A CRITICIAL ANALYSIS OF TATARA BRIDGE, JAPAN

Anthony Wilson

1MEng Undergraduate Student - University of Bath

Abstract: The Tatara Bridge is the ne plus ultra in the world of cable-stayed bridges. It is a technical masterpiece proving that cable supported bridges at the time of construction can span nearly 900m. Being cheaper with better aesthetics, the Tatara Bridge and other modern cable-stayed bridges are becoming a more viable option to suspension bridges. This paper is about the biggest cable-stayed bridge in Japan assessing the loading conditions and analysing the aesthetics and construction methods used.

Keywords: Cable-stayed, viaduct, sea, Japan

1 Introduction

The Honshū-Shikoku Bridge Authority was set up to connect the largest island in Japan, Honshū with the smallest, Shikoku which was previously only reached by ferry. The project consists of three expressways – Central, Eastern and Western. The Tatara Bridge is located on the Western Expressway along with eight other bridges and was completed in 1999. The Western Expressway goes through nine of the Geiyo Islands with the Tatara Bridge connecting two of these archipelagos together.

The completion of the link between the two islands has dramatically decreased the travelling time and costs to Shikoku with an increase in gross production value in the areas affected estimated at ¥889.0 billion (£149 billion). In addition, 120,000 more jobs have been created in the areas [1].

Figure 3: Perspective of Tatara Bridge

Tatara Bridge is located in one of the most geologically active parts of the world and designed for some of the world’s biggest typhoons prevalent in Japan. In addition, it is located in a very geologically active area and has to withstand major earthquakes. The original proposal for the Tatara Bridge was to be a suspension bridge, however, due to the effect it would have on the surrounding national park area it was changed to a cable-stayed bridge.

With the main span of 890m at the time of construction, it was the longest cable-stayed bridge in the world [4]. Tatara Bridge confirmed that a 900m span bridge has the load-bearing capacity needed especially under extreme wind loading.

Figure 1: Location [2] Figure 2: Satellite image showing the local topography [3]

Proceedings of Bridge Engineering 2 Conference 2009 April 2009, University of Bath, Bath, UK

1 Mr Anthony Wilson – aljw21@bath.ac.uk

Figure 4: Dimensions of the Bridge [5]

However, in 2009 it is the second longest with the construction of Sutong Bridge in China completed in 2008 198m longer. The total length of the Tatara Bridge is 1480m with two side spans of different lengths. The main span comprises of a steel box girder with the side spans consisting of steel box and concrete box girders acting as counterweights and against uplift.

Main Span 890m

Side Spans 320m and 270m

Total length 1480m

Width of Deck 30.6m

Depth of Deck 2.7m

Lanes Four lanes of Traffic with two lanes for pedestrians and cyclists

Height of Towers 220m

Cost $605.8 million

2. Aesthetics

The Tatara Bridge is an aesthetic tour de force as well as being a technical achievement. The original design of the bridge in the 1970s was a suspension bridge. However, a cable-stayed bridge was found to be cheaper and less damaging to the surrounding area which is a protected national park. Using the book “Bridges: Aesthetics and Design” by Fritz Leonhardt as a template the aesthetics can be broken down into different areas which are covered in the following chapter.

2.1 Function

The function of the bridge can be clearly seen with the cables in tension transferring the load to the pylons in compression into the foundations. This shows the materials used with a concrete surface for the tower and cables in steel. It is the simplicity of this which produces the elegancy of the bridge. No other elements on the bridge are redundant undoing this clarity.

2.2 Proportions

The proportions of the bridge appear to be correct with a slim deck (span/depth ratio of 1/330 [7]) due to the high number of cables taking most of the load in addition to the slim columns of the towers. The towers are also not too

tall, any shorter the bridge would appear elongated taking it out of proportion. The centre span is also much wider than the side spans drawing the eye from the edge.

2.3 Order

A lot of roads joining the bridge means it can be seen in elevation but most drivers will see it from perspective as shown in the picture. However, with a two planes of cables can produce many different lines that can become crowded when looked from an oblique angle. In addition using fewer cables could also solve this problem but this meant the deck would need to be deeper making it look out of proportion. The smooth fascia of the deck is broken by the cable connections which as they are placed at regular intervals give some order. The cable-fixing parts were stored inside the fairing so that the fixture is not exposed to the outside girder. This is also important for maintenance. It would have been better to cover these connections even more so the smooth fascia was continuous.

