Catenary Cables and Arches Overview
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Questions and Answers

What is a characteristic of a self-anchored suspension bridge?

  • Main cables require earth anchoring.
  • Main cables may be attached to the end of the road deck. (correct)
  • Main cables do not change shape with load.
  • Main cables are attached to the ground.

Which design configuration resembles a harp in self-anchored bridges?

  • Fan design
  • Mono design
  • Harp design (correct)
  • Star design

What might occur due to uneven loading on cables in suspension bridges?

  • Destruction due to wind and vibration. (correct)
  • Increased stability of the structure.
  • Enhanced flexibility of the cables.
  • Reduction in the cable’s curvature.

What is one proposed method to stabilize a clothesline against wind loads?

<p>Add weights to hold down the clothesline. (C)</p> Signup and view all the answers

Which method is used to stabilize cable-stayed structures?

<p>Employ pre-tension cables with reverse curvature. (A)</p> Signup and view all the answers

What is a consequence of resonance in building materials?

<p>Destruction of the material. (D)</p> Signup and view all the answers

How do arches primarily function in structures?

<p>To redirect forces into axial compression. (B)</p> Signup and view all the answers

What kind of loads may cause cables in structures to shift shape?

<p>Dynamic loads and vibrations. (C)</p> Signup and view all the answers

What is a potential destruction risk for a cable-stayed roof structure?

<p>Tuning due to resonance. (C)</p> Signup and view all the answers

Which of the following is NOT a method used for stabilizing cable-stayed structures?

<p>Employing compressive elements. (C)</p> Signup and view all the answers

What is the primary characteristic of a funicular arch?

<p>It carries loads only in axial compression. (A)</p> Signup and view all the answers

If a load is distributed uniformly along the span of an arch, which shape does the arch resemble?

<p>A parabola (B)</p> Signup and view all the answers

What happens to the shape of an arch if the loading conditions change?

<p>It will no longer be funicular and may fail. (C)</p> Signup and view all the answers

Who studied the catenary forms of hanging chains in the 17th century?

<p>Robert Hooke (D)</p> Signup and view all the answers

Which type of cable structure primarily spans between parallel supports and carries the deck directly?

<p>Single-curvature structures (C)</p> Signup and view all the answers

What is the economic span range most suitable for a cable-stayed structure?

<p>50 to 500 ft (A)</p> Signup and view all the answers

What is a well-known example of a single-curvature cable structure?

<p>Golden Gate Bridge (C)</p> Signup and view all the answers

Which type of structure is primarily subject to axial compression according to the principles discussed?

<p>Funicular arches (B)</p> Signup and view all the answers

What is the recommended sag to span ratio for structures?

<p>1:10 (C)</p> Signup and view all the answers

What is the purpose of adding stabilizing cables in double-cable structures?

<p>Resist wind uplift (C)</p> Signup and view all the answers

Which materials are commonly used for making structural cables?

<p>High strength steel and polypropylene (D)</p> Signup and view all the answers

Which of the following statements best describes catenary arches?

<p>They only experience axial compression. (B)</p> Signup and view all the answers

What forces must the anchorage system in cable-supported structures resist?

<p>Horizontal thrust from the main cables (A)</p> Signup and view all the answers

What form does a hanging chain take when forces acting on it change?

<p>It adapts to remain in tension. (C)</p> Signup and view all the answers

How do double-curvature structures differ from double-cable structures?

<p>Double-curvature structures sag similarly to single-curvature ones (B)</p> Signup and view all the answers

Why do arches typically experience both compression and bending forces?

<p>Because they cannot adjust to changing loads. (C)</p> Signup and view all the answers

What is a significant characteristic of the materials used in cable structures?

<p>They can be twisted or bound strands (B)</p> Signup and view all the answers

What type of vertical support may be used in cable-supported structures?

<p>Various types including masts and diagonal struts (A)</p> Signup and view all the answers

What is the common breaking stress for steel used in cable structures?

<p>Around 200,000 psi or more (A)</p> Signup and view all the answers

What is the primary function of vertical supports in a cable-supported structure?

<p>To provide essential reactions and keep cables elevated (D)</p> Signup and view all the answers

What type of loads can cables resist?

<p>Axial tensile forces (B)</p> Signup and view all the answers

Under what load condition do cables form a catenary shape?

<p>Under a uniformly distributed load (C)</p> Signup and view all the answers

What is the primary structural design consideration influenced by the sag-to-span ratio in catenary cable structures?

<p>The tensile force in the cable (B)</p> Signup and view all the answers

What is the optimum sag-to-span ratio for a uniformly loaded parabolic cable?

