**2. Structural system**

stiff as the stiffening contribution of the deck becomes negligible [1]. Therefore, strong but

There are many new high-strength materials with low density like carbon fibre with epoxy, graphene oxide and alumina-polymer composites. Some materials have much better mechanical performances than steel or concrete but are only used in some high-tech industries such as aerospace, wind energy and automotive industries due to their high price. By 2050, the new materials are likely to be used extensively in construction due to the reduced cost in the development process of new materials [2]. This paper presents and analyses a super-long-span bridge design which has a total span of 4440 m with 40 m width deck and two 702-m-high pylons. The bridge design is based on the Golden Gate Bridge and a finite element model is created in Strand7 [3] which is a modification to the Golden Gate Bridge model developed by [4]. The central span of the bridge is 3780 m, which is three times the span of the Golden Gate Bridge of 1260 m, while the length of the two end spans is the same at 330 m. Previous studies have been conducted on super-long cable-stayed bridges using carbon fibre reinforced polymer [5] and on long-span suspension bridges using fibre-reinforced polymer [6]. Special techniques are adopted in this design where the bridge combines the advantages of a suspension bridge and a cable-stayed bridge to minimise the deflection of the superstructure and the pylons. The material of the catenary cables and stay cables are changed to a lightweight fibre carbon composite [7] with high stiffness and high strength, and standard carbon fibre is used in the superstructure and the

vertical hangers. Finally, the stayed-cables of the bridge are pre-strained in this design.

600 GPa, tensile strength of 8.7 GPa, surface area 40 m2

Carbon nanofibres have cylindrical shapes with graphene layers constructed in the morphology of cones or plates or sheets, with an average diameter of 50–100 nm and an average length of 50–200 um, exceptional thermal and mechanical properties (as high as elastic modulus of

tions in the civil engineering discipline (e.g. bridges, roads, railways, tunnels, airports, ports and harbours), and other areas such as aerospace, automotive, sports goods material, and so on. Reinforcement of such new nanocarbons with polymeric materials further boosts their mechanical properties through different fabrication technologies such as wet/hand lay-up/ spray lay-up, autoclave curing, filament winding, pultrusion, wet/hand lay-up, and so on. These extraordinary properties of advanced hybrid composites have enabled the design engineers to use them in the renewal of civil infrastructure ranging from the strengthening of reinforced concrete, steel and iron, and for replacement of bridge decks in rehabilitation (seismic repair, strengthen or retrofitting) to the construction of new ultra super-long bridge and building structures with less cost. In 1972, high strength polymeric material roof structure with the shape of an umbrella was manufactured via hand lay-up fabrication process and transported from the UK to be erected at the international airport of Dubai. In 1990s, it was replaced by advanced composites that were made with sophisticated glass fibre-reinforced plastics. Such advanced polymer composites with nanofillers (e.g., nanocarbons, glass fibre) are used for the development of building systems and building blocks using an automated construction system (ACS), which consists of a number of interlocking fibre-reinforced polymers (e.g., aramid) that can assemble into a large number of different efficient civil structures (e.g., 3D form) for use in the construction industry. Some examples of these ACS systems in the area of bridging engineering are Humber Bridge (1410 m span), Aberfeldy Bridge, Iron Bridge and the Bonds Mill Bridge from UK, and Gilman Bridge (450 m span), George Washington Bridge

/g), which offer a wide range of applica-

light-weight materials must be used in the design of super-long-span bridges.

6 Bridge Engineering

#### **2.1. Structural members**

The design of this long-span bridge is based on the Golden Gate Bridge, therefore structural member types are essentially similar to the Golden Gate Bridge, which consists of a bridge deck with a supporting trusses and beams system, two pylons, catenary cables, vertical hangers and stayed cables and eight lanes of vehicle traffic. The design of the central span between the two pylons is based on a typical suspension bridge, while the two edge spans are similar to a cablestayed bridge. The superstructure spanning between the two pylons is hung by vertical suspenders at 15-m intervals, which is the same as a typical suspension bridge. These vertical hangers carrying the loads on the deck are supported by the catenary cables suspended between the two pylons. Additionally, the stay cables at the two edge spans connecting the top of the pylons and the ends of the bridge are anchored by the abutment anchors at each end of the bridge. The cables directly running from the tower to the deck form a fan-like pattern on a series of parallel lines. Due to the different stress modes on the structural members, different materials are selected for each member based on their properties such as ultimate tensile and compressive strength, density and Young's modulus. The properties of the materials used in the bridge model are listed in **Table 1** [7–9]. The material selection is further discussed for each structural member.