2.4 Integration into the Environment

Cable-stayed Bridges are elegant bridges if they are placed in the right area. As the Tatara Bridge is placed over water it is integrated very well into the environment with the right type of bridge for the location. If the cable-supported bridge was placed over a valley then the aesthetic appeal is lost and an arch would be a better type of bridge. The tall towers also compliment the surrounding hills and mountains so considering the local topography for the design.

2.5 Texture

The piers are given a matt finish with a glossy finish for the deck giving a clear distinction between the different elements of the bridge.

Figure 5: Closer look of one of the towers and deck

Table 1: Main statistics of Tatara Bridge [6]

2.6 Colour

The towers appear to be brighter than the deck so the observer’s eyes look immediately at these, as they are the best looking part of the whole bridge. Additionally the lighter colour of the columns gives the piers a slimmer appearance in keeping with the thin deck. The cables are painted black to blend them blend against the dark background of the mountains as the double plane cables can appear to be cluttered when looked at an oblique angle.

2.7 Character

This is a hard section to comment on with older structures having more character or if there are idiosyncratic features in the design. The towers of the bridge are unique giving a distance look compared with other two plane cable-stayed bridges. This also gives an innovative appearance showing character. In addition, the lines showing where the prefabricated blocks are connected together are a nice feature giving the bridge some character whilst showing the public how it the bridge was built seen on Fig. 5.

2.8 Complexity

This can be a hard area to fulfill with too much intricacy ruining the appearance and too little making it look too simple and uninteresting to the viewer. However, the Tatara Bridge has a simple design with the cables transferring the loads from the deck onto the pylons and then into the foundations but there is enough complexity to make it visually stimulating.

2.9 Nature

Nature has been incorporated into the design with the fan arrangement of the cables all spread out from a point on top of the tower. This gives the appearance of a “bird spreading its wings”.

2.10 Refinements

The bridge is very refined with a high attention to detail. For example, the top of the towers are tapered in section to reduce the wind loading effects but also come to a point to form an A-section, arguably the best looking design for towers. A single plane of cables is often the most elegant design and this has been incorporated in the design with the double plane of cables brought in close together. The cables are attached between the road and the pavement giving the illusion of one central plane, thus keeping in with the refinement of the angled towers.

With relatively wide columns at the base, the fairly aggressive tapering towards the deck really makes the rest of the columns appear very slim. This also shows where the biggest moments of the towers will be reducing higher up therefore using slender sections. The curve at the top where the two columns come together in the tower is reflected at the bottom with the two columns joining at the base. The curves are repeated above showing continuity throughout the design. This is repeated with the piers supporting the side spans at an angle instead of perpendicular from the floor given continuity throughout the bridge. However, the angles of these columns appear to be varying with different spaces between the columns at the base but this maybe because two of the piers are in

water and two are in land but it slightly disrupts the order and repetition of the bridge.

2.11 Summary of Bridge Aesthetics

Using Fritz Leonhardt as a template, the ten points help to identify the beauty of the bridge. A bridge does not have to satisfy all the criteria to be beautiful. However, the Tatara Bridge has successfully fulfilled all the criteria. It is an attestation to both the designers and the engineers to create a bridge that is visually stunning using thousands of tones of steel and concrete as well as structurally flawless.

3. Structure

3.1 Choice of Bridge Type

In 1973, the initial design of the Tatara Bridge was to be a suspension bridge with the cable-stayed technology only able to span medium sized distances. The longest cable-supported bridge in 1974 was Köhlbrandbrücke in Hamburg, Germany spanning 325m [8] so the technology was not there to span nearly 900m. However, Japan put a halt onto building the Tatara Bridge diverting funds to deal with the international oil crisis [6]. In 1989, planning was resumed and decided that the anchorages of the suspension would damage the beauty of the national park at one end. A cable-stayed bridge was chosen as the result of this. In addition, the cable-stayed design brought further advantages in cost and constructing time [9].

The new design using a cable-supported bridge is now cheaper than building a suspension bridge for the same span. This is due to the great expense of spinning of the main cables and has a lot more construction issues getting the cables correct compared with using more cables with smaller diameters. This reason also speeds up construction with a cable-stayed bridge erected faster than a suspension bridge.

