大跨度缆索支撑桥梁：概念与设计

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"Cable Supported Bridges: Concept and Design" 在桥梁体系中，索缆支撑桥以其跨越大跨度的能力而独树一帜。当前，这类桥梁能够适应200米到2000米（甚至更远）的跨度，覆盖了目前大约90%的跨度范围。对于绝大多数索缆支撑桥，其结构系统可以分为四个主要组成部分： 1. 桥面板（或加强梁）：这是桥梁的主要承重部分，通常由混凝土或钢材制成，用于承载交通荷载。 2. 支撑桥面板的索缆系统：包括主缆和吊索，它们通过张力传递荷载到其他组件。 3. 索塔（或塔架）：支撑索缆系统的高耸结构，通常位于桥的两侧，起到垂直支撑的作用。 4. 锚固块（或锚碇墩）：在桥的两端，垂直和（或）水平地支撑索缆系统，确保整个结构的稳定性。《Cable Supported Bridges: Concept and Design》第三版，由NIELS J. GIMSING和CHRISTOS T. GEORGAKIS编写，来自丹麦技术大学土木工程系。这本书的各个版本分别于1983年、1997年和2012年出版，详细介绍了索缆支撑桥的设计原理和技术。书中可能涵盖了以下关键知识点： - 索缆桥的历史和发展：从早期的设计概念到现代技术的进步，包括新材料和新设计方法的引入。 - 结构分析：深入探讨了桥面板、索缆、索塔和锚固块之间的力学关系，以及如何通过这些关系进行结构优化设计。 - 索缆系统设计：讨论了主缆和吊索的几何形状、材料选择、张力分配以及疲劳和耐久性问题。 - 索塔设计：涉及塔的高度、形状、基础类型，以及在风荷载和地震荷载下的稳定性分析。 - 锚固系统：详述了锚固块的设计，包括锚固方式、应力分布和潜在的滑移问题。 - 施工技术和挑战：如如何安装和调整索缆，以及在复杂地形和环境条件下施工的策略。 - 维护与安全：讨论了定期检查、维护的重要性，以及如何预防和处理可能出现的损伤或故障。 - 实例研究：可能包含了一些具有代表性的索缆桥案例，如金门大桥、悉尼海港大桥等，分析它们的设计特点和建造经验。这本书作为专业教材，不仅对工程师和学者有价值，也为对桥梁工程感兴趣的一般读者提供了深入理解这一独特桥梁类型的机会。通过阅读，读者可以全面了解索缆支撑桥的设计理念、工程实践以及面临的挑战。

The chain support was generally preferred by the British engineers of the nineteenth century and a number of notable

bridges were built, among these the famous Clifton Suspension Bridge, initially designed by Isambard Kingdom Brunel,

but not actually constructed until after his death. The bridge was opened to trafﬁc in 1864 and it comprised a main span of

214 m – an impressive span, considering that the strength-to-density ratio of the wrought steel in the chains was less than

one-ﬁfth of the ratio of modern cable steel (Figure 1.2).

To erect the eye-bar chains, a temporary footway had to be established between the supporting points on the pylon tops

and at the anchor blocks. In the case of the Clifton Suspension Bridge, this temporary footway was supported by wire ropes,

so the principle of cable support was actually applied, although only in the construction phase.

A most unusual bridge based on application of eye-bar chains is the Albert Bridge across the Thames in London

(Figure 1.3). The bridge was built from 1871 to 1873 and it is characterized by combining the cable stayed and the

suspension system. A part of the deck load is transferred to the strong top chain through hangers and the rest is carried by a

number of straight chains radiating from the pylon tops. The system is statically indeterminate to such a degree that it was

impossible with the available tools to calculate forces and moments to get even close to the exact values. Nevertheless the

bridge with its 122 m-long main span is still in service although there are restrictions on the trafﬁc allowed to pass

over it (Figure 1.4).

Chain support was also applied in a number of bridges on the European continent, but here it was to a larger extent

in competition with cable supported suspension bridges. Thus the longest free span in Europe was for several decades

found in the wire supported Grand Pont Suspendu across the Sarine Valley at Fribourg in Switzerland. The bridge was

completed in 1834 and it had a main span of 273 m. In the Grand Pont Suspendu, each of the four main cables was composed

of over 1000 wires, grouped in 20 strands, each assembled on the ground and lifted individually into position. The bridge

was in service for almost a century until it was ﬁnally demolished in 1923.

On a global level, the Swiss span record was beaten in 1849 by the completion of the Wheeling Suspension Bridge across

the Ohio River in the USA. This bridge had a main span of 308 m, carried by a total of 12 parallel-wire cables, six on either

side of the roadway.

