A cantilever is a rigid
structural element that extends horizontally and is supported at only 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
Beam may refer to:
Streams of particles or energy
*Light beam, or beam of light, a directional projection of light energy
**Laser beam
*Particle beam, a stream of charged or neutral particles
**Charged particle beam, a spatially localized grou ...
, plate,
truss
A truss is an assembly of ''members'' such as beams, connected by ''nodes'', that creates a rigid structure.
In engineering, a truss is a structure that "consists of two-force members only, where the members are organized so that the assembl ...
, 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
Shear stress, often denoted by (Greek: tau), is the component of stress coplanar with a material cross section. It arises from the shear force, the component of force vector parallel to the material cross section. ''Normal stress'', on the ot ...
and a
bending moment.
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 architecture, a corbel is a structural piece of stone, wood or metal jutting from a wall to carry a superincumbent weight, a type of bracket. A corbel is a solid piece of material in the wall, whereas a console is a piece applied to the s ...
). 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
Scotland (, ) is a country that is part of the United Kingdom. Covering the northern third of the island of Great Britain, mainland Scotland has a border with England to the southeast and is otherwise surrounded by the Atlantic Ocean to the ...
is an example of a cantilever
truss bridge. A cantilever in a traditionally
timber framed building is called a
jetty
A jetty is a structure that projects from land out into water. A jetty may serve as a breakwater, as a walkway, or both; or, in pairs, as a means of constricting a channel. The term derives from the French word ', "thrown", signifying somet ...
or
forebay. In the southern United States, a historic barn type is the cantilever barn of
log construction
A log house, or log building, is a structure built with horizontal logs interlocked at the corners by notching. Logs may be round, squared or hewn to other shapes, either handcrafted or milled. The term "log cabin" generally refers to a sma ...
.
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
Falsework consists of temporary structures used in construction to support a permanent structure until its construction is sufficiently advanced to support itself. For arches, this is specifically called centering. Falsework includes temporary su ...
, 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
Navajo Bridge is the name of twin steel spandrel arch bridges that cross the Colorado River in the Grand Canyon National Park (near Lee's Ferry, Lees Ferry) in northern Coconino County, Arizona, Coconino County, Arizona, United States. The newer ...
) 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
A cable-stayed bridge has one or more ''towers'' (or ''pylons''), from which cables support the bridge deck. A distinctive feature are the cables or stays, which run directly from the tower to the deck, normally forming a fan-like pattern o ...
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
In physics and mechanics, torque is the rotational equivalent of linear force. It is also referred to as the moment of force (also abbreviated to moment). It represents the capability of a force to produce change in the rotational motion of th ...
and rotational equilibrium for their stability.
In an architectural application,
Frank Lloyd Wright
Frank Lloyd Wright (June 8, 1867 – April 9, 1959) was an American architect, designer, writer, and educator. He designed more than 1,000 structures over a creative period of 70 years. Wright played a key role in the architectural movements o ...
's
Fallingwater
Fallingwater is a house designed by the architect Frank Lloyd Wright in 1935 in the Laurel Highlands of southwest Pennsylvania, about southeast of Pittsburgh in the United States. It is built partly over a waterfall on Bear Run in the Mill R ...
used cantilevers to project large balconies.
The East Stand at
Elland Road
Elland Road is a football stadium in Beeston, Leeds, West Yorkshire, England, which has been the home of Premier League club Leeds United since the club's formation in 1919. The stadium is the 14th largest football stadium in England.
The g ...
Stadium in Leeds was, when completed, the largest cantilever stand in the world holding 17,000 spectators.
The
roof
A roof ( : roofs or rooves) is the top covering of a building, including all materials and constructions necessary to support it on the walls of the building or on uprights, providing protection against rain, snow, sunlight, extremes of temper ...
built over the stands at
Old Trafford
Old Trafford () is a football stadium in Old Trafford, Greater Manchester, England, and the home of Manchester United. With a capacity of 74,310 it is the largest club football stadium (and second-largest football stadium overall after Wemb ...