3.2 Design

Due to the long span of the bridge, there are very high wind loads so the towers need to have high lateral stability. For this reason the A-frame design was chosen with its two close sections, the smaller section above the much larger one. This increases the rigidity in bending reducing any rotation [10]. For the towers the inversed ‘Y’ design was used as it has better aerodynamic properties and better aesthetics than the A-shape original design. Additionally, the straight section at the top eases any construction issues connecting all the cables to one part giving the semi-harp arrangement.

Figure 6: View from the towers before opening http://tinyurl.com/dmfwgn

For the stay arrangement the original idea was to choose the fan pattern as it is a more efficient design using lighter cables as less materials are required. The fan design also has additional advantages, such as, the cables are at a much steeper angle to the horizontal compared with the harp arrangement, therefore, the horizontal component is much less in the deck. This configuration also increases the flexibility for horizontal movements improving performance against seismic activity [10].

However, the fan arrangement is a theoretical idea as it is nearly impossible to connect all the cables to one single point. Therefore, to increase the practicality of connecting the cables to the tower the semi-fan configuration is used. This is where the stays are spread down the upper part of the pylon.

With the Tatara Bridge having 42 cables it can produce a thinner deck with more of the load taken by the pylons so they need to be bigger, however, from the aesthetics position they are not too big to be out of proportion. The light deck is an advantage during an earthquake, however, becomes a disadvantage with wind [10] and these are looked at later in the paper.

Cable-stayed bridges have a direct load pathand this makes the bridge a lot stiffer. To minimise bending moments taken by the piers the bridge has to be nearly symmetrical with similar spans either side of the main central span. However, due to the unequal lengths of these side spans Prestressed Concrete (PC) girders balance the weight of deck.

4. Construction

At a cost of $605.8million it was one of the most expensive bridges out of the 18 major bridges built along the new route. The Tatara Bridge was one part of a $27 billion project to connect the islands of Ikunchi and Omishima including 150km of motorways [6].

For the geology, granite is the main source of bedrock. This type of igneous rock has very high strength giving sufficient bearing pressure for the large weight and pressures of the bridge superstructure. Two large caissons, one for each tower were constructed and situated on the granite and filled with concrete. The two legs of each tower then come together and rest on top of the caissons. For the side piers taking less load, piles were constructed into the alluvium with pad foundations for the piers when located on the granite. The good bedrock is very close to the ground surface and so little excavation and drilling is required reducing the time and cost. Additionally, the piers are located in relatively shallow water depths reducing the need for expensive cofferdams and potentially blocking the shipping lanes.

After the caissons had been installed along with the diving installation of underwater and atmospheric concrete the construction of the towers were started. The tower was the largest class ever of a monocell structure.

Figure 8: Location of Tatara Bridge on the Western Expressway http://tinyurl.com/d5n3nm

Figure 7: View for a pedestrian http://tinyurl.com/cgue5c

Figure 10: Construction Sequence [12] [http://tinyurl.com/d5n3nm

Figure 9: Geology under the bridge [9] [http://tinyurl.com/d5n3nm

The tower is 220m high and consisted of 23 blocks with high-strength friction-grip bolts connecting this blocks together [7]. The design thickness of the steel plates was 200mm, with 235mm purchased for tolerances and deformations at welded corners [13]. Floating cranes with a capacity of 3600t erected the two base plates weighing 120t each with the first blocks weighing 240t each, followed by a lower part of the tower weighing approximately 1500t. Afterwards a 2000t, 123m steel girder near the tower with a 163m steel girder weighing nearly 2500t are also erected for balance. Using the new deck for the work yard, 160t lifting capacity tower cranes place the upper blocks of tower one by one. The towers were constructed to the right precision of 1/2000 the tower height with very high quality control from the factories and accurate building operations [7].

Immediately after the towers were completed the PC girders for the side spans were installed with floating cranes used for this. The 109m long 1800t PC girder was put in place in one unit. However, for the other side span was too long for one single element to be installed, therefore balanced construction was used. Four blocks were constructed for the central span with three blocks for the side span to keep the balance and not induce any major hogging moments. Finally a 1500t, 102m block was installed by the floating crane finishing the side span [7].

For the central span, both sides were constructed simultaneously with a crane at each end and the deck launched as a cantilever. The deck was installed in sections with 18 needed for the 2P-side and 15 for the 3P-side [7]. While the cables were being installed, temporary braces supported the girder sections [14].

