Editing Cantilever

{{short description|Beam anchored at only one end}}
{{For|the figure skating element|Cantilever (figure skating)}}
[[Image:Cantilever examples.svg|right|thumb|200px|A schematic image of three types of cantilever. The top example has a full moment connection (like a horizontal flagpole bolted to the side of a building). The middle example is created by an extension of a simple supported beam (such as the way a [[Springboard|diving board]] is anchored and extends over the edge of a swimming pool). The bottom example is created by adding a [[Robin boundary condition]] to the beam element, which essentially adds an elastic spring to the end board.  The top and bottom example may be considered structurally equivalent, depending on the effective stiffness of the spring and beam element.]]

A '''cantilever''' is a rigid [[structural element]] that extends horizontally and is unsupported at one end. Typically it extends from a flat vertical surface such as a wall, to which it must be firmly attached. Like other structural elements, a cantilever can be formed as a [[Beam (structure)|beam]], plate, [[truss]], or [[Concrete slab|slab]].

When subjected to a [[structural load]] at its far, unsupported end, the cantilever carries the load to the support where it applies a [[shear stress]] and a [[bending moment]].<ref>{{Cite book |last1=Hool |first1=George A. |url=https://books.google.com/books?id=wFdDAAAAIAAJ |title=Handbook of Building Construction |last2=Johnson |first2=Nathan Clarke |publisher=[[McGraw-Hill]] |year=1920 |edition=1st |volume=1 |location=New York |page=2 |chapter=Elements of Structural Theory - Definitions |format=Google Books |quote=A cantilever beam is a beam having one end rigidly fixed and the other end free. |access-date=2008-10-01 |chapter-url=https://books.google.com/books?id=wFdDAAAAIAAJ&pg=PA2}}</ref>

Cantilever construction allows overhanging structures without additional support.

==In bridges, towers, and buildings==
Cantilevers are widely found in construction, notably in [[cantilever bridge]]s and [[balcony|balconies]] (see [[corbel]]). 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 an example of a cantilever [[truss bridge]]. A cantilever in a traditionally [[Timber framing|timber framed]] building is called a [[Jettying|jetty]] or [[Pennsylvania barn|forebay]]. In the southern United States, a historic barn type is the cantilever barn of [[Log cabin|log construction]].

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.g., over a busy roadway or river, or in a deep valley). Therefore, some [[truss arch bridge]]s (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 finally joining. Nearly all [[cable-stayed bridges]] are built using cantilevers as this is one of their chief advantages. Many box girder bridges are built [[Segmental bridge|segmentally]], or in short pieces. This type of construction lends itself well to balanced cantilever construction where the bridge is built in both directions from a single support.

These structures rely heavily on [[torque]] and rotational equilibrium for their stability.

In an architectural application, [[Frank Lloyd Wright]]'s [[Fallingwater]] used cantilevers to project large balconies.<!--Please add content about the structural problems which these have; the people maintaining it would know-->
The East Stand at [[Elland Road]] Stadium in Leeds was, when completed, the largest cantilever stand in the world<ref>{{Cite journal |date=6 February 1992 |title=GMI Construction wins £5.5M Design and Build Contract for Leeds United Football Club's Elland Road East Stand |url=https://www.constructionnews.co.uk/archive/06feb92-uk-gmi-construction-wins-5-5m-design-and-build-contract-for-leeds-united-football-clubs-elland-road-east-stand-06-02-1992/ |journal=Construction News |access-date=24 September 2012}}</ref> holding 17,000 spectators.
The [[roof]] built over the stands at [[Old Trafford]] uses a cantilever so that no supports will block views of the field.
The old (now demolished) [[Miami Stadium]] had a similar roof over the spectator area. The largest cantilevered roof in Europe is located at [[St James' Park]] in [[Newcastle-Upon-Tyne]], the home stadium of [[Newcastle United F.C.]]<ref name="IStructE">IStructE The Structural Engineer Volume 77/No 21, 2 November 1999. James's Park a redevelopment challenge</ref><ref name="highbeamdotcom">[https://web.archive.org/web/20110826052725/http://www.highbeam.com/doc/1P3-898836331.html highbeam.com]; '' The Architects' Journal''. Existing stadiums: St James' Park, Newcastle. 1 July 2005</ref>

Less obvious examples of cantilevers are free-standing (vertical) [[radio masts and towers|radio towers]] without [[guy-wire]]s, and [[chimneys]], which resist being blown over by the wind through cantilever action at their base.

