**3. Theoretical analysis**

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**).

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

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.

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

**2.3. Structural system resisting lateral loads**

**2.4. Loads**

10 Bridge Engineering

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.

#### **3.1. Optimum cable shape**

The shape of a flexible cable under self-weight is a catenary [13]. The equation for a catenary is:

$$y\_c = a \times \cosh\left(\frac{x}{a}\right) \tag{4}$$

to the maximum defection with a specific K value divided by the maximum deflection with K = 0. It is observed that for different K values, the maximum deflections for each case are different, and it reaches a minimum when K is about 0.6. It is also important to note that when the applied load has changed, the optimum K value will change as well. For example, when considering the live load by applying additional uniformly distributed load onto the deck, the optimum value K will increase since the overall load will be closer to a uniformly distributed load where K = 1 (i.e. a parabolic shape will have minimum deflections), so the optimum cable shape would be closer to a parabola. By considering different loading cases while maintaining

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To determine the maximum tensile stress in cables, four assumptions are made to simplify calculations. First, the combination of the self-weights of the cables and the decks is regarded as a uniformly distributed load, which means the consequent cable shape is parabolic. Second, the displacement of the top point of the pylons can be neglected by assuming pin connections between cables and pylons. Third, the deflection of cables under loading is not significant meaning that it will not affect the loads. Fourth, the influence of earth curvature is ignored, which means the gravitational forces are perfectly downwards. The free body diagram of half

load, *L* is the total length of internal span, *h* is the extreme difference of the main cable in the

<sup>2</sup> <sup>×</sup> \_\_*<sup>L</sup>*

By applying the moment equilibrium at the top right corner, it can be obtained that:

is the horizontal tensile force at the midpoint, *w* is the uniformly distributed

<sup>4</sup> <sup>=</sup> <sup>0</sup> <sup>→</sup> *<sup>T</sup>*<sup>0</sup> <sup>=</sup> *<sup>w</sup> <sup>L</sup>*<sup>2</sup> \_\_\_\_

<sup>8</sup>*<sup>h</sup>* (7)

relatively low deflections, a K value of 0.7 was adopted for the design.

**3.2. Maximum tensile stress in main span cables under dead loads**

internal span is shown in **Figure 4**.

vertical direction and *Tmax* is tensile stress at the pylon.

<sup>∑</sup>*<sup>M</sup>* <sup>=</sup> *<sup>T</sup>*<sup>0</sup> <sup>×</sup> *<sup>h</sup>* <sup>−</sup> *<sup>w</sup>* <sup>×</sup> \_\_*<sup>L</sup>*

**Figure 4.** Free body diagram of main cable—Half internal span.

From **Figure 4**, *T*<sup>0</sup>

where the parameter *a* can be determined once the points through the catenary are known.

Alternatively, when the cables are under heavy load (i.e. the self-weight of cables is negligible compared to the applied uniformly distributed load), then the shape becomes a parabola with the equation:

$$\mathbf{y}\_p = \frac{w}{2}\mathbf{r}\_o^2 + \boldsymbol{\beta} \tag{5}$$

where *T*<sup>0</sup> is the tensile force in the middle of the cable, *w* is the uniformly distributed load, and *β* is the distance between the lowest point of the cable and the top surface of the deck. However, in this design of a super-long-span suspension bridge, neither the self-weight of cables nor the applied uniformly distributed load from the deck can be ignored. Therefore, the resulting shape of the catenary cable is between the shape of a parabola and a catenary [14]. To determine the optimum cable shape that results in minimum deflection for the suspension bridge, an interpolation factor, K, is introduced to determine the final cable shape:

$$y = K \times y\_c + (1 - K) \times y\_p \tag{6}$$

where *K* ∈ [0, 1]. Note that the cable shape will be a catenary when K is 1 or a parabola when K is 0.

When only considering dead loads, the normalised maximum deflections of the middle span are plotted against different K values as shown in **Figure 3**. The normalised deflection is equal

**Figure 3.** Normalised maximum deflection under self-weight vs. K.

to the maximum defection with a specific K value divided by the maximum deflection with K = 0. It is observed that for different K values, the maximum deflections for each case are different, and it reaches a minimum when K is about 0.6. It is also important to note that when the applied load has changed, the optimum K value will change as well. For example, when considering the live load by applying additional uniformly distributed load onto the deck, the optimum value K will increase since the overall load will be closer to a uniformly distributed load where K = 1 (i.e. a parabolic shape will have minimum deflections), so the optimum cable shape would be closer to a parabola. By considering different loading cases while maintaining relatively low deflections, a K value of 0.7 was adopted for the design.

#### **3.2. Maximum tensile stress in main span cables under dead loads**

To determine the maximum tensile stress in cables, four assumptions are made to simplify calculations. First, the combination of the self-weights of the cables and the decks is regarded as a uniformly distributed load, which means the consequent cable shape is parabolic. Second, the displacement of the top point of the pylons can be neglected by assuming pin connections between cables and pylons. Third, the deflection of cables under loading is not significant meaning that it will not affect the loads. Fourth, the influence of earth curvature is ignored, which means the gravitational forces are perfectly downwards. The free body diagram of half internal span is shown in **Figure 4**.

From **Figure 4**, *T*<sup>0</sup> is the horizontal tensile force at the midpoint, *w* is the uniformly distributed load, *L* is the total length of internal span, *h* is the extreme difference of the main cable in the vertical direction and *Tmax* is tensile stress at the pylon.

By applying the moment equilibrium at the top right corner, it can be obtained that:

$$
\Sigma M = \ T\_o \times h - \overline{w} \times \frac{L}{2} \times \frac{L}{4} = \begin{array}{c} 0 \ \rightarrow \ T\_o = \frac{\overline{w} \ L^2}{8h} \end{array} \tag{7}
$$

**Figure 4.** Free body diagram of main cable—Half internal span.

**Figure 3.** Normalised maximum deflection under self-weight vs. K.

**3.1. Optimum cable shape**

the equation:

12 Bridge Engineering

where *T*<sup>0</sup>

K is 0.

*yc* = *a* × cosh(

*yp* <sup>=</sup> \_\_\_*<sup>w</sup>*

The shape of a flexible cable under self-weight is a catenary [13]. The equation for a catenary is:

where the parameter *a* can be determined once the points through the catenary are known.

