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Simple suspension bridge
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Simple suspension bridge
A simple suspension footbridge in the Zillertal Alps
A simple suspension footbridge in the Zillertal Alps
Descendant
CarriesPedestrians, livestock
Span rangeshort to medium
MaterialRope (fiber), chain, steel wire rope; appropriate decking material
MovableNo
Design effortlow
Falsework requiredNo

A simple suspension bridge (also rope bridge, swing bridge (in New Zealand), suspended bridge, hanging bridge and catenary bridge) is a primitive type of bridge in which the deck of the bridge lies on two parallel load-bearing cables that are anchored at either end. They have no towers or piers. The cables follow a shallow downward catenary arc which moves in response to dynamic loads on the bridge deck.

The arc of the deck and its large movement under load make such bridges unsuitable for vehicular traffic. Simple suspension bridges are restricted in their use to foot traffic. For safety, they are built with stout handrail cables, supported on short piers at each end, and running parallel to the load-bearing cables. Sometime these may be the primary load-bearing element, with the deck suspended below. Simple suspension bridges are considered the most efficient and sustainable design in rural regions, especially for river crossings that lie in non-floodplain topography such as gorges.

Comparison to other types

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A swingbridge at the Hokitika Gorge on the West Coast of New Zealand.

In some contexts the term "simple suspension bridge" refers not to this type of bridge but rather to a suspended-deck bridge that is "simple" in that its deck is not stiffened.[1][2] Although simple suspension bridges and "simple" suspended deck bridges are similar in many respects, they differ in their physics. On a simple suspension bridge, the main cables (or chains) follow a hyperbolic curve, the catenary. This is because the main cables are free hanging. In contrast, on a suspended deck bridge (whether "simple" or not) the main cables follow a parabolic curve. This is because the main cables are tied at uniform intervals to the bridge deck below (see suspension bridge curve).

The differences between these two curves were a question of importance in the 17th century, worked on by Isaac Newton.[3] The solution was found in 1691, by Gottfried Leibniz, Christiaan Huygens, and Johann Bernoulli who derived the equation in response to a challenge by Jakob Bernoulli.[4] Their solutions were published in the Acta Eruditorum for June 1691.[5][6]

A stressed ribbon bridge also has one or more catenary curves and a deck laid on the main cables. Unlike a simple suspension bridge however, a stressed ribbon bridge has a stiff deck, usually due to the addition of compression elements (concrete slabs) laid over the main cables. This stiffness allows the bridge to be much heavier, wider, and more stable.

History

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The simple suspension bridge is the oldest known type of suspension bridge and, ignoring the possibility of pre-Columbian trans-oceanic contact, there were at least two independent inventions of the simple suspension bridge, in the wider Himalaya and East Asian region and in South America.[7]

18th-century rope bridge in Srinagar, Garhwal Kingdom

The earliest reference to suspension bridges appear in Han dynasty records on the travels of Chinese diplomatic missions to the countries on the western and southern fringe of the Himalaya, namely the Hindukush range in Afghanistan, and the lands of Gandhara and Gilgit.[8] These were simple suspension bridges of three or more cables made from vines, where people walked directly on the ropes to cross. Later, they also used decking made from planks resting on two cables.[8]

1952, suspension bridge over Cuanana river, Yosondua, Oaxaca, Mexico.

In South America, Inca rope bridges predate the arrival of the Spanish in the Andes in the 16th century. The oldest known suspension bridge, reported from ruins,[clarification needed] dates from the 7th century in Central America (see Maya Bridge at Yaxchilan).

Simple suspension bridges using iron chains are also documented in Tibet and China. One bridge on the upper Yangtze dates back to the 7th century. Several are attributed to Tibetan monk Thang Tong Gyalpo, who reportedly built several in Tibet and Bhutan in the 15th century, including Chushul Chakzam and one at Chuka.[7] Another example, the Luding Bridge, dates from 1703, spanning 100 m using 11 iron chains.[7]

Jurong Bird Park -rope bridge

Industrial Revolution

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Development of wire cable suspension bridges dates to the temporary simple suspension bridge at Annonay built by Marc Seguin and his brothers in 1822. It spanned only 18 m.[7] However, simple suspension bridge designs were made largely obsolete by the 19th century invention and patent of the suspended deck bridge by James Finley.[9] A late 18th century English painting of a bridge in Srinagar[citation needed], then part of the Garhwal Kingdom, anticipates the invention of the suspended deck bridge. This unusual bridge, built on a floodplain, had suspended deck ramps used to access a simple suspension bridge supported from towers.

