Neutral plane

In mechanics, the neutral plane or neutral surface is a conceptual plane within a beam or cantilever. When loaded by a bending force, the beam bends so that the inner surface is in compression and the outer surface is in tension. The neutral plane is the surface within the beam between these zones, where the material of the beam is not under stress, either compression or tension.

As there is no lengthwise stress force on the neutral plane, there is no strain 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, it is obvious that 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 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.

The location of the neutral plane can be an important factor in monocoque structures and pressure vessels. 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 submarines 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 scantlings. The designer Andrew I. McKee at Portsmouth Naval Shipyard 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.

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Wikipedia