Alternatively, when the cables are under heavy load (i.e. the self-weight of cables is negligible compared to the applied uniformly distributed load), then the shape becomes a parabola with

2 *T*<sup>0</sup>

and *β* is the distance between the lowest point of the cable and the top surface of the deck. However, in this design of a super-long-span suspension bridge, neither the self-weight of cables nor the applied uniformly distributed load from the deck can be ignored. Therefore, the resulting shape of the catenary cable is between the shape of a parabola and a catenary [14]. To determine the optimum cable shape that results in minimum deflection for the suspension bridge, an interpolation factor, K, is introduced to determine the final cable shape:

*y* = *K* × *yc* + (1 − *K*) × *yp* (6)

where *K* ∈ [0, 1]. Note that the cable shape will be a catenary when K is 1 or a parabola when

When only considering dead loads, the normalised maximum deflections of the middle span are plotted against different K values as shown in **Figure 3**. The normalised deflection is equal

is the tensile force in the middle of the cable, *w* is the uniformly distributed load,

\_\_*x*

*<sup>a</sup>*) (4)

*x*<sup>2</sup> + *β* (5)

Then, by applying Pythagorean theorem, the *Tmax* is obtained:

$$T\_{\max} = \sqrt{T\_0^2 + \left(\frac{wL}{2}\right)^2} = \sqrt{\frac{w^2L^4}{64\,h^2} + \frac{w^2L^2}{4}}\tag{8}$$

subdivided the deck plate, resulting in a relatively coarse mesh. Since the bridge deck is not a critical component in the analysis process, the mesh quality of plate elements is not an issue.

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For the bridge superstructure, the bridge lanes are modelled by plate elements having concrete material properties. The components of the truss system supporting the concrete deck are modelled as beam elements in the shape of I sections or rectangular hollow sections (RHS). In addition, the pylons, pylon diagonal bracings and pylon cross bracings are modelled as B2

The catenary cable is modelled using cut-off bar elements which are connected between nodes with coordinates that are determined by a theoretical analysis using both catenary curve and parabolic curve equations. The optimum cable shape results in an acceptable maximum deflection. The nodes for the catenary cables were imported into the Strand7 model, and were then joined by B2 cut-off bar elements to form the catenary cables. The vertical cables are also modelled by connecting the nodes on the catenary cables and bridge deck by using cut-off bar elements. Similarly, the stay cables are also modelled by connecting the nodes on the pylons and edge span bridge decks with cut-off bars. The reason for selecting cut-off bar is that this type of beam element only allows axial forces and allows users to set the tensile or compressive capacity of the bar. Therefore, all of the cables can be set to have zero compressive capacities. The nodes on the base of the pylons were completely fixed in all six degrees of freedom, which includes DX, DY and DZ as well as RX, RY and RZ, which is consistent with real structural behaviours with a deep and strong foundation system. Meanwhile, four giant anchors located at the ends of the bridge span are also fully fixed to prevent bridge movements in all directions.

Both the static solver and the dynamic solver are used in the numerical analysis. The deflection of the bridge and the stress within the structure members under dead load, live load, wind load and their combinations are determined by the linear static solver. The non-linear static solver is used to guarantee the maximum stresses within the members are below the

The Natural Frequency Solver is used to determine the natural frequencies of the bridge based on the results of linear static analysis. Linear static analysis under the G+Q load is conducted first since the tension and compression within structural members would have significant impacts on its natural frequencies. Up to 50 frequency modes are analysed in order to obtain

Once the natural frequency analysis is completed, the harmonic response analysis is performed to determine the mass participation of the bridge and its displacements under wind load. Case factor is set as 1.0 for wind load only, a 5% modal damping is applied in harmonic analysis and all 50 natural frequencies are investigated. The resonance frequency and the cor-

responding deflection can be obtained in the harmonic response analysis.

elements (beam element) with solid rectangular sections.

**4.2. Element types**

**4.3. Solvers used in the analysis**

yield stress of the corresponding materials.

the sufficient mass participation of the bridge.

From Strand7, the dead load of the deck and cables is obtained: *w* = 485.275 *kN*/*m*. With *L* = 3780 m, *<sup>h</sup>* = 443.5 m, the horizontal tensile force is calculated to be *T*<sup>0</sup> = 1954.29 kN, and *Tmax* = 2158.80 kN. Then, for a cable with diameter D = 2.2 m, the stresses are calculated by dividing the force by the cross-sectional area of cable: *σ*<sup>0</sup> <sup>=</sup> *<sup>T</sup>* \_\_0 *<sup>A</sup>* <sup>=</sup> <sup>515</sup> MPa, and *σmax* <sup>=</sup> *<sup>T</sup>* \_\_\_\_ *max <sup>A</sup>* <sup>=</sup> 568 MPa.

#### **3.3. Bridge natural frequency**

The natural frequency of bridges is affected by different material and geometric properties:

$$n = f(E, I, \rho, k, L) \tag{9}$$

where *E* is elastic modulus, *I* is the second moment of area, *ρ* is the density of materials, *k* is the factor depending on the boundary condition and *L* is the span distance of the bridge.

Since the equation for the natural frequency for a complete representation of the suspension bridge is extremely complicated, a simplified method was adopted under the following three assumptions. First, the oscillation mode will be such that the bridge will deflect in the transverse direction, which is consistent with the first mode determined from the numerical analysis presented. Second, the geometric structure of the deck will be regarded as a simple beam. Third, the cables provide no significant effect on the oscillation frequency in the transverse direction. By applying a simplified equation:

$$m = \frac{K}{2\pi L^2} \sqrt{\frac{EI}{m}}\tag{10}$$

where K is a constant depending on the mode of vibration mode, m is the mass per metre for the deck, then the natural frequency of the first mode is determined to be 0.0212 Hz.

#### **4. Numerical analysis**

A detailed finite element model of the structure was created in Strand7 [3], and details of the model are described.

#### **4.1. Mesh and mesh quality**

In Strand7, plate elements are used to model the bridge concrete deck, while the remainder of bridge elements use cut-off bars and beam elements. Only the plate elements within the model need meshing as cut-off bars and beam elements in the truss system do not require meshing. However, the node positions of truss members below the bridge deck have already subdivided the deck plate, resulting in a relatively coarse mesh. Since the bridge deck is not a critical component in the analysis process, the mesh quality of plate elements is not an issue.

