Cable-Stayed Bridges

Solution

1. What is a Cable-Stayed Bridge?

A cable-stayed bridge is a cable supported bridge in which one or multiple pylons are installed in the middle of the bridge and girder segments are connected to the pylons by a cable. In cable-stayed bridges, the shape of pylons, the shape of girders, and the cable arrangement can be freely designed; therefore, various structural systems can be applied. For example, adjusting the tension of the cable forces can reduce the size of the bending moment of the girder. This allows for a more economical design. Furthermore, different cable arrangements and shapes for pylons can be planned for a more aesthetic bridge design suitable for the surrounding environment. However, even with various structural advantages, only a small number of cable-stayed bridges were designed and built in the past due to limitations in materials and construction methods. Today, the emergence of high-strength cables, the advancement of structural analysis software, the establishment of wind-resistant design methods through wind tunnel tests, and the development of construction technology have placed cable-stayed bridges, along side with suspension bridges, responsible for the future of long-span bridges.

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  • Fig. Cable-stayed bridge (Incheon bridge, Korea)

2. Components of a Cable-Stayed Bridge

The main components of a cable-stayed bridge are as follows:

  • Pylon/Tower

  • Girder/Deck

  • Cable stay

  • Cable Anchorage

  • Support system

 

A. Pylon/Tower

Pylons, or towers, play the role of supporting the cables and transferring the loads transmitted through the cables all the way to the ground. The shape of the pylons/towers can be freely planned according to the shape of the cable stays. If cable stays are arranged on a single plane, different shapes of pylons/towers such as single column types, A-types, reverse Y-types, and diamond types can be used. If cable stays are arranged on a double plane, a variety of pylon/tower shapes can be used except for the single column type. The most representative shapes of pylons/towers can be found in the figures below. Additionally, pylons are designed in various shapes to emphasize aesthetics while providing structural integrity.

 

  • Fig. H-shape (Seohae Grand bridge)

  • Fig. A-shape (Severinsbrücke bridge)

  • Fig. Reverse Y-shape (Guadiana international bridge)

  • Fig. Diamond shape (New cooper river bridge)

  • Fig. I-shape (Stonecutters bridge)

  • Fig. X-shape (Octávio Frias de Oliveira bridge)

B. Girder/Deck

Girders or decks of cable-stayed bridges can be designed using various shapes and materials. Typical examples are steel girders, steel composite girders, and concrete girders. Alternatively, there can be different types of girders for the main span and the approach span. This is often used to increase the length of the main span by taking advantage of concrete being heavier than steel. The shape of the girder should be carefully planned because the cable arrangement method, spacing, anchorage design, analysis technique, and construction method are determined by what kind of girder is planned.

 

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  • Fig. Classification of griders

B-1. Steel Girder

Steel girders are one of the oldest types of girders used on cable-stayed bridges. These types of girders and decks are made entirely out of steel. The shape of the girder changes to secure torsional stiffness and sectional stiffness according to the shape of the cable arrangement. Since steel is lighter than concrete, steel girders can be used to plan for long-span bridges. However, steel girders must be reviewed for buckling since they are weak against the compressive forces caused by the cable stays.

 

Box Girder

Box girders are composed multiple stiffeners and a closed box with single/multiple cells. The shape of the box has high torsional stiffness, providing excellent aerodynamic stability. Furthermore, due to its high torsional stiffness, it has freedom in regards to its cable arrangement. Therefore, the cable arrangement can be freely planned as a single plane or double plane.

 

  • Fig. Bridges single cell box girder (New Queensferry Crossing)

Twin Box Girder

Twin box girders have boxes at both ends of the girder, with crossbeams and multiple stiffeners placed between them. The double-plane cable arrangement is often proposed to anchor cable stays at the girder. The double-plane cable arrangement suppresses torsional deformation of the cables, so the shape of the twin box girder along with the cable arrangement provide excellent aerodynamic stability.

 

  • Fig. Twin box girder (Big Obukhovsky bridge)

B-2. Steel Composite Girder

After the late 1960s, reinforced concrete decks or prestressed concrete decks were used, and steel composite girders started to be implemented on cable-stayed bridges. In terms of material properties, steel is strong in tension and concrete is strong in compression; therefore, a proper synthesis between these two materials produces a lightweight and durable girder.

 

Edge I Girder

Edge I girders consist of two main girders located at both ends and a number of crossbeams, stringers, stiffeners, and concrete slabs. Edge I girders have a relatively simple cross-sectional configuration, so they are relatively light and have low steel content, making them economically advantageous. However, since the anchorages are exposed, special maintenance is required. Furthermore, torsional and flexural stiffness of the cross-section is small, so aerodynamic stability as well as lateral buckling stability must be carefully examined.

 

  • Fig. Edge I girder

Twin Box Girder

Twin box girders consist of two box girders, crossbeams, stiffeners, and concrete slabs. Box-shape cross-sections have great torsional and flexural stiffness, so they have excellent aerodynamic stability and lateral buckling resistance. Since the cables are anchored inside the box, sufficient space is required inside the box for installation and maintenance.

