A schematic image of two cantilevers. The top example has a full moment connection (like a flag pole bolted to the side of a building). The bottom example is created by an extension of a simply supported beam (such as the way a diving-board is anchored and extends over the edge of a swimming pool).

A cantilever is a beam supported on only one end. The beam carries the load to the support where it is resisted by moment and shear stress. In Physics, the moment of force (often just moment, though there are other quantities of that name such as Moment of inertia) is a Pseudovector A shear stress, denoted \tau\ ( Tau) is defined as a stress which is applied Parallel or tangential to a face of a material Cantilever construction allows for overhanging structures without external bracing. Cantilevers can also be constructed with trusses or slabs. In Architecture and Structural engineering, a truss is a structure comprising one or more triangular units constructed with straight slender members whose A Concrete slab is a common structural element of modern buildings

This is in contrast to a simply supported beam such as those found in a post and lintel system. For lintel as a decorative element see Lintel (architecture For beam as load-bearing member see beam A simply supported beam is supported at both ends with loads applied between the supports.

In bridges, towers, and buildings

Cantilevers are widely found in construction, notably in cantilever bridges and balconies. A cantilever bridge is a Bridge built using Cantilevers structures that project horizontally into space supported on only one end Balcony (from Italian balcone, scaffold cf High German balcho, beam balk probably cognate with Persian term بالكانه In cantilever bridges the cantilevers are usually built as pairs, with each cantilever used to support one end of a central section. The Forth Bridge in Scotland is a famous example of a cantilever truss bridge. For the nearby road bridge see Forth Road Bridge. The Forth Bridge is a cantilever Railway Bridge over the Scotland ( Gaelic: Alba) is a Country in northwest Europethat occupies the northern third of the island of Great Britain.

Temporary cantilevers are often used in construction. The partially constructed structure creates a cantilever, but the completed structure does not act as a cantilever. This is very helpful when temporary supports, or falsework, cannot be used to support the structure while it is being built (e. Falsework consists of temporary structures used in Construction to support spanning or arched structures in order to hold the component in place until its construction is sufficiently g. , over a busy roadway or river, or in a deep valley). So some truss arch bridges (see Navajo Bridge) are built from each side as cantilevers until the spans reach each other and are then jacked apart to stress them in compression before final joining. A truss arch Bridge combines the elements of the Truss bridge and the Arch bridge. Navajo Bridge crosses the Colorado River 's Marble Canyon near Lee's Ferry in the U Nearly all cable-stayed bridges are built using cantilevers as this one is one of their chief advantages. A Many box girder bridges are built segmentally, or in short pieces. As its name implies a segmental bridge is a Bridge built in short sections (called segments i This type of construction lends itself well to balanced cantilever construction where the bridge is built in both directions from a single support.

In an architectural application, Frank Lloyd Wright's Fallingwater used cantilevers to project large balconies. Frank Lloyd Wright (June 8 1867 &ndash April 9 1959 was an American (of Welsh descent Architect, Interior designer, Writer, and educator who Fallingwater, also known as the Edgar J Kaufmann Sr Residence, is a House designed by American Architect Frank Lloyd Wright The roof built over the stands at Old Trafford Football Ground uses a cantilever so that no supports will block views of the field. Vietnam roofjpg|thumb|The roofs of Vietnam.]] A roof is the covering on the uppermost part of a Building.

The Forth Bridge, a cantilever truss bridge. For the nearby road bridge see Forth Road Bridge. The Forth Bridge is a cantilever Railway Bridge over the

This concrete balanced cantilever bridge under construction employs movable cantilevers to support formwork.

A notable cantilever balcony of the Fallingwater house, by Frank Lloyd Wright. Fallingwater, also known as the Edgar J Kaufmann Sr Residence, is a House designed by American Architect Frank Lloyd Wright Frank Lloyd Wright (June 8 1867 &ndash April 9 1959 was an American (of Welsh descent Architect, Interior designer, Writer, and educator who

A balcony created by a cantilever slab.