## **4.2. Element types**

Then, by applying Pythagorean theorem, the *Tmax* is obtained:

*<sup>h</sup>* = 443.5 m, the horizontal tensile force is calculated to be *T*<sup>0</sup>

\_\_\_\_\_\_\_\_\_

From Strand7, the dead load of the deck and cables is obtained: *w* = 485.275 *kN*/*m*. With *L* = 3780 m,

Then, for a cable with diameter D = 2.2 m, the stresses are calculated by dividing the force by

The natural frequency of bridges is affected by different material and geometric properties:

*n* = *f*(*E*, *I*, *ρ*, *k*, *L*) (9)

where *E* is elastic modulus, *I* is the second moment of area, *ρ* is the density of materials, *k* is the

Since the equation for the natural frequency for a complete representation of the suspension bridge is extremely complicated, a simplified method was adopted under the following three assumptions. First, the oscillation mode will be such that the bridge will deflect in the transverse direction, which is consistent with the first mode determined from the numerical analysis presented. Second, the geometric structure of the deck will be regarded as a simple beam. Third, the cables provide no significant effect on the oscillation frequency in the transverse

2*πL*<sup>2</sup> √

where K is a constant depending on the mode of vibration mode, m is the mass per metre for

A detailed finite element model of the structure was created in Strand7 [3], and details of the

In Strand7, plate elements are used to model the bridge concrete deck, while the remainder of bridge elements use cut-off bars and beam elements. Only the plate elements within the model need meshing as cut-off bars and beam elements in the truss system do not require meshing. However, the node positions of truss members below the bridge deck have already

the deck, then the natural frequency of the first mode is determined to be 0.0212 Hz.

\_\_ \_\_ *EI*

factor depending on the boundary condition and *L* is the span distance of the bridge.

*<sup>A</sup>* <sup>=</sup> <sup>515</sup> MPa, and *σmax* <sup>=</sup> *<sup>T</sup>*

\_\_\_\_\_\_\_\_\_ *w*<sup>2</sup> *L*<sup>4</sup> \_\_\_\_ <sup>64</sup> *<sup>h</sup>*<sup>2</sup> <sup>+</sup> *<sup>w</sup>*<sup>2</sup> *<sup>L</sup>*<sup>2</sup> \_\_\_\_

\_\_\_\_ *max*

*<sup>A</sup>* <sup>=</sup> 568 MPa.

<sup>4</sup> (8)

= 1954.29 kN, and *Tmax* = 2158.80 kN.

*<sup>m</sup>* (10)

*T*0 <sup>2</sup> + ( \_\_\_ *wL* <sup>2</sup> ) 2 <sup>=</sup> <sup>√</sup>

\_\_0

*Tmax* <sup>=</sup> <sup>√</sup>

14 Bridge Engineering

the cross-sectional area of cable: *σ*<sup>0</sup> <sup>=</sup> *<sup>T</sup>*

direction. By applying a simplified equation:

**4. Numerical analysis**

**4.1. Mesh and mesh quality**

model are described.

*<sup>n</sup>* <sup>=</sup> \_\_\_\_ *<sup>K</sup>*

**3.3. Bridge natural frequency**

For the bridge superstructure, the bridge lanes are modelled by plate elements having concrete material properties. The components of the truss system supporting the concrete deck are modelled as beam elements in the shape of I sections or rectangular hollow sections (RHS). In addition, the pylons, pylon diagonal bracings and pylon cross bracings are modelled as B2 elements (beam element) with solid rectangular sections.

The catenary cable is modelled using cut-off bar elements which are connected between nodes with coordinates that are determined by a theoretical analysis using both catenary curve and parabolic curve equations. The optimum cable shape results in an acceptable maximum deflection. The nodes for the catenary cables were imported into the Strand7 model, and were then joined by B2 cut-off bar elements to form the catenary cables. The vertical cables are also modelled by connecting the nodes on the catenary cables and bridge deck by using cut-off bar elements. Similarly, the stay cables are also modelled by connecting the nodes on the pylons and edge span bridge decks with cut-off bars. The reason for selecting cut-off bar is that this type of beam element only allows axial forces and allows users to set the tensile or compressive capacity of the bar. Therefore, all of the cables can be set to have zero compressive capacities.

The nodes on the base of the pylons were completely fixed in all six degrees of freedom, which includes DX, DY and DZ as well as RX, RY and RZ, which is consistent with real structural behaviours with a deep and strong foundation system. Meanwhile, four giant anchors located at the ends of the bridge span are also fully fixed to prevent bridge movements in all directions.

#### **4.3. Solvers used in the analysis**

Both the static solver and the dynamic solver are used in the numerical analysis. The deflection of the bridge and the stress within the structure members under dead load, live load, wind load and their combinations are determined by the linear static solver. The non-linear static solver is used to guarantee the maximum stresses within the members are below the yield stress of the corresponding materials.

The Natural Frequency Solver is used to determine the natural frequencies of the bridge based on the results of linear static analysis. Linear static analysis under the G+Q load is conducted first since the tension and compression within structural members would have significant impacts on its natural frequencies. Up to 50 frequency modes are analysed in order to obtain the sufficient mass participation of the bridge.

Once the natural frequency analysis is completed, the harmonic response analysis is performed to determine the mass participation of the bridge and its displacements under wind load. Case factor is set as 1.0 for wind load only, a 5% modal damping is applied in harmonic analysis and all 50 natural frequencies are investigated. The resonance frequency and the corresponding deflection can be obtained in the harmonic response analysis.

Spectral response solver is used to investigate the dynamic response to wind load, with the aid of a power spectral density curve. A 5% modal damping is applied and the results are calculated based on square root of the sum of the squares (SRSS) approach.

