mechanics Mechanics (from Ancient Greek: μηχανική, ''mēkhanikḗ'', "of machines") is the area of mathematics and physics concerned with the relationships between force, matter, and motion among physical objects. Forces applied to objects r ...

, the neutral plane or neutral surface is a conceptual

plane Plane(s) most often refers to: * Aero- or airplane, a powered, fixed-wing aircraft * Plane (geometry), a flat, 2-dimensional surface Plane or planes may also refer to: Biology * Plane (tree) or ''Platanus'', wetland native plant * Planes (gen ...

within 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 ...

cantilever 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 canti ...

. When loaded by a bending force, the beam bends so that the inner surface is in

compression Compression may refer to: Physical science *Compression (physics), size reduction due to forces *Compression member, a structural element such as a column *Compressibility, susceptibility to compression *Gas compression *Compression ratio, of a c ...

and the outer surface is in

tension Tension may refer to: Science * Psychological stress * Tension (physics), a force related to the stretching of an object (the opposite of compression) * Tension (geology), a stress which stretches rocks in two opposite directions * Voltage or el ...

. The neutral plane is the surface within the beam between these zones, where the material of the beam is not under

stress Stress may refer to: Science and medicine * Stress (biology), an organism's response to a stressor such as an environmental condition * Stress (linguistics), relative emphasis or prominence given to a syllable in a word, or to a word in a phrase ...

, either compression or tension. As there is no lengthwise stress force on the neutral plane, there is no

strain Strain may refer to: Science and technology * Strain (biology), variants of plants, viruses or bacteria; or an inbred animal used for experimental purposes * Strain (chemistry), a chemical stress of a molecule * Strain (injury), an injury to a mu ...

or extension either: when the beam bends, the length of the neutral plane remains constant. Any line within the neutral plane parallel to the axis of the beam is called the deflection curve of the beam. To show that every beam must have a neutral plane, the material of the beam can be imagined to be divided into narrow fibers parallel to its length. When the beam is bent, at any given cross-section the region of fibers near the concave side will be under compression, while the region near the convex side will be under tension. Because the stress in the material must be

continuous Continuity or continuous may refer to: Mathematics * Continuity (mathematics), the opposing concept to discreteness; common examples include ** Continuous probability distribution or random variable in probability and statistics ** Continuous ...

across any cross section, there must be a boundary between the regions of compression and tension at which the fibers have no stress. This is the neutral plane.

Structural design

The location of the neutral plane can be an important factor in

monocoque Monocoque ( ), also called structural skin, is a structural system in which loads are supported by an object's external skin, in a manner similar to an egg shell. The word ''monocoque'' is a French term for "single shell". First used for boats, ...

structures and

pressure vessel A pressure vessel is a container designed to hold gases or liquids at a pressure substantially different from the ambient pressure. Construction methods and materials may be chosen to suit the pressure application, and will depend on the size o ...

s. If the structure is a membrane supported by strength ribs, then placing the skin along the neutral surface avoids either compression or tension forces upon it. If the skin is already under external pressure, then this reduces the total force to which it is subject. In the design of submarines this has been an important, although subtle, issue. The US

Fleet submarine A fleet submarine is a submarine with the speed, range, and endurance to operate as part of a navy's battle fleet. Examples of fleet submarines are the British First World War era K class and the American World War II era ''Gato'' class. The t ...

s of World War II had a hull section that was not quite circular, causing the nodal circle to separate from the neutral plane, giving rise to additional stresses. The original design was framed internally: this needed trial-and-error design refinement to produce acceptable dimensions for the rib

scantling Scantling is a measurement of prescribed size, dimensions, or cross sectional areas. Shipping In shipbuilding, the scantling refers to the collective dimensions of the framing (apart from the keel) to which planks or plates are attached to form th ...

s. The designer Andrew I. McKee at

Portsmouth Naval Shipyard The Portsmouth Naval Shipyard, often called the Portsmouth Navy Yard, is a United States Navy shipyard in Kittery on the southern boundary of Maine near the city of Portsmouth, New Hampshire. Founded in 1800, PNS is U.S. Navy's oldest continuo ...

developed an improved design. By placing the frames partly inside the hull and partly outside, the neutral axis could be rearranged to coincide with the nodal circle once more. This gave no resultant bending moment on the frames and so allowed a lighter and more efficient structure.

Metrology

The property of remaining a constant length under load has been made use of in length

metrology Metrology is the scientific study of measurement. It establishes a common understanding of units, crucial in linking human activities. Modern metrology has its roots in the French Revolution's political motivation to standardise units in Fran ...

. When metal bars were developed as physical standards for length measures, they were calibrated as marks made on a length measured along the neutral plane. This avoided the minuscule changes in length, owing to the bar sagging under its own weight. The first length standards to use this technique were rectangular section solid bars. A blind hole was bored at each end, to the depth of the neutral plane, and the calibration marks were made at this depth. This was inconvenient, as it was impossible to measure directly between the two marks, but only with an offset trammel down the wells. Platinum-Iridium meter bar

A more convenient approach was used for the

international prototype metre The history of the metre starts with the Scientific Revolution that is considered to have begun with Nicolaus Copernicus's publication of ''De revolutionibus orbium coelestium'' in 1543. Increasingly accurate measurements were required, and sc ...

of 1870, a bar of platinum-iridium alloy which served as the definition of the meter from 1889 to 1960. This was made with a splayed H-shaped cross section, called the Tresca section. One surface of the centre crossbar of the H was designed to coincide with the neutral plane, and the calibration marks defining the meter were scribed into this surface.

References

{{Reflist Statics

Structural design

Metrology

See also

References