<gallery mode="nolines">
Image:ForthBridgeEdinburgh.jpg|The [[Forth Bridge]], a cantilever truss bridge
Image:Pierre Pflimlin Bridge UC Adjusted.jpg|This [[Pierre Pflimlin Bridge|concrete bridge]] temporarily functions as a set of two balanced cantilevers during construction – with further cantilevers jutting out to support [[formwork]].
File:Howrah Bridge.jpg|[[Howrah Bridge]] in [[India]], a cantilever bridge
Image:FallingwaterCantilever570320cv.jpg|A cantilevered balcony of the [[Fallingwater]] house, by [[Frank Lloyd Wright]]
File:Canton Viaduct, Southern view, west side.JPG|A cantilevered railroad deck and fence on the [[Canton Viaduct]]
File:Cantilever-barn-moa-tn1.jpg|A cantilever barn in rural [[Tennessee]]
File:18-22-186-cades.jpg|Cantilever barn at [[Cades Cove]]
File:DoubleJettiedBuilding.jpg|A double jettied building in Cambridge, England
File:Cantilever Jenga.JPG|Cantilever occurring in the game "[[Jenga]]"
File:Busan_Film_Center.jpg|[[Busan Cinema Center]] in Busan, South Korea, with the world's longest cantilever roof
File:Riverplace Tower in Jacksonville.jpg|Cantilever facade of [[Riverplace Tower]] in [[Jacksonville, Florida]], by [[Welton Becket]] and [[KBJ Architects]]
File:Cantilever crown.png|This [[radiograph]] of a "bridge" dental restoration features a cantilevered crown to the left.
File:Ronan Point collapse closeup.jpg|[[Ronan Point]]: Structural failure of part of floors cantilevered from a central shaft.
File:Fiat tagliero, 08.JPG|[[Fiat Tagliero]], a [[Futurist architecture|Futurist-style]] [[Filling station|service station]] in [[Asmara]], [[Eritrea]], has a mirrored cantilevered roof.
</gallery>

==In aircraft==
[[File:Junkers J 1 at Döberitz 1915.jpg|thumb|left|200px|The pioneering [[Junkers J 1]] all-metal monoplane of 1915, the first  aircraft to fly with cantilever wings]]

The cantilever is commonly used in the wings of [[fixed-wing aircraft]]. Early aircraft had light structures which were braced with [[Flying wires|wires]] and [[Strut#Aircraft|strut]]s. However, these introduced aerodynamic drag which limited performance. While it is heavier, the cantilever avoids this issue and allows the plane to fly faster.

[[Hugo Junkers]] pioneered the cantilever wing in 1915. Only a dozen years after the [[Wright Brothers]]' initial flights, Junkers endeavored to eliminate virtually all major external bracing members in order to decrease airframe drag in flight. The result of this endeavor was the [[Junkers J 1]] pioneering all-metal monoplane of late 1915, designed from the start with all-metal cantilever wing panels. About a year after the initial success of the Junkers J 1, [[Reinhold Platz]] of [[Fokker]] also achieved success with a cantilever-winged [[sesquiplane]] built instead with wooden materials, the [[Fokker V.1]].

[[File:De Havilland DH88 Comet.jpg|thumb|200px|[[de Havilland DH.88 Comet]] G-ACSS, winner of the [[MacRobertson_Air_Race|Great Air Race of 1934]], showing off its cantilever wing]]
In the cantilever wing, one or more strong beams, called ''[[spar (aviation)|spars]]'', run along the span of the wing. The end fixed rigidly to the central fuselage is known as the root and the far end as the tip. In flight, the wings generate [[lift (force)|lift]] and the spars carry this load through to the fuselage.

To resist horizontal shear stress from either drag or engine thrust, the wing must also form a stiff cantilever in the horizontal plane. A single-spar design will usually be fitted with a second smaller drag-spar nearer the [[trailing edge]], braced to the main spar via additional internal members or a stressed skin. The wing must also resist twisting forces, achieved by cross-bracing or otherwise stiffening the main structure.

