Imagine a steel dragon spanning across rivers, both lightweight and powerful. This is the cable-stayed bridge – a structural marvel that perfectly combines engineering mechanics with architectural beauty. More than just a passage connecting two shores, it stands as a testament to human ingenuity and creativity.

True to its name, a cable-stayed bridge consists of continuous girders (or deck) supported by inclined cables. These cables, resembling harp strings, connect the deck to towering pylons, forming a stable yet graceful whole. From a mechanical perspective, cable-stayed bridges function as elastically supported continuous beam bridges, with their unique configuration offering distinct advantages within specific span ranges.

Among bridge types, cable-stayed bridges excel in spanning capabilities. They particularly shine for spans between 150 to 600 meters, where they outperform cantilever, truss, arch, and box girder bridges in both economic and aesthetic terms. While their spanning capacity doesn't match suspension bridges, their relatively shallow girder depth creates a more visually lightweight appearance. With advancing design and construction technologies, cable-stayed bridges continue to break span records, exemplified by Russia's Russky Bridge with its 1,104-meter main span – currently the world's longest cable-stayed bridge.

The design philosophy of cable-stayed bridges is elegantly efficient. Each component primarily handles either tension or compression forces, maximizing material usage. The stay cables provide elastic support to the deck, effectively extending the bridge's span. To bear deck loads, these cables must withstand tremendous tension, which in turn transforms into compression forces within the pylons and main girders. While bending moments and other forces do affect pylons and girders, axial forces typically dominate. Since axially loaded members outperform bending members in efficiency, this explains the structural and economic advantages of cable-stayed bridges.

The concept of cable-stayed bridges dates back to 1595, documented in Machinae Novae. Early 19th century saw several constructions, but it wasn't until the 1950s that they gained popularity alongside truss, arch, and suspension bridges. Early failures stemmed from insufficient understanding of the structural system – particularly inadequate resistance and inability to tension cables properly, causing slackness under various loads. The 1883 Brooklyn Bridge marked significant improvements. Modern cable-stayed bridges emerged in 1950s Germany, with Sweden's Strömsund Bridge (1955) becoming the first modern example. Since then, design and construction techniques have advanced rapidly, making cable-stayed bridges a global phenomenon.

Cable-stayed bridges can be categorized in multiple ways, with cable arrangement being the most common method.

Based on longitudinal arrangement, cable-stayed bridges fall into four types: single cable, fan, modified fan, and harp configurations. While these systems show minimal differences in overall performance – especially for long spans – each offers unique characteristics.

• Single Cable System: This rare configuration uses single cables connecting pylon to deck. Germany's Neckar River Bridge exemplifies this type. Early designs with fewer cables led to higher construction costs, while modern bridges favor more cables for better economics.
• Fan System: All cables converge at or pass through the pylon top. This structurally superior design minimizes pylon bending moments. The steep cable angles efficiently handle vertical loads while imposing minimal axial forces on girders. However, concentrated forces at pylon tops can cause corrosion and fatigue issues, requiring complex anchorages and additional pylon reinforcement.
• Modified Fan System: Developed to address fan system challenges, this variation spaces cables sufficiently near the pylon top for better force distribution, easier maintenance, and individual cable inspection. Hong Kong's Ting Kau Bridge successfully employs this system.
• Harp System: Featuring nearly parallel cables, this arrangement creates a visually orderly pattern. The lower starting point of cable anchors allows earlier construction commencement. The Hong Kong-Zhuhai-Macao Bridge's Jiuzhou Channel Bridge showcases this elegant system.

Transversely, cables can be arranged in: a single central plane, dual edge planes (vertical or inclined), or triple planes connecting centerline to both edges. This arrangement impacts structural behavior, construction methods, and architectural expression. Dual-plane systems are most common, though single central planes work when using torsion-resistant box sections. For exceptionally wide decks or combined rail-road bridges, triple-plane systems may be employed.