#### **5. Structural design**

In terms of structural design of the bridge, the capacity is defined as the strength limit state by the critical members which experience maximum axial force, bending moment or shear force. The serviceability limit state is also considered; therefore, the deflections of the deck are checked. In particular, carbon fibre has no yielding behaviours, so there will be no sign of failure in the carbon fibre cables. For members consisting of standard carbon fibre and M55\*\*UD carbon fibre composite, the tensile strength is reduced by 80% due to this brittle nature. For steel members, the section yield stress is factored down to 90% of full yielding. According to the Steel Structures design code AS4100 [8], the nominal section capacity for members subject to axial tension and compression is calculated using the equations:

$$f\_{\iota}^{\*} = 0.85 \,\mathcal{Q} \, k\_{\iota} f\_{\iota} \tag{11}$$

**5.1. Cable design**

ties in **Table 3**.

**5.2. Deck design**

analytical results in later sections.

**Member type Member dimensions (m in diameter)**

For bridges with super-long spans, the most challenging and critical members are vertical cables and catenary cables because the dead and live loads acting on the bridge deck are mainly transferred to the vertical cables and further to the catenary cables, which result in large tensile stresses in those cables. As specified above, the vertical cables and catenary cables are cut-off bars, which only resist axial tensile force. The Strand7 linear static analysis results under the G + Q case give the maximum tensile stresses in the cables compared to the capaci-

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For catenary cables, the maximum tensile stress is applied at the end segments near the pylons, which is reasonable since loads on the catenary cables are transferred to the pylons and further to the stayed cables. The last column in **Table 3** is the percentage of maximum applied stress to the tensile capacity. The results show that the current cable design is optimistic as the applied stresses are extremely close to the cable capacity, and the maximum bridge deflection under G+Q is relatively close to the AS5100 [11] limit. However, it is significant to note that the dimension of the catenary cable is relatively large compared to the original design, as it was increased from 1.20 to 2.20 m in diameter. To prove the validity of the Strand7 model, the maximum applied stress in the catenary cables in Strand7 analysis is compared with the

In terms of the deck design, the deck members are divided into two groups: truss members and flexural members. Truss members such as the top and bottom chords resist axial load only, so the tensile and compressive axial strength for each type is compared with the maximum applied axial loads under the most critical load combination (G+Q). Flexural members such as the top and bottom cross girders also experience significant bending moments; thus, the calculated moment section capacity for each type of member is further compared with the maximum applied bending moments under the G+Q case. In particular, for a conservative

The last column in **Table 4** indicates the larger percentages of applied axial stress to the axial capacity of critical axial force in terms of tension or compression. All truss members have a

**(MPa)**

Vertical cables 0.16 459 416 90.63 Catenary cables 2.20 1224 1154 94.28 Stayed cables 0.15 1224 1152 94.11

**Table 3.** Comparison of tensile capacity to maximum applied stress (suggested design).

**Tensile capacity** 

**Maximum stress** 

**Capacity (%)**

**(MPa)**

design, the axial and bending capacities in **Table 4** are factored into capacities.

$$f\_c^\* = \bigotimes k\_i f\_y \tag{12}$$

Assuming the tensile load is distributed uniformly to the catenary cable, the value of *k t* equals to 1. As the catenary cables made of M55\*\*UD carbon fibre composite are only subjected to tensile forces, the factored tensile capacity *f <sup>t</sup>*\_*cc* can be obtained as:

$$f\_{t\_{\rm u}w} = 0.85 \times 0.9 \times 1600 = 1224 \text{ MPa} \tag{13}$$

Similarly, for the truss members and vertical cables which are made up of standard carbon fibre, it is assumed that their effective cross-sectional area equals their total cross-sectional area (*k <sup>f</sup>* <sup>=</sup> 1). Therefore, the factored tensile capacity *<sup>f</sup> t*\_*c* and compressive capacity *f <sup>c</sup>*\_*<sup>c</sup>* can be obtained as:

$$f\_{t\_{\zeta}} = 0.85 \times 0.9 \times 600 = 459 \text{ MPa} \tag{14}$$

$$f\_{\epsilon\_{\varsigma}} = 0.9 \times 570 = 513 \text{ MPa} \tag{15}$$

Pylons are made up of Grade 350 steel, where the factored yield capacity *f c*\_*p* is calculated as:

$$f\_{c,p} = 0.8 \times 350 = 315 \text{ MPa} \tag{16}$$

### **5.1. Cable design**

Spectral response solver is used to investigate the dynamic response to wind load, with the aid of a power spectral density curve. A 5% modal damping is applied and the results are

In terms of structural design of the bridge, the capacity is defined as the strength limit state by the critical members which experience maximum axial force, bending moment or shear force. The serviceability limit state is also considered; therefore, the deflections of the deck are checked. In particular, carbon fibre has no yielding behaviours, so there will be no sign of failure in the carbon fibre cables. For members consisting of standard carbon fibre and M55\*\*UD carbon fibre composite, the tensile strength is reduced by 80% due to this brittle nature. For steel members, the section yield stress is factored down to 90% of full yielding. According to the Steel Structures design code AS4100 [8], the nominal section capacity for members subject

<sup>∗</sup> <sup>=</sup> 0.85 <sup>∅</sup> *kt <sup>f</sup>*

<sup>∗</sup> <sup>=</sup> <sup>∅</sup> *kt <sup>f</sup>*

to 1. As the catenary cables made of M55\*\*UD carbon fibre composite are only subjected to

Similarly, for the truss members and vertical cables which are made up of standard carbon fibre, it is assumed that their effective cross-sectional area equals their total cross-sectional

*<sup>t</sup>*\_*cc* can be obtained as:

*t*\_*c*

*<sup>t</sup>*\_*cc* = 0.85 × 0.9 × 1600 = 1224 MPa (13)

*<sup>t</sup>*\_*<sup>c</sup>* = 0.85 × 0.9 × 600 = 459 MPa (14)

*<sup>c</sup>*\_*<sup>c</sup>* = 0.9 × 570 = 513 MPa (15)

*<sup>c</sup>*\_*<sup>p</sup>* = 0.8 × 350 = 315 MPa (16)

*c*\_*p*

and compressive capacity *f*

*<sup>u</sup>* (11)

*<sup>y</sup>* (12)

*t* equals

*<sup>c</sup>*\_*<sup>c</sup>* can be

is calculated as:

calculated based on square root of the sum of the squares (SRSS) approach.

to axial tension and compression is calculated using the equations:

*t*

*c*

Assuming the tensile load is distributed uniformly to the catenary cable, the value of *k*

*f*

*f*

tensile forces, the factored tensile capacity *f*

*<sup>f</sup>* <sup>=</sup> 1). Therefore, the factored tensile capacity *<sup>f</sup>*

Pylons are made up of Grade 350 steel, where the factored yield capacity *f*

*f*

*f*

*f*

*f*

area (*k*

obtained as:

**5. Structural design**

16 Bridge Engineering

For bridges with super-long spans, the most challenging and critical members are vertical cables and catenary cables because the dead and live loads acting on the bridge deck are mainly transferred to the vertical cables and further to the catenary cables, which result in large tensile stresses in those cables. As specified above, the vertical cables and catenary cables are cut-off bars, which only resist axial tensile force. The Strand7 linear static analysis results under the G + Q case give the maximum tensile stresses in the cables compared to the capacities in **Table 3**.

