cantilever - In bridges, towers, and buildings, In aircraft, In MEMS

A horizontal building element where the part hidden within the building bears a downward force, and the other part projects outside without external bracing, and so appears to be self-supporting. It is often used to dramatic effect in modern architecture.

A cantilever is a beam anchored at one end and projecting into space. Cantilever construction allows for long structures without external bracing.

This is in contrast to a post and lintel system where the beam is supported at both ends and loads applied between them.

In bridges, towers, and buildings

Cantilevers are widely found in construction, notably in cantilever bridges and balconies. In cantilever bridges the cantilevers are usually built as balanced pairs, with two such pairs usually used to support a truss central section.

Less obvious examples are free-standing radio towers and chimneys, which resist being blown over by the wind through cantilever action at their base.

In aircraft

Another use of the cantilever is in aircraft design, pioneered by Hugo Junkers in 1915.

It was also desirable to build a monoplane aircraft, as additional drag is formed by having a stack of wings.

The most successful wing design was the cantilever.

Cantilever wings require a much heavier spar than would otherwise be needed in cable-stayed designs. 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.

In MEMS

Cantilevered beams are the most ubiquitous structures in the field of microelectromechanical systems (MEMS). 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. The first is Stoney's formula, which relates cantilever end deflection δ to applied stress σ:

where ν is Poisson's ratio, E is Young's modulus, L is the beam length and t 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 k to the cantilever dimensions and material constants:

where F is force and w is the cantilever width. The spring constant is related to the cantilever resonant frequency ω0 by the usual harmonic oscillator formula . A change in the force applied to a cantilever can shift the resonant 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.