 

  • Fig. Twin box girder

Truss Girder

Truss girders are composed of truss type main girders and concrete slabs. The shape of the truss makes it possible to assemble small members together to achieve a high stiffness. Single members of truss girders are relatively small compared to other member types, making them advantageous in terms of transportation, manufacturing, and construction. If there is enough space, the carriageway can be installed on the top and bottom chords.

 

  • Fig. Truss girder

B-3. Concrete Girder

Concrete girders have good durability and are strong in compression, enabling efficient cross-sectional planning of compressive forces for cable stays. A concrete girder has a shorter span compared to a steel girder because of its heavier weight. Concrete girders should take into consideration the behavior caused by shrinkage, creep, etc., due to their material properties. In the early days, concrete girders were not used for cable-stayed bridges because there were many failure cases during construction. Currently, the design and construction of cable-stayed bridges with concrete girders are being actively conducted due to the development of new cable stay systems, high strength materials, and construction technology.

Edge Girder

Edge girders consist of main girders, slabs, and crossbeams at both ends of the girder. Since anchorages can be secured at both ends of the girder, double-plane cables can be applied. The height of the girder is low, so it has a slim shape. And the cable anchorage is not exposed, so it has a good appearance. Furthermore, due to the characteristics of concrete, edge girders are durable and provide ease of maintenance. However, in terms of the characteristics of the girder shape, torsional stiffness and flexural stiffness are small, and aerodynamic stability is required.

 

  • Fig. Cross-section of Helgeland bridge

  • Fig. Helgeland bridge

Box Girder

Box girders have the advantages of concrete materials. Furthermore, since the box shape has high torsional stiffness, it has excellent aerodynamic stability, and cables can be arranged in single or double-planes. However, the weight of the girder itself can increase the size of the substructure. To enhance economic feasibility while taking advantage of the box girders, part of the girder sections can be replaced with steel struts or diaphragms. By installing struts on the inside and outside of the girders, the weight of the girders can be reduced, enabling efficient cross-sectional planning. If struts are installed, detailed review of the anchorages and landscapes is additionally required.

 

  • Fig. Cross-section of Skarnsundet bridge

  • Fig. Skarnsundet bridge

  • Fig. Cross-section of Centennial bridge

  • Fig. Centennial bridge

 

C. Cable Stay

Cables used on cable-stayed bridges are tension members that cannot resist bending or compression, such as ropes, wires, and chains, and can only support axial tension. The tensile strength of the cables is usually around 1,600 to 1,860 MPa, but with advances in technology, cables with higher tensile strength are being developed.

 

C-1. LCS (Locked Coil Strand)

Locked Coil Strand (LCS) are composed of spirally braided wires that composes the central core, and trapezoidal or z-shaped cross-sectional wires that wrap around the outside in several layers. The elastic modulus, tensile strength, and fatigue resistance are inferior compared to other cables. Furthermore, LCS is currently not being used because corrosion prevention is difficult, and packaging and transportation are expensive.

 

  • Fig. Section of locked coil strand

C-2. PWS (Parallel Wire Strand)

Parallel Wire Strand (PWS) is parallel wires bundled together in the shape of a circle or hexagon coated in polyethylene. The cross-section of the cables is small, providing excellent aerodynamic stability. PWS is manufactured in control environments, so quality control is simple. And if ease transportation is available, the construction period can be shortened. However, since the strands are tensioned together as a bundle, a heavy strand jack is required. Furthermore, since the anchorage system is integrated, it is difficult to inspect when the anchorage system is damaged.

 

  • Fig. Section of parallel wire strand

C-3. MS (Multi Strand)

Multi Strands (MS) consist of bundles of strands consisting of seven wires. MS cables are tensioned individually so a light strand jack is required. Furthermore, individual replacement of strands is relatively easy; however, since the cable cross-section is relatively large, aerodynamic stability becomes inefficient.

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  • Fig. Section of multi strand

D. Cable Anchorage

 

D-1. Cable Anchorages at Girders

Cable anchorages located on the girders anchors the cables. At the anchorages, the tensile forces on the cables are divided into horizontal and vertical components, which are then transmitted to the girders. The horizontal components of the tensile forces generate axial forces in the girder, and the vertical components of the tensile forces create shear forces in the girder. The structure of the anchorage is determined by various ways such as the cable arrangement (positional relationship between the transverse arrangement and the main girder), the number of strands, the shape of the main girder and the slab system, the structure of the cable cross-section, the magnitude of the tensile forces and the implementation method, and etc.

 

 

D-2. Cable Anchorages at Pylons

The cable anchorages of pylons/towers are important structures that have the role of transferring the locally concentrated cable tensile forces directly to the pylons/towers. The structure of the anchorages considers various situations such as the cable arrangement, the shape of the socket and the number of strands, the structure of the pylon/tower, the cable jacking operation, and the method of introducing and adjusting the tensile forces.