Less obvious examples of cantilevers are free-standing radio towers without guy-wires and chimneys, which resist being blown over by the wind through cantilever action at their base. Radio masts and towers are typically tall structures designed A guy-wire or guy-rope is a tensioned cable designed to add stability to structures (frequently ship masts, radio masts, Wind turbines, A chimney is a system for venting hot Flue gases or Smoke from a Boiler, Stove, Furnace or Fireplace to the outside

In aircraft

Another use of the cantilever is in fixed-wing aircraft design, pioneered by Hugo Junkers in 1915. Overview Fixed-wing aircraft range from small training and recreational aircraft to Wide-body aircraft and military cargo aircraft. Hugo Junkers ( 3 February 1859 - 3 February 1935) was an innovative German Engineer, as his many Patents Early aircraft wings typically bore their loads by using two (or more) wings in a biplane configuration braced with wires. A biplane is a Fixed-wing aircraft with two main Wings The first powered heavier-than-air Aircraft, the Wright brothers' Wright Flyer They were similar to truss bridges, having been developed by Octave Chanute, a railroad bridge engineer. A truss bridge is a Bridge composed of connected elements (typically straight which may be stressed from tension, compression, or sometimes both in response Octave Chanute, (February 18 1832 &ndash November 23 1910 was a French-born American Railroad engineer and Aviation pioneer The wings were braced with crossed wires so they would stay parallel, as well as front-to-back to resist twisting. The cables generated considerable drag, and there was constant experimentation on ways to eliminate them.

It was also desirable to build a monoplane aircraft, as the airflow around one wing negatively affects the other in a biplane model. For Félix du Temple 's invention see ''Monoplane'' (1874 Types of monoplane The main distinction in types of monoplane is Early monoplanes used either struts (as do some current light aircraft), or cables (as do some modern home-built aircraft). The advantage in using struts or cables is a reduction in weight for a given strength, but with the penalty of additional drag. This reduces maximum speed, and increases fuel consumption.

A British Hawker Hurricane from World War II with cantilever wings

The most common current wing design is the cantilever. A single large beam, called the main spar, runs through the wing, typically nearer the leading edge at about 25 percent of the total chord. In an aircraft the spar is the main structural member of the wing running widthways across the span of the wing at right angles (or thereabouts to the Fuselage. The leading edge is a line connecting the forward-most points of a Wing 's profile In reference to Aircraft, chord refers to the distance between the leading edge and trailing edge of a Wing, Horizontal stabilizer or Vertical stabilizer In flight, the wings generate lift, and the wing spars are designed to carry this load through the fuselage to the other wing. In the context of a Fluid flow relative to a body the lift force is the component of the Aerodynamic force that is Perpendicular to the flow To resist fore and aft movement, the wing will usually be fitted with a second smaller drag-spar nearer the trailing edge, tied to the main spar with structural elements or a stressed skin. The trailing edge of a Wing is the rear edge of the wing where the airflow separated by the Leading edge rejoins after passing over and under the top and bottom surfaces The wing must also resist twisting forces, done either by a monocoque "D" tube structure forming the leading edge, or by the aforementioned linking two spars in some form of box beam or lattice girder structure. Monocoque, from the French for single ( mono) and shell ( coque) is a construction technique that supports structural load by using an object's external A lattice girder is a Girder where the Flanges are connected by a Lattice web

Cantilever wings require a much heavier spar than would otherwise be needed in cable-stayed designs. However, as the size of an aircraft increases, the additional weight penalty decreases. Eventually a line was crossed in the 1920s, and designs increasingly turned to the cantilever design. By the 1940s almost all larger aircraft used the cantilever exclusively, even on smaller surfaces such as the horizontal stabilizer.