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
Newcastle upon Tyne ( RP: , ), or simply Newcastle, is a city and metropolitan borough in Tyne and Wear, England. The city is located on the River Tyne's northern bank and forms the largest part of the Tyneside built-up area. Newcastle is als ...
, the home stadium of
Newcastle United F.C.
Newcastle United Football Club is an English professional football club, based in Newcastle upon Tyne, that plays in the Premier League – the top flight of English football. The club was founded in 1892 by the merger of Newcastle East End ...
[IStructE The Structural Engineer Volume 77/No 21, 2 November 1999. James's Park a redevelopment challenge][The Architects' Journal](_blank)
Existing stadiums: St James' Park, Newcastle. 1 July 2005
Less obvious examples of cantilevers are free-standing (vertical)
radio towers
Radio masts and towers are typically tall structures designed to support antenna (radio), antennas for telecommunications and broadcasting, including television. There are two main types: guyed and self-supporting structures. They are among the t ...
without
guy-wire
A guy-wire, guy-line, guy-rope, or stay, also called simply a guy, is a tensioned cable designed to add stability to a free-standing structure. They are used commonly for ship masts, radio masts, wind turbines, utility poles, and tents. A thi ...
s, and
chimneys, which resist being blown over by the wind through cantilever action at their base.
Image:ForthBridgeEdinburgh.jpg, The Forth Bridge, a cantilever truss bridge
Image:Pierre Pflimlin Bridge UC Adjusted.jpg, This concrete bridge
Concrete is a composite material composed of fine and coarse aggregate bonded together with a fluid cement (cement paste) that hardens (cures) over time. Concrete is the second-most-used substance in the world after water, and is the most wi ...
temporarily functions as a set of two balanced cantilevers during construction – with further cantilevers jutting out to support formwork
Formwork is Molding (process), molds into which concrete or similar materials are either precast concrete, precast or cast-in-place concrete, cast-in-place. In the context of concrete construction, the falsework supports the shuttering mold ...
.
File:Howrah Bridge.jpg, Howrah Bridge in India
India, officially the Republic of India (Hindi: ), is a country in South Asia. It is the seventh-largest country by area, the second-most populous country, and the most populous democracy in the world. Bounded by the Indian Ocean on the so ...
, a cantilever bridge
Image:FallingwaterCantilever570320cv.jpg, A cantilevered balcony of the Fallingwater
Fallingwater is a house designed by the architect Frank Lloyd Wright in 1935 in the Laurel Highlands of southwest Pennsylvania, about southeast of Pittsburgh in the United States. It is built partly over a waterfall on Bear Run in the Mill R ...
house, by Frank Lloyd Wright
Frank Lloyd Wright (June 8, 1867 – April 9, 1959) was an American architect, designer, writer, and educator. He designed more than 1,000 structures over a creative period of 70 years. Wright played a key role in the architectural movements o ...
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
Tennessee ( , ), officially the State of Tennessee, is a landlocked state in the Southeastern region of the United States. Tennessee is the 36th-largest by area and the 15th-most populous of the 50 states. It is bordered by Kentucky to th ...
File:18-22-186-cades.jpg, Cantilever barn at Cades Cove
Cades Cove is an isolated valley located in the Tennessee section of the Great Smoky Mountains National Park. The valley was home to numerous settlers before the formation of the national park. Today Cades Cove, the single most popular destinati ...
File:DoubleJettiedBuilding.jpg, A double jettied building in Cambridge, England
File:Cantilever Jenga.JPG, Cantilever occurring in the game " Jenga"
File:Riverplace Tower in Jacksonville.jpg, Cantilever facade of Riverplace Tower
The Riverplace Tower is a 28-floor office building on the south bank of the St. Johns River in Jacksonville, Florida. At the time of its construction, it was the tallest building in the state of Florida and was the defining landmark in Jacksonvi ...
in Jacksonville, Florida
Jacksonville is a city located on the Atlantic coast of northeast Florida, the most populous city proper in the state and is the largest city by area in the contiguous United States as of 2020. It is the seat of Duval County, with which the ...
, by Welton Becket
Welton David Becket (August 8, 1902 – January 16, 1969) was an American modern architect who designed many buildings in Los Angeles, California.
