Cantilever
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, plate, truss, or 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.[1]
Cantilever construction allows overhanging structures without additional support.
In bridges, towers, and buildings
Cantilevers are widely found in construction, notably in cantilever bridges and 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 framed building is called a jetty or forebay. In the southern United States, a historic barn type is the cantilever barn of 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
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. The East Stand at Elland Road Stadium in Leeds was, when completed, the largest cantilever stand in the world[2] 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)
Less obvious examples of cantilevers are free-standing (vertical)
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The Forth Bridge, a cantilever truss bridge
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This concrete bridge temporarily functions as a set of two balanced cantilevers during construction – with further cantilevers jutting out to support formwork.
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Howrah Bridge in India, a cantilever bridge
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A cantilevered balcony of the Fallingwater house, by Frank Lloyd Wright
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A cantilevered railroad deck and fence on the Canton Viaduct
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A cantilever barn in rural Tennessee
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Cantilever barn at Cades Cove
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A double jettied building in Cambridge, England
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Cantilever occurring in the game "Jenga"
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Thisradiographof a "bridge" dental restoration features a cantilevered crown to the left.
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Ronan Point: Structural failure of part of floors cantilevered from a central shaft.
Aircraft
The cantilever is commonly used in the wings of
In the cantilever wing, one or more strong beams, called
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 200 miles per hour (320 km/h) 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.[5] 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 England-Australia air race of 1934, which was won by a de Havilland DH.88 Comet.[6]
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
Cantilever in microelectromechanical systems
Cantilevered beams are the most ubiquitous structures in the field of
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 is Poisson's ratio, is Young's modulus, is the beam length and 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
where is force and is the cantilever width. The spring constant is related to the cantilever resonance frequency by the usual harmonic oscillator formula . 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.[9] However, it has been shown that microcantilever thicknesses can be precisely measured and that this variation can be quantified.[10] Controlling residual stress can also be difficult.
Chemical sensor applications
A
See also
References
- McGraw-Hill. p. 2. Retrieved 2008-10-01.
A cantilever beam is a beam having one end rigidly fixed and the other end free.
- ^ "GMI Construction wins £5.5M Design and Build Contract for Leeds United Football Club's Elland Road East Stand". Construction News. 6 February 1992. Retrieved 24 September 2012.
- ^ IStructE The Structural Engineer Volume 77/No 21, 2 November 1999. James's Park a redevelopment challenge
- ^ highbeam.com; The Architects' Journal. Existing stadiums: St James' Park, Newcastle. 1 July 2005
- ^ Stevens, James Hay; The Shape of the Aeroplane, Hutchinson, 1953. pp.78 ff.
- ^ Davy, M.J.B.; Aeronautics – Heavier-Than-Air Aircraft, Part I, Historical Survey, Revised edition, Science Museum/HMSO, December 1949. p.57.
- ^ ELECTROMECHANICAL MONOLITHIC RESONATOR, US Pat.3417249 - Filed April 29, 1966
- ^ 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)
- ^ 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)
- ^ 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)
- ^ Patrick C. Fletcher; Y. Xu; P. Gopinath; J. Williams; B. W. Alphenaar; R. D. Bradshaw; Robert S. Keynton (2008). Piezoresistive Geometry for Maximizing Microcantilever Array Sensitivity. IEEE Sensors.
- ISBN 978-1-118-35423-0.
- PMID 36133213.
- .
Sources
- Inglis, Simon: Football Grounds of Britain. CollinsWillow, 1996. page 206.
- Madou, Marc J (2002). Fundamentals of Microfabrication. Taylor & Francis. ISBN 0-8493-0826-7.
- Roth, Leland M (1993). Understanding Architecture: Its Elements History and Meaning. Oxford, UK: Westview Press. pp. 23–4. ISBN 0-06-430158-3.
- Sarid, Dror (1994). Scanning Force Microscopy. Oxford University Press. ISBN 0-19-509204-X.
External links
- Media related to Cantilever beams at Wikimedia Commons