girder but with a downward sloping edge extension, which serves the purpose of balancing the horizontal wind load that strikes on the upper and lower part of the section, thus limits the rotation of the deck. A possible improvement in the pylon design is to use A-frame pylons. This may not be necessary for this bridge because of its moderate span, but becomes all-time important for very long span bridges when aerodynamic stability is paramount. Such systems involve a deck with two planes of inclined cables behaving as a rigid closed section in bending as well as reducing the rotation of the deck. The problem which this design could bring about is the need for extra space in the transverse direction in order to accommodate the pylons, which is less of an issue in a river. The erection of A-frame pylons is generally more complicated than that of vertical pylons. 9 Conclusion The TH Bridge exhibits the primitive characteristics of a modern c-s bridge. These features provided the basis for which modifications can be made on the structural performance of the present c-s bridges. The aesthetics of the bridge was probably the most important aspect to be considered, since its cable pattern, balance in dimensions, and its overall simplicity provided such a successful signature. The only major downside is that the bridge adopted the stiff deck design rather than the stiff pier design which is generally more appreciable in terms of cost today, because it allows a cheaper concrete deck to be designed and prefabricated. The TH Bridge proves to be serviceable up to this day due to the majority of it being steel, which is durable and simple to maintain and repair. It is unlikely that the bridge will see any future changes since it is capable of facilitating the current mass of traffic. The external surfacing may be changed in terms of repainting or resurfacing to give a fresh colour or texture, but the internal structure shall not require modifications. Acknowledgments This paper represents a student s endeavour in applying the fundamental concepts of bridge engineering on the analysis of the Theodor Heuss Bridge. The informative guidelines given by Professor Tim Ibell for preparing this conference paper was highly beneficial. The author of this paper would like to show his sincere appreciation for his valuable guidance throughout. References [1] Wittfoht, H., Building bridges: history, technology, construction, Beton-Verlag, Dusseldorf, pp. 101, pp. 96. [2] Podolny, W. and Scalzi J.B., Construction and design of cable-stayed bridges, Wiley-Interscience, New York and London, pp. 1, pp. 5, pp [3] %28D%C3%BCsseldorf%2., Text [4] Photograph [5] British Standards Institution., British Standards: Steel, Concrete and Composite Bridges- Part 2: Specification for loads, BS :2006, clause , pp. 3, table 13, pp. 44, figure 13, pp. 50, figure 5, pp. 25, table and figure 9, pp , table 9, pp. 28, figure 6, pp.30, clause B.2 and B.2.3, table B.1-B.3, Figure B.1, pp [6] Ibell, T., Bridge Engineering Notes, Section 5.4 Wind load, pp. 182, maximum vertical acceleration, pp.180