216.45.141.162: Described Explicit Initialization Vectors under CBC mode

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Described Explicit Initialization Vectors under CBC mode

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{{For|the figure skating element|Cantilever (figure skating)}}
[[Image:Cantilever examples.svg|right|thumb|200px|frame|A schematic image of three types of cantilevers. The top example has a full moment connection (like a horizontal flag pole 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 middle and bottom example may be considered structurally equivalent, depending on the effective stiffness of the spring and beam element]]

A '''cantilever''' is a [[Beam (structure)|beam]] anchored at only one end. The beam carries the load to the support where it is forced against by a [[Moment (physics)|moment]] and [[shear stress]].<ref>{{cite book|last1= Hool |first1= George A. |first2= Nathan Clarke |last2= Johnson |title= Handbook of Building Construction |url= http://books.google.com/books?id=wFdDAAAAIAAJ |format= Google Books |accessdate= 2008-10-01 |edition= 1st |volume= vol. 1 |year= 1920 |publisher= [[McGraw-Hill]] |location= New York |oclc= |doi= |id= |page= 2 |chapter= Elements of Structural Theory - Definitions |chapterurl= http://books.google.com/books?id=wFdDAAAAIAAJ&pg=PA2#v=onepage&q&f=false |quote= A cantilever beam is a beam having one end rigidly fixed and the other end free. |ref= }}</ref> Cantilever construction allows for overhanging structures without external bracing. Cantilevers can also be constructed with [[truss]]es or [[Concrete slab|slab]]s.

This is in contrast to a simply supported beam such as those found in a [[post and lintel]] system. 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 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 Rail Bridge|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).
So 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 final 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 are highly based on [[torque]] and rotational equilibrium.

In an architectural application, [[Frank Lloyd Wright]]'s [[Fallingwater]] used cantilevers to project large balconies.
The East Stand at [[Elland Road]] Stadium in Leeds was, when completed, the largest cantilever stand in the world<ref>{{cite journal|title=GMI Construction wins £5.5M Design and Build Contract for Leeds United Football Club's Elland Road East Stand|journal=Construction News|date=6 February 1992|url=http://www.cnplus.co.uk/news/06feb92-uk-gmi-construction-wins-55m-design-and-build-contract-for-leeds-united-football-clubs-elland-road-east-stand/1047354.article|accessdate=24 September 2012}}</ref> holding 17,000 spectators.
The [[roof]] built over the stands at [[Old Trafford (football ground)|Old Trafford Football Ground]] 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 cantilever 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>[http://www.highbeam.com/doc/1P3-898836331.html 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>
Image:ForthBridgeEdinburgh.jpg|The ''[[Forth Bridge (railway)|Forth Bridge]]'', a cantilever truss bridge.
Image:Pierre Pflimlin Bridge UC Adjusted.jpg|This 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 cantilever 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 [[Appalachia]]
File:DoubleJettiedBuilding.jpg|A double jettied building in 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.
</gallery>

==Aircraft==

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

Another use of the cantilever is in [[fixed-wing aircraft]] design, pioneered by [[Hugo Junkers]] in 1915. Early aircraft wings typically bore their loads by using two (or more) wings in a [[biplane]] configuration braced with wires and struts.
They were similar to [[truss bridge]]s, having been developed by [[Octave Chanute]], a railroad bridge engineer. The wings were braced with crossed wires so they would stay parallel, as well as front-to-back to resist twisting, running diagonally between adjacent strut anchorages. The cables and struts 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's airframe design. Early monoplanes used either [[strut]]s (as do some current light aircraft), or cables like the 1909 [[Bleriot XI]] (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.
[[Image:Hawker Hurricane03.jpg|thumb|200px|A British [[Hawker Hurricane]] from [[World War II]] with cantilever wings]] [[Hugo Junkers]] endeavored to eliminate virtually all major external bracing members, only a dozen years after the [[Wright Brothers]]' initial flights, to decrease airframe drag in flight, with the result being 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 [[Biplane#Sesquiplane or sesquiwing|sesquiplane]] built instead with wooden materials, the [[Fokker V.1]].

The most common current wing design is the cantilever. A single large beam, called the ''main [[spar (aviation)|spar]]'', runs through the wing, typically nearer the [[leading edge]] at about 25 percent of the total [[chord (aircraft)|chord]].
In flight, the wings generate [[lift (force)|lift]], and the wing spars are designed to carry this load through the fuselage to the other wing.
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 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.

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, with the [[Messerschmitt Bf 109 variants#Bf 109E "Emil"|Messerschmitt Bf 109E]] of 1939-41 being one of the last World War II fighters in frontline service to have bracing struts for its stabilizer.

==In 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|filter]]s 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} \left(\frac{L}{t}\right)^2
</math>

where ν 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. Controlling [[residual stress]] can also be difficult.

[[Image:MEMS Microcantilever in Resonance.png|thumb|MEMS cantilever in resonance<ref>P. C. Fletcher, Y. Xu, P. Gopinath, J. Williams, B. W. Alphenaar, R. D. Bradshaw, R. S. Keynton, "Piezoresistive Geometry for Maximizing Microcantilever Array Sensitivity," presented at the IEEE Sensors, Lecce, Italy, 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=Bǎnicǎ|first=Florinel-Gabriel|title=Chemical Sensors and Biosensors:Fundamentals and Applications|year=2012|publisher=John Wiley & Sons|location=Chichester, UK|isbn=9781118354230|pages=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]].

==In storage applications==

===Warehouse storage===
A cantilever rack is a type of [[warehouse]] storage system consisting of the vertical column, the base, the arms, and the horizontal and/or cross bracing.
These components are fabricated from both roll formed and structural steel.
The horizontal and/or cross bracing are used to connect two or more columns together.
They are commonly found in [[lumber yard]]s, woodworking shops, and plumbing supply warehouses.

===Portable storage===
A folding cantilever tray is a type of stacked shelf that can be unfolded to allow convenient access to items on multiple tiers simultaneously.
The shelves can be collapsed when not in use for more compact storage.
Because of these properties folding cantilever trays are often used in [[baggage]] and [[toolbox]]es.

==See also==
* [[Applied mechanics]]
* [[Beam theory]]
* [[Bicycle brake#The cantilever brake design|Cantilever bicycle brakes]]
* [[Bicycle frame#Cantilever|Cantilever bicycle frame]]
* [[Cantilever bridge]]
* [[Cantilever chair]]
* [[Cantilever mechanics (orthodontics)]]
* [[Grand Canyon Skywalk]]
* [[Knudsen force]] in the context of microcantilevers
* [[Moment (physics)]]
* [[Statics]]

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

==External links==
* [http://www.efunda.com/formulae/solid_mechanics/beams/casestudy_bc_cantilever.cfm Cantilever Beam Loading Options]—Loading scenarios with solutions and calculator available

[[Category:Architectural elements]]
[[Category:Nanotechnology]]
[[Category:Structural system]]

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216.45.141.162: Described Explicit Initialization Vectors under CBC mode

en>Yamla: Remove uncited information

en>Mitch Ames: /* Common modes */ c/e