The superstructure of the bridge consists of four major components: the bridge deck, permanent formwork, the cross girder and the deck truss system. The 0.5-m-thick bridge deck is made up of reinforced concrete while the material applied to the rest of the components of the superstructure is standard carbon fibre to reduce the self-weight of the superstructure. **Figure 1** shows the details of the arrangement of the structural members in the superstructure (without the bridge deck). As shown in **Figure 1**, the truss system resisting tensile or compressive force is attached to the cross girders running across the driving direction of the bridge.


catenary shape and the parabolic shape. The detailed explanation of this process is introduced in Section 3. The catenary cables are formed by connecting the coordinates that mimicked the shape of the cable, so the cables are segmented instead of smooth. Secondly, there are 252 pairs of vertical hangers at 15-m intervals at the central span. The diameter of the vertical hangers is 0.16 m. Standard carbon fibre is used in vertical hangers due to the relatively low tensile stress. Thirdly, the stayed cables at the two side spans are made up of M55\*\*UD with

The Feasibility of Constructing Super-Long-Span Bridges with New Materials in 2050

http://dx.doi.org/10.5772/intechopen.75298

9

Two pylons are also built up at positions which are 330 m from each end of the bridge. The total height of a pylon is 702 m. The superstructure is connected to the pylons at 216 m from the foundations of the pylons. The loads on the catenary cables and the stayed cables are transferred to the pylons as a compressive force; therefore, Grade 350 steel is used as the mate-

The sizes and materials of the structural elements of the long-span bridge are shown in **Table 2**.

The vertical loads acting on the bridge mainly consist of the self-weight of the structural members, the live load due to traffic and the vertical wind load. The vertical loads applied to the bridge deck are firstly carried by the reinforced concrete deck through bending, where the deck is directly supported every 5 m by the cross girders (I beams) with web stiffeners. The web stiffeners act to increase the shear capacity of the deep I beams and decrease the chance of shear

**Structural elements details Material Suggested structural element sizes**

Bridge deck Reinforced concrete 0.5 m thick Cross girder 1 Standard carbon fibre fabric 2500UB3650 Cross girder 2 Standard carbon fibre fabric 1200×500×50 RHS Top and bottom chords (blue) Standard carbon fibre fabric 2000×2000×200 SHS Top/Bottom cross bracing (yellow) Standard carbon fibre fabric 1200×500×50 RHS Side cross bracing (green) Standard carbon fibre fabric 1000×500×50 RHS Main girders (blue) Standard carbon fibre fabric 1400×700×75 RHS Vertical members (pink) Standard carbon fibre fabric 1500UB1420 Catenary cables Carbon fibre composite (M55\*\* UD) 2.2 m diameter Vertical hangers Standard carbon fibre fabric 0.16 m diameter Stayed-cables Carbon fibre composite (M55\*\* UD) 0.15 m diameter Pylons Steel (Grade 350) 16,000×10,000 Pylon diagonal bracing Steel (Grade 350) 5000×5000 Pylon cross bracing Steel (Grade 350) 8000×16,000

a diameter of 0.15 m.

rial of the pylons [10].

**2.2. Structural system resisting vertical loads**

**Table 2.** Structural elements for the super-long-span bridge.

**Table 1.** Properties of the material used in the model.

A 2.5 m-deep UB section is selected for the cross girders to carry flexural loads and then to transfer the loads into the truss system below. The concrete bridge deck sits on top of the truss system and cross girders, and the live load and vertical wind load are directly applied on the top of the bridge deck. Furthermore, the rectangular hollow section cross bracings distribute the loads on the deck onto the cross girders, and they also perform as the tensile reinforcement for the bridge deck above.

The design uses three types of cables: catenary cables, vertical hangers and stayed cables. In the central suspended deck, cables suspended via pylons hold up the road deck, and the weight and the vertical loads are transferred by the cables to the towers, which in turn transfer to the pylons and the anchorages at the end of the bridge. Since all of the cables are in tension, a lightweight carbon fibre or carbon fibre composite should be used in the cables based on material properties in **Table 1**.

Firstly, the catenary cables with a diameter of 2.2 m are suspended between the pylons, with a total cable length of 3915 m and further extend and transfer the loads to the anchorages at the bank. Carbon fibre composite (i.e., M55\*\*UD) is used in the catenary cables. The shape of the catenary cables is determined by selecting an appropriate interpolated shape between the

**Figure 1.** Details of the bridge superstructure.

catenary shape and the parabolic shape. The detailed explanation of this process is introduced in Section 3. The catenary cables are formed by connecting the coordinates that mimicked the shape of the cable, so the cables are segmented instead of smooth. Secondly, there are 252 pairs of vertical hangers at 15-m intervals at the central span. The diameter of the vertical hangers is 0.16 m. Standard carbon fibre is used in vertical hangers due to the relatively low tensile stress. Thirdly, the stayed cables at the two side spans are made up of M55\*\*UD with a diameter of 0.15 m.