During the most vulnerable stage of construction two typhoons hit between the end of June and end of July in 1997 [7]. Typhoon 9 which hit at the end of July was the more furious of the two and while the typhoon was being tracked wind tunnel tests showed that the travelling cranes needed to be moved back 50m to keep the displacements within acceptable limits [14]. The bridge construction was delayed by a week and the cranes moved and retracted to lessen the projected area normal to the wind direction. The typhoon lasted for two days but no damage was done with the extra actions put in place, such as, anti-vibration measures of the cables and rolling up the safety nets of the railings [7].

After the typhoon had left the construction continued after the inspections, the last girder was put in place closing the span in beautiful weather on July 30, 1997 [14]. There were no accidents during the 6 years of construction, a real testament to the skill of the engineers and construction workers. Tatara Bridge was finally opened on schedule May 1, 1999 [6].

5. Loading

This is paramount to see how the bridge reacts under different load conditions. A 1:50 model was created and tested to determine the ultimate strength capacity using hydraulic jacks to simulate the dead and live loading along the whole bridge [14]. The bridge is tested to two different conditions – Serviceability Limit State (SLS) and Ultimate Limit State (ULS). SLS makes sure the bridge is still serviceable from the deflections of the load added and ULS to make sure the loads do not cause any plastic deformation which could lead to collapse. Different loads are added together to give the worst case scenario. However, some loads when added give favourable effects, for example, wind uplift against dead loads so the wind uplift is ignored. Two factors of safety are added for the dead loads, γfl is for loads and γf3 is for how well the bridge can be analysed. All the factored loads are measured as load per metre length along the bridge.

5.1 Dead Load

This load is the weight of the actual bridge elements required so not to cause the collapse of the bridge. For the steel girder 15,860t of steel was used over a length of 1,312m [7], gives a dead load of 120.9 kN/m.

Multiplying by the safety factors of γfl = 1.05 and γf3 = 1.10 gives a factored dead load for the steel deck of 139.6 kN/m

For the PC girder 6610m3 of concrete was used for a length of 168m [7] so 39.3m3 of concrete per metre used at a density of 24kN/m3 gives a dead load of 943.2kN/m.

Figure 13: During construction showing the travelling crane http://tinyurl.com/cbg6jp

Figure 11: Cross section of a PC girder [12]

Figure 12: Cross section of a steel girder [12]

Multiplying by the safety factors of γfl = 1.15 and γf3 = 1.10 gives a factored dead load for the concrete deck of 1193.1 kN/m

5.2 Superimposed Dead Load

This is what makes the bridge usable, such as, the serving, asphalt, lighting and this load here considers these.

70mm asphalt is used for the bridge [12] and assumed same thickness used across the bridge.

0.07m x 30.6m width of bridge x 23kN/m3 = 49.3kN/m

Assume another 10.7kN/m for the parapets, services and lighting giving 60kN/m unfactored.

γfl = 1.75 therefore factored load is 105kN/m.

5.3 Live Loading

This load takes into account the traffic loading on the bridge. As the author is unfamiliar with the Japanese traffic codes the British Standards BS5400-2: 2006 Specification for loads will be used instead. The traffic loading comes into two froms, HA and HB loading.

5.3.1 HA Loading

This loading simulates the general traffic and small trucks going across the bridge. The width of the carriageway for traffic going in both directions is 20m; therefore, there are six notional lanes with a width of 3.33m per notional lane.

The loaded length is above 380m, therefore, the HA unfactored loading is 9kN/m. Knife Edge Loading also added and taken at 120kN per notional lane.

The safety factors for HA loading is γfl = 1.25 and γf3 = 1.10.

Factored HA loading is 9 kN * 1.25 * 1.10 = 12.4kN/m (per metre of lane)

Factored KEL loading is 120 kN * 1.25 * 1.10 = 165kN

To give the worst torsional effects full HA and KEL loading is added for 2 lanes with the rest at 1/3 HA and 1/3 KEL loading. In addition, this also simulates where the heavier, slower trucks would drive on the outside lanes of the carriageway in the slow lanes, shown in Fig. 14.

Total HA loading = (2 * HA + 4 * 1/3HA) = 41.3kN/m

Total KEL loading = (2 * KEL + 4 * 1/3KEL) = 550kN

The position of KEL is different whether for looking for maximum shear or maximum bending. For example, for maximum shear the KEL is placed over the part of the deck connected by the cable-stays with the maximum sagging moment the KEL is placed in the middle between the two sets of stays.