The Wheeling Bridge is still in existence, although not in its original version. Five years after its completion, in 1854, a

violent gale blew the bridge down. Subsequently it was reconstructed and later, in 1872, further strengthened by a fan-

shaped system of stays. The principle of strengthening the suspension system with stays was originally introduced during

the construction of the suspension bridge across the Niagara Gorge. This bridge was designed by the famous

bridge designer John A. Roebling, who was born in Germany but emigrated to the United States of America at the

Figure 1.2 Clifton Suspension Bridge (UK)

8 Cable Supported Bridges: Concept and Design

Based on his experience during design and construction of several suspension bridges, and through his investigations

into accidents such as the collapse of the Wheeling Bridge in 1854, Roebling had acquired a profound understanding of the

aerodynamic problem. This is clearly indicated in his own description of the Brooklyn Bridge concept:

But my system of construction differs radically from that formerly practised, and I have planned the East River

Bridge [as the Brooklyn Bridge was initially called] with a special view to fully meet the destructive forces of a

severe gale. It is the same reason that, in my calculation of the requisite supporting strength so large a proportion has

been assigned to the stays in place of cables.

This description proves that Roebling knew very well that a cable stayed system is stiffer than the suspension system, and

the fact that the stays of the Brooklyn Bridge carry a considerable part of the load can be detected by the conﬁguration of the

main cable having a smaller curvature in the regions where the stays carry a part of the permanent load than in the central

region, where all load is carried exclusively by the main cable.

The efﬁciency of the stay cables (Figure 1.7) is clearly demonstrated by the following remark by Roebling: ‘The

supporting power of the stays alone will be 15 000 tons; ample to hold up the ﬂoor. If the cables were removed, the bridge

would sink in the center but would not fall.’

Roebling had started his engineering career at a time when the design of bridges was still more of an art, requiring

intuition and vision, than a science. Therefore, he had to acquire a profound understanding of the structural behaviour of

cable supported bridges through observations and by experience. He gradually learned how to design structures of great

complexity, as he could combine his intuitive understanding with relatively simple calculations, giving adequate

dimensions for all structural elements.

In the case of the Brooklyn Bridge, the system adopted is one of high indeterminateness as every stay is potentially a

redundant. A strict calculation based on the elastic theory with compatibility established between all elements would involve

numerical work of an absolutely prohibitive magnitude, but by stipulating reasonable distributions of forces between

elements and always ensuring that overall equilibrium was achieved, the required safety against failure could be attained.

After Roebling, the next generation of engineers was educated to concentrate their efforts on the calculations, which

required a stricter mathematical modelling. As systems of high statical indeterminateness would involve an insuperable

amount of numerical work if treated mathematically stringently, the layout of the structures had to be chosen with due

respect to the calculation capacity, and this was in many respects a step backwards. Consequently, a cable system such as

that used in the Brooklyn Bridge had to be replaced by much simpler systems.

The theories available for the calculation of suspension bridges in the second half of the nineteenth century were all

linear elastic theories, such as the theory by Rankine from 1858, dealing with suspension bridges where the deck comprised

Figure 1.7 The cable system of the Brooklyn Bridge at the pylon (USA)

Evolution of Cable Supported Bridges 11

two- and three-hinged girders. The theory was the ﬁrst to take into account rationally the interaction between the cable and

the deck. Later, in 1886, the linear elastic theory was further developed by Maurice Levy in his paper, ‘M



emoires sur le

calcul des ponts suspendus rigides’.

Williamsburg Bridge

The trend to let the calculations inﬂuence the layout of the structure is clearly seen in the Williamsburg Bridge, the second

bridge to span the East River in New York (Figure 1.8). Opened to trafﬁc in 1903, this bridge had a main span of 488 m, just

2 m more than the Brooklyn Bridge.

The structural system with unsuspended side spans and only one well-deﬁned, simply supported suspended main span

without any additional stays, clearly shows the strive towards a practicable mathematical model. Also, the extreme depth of

the stiffening truss, one-fortieth of the span, can be seen as a result of the attempt to match the behaviour of the real structure

to agree with the mathematical model that took only linear elastic effects into account (i.e. neglecting the change of

geometry due to node displacements).

That the ﬁnal result will often be less satisfactory when calculations govern the design is well demonstrated by the

Williamsburg Bridge, especially in comparison with the Brooklyn Bridge. In his book, Bridges and Their Builders [57.1],

D. B. Steinman wrote about the Williamsburg Bridge:

With the ungainly tower design and the excessively deep trusses, the structure presents an appearance of angularity

and clumsiness. It marked one extreme of the swing of the pendulum; thereafter there was a reversal of trend, toward

progressively increasing slenderness and grace in the design of suspension bridges.

One feature that the Brooklyn Bridge and the Williamsburg Bridge has in common is the arrangement of the main cables at

midspan in relation to the stiffening truss. In both bridges, the cables pass beneath the top chord of the truss and are led down

to the bottom chord at the centre of the main span. This arrangement is very well justiﬁed from an economic point of view as

the height of towers and the length of hangers, for a given sag of the main cable, are reduced by a distance equal to the depth

of the truss, as illustrated in Figure 1.9. In modern suspension bridges the main cable will in general be positioned

Figure 1.8 Williamsburg Bridge, second bridge to span the East River in New York (USA)

+k+d

Figure 1.9 Position of the main cable in relation to the stiffening truss: (left) position favoured in the early suspension bridges;

(right) position preferred today

12 Cable Supported Bridges: Concept and Design

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