Cable-stayed bridges can be designed with single, double, triple, or multiple spans. Three or two cable-supported spans are more typical, as cables and anchor piers are crucial for pylon stability. Single-pylon examples include Rotterdam's Erasmus Bridge and Tokyo's Central Bridge. For spans exceeding three, the main challenge involves insufficient longitudinal restraint at intermediate pylon tops. Solutions include: increasing pylon stiffness (using A-frame supports), connecting pylon tops with horizontal ties, adding stabilizing cables between pylons, incorporating midspan ties, or using crossing cables extending about 20% beyond midspan – as demonstrated by Ting Kau Bridge's 464.6-meter longitudinal stabilizing cables.

Cable-stayed bridges rely on three fundamental elements that work in concert: cables, pylons, and decks.

As critical load-bearing members, modern cables have overcome early deficiencies in anchorage systems, materials, and corrosion protection. Current options include: pre-fabricated locked-coil strands (with 1,770 N/mm² tensile strength), pre-fabricated spiral strands (using 5mm wires at 1,570/1,770 N/mm²), bar cables (1,230 N/mm²), parallel wire strands (7mm galvanized wires at 1,570 N/mm²), parallel strand cables (15.2/15.7mm galvanized strands at 1,770 N/mm²), and advanced composite cables.

Pylons may be single columns through deck centers or offset for curved bridges. Dual-column arrangements (with or without crossbeams) create H-frame, A-frame, inverted Y-frame, diamond, or double-diamond configurations. Early steel pylon designs prioritized fast fabrication but faced buckling concerns. Modern trends favor reinforced/prestressed concrete for cost efficiency, despite greater weight. Concrete technology advancements now enable complex pylon forms. Typical pylon heights range from 0.2-0.25 times main span length, with cable angles between 25-65 degrees maintaining efficiency. External factors like airport proximity may dictate lower pylons, as seen in Kawasaki's planned bridge near Haneda International Airport.

Unlike suspension bridge decks, cable-stayed decks must resist bending moments from self-weight/live loads and axial forces from cable horizontal components, allowing varied cross-sections:

• Steel Decks: Favored in early designs for high strength-to-weight ratios and long inter-cable spans. Orthotropic steel decks combine thin wearing surfaces with longitudinal stiffeners supported by transverse floor beams. The Kurushima-Kaikyo Bridge exemplifies how reduced deck weight enables economical long-span designs.
• Concrete Decks: Suitable for medium spans using precast or cast-in-place reinforced/prestressed concrete. While cost-effective, increased weight demands larger cables, pylons, piers, and anchorages. Single-plane cable systems require torsion-resistant box sections, whereas multi-cable systems permit open beam sections with high torsional rigidity for very long spans.
• Composite Decks: Combining steel and concrete advantages, composite sections offer safety and economy. Options include steel orthotropic decks with concrete slabs or mixed configurations – heavier concrete/composite sections for side spans (reducing upward deflection) and lighter steel sections for main spans (minimizing downward deflection).

Modern cable-stayed bridge analysis requires finite element methods. The "fishbone" model typically represents pylons, decks, and cables, with specialized elements accounting for cable sag effects using modified elastic modulus. Stage-by-stage analysis is essential to simulate construction sequencing and load redistribution. Both linear and nonlinear analyses should be performed, complemented by dynamic analysis to determine natural frequencies and vibration modes.

Cable-stayed bridges owe their success to efficient erection procedures, primarily:

• Temporary Support Method: Deck erection occurs on temporary supports before cable installation and tensioning. This straightforward approach requires consideration of support needs and navigation clearance during construction.
• Free Cantilever Method: The preferred modern technique where cables directly support the deck during construction. The bridge remains cantilevered until deck completion. This method demands careful safety verification, especially during maximum cantilever conditions before midspan closure.

1. Describe the structural components of a typical cable-stayed bridge and the internal forces they must withstand.
2. Explain possible transverse and longitudinal cable arrangement patterns in cable-stayed bridges.