Solution | Suspension Bridges

1. What is a Suspension Bridge?

A suspension bridge is referred to a type bridge supported by cables. This type of bridge has been with mankind since ancient times. Today’s large and magnificent suspension bridges were made possible through the establishment of structural analysis methods, material developments, construction methods, and computer technology developments. Suspension bridges are one of the most beautiful special bridges, and are considered one of the types of bridges many structural engineers dream to design.

Fig. Suspension bridge

2. Planning of Suspension Bridges

A. Components of a Suspension Bridge

A suspension bridge is composed of the following members:

- Girder

- Main cable

- Pylon

- Suspender

- Anchorage

- Saddle

Fig. Components of a suspension bridge

B. Types of Suspension Bridges

Today’s suspension bridges can be classified by the following criteria:

a. Girder Type: 2 hinged stiffening, 3 hinged stiffening, Continuous

b. Cable anchor method: Externally-anchored type, Self-anchored type

c. Cable and hanger method: Vertical suspenders, Diagonal suspenders, Combined suspension & cable-stayed system

B-1. Classification according to Girder Type

The classification according to the girder type is based on the degree of freedom of the suspension bridge girder. The 3 hinged stiffening girder type is interpreted as a statically determinate structure, and the 2 hinged stiffening girder and continuous girder type are interpreted as statically indeterminate structures. Continuous girder types are used when external loads are large, such as in road rail bridges, because they increase the stiffness of suspension bridges and reduce the amount of deflection.

Fig. 2hinged stiffening girder, 3 hinged stiffening girder, and continuous girder

B-2. Classification according to Cable Anchoring Method

Externally-Anchored Type

An earth-anchored suspension bridge is a type of bridge in which the main cables are anchored on large concrete blocks, or on the ground, located at the ends of the bridge. External loads applied to suspension bridges are transferred to the suspenders main cables anchorages & pylons and finally to the ground.

Fig. Externally-anchored suspension bridge

Self-Anchored Type

A self-anchored suspension bridge is a type of bridge supported by the main cables anchored to the girder. External loads applied to suspension bridges are transferred to the girder through the suspenders main cables pylons and anchorage inside the girder. Therefore, unlike earth-anchored types, girders behave as bending and compression members.

Fig. Self-anchored suspension bridge

B-3. Classification according to Cable and Suspender Type

Suspenders/Hangers of suspension bridges are usually used with vertical suspenders, and diagonal suspenders can be used to increase the damping on bridges. However, an evaluation of slacking and early fatigue due to the large tensile forces is required. In order to take advantage of cable-stayed bridges and suspension bridges, a hybrid bridge system, in which a cable-stayed system and suspension system are used together, can be implemented.

Fig. Golden Gate Bridge with vertical suspenders
Fig. Bosphorus Bridge with diagonal suspenders
Fig. Yavuz Sultan Selim Bridge, Hybrid cable-stayed and suspension bridge

3. Main Components of Suspension Bridges

A. Stiffening Girder

Stiffening girders of suspension bridges are longitudinal structures that support or distribute vehicle loads. Furthermore, since the stiffening girders are supported by cables, aerodynamic stability is required. In the past, I-girders were mostly used for stiffening girders, but later they were developed into truss structures due to aerodynamic stability problems, and most recently been developed into box-shape cross-sections.

A-1. Truss Girder

Truss girders are proposed for stiffening girders because plate I-girders are disadvantageous with regards to aerodynamic stability. One example in which plate I-girders were used is the Tacoma Narrows Bridge, which is famous for its collapse due to aerodynamic instability. Truss girders can increase the torsional stiffness of suspension bridges by raising the vertical height of the girder and installing horizontal lower bracings. Furthermore, the top and bottom layers of the girder can be used by taking advantage of the height. However, truss girders have large drag due to their heavy weight and long span.

Fig. Truss girders of suspension bridges

A-2. Box Girder

Box girders are cross-sectional stiffening girder types developed to improve the shortcomings of truss-type girders. Box girders have box shaped with orthogonal anisotropic reinforced sheet materials closed in a streamlined fashion. Compared to truss type girders, box girders are lighter and have closed shapes, resulting in high torsional stiffness. Furthermore, the streamlined shapes cause the girders to have low drag.

Fig. Great Belt Bridge and Cross-section of the bridge

A-3. Multi-box Girder

As bridges get longer, it is necessary to secure the torsional stiffness of girders in order to resist aerodynamic loads. This means that it is important to optimize the shape of girders in order to increase the limit wind speed that causes the girder to flutter. Multi-box girders are girder types that secure aerodynamic stability in modern long bridges. Multi-box girders are low in height and light in weight, which reduces the size of cables, pylons/towers, and anchorages, leading to a much economical bridge design.