5.3.2 HB Loading

HB loading takes into account the load from very large lorries with abnormal loads on them. In accordance to BS5400-2: 2006 HB loading is considered as 30 units. However, this can be increased to 45 units on the authority of the relevant highway services with the bridge shut and the lorry going along as near to the middle of the bridge as possible. One unit of HB loading is taken as 10kN per axle (i.e. 2.5kN per wheel). Both the front pair and back pair of axles are 1.8m apart but 21m from the pair of axles as this would give the most onerous case between the stays which are 21m apart. The HB load can be placed either on one lane or straddle between two lanes.

However, HB loading is not always used for analysis due to the fact 25m either side of the abnormal load is clear to model the police escort and therefore there are large areas of the carriageway unloaded and so not the worst case scenario.

5.3.3 Secondary Loading

As the bridge is straight with no bends then horizontal centrifugal loading is ignored.

For the braking forces it is taken as the greater value of either 8kN/m along a single notional lane + 200kN point load or 25% of the total nominal HB load applied over two axles.

5.3.4 Parapet Loading

This is from accidental loading of vehicles hitting the parapets. The design speed of the bridge is 80km/h or 50mph [12] which equals 22.2ms-1.

With 1kN deflects the parapet by 3mm the maximum deflection is 450mm from a 150kN point load. It is assumed that the 20t lorry would hit at 20o, giving a force perpendicular to the parapet of 22.2*sin20 = 7.6 ms1.

It is assumed that 90% of the energy is dissipated due to crumpling of the truck.

FΔt = MΔv (1)

Figure 15: Example of HB Loading, section 6.4 BS5400-2: 2006

Figure 14: Drawing of the traffic loading across the bridge

Full HA Loading

1/3 HA Loading

1/3 KEL Loading

Full KEL Loading

Where FΔt is the impulse and this has the value of 10% of the momentum with 90% of the energy already lost. The mass, m is 20,000 and a normal velocity into the parapet of 7.6ms-1. This gives a value of FΔt as 15,200 kgms-1.

To work out t to work out the force on the parapet found from Eq. 2.

v = u + at (2)

The initial velocity, u is 7.6ms-1 with the final velocity, v being zero ms-1 as the lorry has come to a complete standstill. This then gives the acceleration, a in terms of t, a = -7.6/t.

s = ut + ½ at2 (3)

Putting the value for acceleration in to equation 3 gives a value for the displacement, s as 3.8 * t, with the displacement known as 450mm t is equal to 0.118 seconds. The force is then the impulse divided by time to give the force, which is 129kN. Therefore, the parapet has deflected by 387mm below the maximum value of 450mm. From visual inspection there are three parapets between the traffic lane and the edge of the bridge to stop any traffic involved in a collision.

5.4 Wind Loading

Wind can have one of the biggest effects on a bridge, causing damage to structural elements or creating vibration, which can lead to collapse as seen with the Tacoma Narrows Bridge. The location of Tatara bridge is in a high risk area with lots of major typhoons which could damage or collapse the bridge. Due to this extensive wind tunnel testing was performed using a 1/70 scale model to ensure safety. On top of this, a 1/100 scale model was also created to the test the aerodynamic stability during construction stages [14]. From computer analysis and using physical models the bridge is designed to withstand gusts of up to 63.6ms-1 (142mph) [6]. The horizontal wind load is defined using Eq. 4.

Pt = qA1CD (4)

Where q is the dynamic head pressure worked out in Eq.5, A1 is the solid horizontal area projected in m2 with CD the function of the b/d ratio and gives the drag coefficient. With breadth of the deck at 30.6m and the depth 2.7m, the ratio gives CD as 1.3 the minimum coefficient for decks supported by box girders.

q = 0.613νc2

(5)

νc is at 63.6ms-1 giving q as 2,480. The horizontal projected area is 3,996m2 worked out by multiplying the length of the bridge (1480m) by the depth of the deck (2.7m). This then gives Pt as 12.8MN which the deck spanning 890m and the pylons resist. This then gives a horizontal uniformly distributed load (UDL) of 14.4kN/m. The deck is then assumed to be simply supported with the pylons as supports in the horizontal plane. With this assumption, the maximum bending moment is found from Eq. 6.

MMAX = (wL2) / 8 (6)

Where w is the UDL, L is the length of the main span and this gives a maximum sagging moment of 1426 kNm.