Biography
Becket was born in Seattle, Washington and graduated from the University of Washingt ...
and KBJ Architects
KBJ Architects, Inc. (KBJ) is an American architectural firm based in Jacksonville, Florida. The firm designed 17 of the city's 30 tallest buildings and "created Jacksonville's modern skyline", according to ''The Florida Times-Union'' newspaper.Ker ...
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
Ronan Point was a 22-storey tower block in Canning Town in Newham, East London, that partly collapsed on 16 May 1968, only two months after it had opened. A gas explosion blew out some load-bearing walls, causing the collapse of one entire corn ...
: Structural failure of part of floors cantilevered from a central shaft.
Aircraft
![Junkers J 1 at Döberitz 1915](https://upload.wikimedia.org/wikipedia/commons/d/db/Junkers_J_1_at_D%C3%B6beritz_1915.jpg)
The cantilever is commonly used in the wings of
fixed-wing aircraft
A fixed-wing aircraft is a heavier-than-air flying machine, such as an airplane, which is capable of flight using wings that generate lift caused by the aircraft's forward airspeed and the shape of the wings. Fixed-wing aircraft are distinc ...
. 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
Reinhold Platz (16 January 1886 – 15 September 1966) was a German aircraft designer and manufacturer in service of the Dutch company Fokker.
Platz was hired by Fokker in 1912 as a welder. His first hands-on projects were to weld the frame pa ...
of
Fokker
Fokker was a Dutch aircraft manufacturer named after its founder, Anthony Fokker. The company operated under several different names. It was founded in 1912 in Berlin, Germany, and became famous for its fighter aircraft in World War I. In 1919 ...
also achieved success with a cantilever-winged
sesquiplane
A biplane is a fixed-wing aircraft with two main wings stacked one above the other. The first powered, controlled aeroplane to fly, the Wright Flyer, used a biplane wing arrangement, as did many aircraft in the early years of aviation. While a ...
built instead with wooden materials, the
Fokker V.1
The Fokker V.1 was a small German sesquiplane experimental fighter prototype built in 1916 by the Fokker-Flugzeugwerke. Sporting a parasol wing, it was the first Fokker aircraft purportedly designed by Reinhold Platz—the respective roles played ...
.
![De Havilland DH88 Comet](https://upload.wikimedia.org/wikipedia/commons/9/94/De_Havilland_DH88_Comet.jpg)
In the cantilever wing, one or more strong beams, called ''
spars
The United States Coast Guard (USCG) Women's Reserve, also known as the SPARS (SPARS was the acronym for "Semper Paratus—Always Ready"), was the women's branch of the United States Coast Guard Reserve. It was established by the United States ...
'', 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 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. 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
The de Havilland DH.88 Comet is a British two-seat, twin-engined aircraft built by the de Havilland Aircraft Company. It was developed specifically to participate in the 1934 England-Australia MacRobertson Air Race from the United Kingdom to A ...
.
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.
In microelectromechanical systems
Cantilevered beams are the most ubiquitous structures in the field of
microelectromechanical systems
Microelectromechanical systems (MEMS), also written as micro-electro-mechanical systems (or microelectronic and microelectromechanical systems) and the related micromechatronics and microsystems constitute the technology of microscopic devices, ...
(MEMS). An early example of a MEMS cantilever is the Resonistor, an electromechanical monolithic resonator. MEMS cantilevers are commonly fabricated from
silicon
Silicon is a chemical element with the symbol Si and atomic number 14. It is a hard, brittle crystalline solid with a blue-grey metallic luster, and is a tetravalent metalloid and semiconductor. It is a member of group 14 in the periodic tab ...
(Si),
silicon nitride (Si
3N
4), or
polymer
A polymer (; Greek '' poly-'', "many" + ''-mer'', "part")
is a substance or material consisting of very large molecules called macromolecules, composed of many repeating subunits. Due to their broad spectrum of properties, both synthetic a ...
s.