<p>33% (B)</p> Signup and view all the answers

What does a catenary cable primarily depend upon?

<p>The self-weight of the cable (B)</p> Signup and view all the answers

What happens to cable forces as the sag-to-span ratio increases?

<p>They decrease inversely (C)</p> Signup and view all the answers

In which type of load does a cable under a point load form a polygon shape?

<p>Under multiple point loads (B)</p> Signup and view all the answers

What is a significant difference between a catenary and a parabolic cable under loading conditions?

<p>A parabolic shape is ideal when self-weight is insignificant compared to given loads (B)</p> Signup and view all the answers

What is the relationship between cable diameter and cable length in cable structures?

<p>A greater diameter is needed as cable length decreases (B)</p> Signup and view all the answers

Why is it simpler to utilize a parabola for analysis when the sag-to-span ratio exceeds 5?

<p>The shapes are nearly identical (A)</p> Signup and view all the answers

Flashcards

Single-Curvature Cable Structures

A cable structure where a series of parallel catenary cables span between primary supports and hold a deck directly or through secondary vertical cables.

Double-Cable Structures

A cable structure with additional stabilizing cables below the primary suspension cables to resist wind uplift. These cables span between a compression ring and a tension ring.

Double-Curvature Cable Structures

A cable structure where primary suspension cables sag between supports forming a saddle shape, with stabilizing cables running perpendicular with an opposite curvature.

High-Strength Steel

The most common material for cable structures due to its strength and cost-effectiveness.

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Main Cables

The main load-carrying cables that support the deck in a cable-supported structure.

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Vertical Supports

Vertical supports that hold the main cables above the ground and provide essential reactions in a cable-supported structure.

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Anchorages

Elements that anchor the horizontal thrust of the main cables in a cable-supported structure.

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Stabilizers

Additional cables that help resist wind uplift and provide stability in a cable-supported structure.

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Wind Uplift

The vertical force acting on a structure caused by wind pressure pushing upward on the structure.

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Horizontal Thrust

The tendency of a cable structure to spread outwards horizontally due to the tension in the cables.

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Self-anchored suspension bridge

A type of suspension bridge where the main cables are attached to the end of the road deck, eliminating the need for separate anchorages.

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Harp design (self-anchored bridge)

A type of self-anchored suspension bridge where multiple primary cables support the deck, forming a pattern resembling a harp.

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Fan design (self-anchored bridge)

A type of self-anchored suspension bridge where multiple primary cables support the deck, forming a pattern resembling a fan.

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Star design (self-anchored bridge)

A type of self-anchored suspension bridge where multiple primary cables support the deck, forming a pattern resembling a star.

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Cable flexibility

The tendency of cables to change shape due to shifting loads, requiring stabilization methods to maintain structural integrity.

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Stabilizer (cable-stayed structures)

A structural element used to stiffen cables and resist wind loads, preventing deformation and potential damage.

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Stiffening through construction (cable-stayed structures)

Using the dead weight of the roof or deck construction to stabilize cables, relying on the inherent weight to counter external forces.

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Spreading against a cable with opposite curvature (cable-stayed structures)

A method of stabilizing cables by using a cable with an opposite curvature, creating a counterbalance.

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Tensioning against a cable with opposite curvature (cable-stayed structures)

Stabilizing cables by pre-tensioning a cable with an opposite curvature, creating a tension force to counteract loads.

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Catenary arch

A structural shape that redirects forces into axial compression, creating a strong and efficient load-bearing form.

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Cable Efficiency

Cables are structural elements capable of withstanding significant tensile forces with a minimal cross-sectional area, making them efficient and economical for spanning large distances.

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Catenary Shape

A catenary is the shape a cable takes when only its own weight is considered. It's a smooth curve that sags under the distributed weight, transferring the load evenly to the supports.

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Parabolic Shape

A parabola is the shape a cable takes when it's loaded uniformly across its span, provided its own weight is negligible compared to the load.

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Sag-to-Span Ratio

The ratio of sag to span is crucial for cable design. A higher ratio means less cable force, but also longer cables. It affects the cable's required diameter, tower height, and compression forces.

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Optimum Sag-to-Span Ratio

For a uniformly loaded parabolic cable, the ideal sag-to-span ratio is 33%. Most suspended roof structures have a ratio of 1:8 to 1:10.

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Inward Thrust

The inward force exerted by a cable on its supports is known as inward thrust. It's a key consideration in cable structure design to ensure stability.

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Cable Structure Classification

Classifying cable structures by topology helps understand their behavior and choose appropriate design techniques. It's a structured way to categorize different cable configurations.