However, additional wind actions are also looked at such as wind uplift or a vertical downward force. The is calculated by using Eq. 7.

Pv = q A3 CL (7)

Where q worked out earlier as 2,480, A3 is the plan area is 45,288 m2 derived by the length of the bridge (1480m) multiplied by the width of the deck (30.6m). CL depends on the b/d ratio (11.3) giving CL as 0.29. This then gives Pv as 32,570MN with a UDL of 36.6kN/m. Again using Eq. 6 gives the maximum bending moment of 3.62 MNm.

Combinations of the wind loading taken to give the most onerous case:

1. Pt alone;

2. Pt in combination with ±Pv;

3. PL alone;

4. 0.5Pt in combination with PL ± 0.5Pv.

Combination 2 gives the worst-case scenario for wind loading. For the longitudinal wind loading this is a smaller due to less surface area and can be ignored.

It was found that there were large vibrations in the cables during high wind and rain conditions. To stop this the surface of the cable was indented, Fig.16. The dimples are similar to those found on a golf ball and help to reduce vibrations from these weather conditions [5].

5.6 Seismic Effects

Tatara Bridge is designed for an 8.5 magnitude earthquake with an epicentre 200km away. The fundamental period of the bridge in the longitudinal sway mode is 7.2 seconds [15].

During an earthquake a flexible structure reacts better with the deck being lightweight also an advantage compared with a rigid structure. Cable-stayed bridges are indeed flexible which improves seismic performance. It is assumed there are no expansion joints as with them can cause crushing of the deck. As the deck is kept free it can pass through the pylons on bearings allowing the cables to absorb the seismic instead of the pylons. However, to assess the bridge’s seismic response is difficult with complex 3D interactions. Physical and computer models would therefore be required.

5.7 Temperature

The average yearly temperature of Shikoku, the island just to the south of Tatara Bridge is approximately 16oC [16]. To work out the effect from temperature effects a temperature increase of 30oC (ΔT) will be used for a high diurnal change in temperature. The expansion of the bridge is assumed when the expansion joints are defective or stuck.

Figure 16: The indented surface of the cable [5]

The length of the bridge from steel girders is 1,312m and 168m as PC girders. Due to the coefficient of thermal expansion, α the same for both steel and concrete at 12 x 10-6 / oC the length, l for Eq. 8 is 1480m.

δ = α * l * ΔT (8)

The expansion of the bridge, δ is 532.8mm, which equates to a 0.036% expansion. This becomes a problem where there is no place for the bridge to expand. As the piers are stiff, they have to withstand the additional stresses. To work out the stresses in both the steel and concrete Eq. 9 is used. The Young’s Modulus, E for steel is 200,000 N/mm2 and for concrete is 30,000 N/mm2.

σ = ε * E (9)

The strain, ε is the result of the thermal expansion multiplied by the temperature giving 360 µε. By multiplying the strain by the Young’s Modulus gives you the stress. For steel, the stress is 72 N/mm2 and for concrete, the stress is 10.8 N/mm2. This is unacceptable, for the concrete near 50% of the 24 N/mm2, strength is just from the temperature effects and none from the loading causing cracking drastically shortening the life of the bridge. Due to the slenderness of the deck the additional horizontal compression could induce buckling. To prevent this the horizontal direction cannot be restrained so the piers put on rollers or allow the piers to be flexible enough to allow expansion of the deck longitudinally. To stop any high temperature induced forces the girder is kept free from the towers.

6 Strength

In this section, structural analysis is performed for the bridge to determine whether the deck and cables can sufficiently take the worst case loading. The worst case sagging and hogging moments are shown in Fig.16 and Fig.17. For the maximum sagging moments, any hogging moments are relived as much as possible with the adjacent loaded as lightly as possible. Then for the maximum hogging moment the two interior spans are loaded as much as possible with minimum loading on the outer spans stopping any relieving action. The KEL from traffic is put in the middle of the span as this gives the biggest moments. To simulate pedestrians and cyclists on the walkways to the sides of the main carriageway an intensity of 5kN/m2 is added. With the two pavements each 2.5m wide an additional 25kN/m length of the bridge is included to the other loadings. Finally, the worst case wind loading, Pt, 11.4kN/m is also added to the loading to give 322.3kN/m UDL with a 550kN point load.