Two pylons are also built up at positions which are 330 m from each end of the bridge. The total height of a pylon is 702 m. The superstructure is connected to the pylons at 216 m from the foundations of the pylons. The loads on the catenary cables and the stayed cables are transferred to the pylons as a compressive force; therefore, Grade 350 steel is used as the material of the pylons [10].

The sizes and materials of the structural elements of the long-span bridge are shown in **Table 2**.

#### **2.2. Structural system resisting vertical loads**

The vertical loads acting on the bridge mainly consist of the self-weight of the structural members, the live load due to traffic and the vertical wind load. The vertical loads applied to the bridge deck are firstly carried by the reinforced concrete deck through bending, where the deck is directly supported every 5 m by the cross girders (I beams) with web stiffeners. The web stiffeners act to increase the shear capacity of the deep I beams and decrease the chance of shear


**Table 2.** Structural elements for the super-long-span bridge.

**Figure 1.** Details of the bridge superstructure.

ment for the bridge deck above.

**Table 1.** Properties of the material used in the model.

Carbon fibre composite (M55\*\*

UD)

8 Bridge Engineering

**Materials Ultimate tensile/compressive strength (MPa)**

Steel (Grade 350) 350 (C/T) 8000 207 Reinforced concrete 25.5 (C) 2500 34.5 Standard carbon fibre fabric 600 (T) 1600 70

material properties in **Table 1**.

A 2.5 m-deep UB section is selected for the cross girders to carry flexural loads and then to transfer the loads into the truss system below. The concrete bridge deck sits on top of the truss system and cross girders, and the live load and vertical wind load are directly applied on the top of the bridge deck. Furthermore, the rectangular hollow section cross bracings distribute the loads on the deck onto the cross girders, and they also perform as the tensile reinforce-

1600 (T) 1650 300 (0°)

**Density (kg/ m3 )**

**Young's modulus** 

**(GPa)**

The design uses three types of cables: catenary cables, vertical hangers and stayed cables. In the central suspended deck, cables suspended via pylons hold up the road deck, and the weight and the vertical loads are transferred by the cables to the towers, which in turn transfer to the pylons and the anchorages at the end of the bridge. Since all of the cables are in tension, a lightweight carbon fibre or carbon fibre composite should be used in the cables based on

Firstly, the catenary cables with a diameter of 2.2 m are suspended between the pylons, with a total cable length of 3915 m and further extend and transfer the loads to the anchorages at the bank. Carbon fibre composite (i.e., M55\*\*UD) is used in the catenary cables. The shape of the catenary cables is determined by selecting an appropriate interpolated shape between the

the structure's mass automatically after input of the material density and geometry. Dead

The Feasibility of Constructing Super-Long-Span Bridges with New Materials in 2050

http://dx.doi.org/10.5772/intechopen.75298

11

According to AS5100.2 Bridge Design Codes [11], the live load (Q) applying on the bridge deck is the load resulting from the passage of vehicles and pedestrians, which is SM1600 loading. However, for simplicity, the live load is considered as a pressure acting on the bridge deck in the Strand7 model. The most severe load specified in AS5100.2 is added together and averaged as a pressure load over the bridge deck, resulting in a surface pressure of 10.416 kPa. It is recommended that the Load Influence solver in Strand7 can be used to determine the

Wind load is the dominant impact on super-long bridges. The first step is to obtain the design wind speed calculated as specified in AS/NZS1170.2 [12], which is derived from regional basic wind speed after adjustment for average return interval, geographical location, terrain

*Vsit*,*<sup>β</sup>* = *VR Md*(*Mz*,*cat Ms Mt*) (1)

Since most of the factors vary with different site conditions, and the location of the bridge is not determined yet, by looking at a bridge over Bemboka River in New South Wales, a serviceability design wind speed *<sup>V</sup> <sup>s</sup>* =37 m/s and an ultimate design wind speed *<sup>V</sup> <sup>u</sup>* =48 m/s are used in the design. According to AS5100.2 [11], the ultimate design transverse wind load and ultimate

coefficient. Then the wind load applied on each structure member can be calculated for each structural member. For simplicity, the transverse wind load is assumed to only act on the

AS5100.2 Clause 23 [11] specifies that for *Ultimate Limit State (ULS)* analysis, the load combinations should include Permanent Effect + Road/rail traffic load and Permanent Effect + Wind load. Therefore, in the static analysis and dynamic analysis, the load combinations of G+Q

By applying fundamental principles in engineering design, analytical calculations were carried out to determine the optimum cable shape for the suspension bridge and to predict and verify the maximum stresses in the catenary cables and the natural frequency of the structure.