Materials

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This type of bridge is known as a rope bridge due to its historical construction from rope. Inca rope bridges still are formed from native materials, chiefly rope, in some areas of South America. These rope bridges must be renewed periodically owing to the limited lifetime of the materials, and rope components are made by families as contributions to a community endeavor.

Simple suspension bridges, for use by pedestrians and livestock, are still constructed, based on the ancient Inca rope bridge but using wire rope and sometimes steel or aluminium grid decking, rather than wood.

Living root bridges in Nongriat village, Meghalaya

In modern bridges, materials used instead of (fiber) rope include wire rope, chain, and special-purpose articulated steel beams.

Living bridges

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In the northeast Indian state of Meghalaya, Khasi and Jaintia[10] tribal people have created living root bridges, which are a form of tree shaping. Here, simple suspension bridges are made by training the roots of the Ficus elastica species of banyan tree across watercourses.[11] There are examples with a span of over 170 feet (52 m).[12] They are naturally self-renewing and self-strengthening as the component roots grow thicker and some are thought to be more than 500 years old.[13][14][15]

In the Iya Valley of Japan, bridges have been constructed using wisteria vines. To build such a bridge, these vines were planted on opposite sides of a river and woven together when they grew long enough to span the gap. The addition of planks produced a serviceable bridge.[16][17]

Design

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In a simple suspension bridge the deck lies on the main cables
In a suspended deck bridge the deck is carried below the main cables by vertical "suspenders"
Comparison of a catenary (black dotted curve) and a parabola (red solid curve) with the same span and sag. The catenary represents the profile of a simple suspension bridge, or the cable of a suspended-deck suspension bridge on which its deck and hangers have negligible mass compared to its cable. The parabola represents the profile of the cable of a suspended-deck suspension bridge on which its cable and hangers have negligible mass compared to its deck.

The very lightest bridges of this type consist of a single footrope and nothing more. These are tightropes and slacklines, and require skill to use. More commonly, the footrope is accompanied by one or two handrail ropes, connected at intervals by vertical side ropes. This style is used by mountaineers and is employed extensively in New Zealand on lesser backcountry walking tracks where examples are referred to as 'three wire bridges'. A slightly heavier variation has two ropes supporting a deck, and two handrail ropes. Handrails are necessary because these bridges are prone to oscillate side to side and end to end. Rarely, the footrope (or footrope plus handrails) is combined with an overhead rope similar to a zip-line or cableway.

In some cases, such as the Capilano Suspension Bridge, the primary supports form the handrails with the deck suspended below them. This makes for more motion side-to-side in the deck than when the primary supports are at deck level, but less motion in the handrails.

Disadvantages connected with simple suspension bridges are very great. The location of the deck is limited, massive anchorages and piers generally are required, and loading produces transient deformation of the deck.[18] Solutions to these problems led to a wide variety of methods of stiffening the deck,[18][19] resulting in several other types of suspension bridge. These include a stressed ribbon bridge, which is closely related to a simple suspension bridge but has a stiffened deck suitable for vehicle traffic.

A very light bridge, constructed with cables under high tension, may approach a suspended deck bridge in the nearly horizontal grade of its deck.

The bridge may be stiffened by the addition of cables that do not bear the primary structural or live loads and so may be relatively light. These also add stability in wind. An example is the 220-meter-long (720 ft) bridge across the river Drac at Lac de Monteynard-Avignonet: this bridge has stabilizing cables below and to the side of the deck.

To reduce twisting motion in response to users a bridge may employ vertical drop cables from each side at the center of the bridge, anchored to the ground below.

Use

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The lightest of these bridges, without decking, are suitable for use only by pedestrians. Light bridges with decking, and sufficient tension that crossing the bridge does not approach climbing, may be used also by pack horses (and other animals), equestrians, and bicycle riders. To walk a lighter bridge of this type at a reasonable pace requires a particular gliding step, as the more normal walking step will induce traveling waves that can cause the traveler to pitch (uncomfortably) up and down or side-to-side. The exception is a stabilized bridge, which may be quite stable.