There are 21 cables supporting each half of the central span (445m), it is assumed that the spacing between stays are 21.2m. The longest cable is 460m long with the towers at 220m [6] the horizontal plan distance is 404m by using Pythagoras Theorem. Therefore, the longest proportion of the deck unsupported by the cables is 82m and this is where the largest moments will be generated.

By using statics the unsupported 82m deck, l is assumed to have two fixed ends where the stays are connected and the maximum hogging and sagging moments can be derived from Table 2.

Load Moment Equation MNm

UDL Hogging wl2/12 180.60

UDL Sagging wl2/24 90.30

Point Load Hogging Pl/8 5.64

Point Load Sagging Pl/8 5.64

This then gives a maximum sagging moment of 95.94MNm and a maximum hogging moment of 186.24MNm. To work out the maximum bending moment capacity of the deck, the second moment of area, I has to be calculated first using Eq. 10.

I = bd3/12 (10)

Where b is the breadth and d is the depth. To simplify the calculations the box girder is assumed as shown in Fig.19.

Table 3 shows the calculations for the different I values of the girder. The total I value in the x-axis of the girder is 6 x 1012 mm4. The second moment of area, I is then substituted into Eq.11 to get the bending moment capacity of the deck.

M = (σs * Ixx) / y (11)

Shape b (mm) d (mm) Ixx (mm4)

Top Plate 21600 75 759.4 x 106

Outside Box 21600 2700 3.54 x 1013

Interior Chambers 7100 2550 2.94 x 1013

82m

550kN (KEL)

322.3 kN/m

Figure 18: where w = 310.9kN/m and P = 550kN

Table 2: Shows the moments from each component

Table 3: I values for the different parts of the girder

Figure 19: Assumed dimensions of the box girder

Figure 16 and 17: Diagrams of the worst case sagging and hogging moments respectively

Where M is the bending moment capacity, σs is the design strength of steel, 275N/mm2; Ixx was calculated from table 3 and y is to the centroid of the girder which is in this case is assumed half the depth of the girder, 1350mm. This gives a value of M of 1220MNm which is a lot higher than either the maximum sagging or hogging moments.

As seen in the temperature section, 5.7 a 30oC change in temperature can add 72N/mm2 stress to the steel which would then reduce the deck’s moment capacity. The design stress would then be 203N/mm2 giving a capacity of 902MNm. This is still higher than the maximum moment experienced by the deck.

For the strength of the cables the reaction force at either end of the 82m span is the total weight of the span (26980kN) divided by two 13490kN. There are two planes of cables so 13490kN is divided by two to get 6745kN which each stay has to be able to take. The longest cable, 460m long also has the acutest angle, sin-1 (220/460), gives 28.6o and therefore the least efficient. This cable has the most onerous loading out of all the other cables. To calculate the tension in the stay the reaction force, 6745kN is divided by sin 28.6 with the answer of 14,090kN or 14.09MN.

To work out if the stay can take this amount of tension the design stress is required, σcable = 640N/mm2 with the outer coating assumed to have no structural strength. 7mm diameter galvanised steel wires are bundled together in the factory with 349 of them required to make the 170mm stay diameter [7]. This then gives an area of 22698mm2.

22698mm2 * 640N/mm2 = 14.5MN tension capacity. The 460m long cable can take the loading on the deck.

For the wind loading which was added only the Pt component. In true typhoon conditions there would be both large Pt and Pv values, however, the live loading would not exist as the bridge would likely be closed to stop any vehicles being blown off. Furthermore, the Pt being a fairly large value with the most onerous loaded cable having 400kN design capacity still remaining, it can be assumed it comprises of both Pt and Pv values for slower wind speeds where the bridge would remain open.

7 Natural Frequency

The effects from vibrations are important when designing the bridge. The natural frequency should be between 5–75Hz. If it is less than 5Hz then wind could excite the bridge causing resonance as the bridge absorbs the energy by oscillating at the same frequency as the natural frequency and the could cause collapse. There are pavements for people to walk and cycle down, therefore, the natural frequency has to be below 75Hz. Above this frequency will not cause collapse but will make people feel nauseous and anxious. To work out the natural frequency a simplified equation is used from BS5400-2:2006 Appendix B 2.3, Eq.12. Further analysis using computer software should be used to verify the result.