<sup>2</sup> *At Cd* = 1.935 *At* (2)

<sup>2</sup> *Ap CL* = 1.037 *At* (3)

is the drag coefficient, and *CL* <sup>=</sup> 0.75 is the lift

load is then calculated by multiplying the density by the gravitational acceleration.

critical point for the live load and the sensitivity of structure members.

category and height above ground. The site wind speed is calculated as:

<sup>∗</sup> = 0.0006 *Vu*

<sup>∗</sup> = 0.0006 *Vu*

are the bridge area in plan, *Cd*

vertical wind load are

and *Ap*

and G+W are considered.

**3. Theoretical analysis**

where *At*

*Wt*

*Wv*

superstructure and the pylons.

**Figure 2.** Side views and 3D view of the Strand7 model (a) Longitudinal view, (b) Details of Pylon, (c) 3D view.

buckling in the web. Then the cross girders transfer loads from the bridge deck to the truss system below the deck through bending. In the Strand7 model, the truss members are modelled as rectangular hollow sections to simplify the design. The members of the truss system can only carry axial force, so the top chords are in compression, and the bottom chords are in tension.

The loads on the truss system are spread along the main longitudinal truss members, and further transferred to the vertical hangers which are hanging off the corresponding superstructure every 15 m. These cables carry the loads from the bridge deck up to the catenary cables and the stayed cables through pure tension. On the Golden Gate Bridge, each catenary cable is made up of 27,572 galvanised steel cables which are grouped into 61 cable groups, which are then bunched together to form the 0.92 m diameter cable. For the super-long-span design, the larger diameter of catenary cables and stayed cables requires more galvanised steel cables to group larger cables. These stayed cables are also anchored at the abutments to keep them in tension and to pass the tensile load into the ground through the abutments. The pylons supporting the catenary cables, the stayed cables and the bridge deck are loaded in compression (**Figure 2**).

#### **2.3. Structural system resisting lateral loads**

Only wind load is considered as the lateral load acting on the bridge. Because this bridge is very long, the frequency of earthquakes is not consistent with the resonant frequency of the bridge. Therefore, the action of the earthquake load is not significant in this design. For simplicity, it is assumed that the transverse wind load only acts on the superstructure and the pylons. Therefore, the primary system used to resist transverse wind loads consists of the superstructure at the central span which is mainly restrained by the two pylons, the vertical hangers which are further suspended from the catenary cables and two pylons resisting the wind transverse wind load.

#### **2.4. Loads**

Dead load (G) accounts for the self-weight of the entire structure, which is calculated by multiplying member dimensions with the corresponding density. The Strand7 model calculated the structure's mass automatically after input of the material density and geometry. Dead load is then calculated by multiplying the density by the gravitational acceleration.

According to AS5100.2 Bridge Design Codes [11], the live load (Q) applying on the bridge deck is the load resulting from the passage of vehicles and pedestrians, which is SM1600 loading. However, for simplicity, the live load is considered as a pressure acting on the bridge deck in the Strand7 model. The most severe load specified in AS5100.2 is added together and averaged as a pressure load over the bridge deck, resulting in a surface pressure of 10.416 kPa. It is recommended that the Load Influence solver in Strand7 can be used to determine the critical point for the live load and the sensitivity of structure members.

Wind load is the dominant impact on super-long bridges. The first step is to obtain the design wind speed calculated as specified in AS/NZS1170.2 [12], which is derived from regional basic wind speed after adjustment for average return interval, geographical location, terrain category and height above ground. The site wind speed is calculated as:

$$V\_{s\text{it},\mathfrak{s}} = \,^\vee V\_\text{\tiny{}^\text{M}}(M\_{z,\text{at}}M\_\text{s}M\_\text{t})\tag{1}$$

Since most of the factors vary with different site conditions, and the location of the bridge is not determined yet, by looking at a bridge over Bemboka River in New South Wales, a serviceability design wind speed *<sup>V</sup> <sup>s</sup>* =37 m/s and an ultimate design wind speed *<sup>V</sup> <sup>u</sup>* =48 m/s are used in the design. According to AS5100.2 [11], the ultimate design transverse wind load and ultimate vertical wind load are

$$W\_i^\* = 0.0006 \, V\_u^2 \, A\_i \, \text{C}\_d = 1.935 \, A\_i \tag{2}$$

$$W\_v^\* = 0.0006 \, V\_u^2 \, A\_p \, \text{C}\_L = 1.037 \, A\_l \tag{3}$$

where *At* and *Ap* are the bridge area in plan, *Cd* is the drag coefficient, and *CL* <sup>=</sup> 0.75 is the lift coefficient. Then the wind load applied on each structure member can be calculated for each structural member. For simplicity, the transverse wind load is assumed to only act on the superstructure and the pylons.

AS5100.2 Clause 23 [11] specifies that for *Ultimate Limit State (ULS)* analysis, the load combinations should include Permanent Effect + Road/rail traffic load and Permanent Effect + Wind load. Therefore, in the static analysis and dynamic analysis, the load combinations of G+Q and G+W are considered.