Simple suspension bridges have applications in outdoor recreation. They are a popular choice for tree-top trails[20] and, where the terrain is suitable, for stream crossings.[21] They may be designed without stabilizing so that the free movement of the bridge provides a more interesting experience for the user.[21]

In French, a rudimentary simple suspension bridge is known by one of three names, depending on its form: pont himalayen ("Himalayan bridge": a single footrope and handrails on both sides, usually without a deck); pont de singe ("monkey bridge: a footrope with overhead rope); and tyrolienne ("Tyrolean": a zip-line).[22] Zip-lines can be traversed by hanging below, or walked (by individuals with exceptional balance). A more developed version of the pont himalayen, provided with a deck between a pair of main cables, is known as a passerelle himalayenne (French, "Himalayan footbridge").[23] Examples of this type include two bridges at Lac de Monteynard-Avignonet in the French Alps; these bridges are exceptionally long, for bridges of this type.

In the arts

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A simple rope bridge used to cross a river in India is pictured by W. Purser with a poetical illustration by Letitia Elizabeth Landon, as Crossing the River Tonse by a Jhoola. in Fisher's Drawing Room Scrap Book, 1839.[24]

Notable bridges

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Notable simple suspension bridges include:

Name Span length Year built
Capilano Suspension Bridge 140 metres (460 ft) 1889
Arroyo Cangrejillo Pipeline Bridge 337 metres (1,106 ft) 1998[25]
Lac de Monteynard-Avignonet Drac bridge 220 metres (720 ft) 2007
Carrick-a-Rede Rope Bridge 20 metres (66 ft) rebuilt 2008
Ponte tibetano Cesana Torinese-Claviere 478 metres (1,568 ft) 2006[26]
Ponte nel Cielo 234 metres (768 ft) 2018[27]
Charles Kuonen Suspension Bridge 494 metres (1,621 ft) 2017[28]
Gandaki Golden Footbridge 567 metres (1,860 ft) 2020[29]
Arouca 516 516 metres (1,693 ft) 2021[30]
Ponte tibetano di Castelsaraceno 586 metres (1,923 ft) 2021[31]
Sky Bridge 721 721 metres (2,365 ft) 2022
Bridge of National Unity 723 metres (2,372 ft) 2024
Ponte tibetano di Sellano 517.5 metres (1,698 ft)[32] 2024[33]
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See also

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References

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Revisions and contributorsEdit on WikipediaRead on Wikipedia

Simple suspension bridge

View on Grokipedia
from Grokipedia
A simple suspension bridge is a fundamental type of bridge in which a flexible deck is suspended directly from main cables anchored at each end of the span, without intermediate towers, piers, or vertical , causing the roadway to conform to the natural curve of the cables. Unlike more complex suspension bridges that use towers and vertical to support a stiffened deck, or cable-stayed bridges that rely on towers with cables directly attached to the deck, simple suspension bridges minimize structural elements, relying solely on the tensile strength of the main cables. This design distinguishes them from other types by their primitive simplicity and flexibility. This type represents one of the oldest known bridge forms, originating in ancient civilizations, and continues to be used in both traditional and modern contexts with updated materials.

Introduction and Classification

Definition and Characteristics

A simple suspension bridge is a structural form in which the deck is hung below two parallel main cables that assume a curve under their own weight, with the cables anchored directly into the ground or abutments at each end and without the use of intermediate towers or stiffening trusses. This design relies on the tensile strength of the cables to transfer loads to the anchors, creating a lightweight and economical crossing primarily for short to medium distances. Key characteristics of simple suspension bridges include their inherent flexibility, which allows for some swaying under load or wind, making them suitable for traffic only. Historically, these bridges were limited to spans under 100 meters due to material constraints, though modern examples using high-strength cables have extended versions to over 700 meters, such as the 721-meter in the . Their emphasizes simplicity and minimal material use, often resulting in a profile that optimizes load distribution along the cable length. The basic components consist of the two main load-bearing cables, typically made from , , or wire in traditional forms; a flexible deck often composed of wooden planks or lightweight panels that rests directly on the main cables; and robust anchorages at each end to secure the cables against tension forces. Unlike more advanced suspension designs, simple bridges lack horizontal stiffening girders, which contributes to their but also their dynamic response to loads. These bridges are designed primarily for foot traffic or pack animals, with load capacities supporting distributed weights of several tons in modern tourist applications, such as groups of pedestrians on reinforced decks. Simple suspension bridges originated in ancient cultures, including the Inca civilization's rope bridges in the , where they facilitated crossings over challenging terrain.

