Beam anchored at only one end
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
[
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]
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
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 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 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
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.
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)
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.
[3]
[4]
Less obvious examples of cantilevers are free-standing (vertical)
radio towers
without
guy-wires
, and
chimneys
, which resist being blown over by the wind through cantilever action at their base.
Aircraft
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The cantilever is commonly used in the wings of
fixed-wing aircraft
. Early aircraft had light structures which were braced with
wires
and
struts
. 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
.
In the cantilever wing, one or more strong beams, called
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
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 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
ultralight
class.
Cantilever in microelectromechanical systems
[
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]
Cantilevered beams are the most ubiquitous structures in the field of
microelectromechanical systems
(MEMS). An early example of a MEMS cantilever is the Resonistor,
[7]
[8]
an electromechanical monolithic resonator. MEMS cantilevers are commonly fabricated from
silicon
(Si),
silicon nitride
(Si
3
N
4
), or
polymers
.
The fabrication process typically involves undercutting the cantilever structure to
release
it, often with an anisotropic wet or
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
biosensors
for medical diagnostic applications. MEMS cantilevers are also finding application as
radio frequency
filters
and
resonators
.
The MEMS cantilevers are commonly made as
unimorphs
or
bimorphs
.
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
spring constant
to the cantilever dimensions and material constants:
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
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]
A
chemical sensor
can be obtained by coating a recognition receptor layer over the upper side of a microcantilever beam.
[12]
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.
[13]
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.
[14]
See also
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References
[
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]
- ^
Hool, George A.; Johnson, Nathan Clarke (1920).
"Elements of Structural Theory - Definitions"
.
Handbook of Building Construction
(Google Books)
. Vol. 1 (1st ed.). New York:
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.
- ^
B?nic?, Florinel-Gabriel (2012).
Chemical Sensors and Biosensors:Fundamentals and Applications
. Chichester, UK: John Wiley & Sons. p. 576.
ISBN
978-1-118-35423-0
.
- ^
Noyce, Steven G.; Vanfleet, Richard R.; Craighead, Harold G.; Davis, Robert C. (1999-02-22).
"High surface-area carbon microcantilevers"
.
Nanoscale Advances
.
1
(3): 1148?1154.
doi
:
10.1039/C8NA00101D
.
PMC
9418787
.
PMID
36133213
.
- ^
Zhao, Yue; Gosai, Agnivo; Shrotriya, Pranav (1 December 2019).
"Effect of Receptor Attachment on Sensitivity of Label Free Microcantilever Based Biosensor Using Malachite Green Aptamer"
.
Sensors and Actuators B: Chemical
.
300
.
doi
:
10.1016/j.snb.2019.126963
.
Sources
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External links
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