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
Atomic force microscopy (AFM) or scanning force microscopy (SFM) is a very-high-resolution type of scanning probe microscopy (SPM), with demonstrated resolution on the order of fractions of a nanometer, more than 1000 times better than the op ...
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
Radio frequency (RF) is the oscillation rate of an alternating electric current or voltage or of a magnetic, electric or electromagnetic field or mechanical system in the frequency range from around to around . This is roughly between the upp ...
filters
Filter, filtering or filters may refer to:
Science and technology
Computing
* Filter (higher-order function), in functional programming
* Filter (software), a computer program to process a data stream
* Filter (video), a software component tha ...
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
Deflection or deflexion may refer to:
Board games
* Deflection (chess), a tactic that forces an opposing chess piece to leave a square
* Khet (game), formerly ''Deflexion'', an Egyptian-themed chess-like game using lasers
Mechanics
* Deflection ...
δ to applied stress σ:
:
where
is
Poisson's ratio,
is
Young's modulus
Young's modulus E, the Young modulus, or the modulus of elasticity in tension or compression (i.e., negative tension), is a mechanical property that measures the tensile or compressive stiffness of a solid material when the force is applied leng ...
,
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
In classical mechanics, a harmonic oscillator is a system that, when displaced from its Mechanical equilibrium, equilibrium position, experiences a restoring force ''F'' Proportionality (mathematics), proportional to the displacement ''x'':
\v ...
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. However, it has been shown that microcantilever thicknesses can be precisely measured and that this variation can be quantified. Controlling
residual stress can also be difficult.
Chemical sensor applications
A
chemical sensor
A sensor is a device that produces an output signal for the purpose of sensing a physical phenomenon.
In the broadest definition, a sensor is a device, module, machine, or subsystem that detects events or changes in its environment and sends ...
can be obtained by coating a recognition receptor layer over the upper side of a microcantilever beam. A typical application is the immunosensor based on an
antibody
An antibody (Ab), also known as an immunoglobulin (Ig), is a large, Y-shaped protein used by the immune system to identify and neutralize foreign objects such as pathogenic bacteria and viruses. The antibody recognizes a unique molecule of the ...
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.
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.
[Yue Zhao,Agnivo Gosai, Pranav Shrotriya : Effect of Receptor Attachment on Sensitivity of Label Free Microcantilever Based Biosensor Using Malachite Green Aptamer https://doi.org/10.1016/j.snb.2019.126963]
See also
*
Applied mechanics
Applied mechanics is the branch of science concerned with the motion of any substance that can be experienced or perceived by humans without the help of instruments. In short, when mechanics concepts surpass being theoretical and are applied and e ...
*
Cantilever bicycle brakes
*
Cantilever bicycle frame
*
Cantilever chair
A cantilever chair is a chair whose seating and framework are not supported by the typical arrangement of 4 legs, but instead is held erect and aloft by a single leg or legs that are attached to one end of a chair's seat and bent in an L shape, thu ...
*
Cantilever method
*
Cantilevered stairs
*
Corbel arch
A corbel arch (or corbeled / corbelled arch) is an arch-like construction method that uses the architectural technique of corbeling to span a space or void in a structure, such as an entranceway in a wall or as the span of a bridge. A corbel v ...
*
Euler–Bernoulli beam theory
Euler–Bernoulli beam theory (also known as engineer's beam theory or classical beam theory) is a simplification of the linear theory of elasticity which provides a means of calculating the load-carrying and deflection characteristics of beams. ...
*
Grand Canyon Skywalk
*
Knudsen force in the context of microcantilevers
*
Orthodontics
Orthodontics is a dentistry specialty that addresses the diagnosis, prevention, management, and correction of mal-positioned teeth and jaws, and misaligned bite patterns. It may also address the modification of facial growth, known as dentofacial ...
*
Statics
Statics is the branch of classical mechanics that is concerned with the analysis of force and torque (also called moment) acting on physical systems that do not experience an acceleration (''a''=0), but rather, are in static equilibrium with ...
References
Sources
* Inglis, Simon: ''Football Grounds of Britain''. CollinsWillow, 1996. page 206.
*
*
*
{{Authority control
Architectural elements
Structural system
Bridge components