Neutralachse

Neutralachse, in mechanics often called the neutral axis, is the line within a beam’s cross-section along which the longitudinal strain is zero when the beam carries bending moments. Under bending, fibers above the neutral axis shorten (compression) while fibers below it elongate (tension); points on the neutral axis experience no change in length. The concept relies on the assumption that cross-sections remain plane and perpendicular to the beam axis (the Euler-Bernoulli hypothesis).

In a homogeneous, isotropic beam undergoing pure bending, the neutral axis coincides with the centroidal axis of the cross-section. The stress at a distance y from the neutral axis is given by σ = M y / I, where M is the bending moment and I is the second moment of area about the neutral axis. The sign convention assigns compression and tension depending on the side of the axis.

In composite or nonuniform cross-sections, the neutral axis generally shifts away from the geometric centroid. It is found by transforming all materials to a common modulus (transformed-section method) and locating the centroid of the transformed area, or by solving for the neutral-axis position y_NA that yields zero net axial force: ∑ E_i ∫ (y − y_NA) dA_i = 0. Equivalently, y_NA = (∑ E_i A_i y_i) / (∑ E_i A_i), where A_i and y_i are the area and its centroid of each material region relative to a reference axis.

The neutral axis is a key concept in beam design and analysis, and its location influences the distribution of bending stresses. In real structures with axial loads, shear, or material anisotropy, the neutral axis must be determined from the complete stress-strain state rather than from pure bending alone.