 

Steel Pylon Anchorage

- Saddle type

- Anchor girder type

- Bearing plate type

- Pin socket type

 

Concrete Pylon Anchorage

- Saddle type

- Overlapped type

- Inside type

- Insider with bracket and link type

 

 

 

E. Support System

The boundary conditions between the crossbeams of a pylon and the stiffened girders affect the behavior of the entire bridge structure. The boundary conditions are classified into three categories: a floating system without a support, a support system, and a frame system with stiffened girders and pylons.

 

E-1. Floating System

The floating system is a structure that supports the load of the superstructure by additionally installing stay cables instead of omitting the vertical supports. Since the torsional load acting on the main girder can be solved by the axial force on the cable, the main girder structure without torsional stiffness is established, and it is a boundary condition for flexible vertical behavior because there is no support for the pylon.

Furthermore, the negative moment of the stiffening girder near the pylon is reduced, and the crossbeam of the pylon can be excluded by not installing the vertical supports on the pylon; thus, improving maintenance. On the other hand, separate countermeasures and large-scale expansion joints are required for displacements caused by horizontal loads such as earthquakes. Additionally, since there are no supports on the pylons, the vertical loads acting on the cables create much larger fatigue loads.

 

  • Fig. Concept of floating system

E-2. Shoe System

The Shoe Support (bearing) System is a structural system in which stiffening girders and pylons are separated and vertical supports and wind shoes are installed. This system supports the vertical and horizontal reaction forces caused by the vertical supports installed on the top of the pylon crossbeams and the horizontal supports installed on the side of the pylons. Supports are placed on pylons, the vertical loads borned by the cables are relatively reduced. Furthermore, permanent bearings can be installed during the construction stage, but additional restraining devices must be installed for deflection. If the span length is long or the self-weight of superstructure increases, the negative moment tends to be excessive because the deck acts as a continuous beam. Since vertical and horizontal supports are installed on the pylons, it is disadvantageous in terms of maintenance, and it can reduce drivability near the pylons.

 

  • Fig. Concept of shoe system

E-3. Frame System

The frame system is a structural system in which pylon crossbeams, stiffening girders, and piers are integrated and converged together so that they can behave as one. This structural system is easy to maintain because there is no need for bridge supports, and it has excellent wind stability as it does not need to control the displacement in the bridge longitudinal direction during construction. And this system is stable under the construction and service. However, the effect of creep, shrinkage and thermal load should be examined.

 

  • Fig. Concept of frame system

3. Design of Cable-Stayed Bridges

The design of a cable-stayed bridge requires considerable insight as there are many factors to be considered during design, including the many irregularities of the bridge itself. The conceptual review items required for design are as follows:

 

  • Fig. Design steps for cable-stayed bridges

4. Structural Analysis of Cable-Stayed Bridges

When performing structural design of cable-stayed bridges, structural analysis of dead loads as well as structural analysis of live loads, or dynamic loads, such as natural vibration analysis, earthquake load analysis, and wind load analysis must be performed during the final stage. In general, in the design of cable-stayed bridges, the service stage analysis calculates the dimensions of the structure as well as the cross-section and tensile forces of the cables. A typical analysis flow chart of cable-stayed bridges is shown below.

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  • Fig. Structural analysis flow chart of cable-stayed bridges

A. Structural Analysis for the Initial Shape

The structural analysis for the initial shape is performed to optimizing member forces of girders, and pylons, tensile forces of cables, and reaction forces. The analysis is referred to as the introduction of tensile forces to each cable so that the dead loads are balanced with the initial cable tensile forces. The entire model of cable-stayed bridges is a high-order, statically indeterminate structure, so obtaining the initial values required repetitive calculations. Furthermore, since the tension of each cable does not exist as the only solution, different cable tensioning plans can be made for each designer for the same cable-stayed bridge. In particular, in the case of concrete structures, stress is redistributed over time in the final stage due to the effects of creep and shrinkage, leading to deformation of the structure. Therefore, it is also important to determine when the design longitudinal curve is satisfied. These are the three initial value analysis methods:

 

- Zero Displacement Method

- Force Equilibrium Method

- Force Method

 

 

B. Construction Stage Analysis

In order to determine the cable tension introduced during the cable installation in cable-stayed bridges, it is necessary to first determine the initial equilibrium state for the dead loads in the service stage (completed state). Thereafter, the construction stage analysis according to the construction process must be performed.

 

In general, when designing cable-stayed bridges, in the structural analysis of the final stage, the specifications of the structure as well as the cross-section and tension of the cables are calculated. Furthermore, in the construction stage analysis, the installed tension of the cable at each stage as well as the pre-camber of the girder and the construction camber are determined. Through the construction stage analysis, the stress generated in each member is also examined. Moreover, using the review results, the assumed construction sequence and the constructability for the work load are identified in advance, and the optimal construction method is then selected.

 

The construction stage analysis can be classified into backward analysis and forward analysis according to the order of the analysis. In contrast to the construction analysis, backward analysis is a method of performing analysis by removing construction members and loads in the backward direction of construction from structures in which the final stage of the initial equilibrium state is determined. Forward analysis in the other hand is a method of performing analysis in the order in which construction proceeds.