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Cable Forces and Sag

The relationship between cable forces and sag-to-span ratio: higher sag = lower cable forces.

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Cable Length and Diameter

The relationship between cable length and diameter: shorter cable = thicker diameter.

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Funicular Arch

The inverted compressive equivalent of a suspension cable, where the arch carries only axial compression and no bending forces.

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Catenary

The shape of a hanging chain, used in arch design.

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Parabolic Arch

An arch that is shaped like a parabola, allowing for uniform load distribution along the span.

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Load Adaptability

The ability of a cable or arch to adjust its shape to accommodate changing load conditions. Arches generally lack this.

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Economic Span of Cable-Stayed Structures

A principle stating that the economic span for a cable-stayed structure is between 50 and 500 feet.

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Span Table for Structural Systems

The table provided specifies suitable spans for different structural systems, such as arches, vaults, cable-stayed, and suspension bridges. This table is useful for choosing the appropriate structure based on the required span.

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Axial Compression

The ability of an arch or structure to withstand compression forces without bending.

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Bending Forces in Arches

The bending of a structure due to applied forces, which is generally undesirable in arches.

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Funicular Form

The ability to carry loads in compression without bending, a property particularly significant for arches. A funicular arch achieves this perfectly.

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Study Notes

Catenary Cables and Arches

  • Cables are efficient structural components, able to withstand high tensile forces with a small cross-section. They are a cost-effective way to span large distances.

  • Cables can only withstand axial tensile forces, not compression or bending moments. They are flexible and their shape changes under various loads to maintain equilibrium.

  • A single point load on a cable creates two straight lines meeting at the load application point.

  • A uniformly distributed load on a cable results in a catenary or parabolic shape.

  • The sag-to-span ratio of a catenary cable significantly affects cable forces. Higher ratios (generally above 5) lead to shapes nearly identical to parabolas.

  • Cable forces are inversely proportional to sag.

  • To decrease cable length, a larger cable diameter is needed, therefore, there is an impact on compressive forces in the supporting structure.

  • The optimum sag-to-span ratio for uniformly loaded parabolic cables is 33%.

  • Suspension cable structures, often involving a sag-to-span ratio between 1:8 and 1:10, are frequently used for building roofs.

Classification of Cable Structures

  • Single-curvature: Parallel cables spanning between supports, often supporting decks directly in designs like the Dulles Airport Terminal, Akashi Kaikyo Bridge, and the Golden Gate Bridge.

  • Double-cable: Stabilizing cables below the primary suspension cables are added to resist wind uplift forces, for instance, in Utica Memorial Auditorium.

  • Double-curvature: Primary suspension cables sag between supports, and stabilizing cables run perpendicularly with opposite curvature, examples are the roof of Dorton Arena.

Materials

  • Cable materials commonly include mild steel, high-strength steel, stainless steel, polypropylene, fiberglass, and carbon fiber.

  • High tensile strength steel is frequently used for reliability and cost-effectiveness.

  • Structural cables are a series of intertwined small strands.

Cable-Supported Structures

  • Main components of a cable-supported structure include main cables, vertical supports (towers, masts, or piers), anchorages, and stabilizers.

  • Vertical supports support cables and provide essential reactions.

  • The horizontal thrust needs to be resisted via a suitable anchorage system. Earth-anchored systems attach the main cables to the ground; self-anchored cables attach to the deck edge of the bridge.

  • Cable connections to the bridge deck can have various forms (fan, harp, star, etc.) but should resist changes in shape due to load shifts.

Resonance and Durability

  • Materials and structures have natural vibration frequencies. External forces matching these frequencies can cause resonance, leading to destruction.

  • Suspension bridges can be subject to destruction due to external forces such as wind.

  • Stabilizers, pre-tension cables, or other countermeasures are employed to protect the structure against damage from vibrational resonance due to loads, wind, or other factors.

  • Cable removal/replacement during the structure's life is a critical factor in maintenance.

Arches

  • Arches are historically used to redirect forces into compression, enabling them to span openings.

  • A "funicular arch" is the compressive equivalent of an inverted catenary cable.

  • A uniformly distributed load results in a parabolic-shaped arch, whereas a uniformly distributed load creates a catenary arch.

  • During load changes or if outside forces affect the arches, bending and compression are often involved simultaneously.

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Catenary Cables and Arches PDF

Description

This quiz explores the principles of catenary cables and their behavior under various loads. Learn about the efficiency of cables in structural applications, the significance of sag-to-span ratios, and how these elements affect cable forces. Perfect for students in engineering and architecture.

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