Cable Structures and Bridge Engineering

Cable Structures and Trusses

• Cable structures balance masses and manipulate force diagrams, while considering forms

Erasmus Bridge

• The Erasmus Bridge in Rotterdam, NL, designed by architect Ben Van Berkyl, exemplifies cable structure principles
• The bridge's "L" shape counters the deck's loads from supporting people and cars
• This Rotterdam bridge's proximity to water reduces wind uplift effects

Caltrans Bridges

• Caltrans bridges are engineered instead of using strong designer input on the scheme

Cable Structure Properties

• Cable structures are lighter compared to other systems
• These systems are highly efficient structurally
• They must remain in tension
• Cables have small cross-sections relative to their length
• Cables have no Rigidity or stiffness refers to the inability of a material or object to bend easily, resulting in limited flexibility and increased resistance to deformation.

Simple Cables

• Simple cables are highly efficient structural systems used in suspension bridges, roof structures, transmission lines, and guy wires
• Cables or suspension structures are one of the oldest structural systems
• A cable system logically objectifies the laws of statics in visual terms

Cable Engineering

• Cables provide an economical way to span large distances due to steel's tensile strength
• Steel cables reduce the dead load of a structure while providing ample strength to support the design live load
• Cables are light and lack rigidity or stiffness

Cable Load Resistance

• Beams and arches develop bending moments under changing loads; cables change shape in response
• Cables offer superior load resistance in tension but change shape, which can cause problems
• Analysis of the cables' cross-section is always important

Structures Incorporating Cables

• Bridges
• Guy wires
• Roof structures
• Temporary structures
• Transmission lines

Cable Material

• High-strength steel is commonly used for cable structures

Cable Properties

• Bending capacity in cables is negligible due to their small cross-sectional dimension relative to their length
• Cables can carry loads only in tension and must remain in tension for stability
• Tensile structure stability is achieved through shape (geometry) and prestress

Cable Response to Load

• Beams and arches develop bending moments with changing loads whereas cables change shape or configuration

Essential Elements of Suspension Systems

• Every practical suspension system must include all of the following principal elements in one form or another:
• Vertical supports or towers
• These provide the essential reactions that keep the cable system above the ground
• Each system requires some kind of supporting towers
• These may be simple vertical or sloping piers or masts, diagonal struts, or a wall
• Vertical Supports' Axes ideally bisect the angle between the cables that pass over them
• Main cables
• These are the primary tensile elements, carrying the roof (or sometimes floors) with a minimum of material
• Steel used in cable structures has breaking stresses that exceed 200,000 psi (pounds per square inch)
• Anchorages
• Main cables are not usually vertical, so the structure provides a horizontal force resistance
• This is called an anchorage
• the main cables are carried over gently curved saddles on top of the towers and on down into massive concrete abut-ments or into bedrock

Cable-Stayed Bridge System

• Cables on opposite sides of a vertical tower balance each other
• Horizontal thrust is resolved in the longitudinal bridge-deck framework

Building Thrust Resolution

• For buildings, resolution of horizontal thrust can be cumbersome, involving tremendous mass
• It is best either to brace a floor or to make a compression ring if the building has a smooth, closed curve in plan

Stabilizers

• Stabilizers prevent cables from extreme shape changes under varying loads by preventing flutter
• Lightweight roof systems are susceptible to undulation or fluttering under wind forces

Common Frequencies

• If an outside force acting upon a material comes within that frequency range, causing the material to vibrate internally, or flutter, a vibrational state may be reached where the outer and inner forces are in tune (called resonance), and the material undergoes destruction

Cable Structure Problems

• Light, strong materials can be sensitive to uneven loading
• Vibration and flutter become major design considerations
• David Steinman devised a system of damping that subtly outwits the phenomenon without sacrificing weight or economy after 17 years of independent work

Roof Surface Considerations

• Dynamic instability in membrane structures, acting only in tension, can be solved by pretensioning
• Alternatively, wood planking, metal decking, or a thin concrete slab can resist normal forces through bending, minimizing flutter and movement, but surface design remains a concern for the main cables

Factors for Stabilizing Primary Cables

• Dead weight
• A rigid surface that includes the main cables
• A set of secondary pre-tensioned cables with reverse curvature from the main cables
• Restraining cables

Details of the Ice Rink

• The Ice Rink shows consideration of the components but recomposes them to establish a new form
• The load from the planks and roof structure prevent the roof from flapping
• The roof system is in enough tension to create a smooth surface able to take a roof coating
• Also, it is at such an angle that it sheds water at a fast rate, thus avoids the water from pooling

Hyperbolic Structure Characteristics

• Hyperbolic structures use the load characteristics of the catenary to develop a smooth curve
• Structures are in tension and do not flap in the wind, but are also not rigid

Cable Geometry

• A perfectly flexible cable or string will take on a different shape for every variation in loading; it's a funicular or string polygon

Cable Shape

• Under one concentrated load, a cable forms two straight lines at the load's application point
• When two concentrated loads act, three straight lines form
• With uniform horizontal distribution (suspension bridges), a parabola is achieved
• With uniform distribution along the cable's length (suspended chain), a catenary curve results

Cable Shifts

• Changes in shape for asymmetrical loading (snow) are the same as moving loads
• The greater the live load/dead load ratio, the greater the movement

Cable Characteristics

• Most cases of sag to span ratio are small, on the order of 1/10 to 1/15

Snelson Sculpture

• Kenneth Snelson supports elements (bars) by suspending them in space through tension to other members
• He uses cantilevers in this configuration as well

Truss Design

• Buildings and highways are dotted with steel trusses
• Structural steel is good for trusses because it has both high tensile and compressive strength, and it easily and strongly connects
• Steel comes in different shapes, cross-sectional areas, and lengths for easy construction

Truss Mechanics

• Scientists attempted no serious scientific design involving trusses until the 19th century
• The needs of the railways gave the impetus for steel

Truss Definitions

• A truss is a structural system distributing loads through varied members in planar triangles for stable geometric units
• An ideal pin-connected truss consists of elements connected at their ends only with element restrained from rotation about any axis to the framework
• In early trusses, members were joined at their ends by pins and members assumed only tensile or compressive force which created an ideal truss
• Today, bolting, welding, or a combination of the two join truss members

Truss Fasteners

• In real trusses, more than one fastener is needed at a connection and members of a real truss tend to bend
• In well-designed trusses, bending stresses remain below 20 percent of the tensile or compressive stresses and are neglected in preliminary design

Space Framework

• Actual trusses consist of several trusses joined together to form a space framework
• Secondary trussing/cross bracing provides perpendicular stability
• Loads should be applied to the joints and member weights aren't considered because the weights are small compared to the loads

Truss Analysis

• Preliminary truss analysis assumes: linear members with pin connections, neglecting member weight, loads applied at pinned joints, and neglecting secondary stress
• Each truss member is a two-force member with loads at the end pin or hinge and along the axis

FBD properties

• When isolated as an FBD, a two-force member is in equilibrium under two equal, opposite, and collinear forces
• Member cuts have forces acting along the axis

Wood Trusses

• Member sizes and joint details depend on engineering calculations based on truss type, load pattern, span, and wood used
• Wide member faces offer more area for fastenings