For catenary cables, the maximum tensile stress is applied at the end segments near the pylons, which is reasonable since loads on the catenary cables are transferred to the pylons and further to the stayed cables. The last column in **Table 3** is the percentage of maximum applied stress to the tensile capacity. The results show that the current cable design is optimistic as the applied stresses are extremely close to the cable capacity, and the maximum bridge deflection under G+Q is relatively close to the AS5100 [11] limit. However, it is significant to note that the dimension of the catenary cable is relatively large compared to the original design, as it was increased from 1.20 to 2.20 m in diameter. To prove the validity of the Strand7 model, the maximum applied stress in the catenary cables in Strand7 analysis is compared with the analytical results in later sections.

#### **5.2. Deck design**

In terms of the deck design, the deck members are divided into two groups: truss members and flexural members. Truss members such as the top and bottom chords resist axial load only, so the tensile and compressive axial strength for each type is compared with the maximum applied axial loads under the most critical load combination (G+Q). Flexural members such as the top and bottom cross girders also experience significant bending moments; thus, the calculated moment section capacity for each type of member is further compared with the maximum applied bending moments under the G+Q case. In particular, for a conservative design, the axial and bending capacities in **Table 4** are factored into capacities.

The last column in **Table 4** indicates the larger percentages of applied axial stress to the axial capacity of critical axial force in terms of tension or compression. All truss members have a


**Table 3.** Comparison of tensile capacity to maximum applied stress (suggested design).


**Table 4.** Design of deck truss members based on axial capacity (current design).

percentage of capacity less than 100%, which indicates that this design satisfies the strength limit state requirements. However, except for side cross-bracing members, the percentages of capacity for other truss members are less than 15%, which means that these members are over-conservative. Hence, the geometries for those members can be adjusted to achieve a more economical design.

For the deck flexural members under bending, the section capacity can be obtained by:

$$M = \frac{\sigma y}{I} \tag{17}$$

*Mb*\_*<sup>g</sup>* = 0.046 × 459 × 103 = 0.21 × 105 kNm (20)

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Similarly, all deck flexural members have a percentage of capacity less than 100% while for the top and bottom cross girders the value is below 15%, so the member geometries are neces-

Using the linear static solver available in Strand7, the suspension bridge is assessed in terms of deflections and stresses under the G+Q and G+W cases. As specified in AS5100.2 [11], the ratio of the allowable vertical deflection or transverse deflection over the length of the span

<sup>600</sup>, which corresponds to a maximum deflection of 6.3 m. The allowable deflections are

The deflection contour of the suspension bridge under the combination of dead and live loads is shown in **Figure 5**. The maximum vertical deflection occurs at the middle of the central span, which is around 8.3 m downwards. The vertical deflection exceeds the allowable deflection limit, which is 6.3 m, hence more techniques are required to further decrease the vertical

In terms of the stresses shown in **Figure 6**, the maximum stresses occur in the catenary cables and stay cables, with the values of 1154 and 1152 MPa respectively. As calculated in Section 5, the carbon fibre composite (M55\*\*UD) used in catenary and stay cables have a factored tensile capacity of 1224 MPa and can sustain the load without failure. Additionally, the vertical cables within the central span have relatively small stress at around 400 MPa, which is below

sarily optimised to achieve a more economical design.

further compared with the results in Strand7 analysis.

**6. Results and discussion**

**6.1. Static analysis**

*6.1.1. Dead load + live load*

the factored tensile capacity of 459 MPa.

**Figure 5.** Vertical deflection contour under dead + live load.

is \_\_\_1

deflection.

In terms of the section modulus and the axial compression capacity, the section capacity for the top and bottom cross girder and top and bottom chords is calculated as follows (**Table 5**):

$$M\_{\rm \\_g} = 0.262 \times 459 \times 10^3 = 1.203 \times 10^5 \text{ kNm} \tag{18}$$

$$M\_{\varepsilon} = 0.787 \times 459 \times 10^3 = 3.612 \times 10^5 \text{ kNm} \tag{19}$$


**Table 5.** Design of deck flexural members based on moment section capacity (current design).

$$M\_{b\\_g} = 0.046 \times 459 \times 10^3 = 0.21 \times 10^5 \text{ kNm} \tag{20}$$

Similarly, all deck flexural members have a percentage of capacity less than 100% while for the top and bottom cross girders the value is below 15%, so the member geometries are necessarily optimised to achieve a more economical design.

## **6. Results and discussion**

#### **6.1. Static analysis**

Using the linear static solver available in Strand7, the suspension bridge is assessed in terms of deflections and stresses under the G+Q and G+W cases. As specified in AS5100.2 [11], the ratio of the allowable vertical deflection or transverse deflection over the length of the span is \_\_\_1 <sup>600</sup>, which corresponds to a maximum deflection of 6.3 m. The allowable deflections are further compared with the results in Strand7 analysis.

