Biegungen

Biegungen is the plural of Biegung, a German term for bending or curving. It appears across disciplines such as physics, engineering, geometry, and everyday language to denote the departure from straightness of a line, surface, or path, as well as the deformation of a material under load.

In geometry and mathematics, bending is described by curvature. For a smooth plane curve parameterized by arc length, the curvature κ measures how quickly the curve changes direction; the radius of curvature R is the reciprocal of the absolute curvature, R = 1/|κ|. Signed curvature encodes the direction of bending.

In structural engineering and mechanics, Biegung refers to the bending deformation of slender bodies, such as beams, under lateral loads. The curvature of a deflected beam is related to the bending moment M by relationships such as M = E I κ in the Euler-Bernoulli framework, where E is Young’s modulus and I is the second moment of area. Bending also produces stresses described by σ = M y / I, where y is the distance from the neutral axis. Designers specify allowable Biegungen to prevent excessive deformation or failure.

In road design, cartography, and transportation engineering, Biegungen denote curves in roads, railways, and waterways. These curves are characterized by a radius of curvature and, in the traffic context, may be complemented by superelevation and warning signage to ensure safety and travel efficiency.

Etymologically, the term derives from the German verb bie­gen (to bend). Related concepts include curvature, radius of curvature, bending moment, and superelevation.