Fig. Yi Sun Sin Bridge and Cross-section of the bridge

B. Main Cable

The main cables used in suspension bridges are tension members, such as ropes, wires, chains, etc., that cannot resists bending or compression, and can only support axial tension. In general, tensile strength of 1,600 ~ 1,800MPa is used for the main cables, but recently, cable steel wires for bridges with tensile strength of 2,200MPa have been developed. Since parallel cables have greater strength than structural steel, the cross-sectional area of the cables is reduced, and thus, secondary stresses, manufacturing errors, and the amount of main cables are significantly reduced.

Cable construction method is mainly divided into Air Spinning method (hereinafter referred to as AS method) and Prefabricated Wire Strand (hereinafter referred to as PWS method).

B-1. Air Spinning

The AS method uses the cable Hauling system to construct cables in wire units. Wires are formed in strand units at the construction site and constructed as main cables. This method has the advantage of reducing the size of the anchorages. However, wires are sensitive to wind loads and the construction period is longer than wires constructed using the PWS method.

Fig. Air spinning method

B-2. Prefabricated Wire Strand

The PWS method is a method of making a main cable by withdrawing it in strand units. This method shortens the construction period because construction site work is simplified compared to the AS method. Additionally, strands are manufactured in controlled environments, so it is good in terms of quality control. However, the cost of manufacturing and transporting the strands is rather high, and since they are manufactured in strand units, the size of the temporary facilities, such as catwalk towers, can be relatively large.

Fig. Prefabricated wire strand method

C. Suspender/Hanger

Suspenders are cables that connect the main cables to the girders. There are two main types of suspenders: Center Fit Rope Cores (CFRC) and Parallel Wire Strands (PWS). The CFRC hanger (suspender) system is a method of placing high-strength galvanized steel wires twisted in a spiral shape on top of the band of the main cable and fixing the bearing plate at the saddle-type reinforced girder hanger anchorage. The PWS hanger system is a method of pin-anchoring high-strength galvanized steel wires that are tied together parallelly, forming a hanger rope that is covered by Polyethylene, to the cable band sides and the reinforcing girder sides, respectively.

Fig. Section of hanger cables (PWS, CFRC)

There are two types of connections between the girders and suspenders for the main cable: a wrapping method and a pin connection method.

Fig. Suspender connection types

Special types of suspenders are located at the center of any suspension bridge. These are used to restrict the relative displacement between the girders and main cables in order to suppress the deformation in the longitudinal direction of the girders, and alleviate the deflection angle of the suspenders in the lateral direction. There are mainly two types of special suspenders: center stay types and center lock types. Center stays are prestressed cable stays that connect the girder to the main cable. This type of cable stay is suitable for suspension bridges with a main span of 1,000m or less, assuming fracture during earthquakes. Center lock is a structure that connects the girder to the main cable with a steel frame. This structure can resist axial forces, shear forces, and bending. Furthermore, center locks have structures that can withstand earthquakes and are suitable for suspension bridges with long spans.

Fig. Center stay & Center lock

D. Cable Band

Cable bands are members that connect the main cable and the hanger cables. The cable bands wrap the main cable and are fastened by using cable band bolts. These bolts can be fastened horizontally or vertically as shown in the figure below. Horizontally fastened cable band bolts have an advantage in terms of maintenance because they prevent water infiltration, while vertically fastened cable band bolts have the advantage of having fewer bolts for fastening the cable bands, leading to a more economical design.

Fig. Cable bands

E. Saddle

Saddles rest on top of the pylon and anchorage, and directly support the main cable. Its mechanical role is to transfer the loads from the main cable to the pylons and anchorages. Saddles installed on pylons are called pylon saddles, and saddles installed on anchorages are called splay saddles. For pylon saddles, setting the radius of curvature of the saddles is very important. The radius of curvature should be determined in consideration of the bending stresses of the cables and the contact pressures between the cables and the saddles. In the case of splay saddles, the cables can be fixed to the anchorages in a radial shape. Furthermore, when designing the saddles, the horizontal and vertical curvatures of the strand must be properly calculated.

Fig. Pylon saddle & Splay saddle

F. Pylon

Pylons of suspension bridges transmit the loads from the main cable to the ground through the foundations. Stones were the first materials to be used for pylons, but nowadays, materials such as steel and concrete are mostly being used. The shape of the pylon is limited in cross-sectional shape due to the limitations of the construction method, and most of the shapes follow a pattern. The Yeongjong Bridge in Korea has a diamond-shaped pylon, but due its narrow tower top, a three-dimensional main cable was applied. Furthermore, suspension bridges with one main tower can diversify the shape of the main pylon to emphasize its aesthetic appearance. In the table below, steel pylons and concrete pylons are briefly compared:

Classification	Steel Pylon	Concrete Pylon
Structural Integrity	Buckling stability analysis required. Aerodynamic stability analysis required Good earthquake resistance due to light weight	Advantageous to secure required stiffness due to its high rigidity. Good aerodynamic stability. Poor earthquake resistance due to heavy weight.
Constructability	Difficulty in correcting construction errors. Quality assurance through controlled environments. Short construction periods.	Easy to correct construction errors. Quality control required due to on-site installation. Long construction periods.
Durability and Maintenance	Poor durability in coastal environments. Repainting required for maintenance.	Good durability in coastal environments Easy maintenance.