#### *6.1.1. Dead load + live load*

percentage of capacity less than 100%, which indicates that this design satisfies the strength limit state requirements. However, except for side cross-bracing members, the percentages of capacity for other truss members are less than 15%, which means that these members are over-conservative. Hence, the geometries for those members can be adjusted to achieve a

**Truss members Geometry Capacity Loading Capacity (%)**

1200×500×50 RHS 459 513 29 15 6.3

*u\_c* **(MPa) Design** 

**tension (MPa)**

**Design compression (MPa)**

*u\_t* **(MPa)** *f*

Bottom cross girders 1200×500×50 RHS 459 513 53 8 11.5 Top/bottom chords 2000×2000×200 RHS 459 513 72 32 15.7

Side cross bracings 1000×500×50 RHS 459 513 208 285 55.6 Main girders 1400×700×75 RHS 459 513 10 10 2.2 Vertical bracings 500UB667 459 513 66 17 14.4 Top cross girders 2500UB3650 459 513 10 19 3.7

*f*

For the deck flexural members under bending, the section capacity can be obtained by:

In terms of the section modulus and the axial compression capacity, the section capacity for the top and bottom cross girder and top and bottom chords is calculated as follows (**Table 5**):

*Mt*\_*<sup>g</sup>* = 0.262 × 459 × 103 = 1.203 × 105 kNm (18)

*Mc* = 0.787 × 459 × 103 = 3.612 × 105 kNm (19)

**Flexural members Geometry Capacity Loading Capacity (%)**

 **(MPa) Section capacity (kNm)**

 **(m3 )** *f u\_c*

Top cross girder 0.465 0.328 1.25 0.262 459 1.203 × 105 12,025 10 Top/bottom chords 1.440 0.787 1.00 0.787 459 3.612 × 105 315,000 87.2 Bottom cross girder 0.160 0.028 0.60 0.046 459 0.21 × 105 725 3.5

*<sup>I</sup>* (17)

**Design moment (kNm)**

more economical design.

Top/bottom cross bracings

18 Bridge Engineering

*<sup>M</sup>* <sup>=</sup> *y*\_\_\_

**Area (m2 )**

**Ix (m4**

**) y (m) Zx**

**Table 5.** Design of deck flexural members based on moment section capacity (current design).

**Table 4.** Design of deck truss members based on axial capacity (current design).

The deflection contour of the suspension bridge under the combination of dead and live loads is shown in **Figure 5**. The maximum vertical deflection occurs at the middle of the central span, which is around 8.3 m downwards. The vertical deflection exceeds the allowable deflection limit, which is 6.3 m, hence more techniques are required to further decrease the vertical deflection.

In terms of the stresses shown in **Figure 6**, the maximum stresses occur in the catenary cables and stay cables, with the values of 1154 and 1152 MPa respectively. As calculated in Section 5, the carbon fibre composite (M55\*\*UD) used in catenary and stay cables have a factored tensile capacity of 1224 MPa and can sustain the load without failure. Additionally, the vertical cables within the central span have relatively small stress at around 400 MPa, which is below the factored tensile capacity of 459 MPa.

**Figure 5.** Vertical deflection contour under dead + live load.

**Figure 6.** Beam axial stress (kPa) contour under dead and live load combination (G+Q).

#### *6.1.2. Dead load + wind load*

A horizontal wind load is applied onto the deck system and pylons. Under linear static analysis, the transverse deflection contour of the "Dead +Wind" loading case is shown in **Figure 7**. **6.2. Natural frequency analysis**

to find the most disastrous wind speed.

**6.3. Harmonic response analysis**

Natural frequencies of the bridge are solved by Strand7 based on a linear static analysis result under the "Dead load + Live load" case since wind impact is significant when the bridge is in

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In the first mode with a frequency of 0.00338 Hz, the bridge deforms horizontally in a single curvature shape. In the second mode, the bridge deforms horizontally in a double curvature shape, where the frequency is 0.06001 Hz, and in the third mode, the bridge deforms vertically in a double curvature shape, where the frequency is 0.071586 Hz. Further natural frequency modes with higher frequencies are not considered as critical as the first three modes, but the harmonic response solver will be used to investigate the wind impact of these modes

Based on the previous solved natural frequencies, the harmonic response analysis runs under the "wind load only" case with 5% modal damping. **Figure 9** shows that the first mode is the most critical case, since at 0.00338 Hz, the bridge is under resonance and there is a relatively large transverse displacement of 47.6 m at the mid-span of the bridge. Specifically, the wind load is applied as steady sinusoidal force at various frequencies, where each cycle of loading exerts additional energy and increases the vibration amplitude. In this case, when the wind blows in the same frequency as the first natural frequency mode (0.00338 Hz), the bridge is under resonance where the maximum response amplitude occurs and the transverse displacement reaches 47.6 m. Therefore, the super-long bridge is considered to fail when the wind frequency coincides with the first mode of frequency of the bridge. However, the real

**Numerical Analytical Difference (%)**

service. Up to 50 different modes of natural frequencies are solved.

**Figure 8.** Beam axial stress (kPa) contour under dead and wind load combination (G+W).

behaviour of wind loading is further explored in Section 6.4.

**Table 6.** Comparison of numerical and analytical catenary cable stresses.

Tensile stress near pylons (MPa) 714 568 20.4 Tensile stress at midpoint (MPa) 646 515 20.3

It is found that the transverse deflections at the edge span and the central span near the pylons are very small, and the maximum transverse deflection of 30.9 m occurs at the mid-span of the central span. The transverse deflection under the "Dead load + Wind load" case exceeds the allowable value of 6.3 m, since the out of plane stiffness of the deck is insufficient via the lateral wind load. Therefore, the deflection under the "Dead load + Wind load" case is not satisfactory, and further methods should be considered to reduce the transverse deflection such as improving the stiffness of the deck.

In terms of the stress contours shown in **Figure 8**, the maximum stresses in this case are much lower than the stresses under the "Dead load + Live load" case which indicate that the "Dead load + Wind load" case is not the most critical case for element stresses. Hence the structural elements sufficiently sustain the loads without failure under the "Dead load + Wind load" case.

The catenary cable stress at the mid-span from the Strand7 analysis is compared to the analytical results. Under the "Dead load + Live load" case, the maximum catenary cable stress at the mid-span is 714 MPa, which is located at the region near the pylons, and the horizontal stress at the midpoint of the central span is 646 MPa from Strand7 linear static analysis. **Table 6** shows that there is a 20% difference between the numerical and analytical results.

**Figure 7.** Transverse deflection contour under dead load and wind load.

**Figure 8.** Beam axial stress (kPa) contour under dead and wind load combination (G+W).

#### **6.2. Natural frequency analysis**

*6.1.2. Dead load + wind load*

20 Bridge Engineering

such as improving the stiffness of the deck.