Comparison to Other Bridge Types

Simple suspension bridges differ from more advanced suspended-deck suspension bridges primarily in their structural simplicity and load-bearing configuration. In simple designs, the main cables form a natural curve under their own weight and the light deck load, with the deck often suspended directly from these cables without intermediate towers or piers, limiting their use to shorter spans where the cable's self-weight dominates the shape. In contrast, modern long-span suspension bridges, such as the , feature parabolic main cables under uniform heavy deck loads, supported by massive towers and reinforced with stiffening trusses to distribute forces and prevent excessive deflection or vibration. Compared to cable-stayed bridges, simple suspension bridges lack the diagonal stay cables that radiate from central towers to directly support the deck, instead relying solely on the main cables anchored at the ends. This results in simpler anchorage requirements but reduced efficiency for longer spans or heavier vehicular loads, as the tension-only system transfers forces primarily through the main cables rather than compressing the towers like in cable-stayed designs. Cable-stayed bridges offer greater stiffness and are more suitable for spans up to 1,000 m, while simple suspension types excel in minimalistic setups but require careful load management to avoid instability. In relation to arch and beam bridges, simple suspension bridges emphasize tension in the cables as the primary load-carrying mechanism, unlike arch bridges that depend on compressive forces along curved ribs or beam bridges that resist shear and through rigid horizontal members. This tension-based approach makes simple suspension bridges particularly advantageous in rugged or inaccessible where erecting piers or abutments for arches or beams is challenging, though they are more susceptible to oscillatory movements without inherent rigidity. Arch and beam types provide better resistance to localized heavy loads but are generally confined to shorter spans due to material stress limitations in compression or . Simple suspension bridges offer key advantages such as cost-effectiveness in remote or temporary applications and rapid assembly using basic materials, making them ideal for crossings in difficult landscapes. However, their disadvantages include a limited maximum span of approximately 700 m without added stiffening, as well as heightened vulnerability to wind-induced vibrations and dynamic loads that can cause swaying or fatigue in the flexible cables. Within the broader classification of suspension bridges, simple variants serve as the primitive precursor, characterized by direct cable anchorage and absence of advanced features like aerodynamic stabilizers, stiffening trusses, or self-anchored/earth-anchored systems found in earth-anchored or self-anchored modern types, which enable much longer and more stable spans.

Historical Development

Ancient and Traditional Origins

Simple suspension bridges emerged independently in various regions, with early examples relying on natural fibers to span challenging terrains. In the Andean region of , pre-Inca cultures developed rope bridges using vines and grasses as early as the 13th century, which the later expanded into a vital network exceeding 200 major crossings to facilitate communication and trade across steep canyons. These structures, such as those documented in the gorge, typically spanned 30 to 50 meters and were constructed by weaving thick cables from local vegetation like ichu grass or cabuya fibers, forming a basic shape from the natural sag of suspended ropes. In , particularly in during the (206 BCE–220 CE), the earliest recorded prototypes appeared as iron chain suspension bridges, marking a shift from purely organic materials. By the (1368–1644), Tibetan engineer advanced these designs in the , building iron chain bridges that integrated local rope reinforcements for added stability in high-altitude environments. Construction techniques across these cultures emphasized communal labor and renewable materials, such as hand-woven ropes from , , or vines lashed to anchorages on cliffs or trees. In the , communities like those near the Q'eswachaka Bridge in continue a of annual renewal, where families gather for a multi-day to dismantle and rebuild the structure using braided grass cables up to 10 cm thick, ensuring its integrity for pedestrian and livestock passage. Similarly, Himalayan bridges required periodic replacement of fiber elements to combat , with Tibetan examples incorporating iron for longevity in seismic zones. These practices not only addressed the short lifespans of organic components—often 1 to 2 years due to exposure and load stress—but also reinforced social bonds through collective maintenance. Culturally, these bridges were indispensable for mountainous trade routes, enabling the exchange of goods like salt, , and metals in isolated Andean and Himalayan communities. In , they symbolized imperial unity, with bridges like Q'eswachaka serving as sacred links in the Qhapaq Ñan road system, where failure to maintain them could disrupt vital supply lines. Limitations persisted, however, as the perishable materials restricted spans and loads to foot or light animal traffic, precluding heavier carts and necessitating frequent rebuilds in remote areas without metal alternatives until later centuries.