€

f0 =C2

2πl2EIm

(12)

Where fo is the natural frequency, C is the configuration factor for no interior supports is π, the

length l is the main span of 890m, E is the Young’s Modulus of the steel deck is 200x109 N/m2 with the second moment of area, I worked out previously at 6m4. The mass includes dead load and superimposed dead load giving a value of 24,940 kilograms per metre. This gives a natural frequency of 0.01Hz; therefore, resonance is a major problem and will have to use dampers to stop any damage by the wind.

8 Design Life

The design life of the bridge is about 120 years in accordance with BS 5400. However, due to its location in a high risk area from earthquakes and typhoons a major ‘freak’ event from either with the ferocity above the design of the bridge could cause major damage. The Tatara Bridge should be of high importance to fix and reopen due to being a major part of the new $27 billion infrastructure project.

8.1 Durability and Maintenance

Differential settlement of supports can be a problem for cable-stayed bridges due to the cables are in tension and an increase in settlement could increase this tension. However, for large spans this is not a problem with a pier settling by a few centimetres would become negligible across the deck over such a long span. In addition, the relative flexibility of the bridge allows the cables to adapting to the induced internal stress causing no deformations in the deck. To stop any scouring of the seabed which could lead to any settlement the piers should be shaped as a large cylinder or ellipse in plan. This is a more streamlined design stopping any water turbulence with the vortices created causing the scouring. Additionally, scouring material could be added on top of the seafloor to stop any scouring from happening.

With the majority of the deck produced from steel, it has the major long-term advantage of no creep as seen in concrete making steel bridges more durable. However, due to the bridge located in a saline environment, corrosion is a major issue. Like the Golden Gate Bridge in San Francisco being continually painted to stop corrosion, this will have to be done here. Any rust that did appear from the corrosion would dramatically weaken that part of the bridge so has to be continually maintained with a layer of paint or a non-corrosive coating. For the cables, the steel wires are bundled together and to stop them from corroding they are coated with a corrosion inhibitor and covered with a UV-resistant high-density polyethylene [17] Fig.20.

Figure 20: Layout of the galvanised steel wires and protection of the cables [17]

Figure 21: Tatara Bridge at sunset [18]

For the PC deck sections creep deformations can occur but the deck is so massive that it could take the deflections. For the towers the concrete surfacing could eventually erode from the salt from the sea causing cracking and then rainwater and more salt could start corroding the steel towers. To stop this the towers would be painted or coated, however, the concrete should last for a long time before this happens. The creep from the concrete here is neglected due to not being the structural element only the veneer.

8.2 Vandalism and Break Down

Due to its remote location, vandalism is unlikely. However, if graffiti did appear the more likely place would be on the deck instead of the piers in the water. This could happen from people writing on the pavement while walking along or people stopping in their cars and getting out. The bridge should be inspected regularly and include looking for vandalism so any graffiti can be controlled. If it continued to be a problem CCTV should be installed in the worst places. Additionally, any CCTV cameras which are installed could determine the exact location of a motorist’s break down. There would also be telephones located down the bridge for the motorist to inform authorities who would help.

8.3 Monitoring

To monitor the effects during an earthquake seismometers are added to the bridge which measure and records the motions of the ground. Furthermore, accelerometers are added to measure the acceleration during wind or earthquake conditions of the tower and deck. Accelerometers are placed in the at the foundation and where the largest displacements will be felt, the top of the towers and the sides of the girders.

In the future to monitor any plastic deformations with the damage might appear invisible but the strains could increase. An increase in strain could lead to the eventual structural failure. To prevent this Peak Displacement sensors and Electro-Magnetic Stress sensors could be used. Peak displacement sensors can show with high precision the maximum distance a bridge tower or deck deformed during a critical event, such as, a typhoon or earthquake. Therefore, show to engineers if any damage had occurred. The Electro-Magnetic Stress sensors are added to the near top of the each cable and they can accurately show the exact stress the stay is experiencing.

9 Conclusion

This paper provides a summary of the type of loads the Tatara Bridge has and will experience. It had a major test withstanding a typhoon during the most vulnerable stage of construction but still has not had a major earthquake to resist. This bridge showed that long spans could be achieved using cable-stayed technology and now a viable alternative to suspension bridges. With exceptional aesthetics and engineering skill, the Tatara Bridge is an excellent precedent for future long span cable-stayed bridges.

Acknowledgments

Thanks must go to the ICE library in London for their help and sending me the requested research papers.

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