**Figure 7.** Transverse deflection contour under dead load and wind load.

A horizontal wind load is applied onto the deck system and pylons. Under linear static analysis, the transverse deflection contour of the "Dead +Wind" loading case is shown in **Figure 7**. It is found that the transverse deflections at the edge span and the central span near the pylons are very small, and the maximum transverse deflection of 30.9 m occurs at the mid-span of the central span. The transverse deflection under the "Dead load + Wind load" case exceeds the allowable value of 6.3 m, since the out of plane stiffness of the deck is insufficient via the lateral wind load. Therefore, the deflection under the "Dead load + Wind load" case is not satisfactory, and further methods should be considered to reduce the transverse deflection

**Figure 6.** Beam axial stress (kPa) contour under dead and live load combination (G+Q).

In terms of the stress contours shown in **Figure 8**, the maximum stresses in this case are much lower than the stresses under the "Dead load + Live load" case which indicate that the "Dead load + Wind load" case is not the most critical case for element stresses. Hence the structural elements sufficiently sustain the loads without failure under the "Dead load + Wind load" case. The catenary cable stress at the mid-span from the Strand7 analysis is compared to the analytical results. Under the "Dead load + Live load" case, the maximum catenary cable stress at the mid-span is 714 MPa, which is located at the region near the pylons, and the horizontal stress at the midpoint of the central span is 646 MPa from Strand7 linear static analysis. **Table 6**

shows that there is a 20% difference between the numerical and analytical results.

Natural frequencies of the bridge are solved by Strand7 based on a linear static analysis result under the "Dead load + Live load" case since wind impact is significant when the bridge is in service. Up to 50 different modes of natural frequencies are solved.

In the first mode with a frequency of 0.00338 Hz, the bridge deforms horizontally in a single curvature shape. In the second mode, the bridge deforms horizontally in a double curvature shape, where the frequency is 0.06001 Hz, and in the third mode, the bridge deforms vertically in a double curvature shape, where the frequency is 0.071586 Hz. Further natural frequency modes with higher frequencies are not considered as critical as the first three modes, but the harmonic response solver will be used to investigate the wind impact of these modes to find the most disastrous wind speed.

#### **6.3. Harmonic response analysis**

Based on the previous solved natural frequencies, the harmonic response analysis runs under the "wind load only" case with 5% modal damping. **Figure 9** shows that the first mode is the most critical case, since at 0.00338 Hz, the bridge is under resonance and there is a relatively large transverse displacement of 47.6 m at the mid-span of the bridge. Specifically, the wind load is applied as steady sinusoidal force at various frequencies, where each cycle of loading exerts additional energy and increases the vibration amplitude. In this case, when the wind blows in the same frequency as the first natural frequency mode (0.00338 Hz), the bridge is under resonance where the maximum response amplitude occurs and the transverse displacement reaches 47.6 m. Therefore, the super-long bridge is considered to fail when the wind frequency coincides with the first mode of frequency of the bridge. However, the real behaviour of wind loading is further explored in Section 6.4.


**Table 6.** Comparison of numerical and analytical catenary cable stresses.

**Figure 9.** Frequencies vs. nodal displacement (Dx ) at the mid-span.

#### **6.4. Spectral response analysis**

The linear elastic response of a super-long bridge subjected to a particular wind loading in Australia can be assessed by the "Spectral Response Solver" in Strand7, where the input for dynamic wind analysis can be expressed in terms of Power Spectral Density (PSD) curves [3]. The PSD curve (Davenport's equation) can be expressed as:

$$S\_{\mu}(n) = 4 \text{ k } V^2 \xrightarrow[n \text{ } (1+x^2)^4]{\mathbb{Z}^2} \tag{21}$$

**Figure 10** indicates that the wind load factor changes with wind frequencies and the largest wind load factor occurs when the wind frequency is approximately 0.0045 Hz. Based on the factor vs. frequency graph, the natural frequency of the bridge and applied wind pressure, the "Spectral Response Solver" is run and the result is calculated by the square root of the sum of the squares (SRSS) method in which the coupling among different modes is neglected. In addition, 5% modal damping is applied in the analysis. The result of transverse displacement

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The result shows that a maximum transverse deflection of 32.4 m occurs at the mid-span, which is greater than the transverse deflection of 30.9 m obtained from linear static analysis. This phenomenon is reasonable because when the bridge natural frequencies coincide with the heavily factored wind frequencies, the wind impact is severely magnified. As the 32.4 m transverse deflection exceeds the AS5100 limit of 6.3 m, the serviceability criterion is not satisfied. The reason is that the out of plane stiffness of the bridge is insufficient to resist wind forces in this super long bridge. Therefore, further approaches are necessary to increase the lateral stiffness such as increasing the deck width and increasing the depth of the truss system.

Standard and ultra-high stiffness carbon fibres are mainly made for high-tech industries like the aerospace industry. They are very expensive and used in specialised applications such as aerofoils. The price for the ultra-high stiffness is \$2000 USD per kg [15], whereas standard carbon fibre was \$22 USD per kg in 2013 [15]. Currently, ultra-high stiffness is not economical for civil infrastructure. However, **Figure 12** shows the forecast cost of standard carbon fibre. The cost in 2017 is approximately \$12 USD per kg, and it has dropped significantly compared to the price in 2013. **Figure 12** shows that the decreasing price trend could be approximated

*cost* = *k* × *e* <sup>−</sup>0.187×*year* (22)

where k depends on the year of interest. Based on the same trend, in 2050, the cost of standard carbon fibre would be \$0.02 USD per kg and the price of carbon fibre composite would be \$1.26 USD per kg, which are even cheaper than the price of steel now of \$1.60 USD per kg

**Figure 11.** Transverse deflection contour under wind load (spectral response analysis).

is shown in **Figure 11**.

**6.5. Carbon fibre cost**

to an exponential function as:

where *Su* (*n*) is the wind speed power spectral density, *n* is the frequency, *V* is the hourly mean wind speed at a 10-m height from the ground, *<sup>x</sup>* <sup>=</sup> \_\_\_\_\_\_\_\_\_\_ <sup>1200</sup> *<sup>n</sup> <sup>V</sup>* and *k* is the roughness parameter. As a result, the equation for the Wind Force PSD is plotted as the factor vs. frequency graph in Strand7 and shown as **Figure 10**.