Evolution to Modern Forms

The transition from traditional to modern simple suspension bridges began in the with the introduction of metallic components that enhanced durability and span capabilities while retaining the no-tower design. In the United States, James Finley pioneered iron chain designs, constructing the Jacob's Creek Bridge in 1801 with a 70-foot span across a creek in , marking the first iron-chain suspension bridge with a level roadway suitable for carriages. This innovation was followed by the adoption of wire ropes, first used in 1816 for a private toll over the near , built by Josiah White and Erskine Hazard, which demonstrated the feasibility of continuous wire cables for lighter, more flexible structures. In , the Luding Bridge, an iron-chain suspension structure completed in 1706 during the , exemplified early metallic applications with its 13 chains spanning the Dadu River, providing a durable crossing anchored directly to abutments without intermediate supports. The saw significant advancements through wire cables, which allowed for longer spans while maintaining the simplicity of unloaded decks anchored at the ends. Engineers shifted from to high-strength wires, enabling greater tensile strength suitable for pedestrian and light uses. During , prefabricated suspension bridges were deployed by military forces for rapid temporary crossings, with Soviet bloc production emphasizing wire cables for portable assault bridges that could span rivers under combat conditions. These developments prioritized lightweight, modular assembly, retaining the core principles of simple suspension while improving tensile strength and resistance to environmental wear. A key engineering transition involved replacing organic cables—such as vines or bamboo fibers used in ancient designs—with metallic ones, first iron chains and later steel wires, to achieve greater longevity and load-bearing capacity without altering the fundamental unloaded deck configuration or adding towers. Modern simple suspension bridges often incorporate minimal handrails for pedestrian safety, avoiding full stiffening systems to preserve their lightweight, swaying character and "simple" classification. In the , innovations have focused on pedestrian-oriented designs integrated with eco-tourism, emphasizing and environmental harmony. Recent post-2024 examples in highlight this trend, such as hybrid pedestrian bridges in and that blend steel cables with natural materials like bamboo for reduced ecological impact, supporting sustainable tourism in sensitive landscapes.

Materials and Construction

Traditional and Natural Materials

In simple suspension bridges of ancient origins, primary load-bearing cables were typically constructed from natural plant fibers, leveraging their availability and tensile properties in regions like ancient and . In , materials such as fibers and vines were prevalent; for instance, the Anlan Bridge in , dating back to around A.D. 300, utilized ropes woven from , a grass-like material known for its rapid growth and structural versatility. In , particularly among the Inca, cables were made from twisted fibers of ichu grass (Stipa ichu) and cabuya (), hardy Andean plants that provided strong, flexible strands capable of spanning deep canyons. These organic choices reflected local ecosystems, with vines also used in Japanese vine bridges on Shikoku Island, where wild lianas were harvested for their natural elasticity. For the deck and attachments, builders employed readily available wood or planks lashed directly to the main cables to form the walkway, ensuring a lightweight yet supportive surface. In Inca constructions, such as the Q'eswachaka Bridge, the deck consisted of wooden branches or planks lashed to the main floor cables. These natural materials offered high tensile strength relative to their low weight, with hemp ropes—used in some Asian and early global contexts—achieving approximately 500 MPa, enabling efficient load distribution in configurations. Their inherent flexibility facilitated the curved shape essential for suspension stability, while biodegradability necessitated regular community-led replacements, often every few years. Bamboo fibers provided notable tensile strength in woven forms, balancing durability with environmental integration. Sourcing involved communal harvesting from local flora, followed by labor-intensive weaving techniques passed down through generations, including pounding fibers to enhance flexibility and treating them with natural resins for weather resistance. For the Inca, grass was gathered from high-altitude puna grasslands and cabuya from lower slopes, then stripped, twisted into cords, and braided into thick cables by teams using traditional Andean methods, as seen in the annual renewal of the Q'eswachaka Bridge. These processes emphasized , with fibers selected for their resistance to local conditions like humidity and altitude. Despite their ingenuity, these materials had limitations, including susceptibility to rot from and degradation from exposure, which shortened and required vigilant . Consequently, spans were generally restricted to 20-50 meters without additional natural reinforcements, as longer distances risked cable under environmental stress.