Fig. Széchenyi Chain Bridge (stone)

Fig. Golden Gate Bridge (steel)

Fig. Yi Sun Sin Bridge (concrete)

Fig. Yeongjong Grand Bridge (steel)

Fig. Oakland Bay Bridge (steel)

Fig. Gogunsan Bridge (concrete)

G. Anchorage

Anchorages are important structures that transmit the horizontal and vertical forces of the main cable to the foundations. The types of anchorages are classified into gravity-type anchorages, tunnel-type anchorages, and rock anchorages. Gravity-type anchorage consists of a method of resisting the loads from the cables with the self-weight of the foundation and anchor frame. Many suspension bridges use gravity-type anchorages. Tunnel-type anchorage is a method of resisting the loads of the cables by using the shear forces of the outer circumference of the steel frame and the pressure of the plug body. Rock anchorage is a method of resisting the loads of the cable by using the weight, adhesion, and frictional resistance of rock wedges. This method is used in areas with good rock formations.

Fig. Anchorage types

4. Schematic Design Process

Unlike other types of bridges, there are many factors to be considered in advance in the design of suspension bridges. For example, extensive review is needed in the following factors: selection of the shape of suspension bridges, review of girder cross-section in terms of aerodynamics, structural planning considering the construction method, and maintenance plan. Suspension bridges are often used as memorial structures due to their size and appearance, so the entire landscape, including temporary construction sites, must be reviewed in advance. The schematic design process of suspension bridges is as follows:

Fig. Schematic design process of suspension bridges

5. Structural Analysis of Suspension Bridges

Structural analysis of suspension bridges is performed by conducting the displacement method using a frame model consisting of axis lines for the pylons, reinforcement girders, and cables. The cables, which are uncompressed members, can be modeled as truss elements. In this case, compression forces may occur when live loads are applied. These compressive forces only reduce the tensile forces of the cables, and the compressive forces must not be applied to the entire structural system. Furthermore, since the tension and elongation of the cables, due to the cables’ sag, are not in a linear relationship, non-linear characteristics must be considered.

A. Initial Linear Analysis

The initial linear analysis is an analysis that identifies what kind of behavior the structure shows when all processes are finished and the structure is completed. The final stage of the suspension bridge is in equilibrium with respect to the structure’s own weight. This is referred to as the initial equilibrium state of the suspension bridge, and calculating the coordinates and tension of the main cable at this time is called the initial equilibrium state analysis. The initial linear analysis of suspension bridges is an analysis of the behavior of the structure under additional loads, including the initial equilibrium state analysis. Suspension bridges exhibit considerable nonlinearity in the construction stage due to their behavioral characteristics; however, they exhibit linear behavior for additional loads (vehicle loads, wind loads, etc.) under the final stage in which sufficient tension is introduced for the main cables and suspenders. Therefore, the tension of the main cables and hangers(suspenders) introduced in the initial equilibrium is converted into geometric stiffness, enabling linear interpretation of additional static loads. This method of linearized analysis by converting the member forces generated in the initial equilibrium state into geometric stiffness is called the linearized finite displacement method. The linearized finite displacement method is applied to the final stage analysis since a sufficient degree of solution can be obtained. This initial linear analysis is carried out to calculate the shape at completion, and to calculate the shape of the main components such as cables, hangers, and reinforced girders.

B. Global Structural Analysis

Unlike the initial linear analysis for determining the initial shape of the structure due to its self-weight, the global structural analysis is intended to examine the design of the main components of the structure and the stability during use. Therefore, in addition to dead loads, the analysis is carried out by combining different loads such as live loads, wind loads, temperature loads, earthquake loads, and differential settlements.

Fig. Global structural analysis

C. Construction Stage Analysis

The construction stage analysis is carried out to check the cross-sectional forces for safety check of major components such as cables, pylons, reinforcement girders, etc., and to examine the setback amount of saddles. In the construction stage analysis, the displacements at each stage are large, so the large displacement theory (geometric nonlinear theory), which constitutes the equilibrium equation, should be applied to the shape after deformation in the structural analysis. The construction stage analysis of suspension bridges is performed by backward construction stage analysis, which analyzes the construction procedure in reverse order in the initial equilibrium state of the final stage. In other words, using the geometric shape and initial tension in the initial equilibrium state as a reference model, members added to each construction stage are removed, and the self-weight of the removed members is loaded in the opposite direction of gravity.