Cantilever wings require much stronger and heavier spars than would otherwise be needed in a wire-braced design. However, as the speed of the aircraft increases, the drag of the bracing increases sharply, while the wing structure must be strengthened, typically by increasing the strength of the spars and the thickness of the skinning. At speeds of around {{convert|200|mph|kph}} the drag of the bracing becomes excessive and the wing strong enough to be made a cantilever without excess weight penalty. Increases in engine power through the late 1920s and early 1930s raised speeds through this zone and by the late 1930s cantilever wings had almost wholly superseded braced ones.<ref>Stevens, James Hay; ''The Shape of the Aeroplane'', Hutchinson, 1953. pp.78 ff.</ref> Other changes such as enclosed cockpits, retractable undercarriage, landing flaps and stressed-skin construction furthered the design revolution, with the pivotal moment widely acknowledged to be the [[MacRobertson Air Race|MacRobertson England-Australia air race]] of 1934, which was won by a [[de Havilland DH.88 Comet]].<ref>Davy, M.J.B.; ''Aeronautics – Heavier-Than-Air Aircraft'', Part I, Historical Survey, Revised edition, Science Museum/HMSO, December 1949. p.57.</ref>

Currently, cantilever wings are almost universal with bracing only being used for some slower aircraft where a lighter weight is prioritized over speed, such as in the [[ultralight aircraft|ultralight]] class.

==In microelectromechanical systems==<!-- This section is linked from [[Microelectromechanical systems]] -->
[[File:AFM (used) cantilever in Scanning Electron Microscope, magnification 1000x.GIF|right|thumb|[[Scanning electron microscope|SEM]] image of a used [[atomic force microscopy|AFM]] cantilever]]
Cantilevered beams are the most ubiquitous structures in the field of [[microelectromechanical systems]] (MEMS). An early example of a MEMS cantilever is the Resonistor,<ref>ELECTROMECHANICAL MONOLITHIC RESONATOR, US Pat.3417249 - Filed April 29, 1966</ref><ref>R.J. Wilfinger, P. H. Bardell and D. S. Chhabra: The resonistor a frequency selective device utilizing the mechanical resonance of a silicon substrate, IBM J. 12, 113–118 (1968)</ref> an electromechanical  monolithic resonator. MEMS cantilevers are commonly fabricated from [[silicon]] (Si), [[silicon nitride]] (Si<sub>3</sub>N<sub>4</sub>), or [[polymer]]s.   
The fabrication process typically involves undercutting the cantilever structure to ''release'' it, often with an anisotropic wet or [[Reactive ion etching|dry]] etching technique.   Without cantilever transducers, [[atomic force microscopy]] would not be possible.
A large number of research groups are attempting to develop cantilever arrays as [[biosensor]]s for medical diagnostic applications. MEMS cantilevers are also finding application as [[radio frequency]] [[mechanical filter|filters]] and [[resonator]]s.
The MEMS cantilevers are commonly made as [[unimorph]]s or [[bimorph]]s.

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

:<math>
\delta = \frac{3\sigma\left(1 - \nu \right)}{E} \frac{L^2}{t^2}
</math>

where <math>\nu</math> is [[Poisson's ratio]], <math>E</math> is [[Young's modulus]], <math>L</math> is the beam length and <math>t</math> is the cantilever thickness. 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]] <math>k</math> to the cantilever dimensions and material constants:

:<math>
k = \frac{F}{\delta} = \frac{Ewt^3}{4L^3}
</math>

where <math>F</math> is force and <math>w</math> is the cantilever width. The spring constant is related to the cantilever resonance frequency <math>\omega_0</math> by the usual [[harmonic oscillator]] formula <math>\omega_0 = \sqrt{k/m_\text{equivalent}}</math>.      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.

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, particularly the thickness as this is generally difficult to accurately measure.<ref>P. M. Kosaka, J. Tamayo, J. J. Ruiz, S. Puertas, E. Polo, V. Grazu, J. M. de la Fuente and M. Calleja: Tackling reproducibility in microcantilever biosensors: a statistical approach for sensitive and specific end-point detection of immunoreactions, Analyst 138, 863–872 (2013)</ref> However, it has been shown that microcantilever thicknesses can be precisely measured and that this variation can be quantified.<ref>A. R. Salmon, M. J. Capener, J. J. Baumberg and S. R. Elliott: Rapid microcantilever-thickness determination by optical interferometry, Measurement Science and Technology 25, 015202 (2014)</ref> Controlling [[residual stress]] can also be difficult.