Modern and Innovative Materials

In the evolution from traditional natural fibers, modern simple suspension bridges have increasingly adopted galvanized steel wire ropes for their main load-bearing cables, offering enhanced durability and strength. These ropes typically feature a 6x19 strand configuration, consisting of six strands each with 19 wires, which provides a balance of flexibility and resistance to abrasion while supporting high tensile loads up to approximately 1,800 MPa. with zinc coating protects against corrosion in exposed environments, extending service life in pedestrian and light vehicular applications. For even lighter structures, aluminum alloys have been explored in cable designs to reduce overall weight, particularly in temporary or remote installations where transportability is key. Synthetic materials have further expanded options for temporary and portable simple suspension bridges, with and (an fiber) providing high strength-to-weight ratios suitable for rapid deployment. Nylon ropes offer elasticity and shock absorption for dynamic loads in or emergency contexts, while Kevlar cables can achieve tensile strengths up to 10 times that of by weight, making them ideal for lightweight spans in rugged terrains. In recent designs, composite cables incorporating fiber-reinforced polymers (FRP), such as carbon fiber reinforced plastics (CFRP), have gained traction for their superior corrosion resistance and reduced maintenance needs compared to steel. These composites exhibit high modulus and low density, enabling longer spans without significant sagging, and have been implemented in innovative prototypes like the 2025 Oder Bridge, the world's first railway structure using CFRP cables. A unique innovation in sustainable materials is the use of living root systems from trees in , , where communities train over 10-20 years to form self-supporting bridges spanning over 50 meters. These organic structures possess self-regenerating properties, as the roots continue to thicken and heal naturally, providing a biodegradable alternative that integrates with ecosystems and requires no industrial production. For anchors and fittings, modern designs embed main cables into massive concrete blocks or natural rock formations at each end to distribute tensile forces securely, while clamps secure the deck directly to the main cables, resisting . Post-2020 advancements emphasize eco-materials, including bio-based polymers derived from renewable sources like plant starches, which are being tested for cable sheathing to minimize environmental impact. These polymers offer biodegradability and reduced reliance on , addressing gaps in traditional production. Efforts toward carbon-neutral cable manufacturing have accelerated, with techniques like low-emission CFRP fabrication and recycled content integration aligning with 2025 standards for bridge .

Design Principles

Structural Components

The main cables form the primary load-bearing elements of a simple suspension bridge, consisting of a pair of flexible cables draped in a curve between anchorages at each end, without intermediate towers or piers. These cables, often constructed from wire ropes, chains, or natural fibers, support the entire weight of the deck and loads by transferring tensile forces directly to the ground anchors. The length of the main cables is calculated based on the bridge span and the desired sag, with the sag typically amounting to about 1/10 of the span to balance structural efficiency and material use. In simple suspension bridges, the deck is typically constructed by lashing wooden planks or weaving materials directly to the main cables, allowing the structure to follow the curve and transfer loads through direct contact and tension. This direct attachment ensures even distribution of loads along the cables without excessive deflection under pedestrian traffic, while allowing the bridge to sway slightly for stability. The deck is a lightweight platform laid directly on the main cables, commonly constructed from planks, metal , or netting to minimize weight and wind resistance. Designed primarily for use, the deck typically has a width of 1 to 3 meters, providing sufficient space for foot traffic while keeping the structure simple and economical. Anchors and supports secure the ends of the main cables to resist the horizontal tension forces, with end anchors commonly of the deadman type—buried masses such as blocks or logs—or types relying on heavy structures like rock fills. Optional minimal side rails may be added along the deck edges for balance and , though they are not integral to the primary load path. Assembly begins with the installation of the main cables, often using temporary supports or guy lines to position them across the span and achieve the proper shape, followed by direct attachment of the deck materials at intervals along the cables. Once the cables are in place, the deck is built in sections, starting from the center or ends depending on site access, ensuring even tension throughout without the need for central towers.

Mechanics and Stability Considerations

The primary structural element in a simple suspension bridge, the main cable, assumes a shape under its own uniform , governed by the equation y=T0w(cosh⁡(wxT0)−1),y = \frac{T_0}{w} \left( \cosh \left( \frac{w x}{T_0} \right) - 1 \right), where yy represents the vertical sag at horizontal position xx from the lowest point, T0T_0 is the horizontal component of tension at the vertex, and ww is the cable's per unit length. This hyperbolic cosine form arises from balancing the cable's against tension forces in equilibrium. In practice, for bridges where the deck's uniform load dominates over the cable's self-, engineers approximate the cable profile as parabolic to simplify calculations, as the deviation from is minimal under these conditions. Load transfer in simple suspension bridges occurs primarily through direct contact and lashing of the lightweight deck to the main cables. Vertical loads from the deck induce both horizontal and vertical components in the main cable tension, resulting in total tension T=H2+V2T = \sqrt{H^2 + V^2}
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