In microelectromechanical systems

Cantilevered beams are the most ubiquitous structures in the field of microelectromechanical systems (MEMS). Microelectromechanical systems ( MEMS) is the technology of the very small and merges at the nano-scale into Nanoelectromechanical systems (NEMS and Nanotechnology MEMS cantilevers are commonly fabricated from silicon (Si), silicon nitride (SiN), or polymers. Silicon (ˈsɪlɪkən or /ˈsɪlɪkɒn/ silicium is the Chemical element that has the symbol Si and Atomic number 14 Silicon nitride (Si3N4 is a hard solid substance It is the main component in silicon nitride Ceramics which have relatively good shock resistance A polymer is a large Molecule ( Macromolecule) composed of repeating Structural units typically connected by Covalent Chemical bonds The fabrication process typically involves undercutting the cantilever structure to release it, often with an anisotropic wet or dry etching technique. Reactive ion etching ( RIE) is an etching technology used in Microfabrication. Without cantilever transducers, atomic force microscopy would not be possible. The atomic force microscope (AFM or scanning force microscope (SFM is a very high-resolution type of scanning probe microscope, with demonstrated resolution of fractions A large number of research groups are attempting to develop cantilever arrays as biosensors for medical diagnostic applications. A biosensor is a device for the detection of an Analyte that combines a biological component with a physicochemical detector component MEMS cantilevers are also finding application as radio frequency filters and resonators. Radio frequency ( RF) is a Frequency or rate of Oscillation within the range of about 3 Hz to 300 GHz Electronic filters are Electronic circuits which perform Signal processing functions specifically intended to remove unwanted signal components and/or enhance wanted A resonator is a device or system that exhibits Resonance or resonant behavior that is it naturally oscillates at some frequencies, called its resonance

Two equations are key to understanding the behavior of MEMS cantilevers. The first is Stoney's formula, which relates cantilever end deflection δ to applied stress σ:

where ν is Poisson's ratio, E is Young's modulus, L is the beam length and t is the cantilever thickness. Poisson's ratio ( ν) named after Simeon Poisson, is the ratio of the relative contraction strain, or transverse strain (normal to In Solid mechanics, Young's modulus (E is a measure of the Stiffness of an isotropic elastic material Very sensitive optical and capacitive methods have been developed to measure changes in the static deflection of cantilever beams used in dc-coupled sensors.

The second is the formula relating the cantilever spring constant k to the cantilever dimensions and material constants:

where F is force and w is the cantilever width. In Mechanics, and Physics, Hooke's law of elasticity is an approximation that states that the amount by which a material body is deformed (the The spring constant is related to the cantilever resonance frequency ω₀ by the usual harmonic oscillator formula . This article is about the harmonic oscillator in classical mechanics A change in the force applied to a cantilever can shift the resonance frequency. The frequency shift can be measured with exquisite accuracy using heterodyne techniques and is the basis of ac-coupled cantilever sensors. In Radio and Signal processing, heterodyning is the generation of new frequencies by mixing or multiplying two Oscillating waveforms

The principal advantage of MEMS cantilevers is their cheapness and ease of fabrication in large arrays. The challenge for their practical application lies in the square and cubic dependences of cantilever performance specifications on dimensions. These superlinear dependences mean that cantilevers are quite sensitive to variation in process parameters. Controlling residual stress can also be difficult. Residual stresses are stresses that remain after the original cause of the stresses (external forces heat gradient has been removed

MEMS cantilever in resonance[1]

See also

• Applied mechanics
• Moment (physics)
• Statics
• Beam theory
• Cantilever brakes
• Cantilever bridge
• Cantilever chair
• Cantilever mechanics (orthodontics)

References

• Roth, Leland M (1993). Applied mechanics is a branch of the Physical sciences and the practical application of Mechanics. In Physics, the moment of force (often just moment, though there are other quantities of that name such as Moment of inertia) is a Pseudovector Statics is the branch of Mechanics concerned with the analysis of loads ( Force, torque/moment) on Physical systems in Static equilibrium Bicycle brake systems are used to slow down or Brake a Bicycle. A cantilever bridge is a Bridge built using Cantilevers structures that project horizontally into space supported on only one end A cantilever Chair has no back legs relying for support on the properties of the material from which it is made A Cantilever is in principle any piece of wire whose end is inserted on one side into a bracket or a tube or included in the acrylic of a removable appliance while the other one Understanding Architecture: Its Elements History and Meaning. Oxford, UK: Westview Press. ISBN 0-06-430158-3.   pp. 23-4
• Madou, Marc J (2002). Fundamentals of Microfabrication. Taylor & Francis. ISBN 0-8493-0826-7.  
• Sarid, Dror (1994). Scanning Force Microscopy. Oxford University Press. ISBN 0-19-509204-X.  

External links

• diracdelta.co.uk cantilever beam calculation