**Figure 10.** Factor vs. frequency graph for spectral response wind analysis.

**Figure 10** indicates that the wind load factor changes with wind frequencies and the largest wind load factor occurs when the wind frequency is approximately 0.0045 Hz. Based on the factor vs. frequency graph, the natural frequency of the bridge and applied wind pressure, the "Spectral Response Solver" is run and the result is calculated by the square root of the sum of the squares (SRSS) method in which the coupling among different modes is neglected. In addition, 5% modal damping is applied in the analysis. The result of transverse displacement is shown in **Figure 11**.

The result shows that a maximum transverse deflection of 32.4 m occurs at the mid-span, which is greater than the transverse deflection of 30.9 m obtained from linear static analysis. This phenomenon is reasonable because when the bridge natural frequencies coincide with the heavily factored wind frequencies, the wind impact is severely magnified. As the 32.4 m transverse deflection exceeds the AS5100 limit of 6.3 m, the serviceability criterion is not satisfied. The reason is that the out of plane stiffness of the bridge is insufficient to resist wind forces in this super long bridge. Therefore, further approaches are necessary to increase the lateral stiffness such as increasing the deck width and increasing the depth of the truss system.

#### **6.5. Carbon fibre cost**

**6.4. Spectral response analysis**

**Figure 9.** Frequencies vs. nodal displacement (Dx

*Su*

Strand7 and shown as **Figure 10**.

where *Su*

22 Bridge Engineering

The PSD curve (Davenport's equation) can be expressed as:

wind speed at a 10-m height from the ground, *<sup>x</sup>* <sup>=</sup> \_\_\_\_\_\_\_\_\_\_ <sup>1200</sup> *<sup>n</sup>*

**Figure 10.** Factor vs. frequency graph for spectral response wind analysis.

The linear elastic response of a super-long bridge subjected to a particular wind loading in Australia can be assessed by the "Spectral Response Solver" in Strand7, where the input for dynamic wind analysis can be expressed in terms of Power Spectral Density (PSD) curves [3].

) at the mid-span.

(*n*) = 4 *k V*<sup>2</sup> *<sup>x</sup>*<sup>2</sup> \_\_\_\_\_\_\_\_\_\_\_\_

a result, the equation for the Wind Force PSD is plotted as the factor vs. frequency graph in

*n* (1 + *x*2) \_\_4 3

(*n*) is the wind speed power spectral density, *n* is the frequency, *V* is the hourly mean

(21)

*<sup>V</sup>* and *k* is the roughness parameter. As

Standard and ultra-high stiffness carbon fibres are mainly made for high-tech industries like the aerospace industry. They are very expensive and used in specialised applications such as aerofoils. The price for the ultra-high stiffness is \$2000 USD per kg [15], whereas standard carbon fibre was \$22 USD per kg in 2013 [15]. Currently, ultra-high stiffness is not economical for civil infrastructure. However, **Figure 12** shows the forecast cost of standard carbon fibre. The cost in 2017 is approximately \$12 USD per kg, and it has dropped significantly compared to the price in 2013. **Figure 12** shows that the decreasing price trend could be approximated to an exponential function as:

$$\text{cost} = k \times e^{-0.187 \text{year}} \tag{22}$$

where k depends on the year of interest. Based on the same trend, in 2050, the cost of standard carbon fibre would be \$0.02 USD per kg and the price of carbon fibre composite would be \$1.26 USD per kg, which are even cheaper than the price of steel now of \$1.60 USD per kg

**Figure 11.** Transverse deflection contour under wind load (spectral response analysis).

with more optimised structural members, section sizes and geometries are recommended to

, Qile Gao1

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

, Hannah Blum1

, Xu Wang1

, Yang Hu1

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

,

and

25

reduce the vertical deflections as well as the total cost of the bridge.

Faham Tahmasebinia1,2\*, Samad Mohammad Ebrahimzadeh Sepasgozar<sup>3</sup>

\*Address all correspondence to: faham.tahmasebinia@sydney.edu.au

bridges. Engineering Structures. 2000;**22**(12):1699-1706

[3] Strand7 v2.4.6. Sydney, Australia: Strand7 Pty Limited; 2015

AIP Publishing; 2016, August. p. 020005

, Fernando Alonso-Marroquin1

1 School of Civil Engineering, The University of Sydney, Sydney, NSW, Australia

2 School of Mining Engineering, The University of New South Wales, Sydney, NSW,

3 Faculty of Built Environment, The University of New South Wales, Sydney, NSW,

[1] Clemente P, Nicolosi G, Raithel A. Preliminary design of very long-span suspension

[2] Shama Rao N, Simha TGA, Rao KP, Ravi Kumar GVV. Carbon Composites are Becoming

[4] Game T, Vos C, Morshedi R, Gratton R, Alonso-Marroquin F, Tahmasebinia F. Full dynamic model of Golden Gate Bridge. In: AIP Conference Proceedings, Vol. 1762(1).

[5] Zhang XJ. Mechanics feasibility of using CFRP cables in super long-span cable-stayed

[6] Yang Y, Wang X, Wu Z. Evaluation of the static and dynamic behaviours of long-span suspension bridges with FRP cables. Journal of Bridge Engineering. 2016;**21**(12):06016008

[7] ACP Composites Inc. Mechanical Properties of Carbon Fiber Composite Materials, Fiber/Epoxy resin (120°C Cure). [Online]. 2010. Available at: https://www.acpsales.com/ upload/Mechanical-Properties-of-Carbon-Fiber-Composite-Materials.pdf [Accessed: 29

[8] Standards Australia. S4100.2:2016 Steel Structure. Sydney, Australia: Standards Australia;

Competitive and Cost Effective. 2014. White paper from www.infosys.com

bridges. Structural Engineering and Mechanics. 2008;**29**(5):567-579

**Author details**

Kakarla Raghava Reddy1

Zhongzheng Wang1

Australia

Australia

**References**

June 2017]

2016

**Figure 12.** Carbon fibre cost forecast (USD).

[15]. Therefore, carbon fibre could be widely used in civil construction, and this design of a super-long-span bridge may be cost-effective to construct in 2050.