[[Image:MEMS Microcantilever in Resonance.png|thumb|MEMS cantilever in resonance<ref>{{cite conference |author=Patrick C. Fletcher |author2=Y. Xu |author3=P. Gopinath |author4=J. Williams |author5=B. W. Alphenaar |author6=R. D. Bradshaw |author7=Robert S. Keynton |title =Piezoresistive Geometry for Maximizing Microcantilever Array Sensitivity|conference = IEEE Sensors |date = 2008}}</ref>]]

==Chemical sensor applications==
A [[chemical sensor]] can be obtained by coating a recognition receptor layer over the upper side of a microcantilever beam.<ref>{{Cite book |last=Bănică |first=Florinel-Gabriel |title= Chemical Sensors and Biosensors:Fundamentals and Applications |publisher=John Wiley & Sons |year=2012 |isbn=978-1-118-35423-0 |location=Chichester, UK |page=576}}</ref> A typical application is the immunosensor based on an [[antibody]] layer that interacts selectively with a particular [[immunogen]] and reports about its content in a specimen. In the static mode of operation, the sensor response is represented by the beam bending with respect to a reference microcantilever. Alternatively, microcantilever sensors can be operated in the dynamic mode. In this case, the beam vibrates at its resonance frequency and a variation in this parameter indicates the concentration of the [[analyte]].  Recently, microcantilevers have been fabricated that are porous, allowing for a much larger surface area for [[analyte]] to bind to, increasing sensitivity by raising the ratio of the analyte mass to the device mass.<ref name="Noyce Vanfleet Craighead Davis 1999 pp. 1148–1154">{{Cite journal |last1=Noyce |first1=Steven G. |last2=Vanfleet |first2=Richard R. |last3=Craighead |first3=Harold G. |last4=Davis |first4=Robert C. |date=1999-02-22 |title= High surface-area carbon microcantilevers |journal=Nanoscale Advances |volume=1 |issue=3 |pages=1148–1154 |doi=10.1039/C8NA00101D |pmid=36133213 |pmc=9418787 |doi-access=free}}</ref> Surface stress on microcantilever, due to receptor-target binding, which produces cantilever deflection can be analyzed using optical methods like laser interferometry. Zhao et al., also showed that by changing the attachment protocol of the receptor on the microcantilever surface, the sensitivity can be further improved when the surface stress generated on the microcantilever is taken as the sensor signal.<ref>{{cite journal|first1 =Yue|last1= Zhao|first2=Agnivo|last2= Gosai|first3= Pranav|last3= Shrotriya |title = Effect of Receptor Attachment on Sensitivity of Label Free Microcantilever Based Biosensor Using Malachite Green Aptamer |doi = 10.1016/j.snb.2019.126963|journal = Sensors and Actuators B: Chemical|volume = 300|date = 1 December 2019|doi-access = free|bibcode= 2019SeAcB.30026963Z}}</ref>

==See also==
{{div col|colwidth=23em}}
* [[Applied mechanics]]
* [[Bicycle brake#Cantilever brakes|Cantilever bicycle brakes]]
* [[Bicycle frame#Cantilever|Cantilever bicycle frame]]
* [[Cantilever chair]]
* [[Cantilever method]]
* [[Cantilevered stairs]]
* [[Corbel arch]]
* [[Euler–Bernoulli beam theory]]
* [[Grand Canyon Skywalk]]
* [[Knudsen force]] in the context of microcantilevers
* [[Orthodontics]]
* [[Statics]]
{{div col end}}

==References==
{{reflist}}

==Sources==
* Inglis, Simon: ''Football Grounds of Britain''. CollinsWillow, 1996. page 206.
* {{Cite book |last=Madou |first=Marc J |title=Fundamentals of Microfabrication |publisher=Taylor & Francis |year=2002 |isbn=0-8493-0826-7}}
* {{Cite book |last=Roth |first=Leland M |url=https://archive.org/details/understandingarc00roth/page/23 |title=Understanding Architecture: Its Elements History and Meaning |publisher=Westview Press |year=1993 |isbn=0-06-430158-3 |location=Oxford, UK |pages=[https://archive.org/details/understandingarc00roth/page/23 23–4]}}
* {{Cite book |last=Sarid |first=Dror |title=Scanning Force Microscopy |publisher=Oxford University Press |year=1994 |isbn=0-19-509204-X}}

== External links ==

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[[Category:Architectural elements]]
[[Category:Structural system]]
[[Category:Bridge components]]