The mechanics of deformation in curved members, such as beams or arches, under bending moments, involve complex responses. When such a member, symmetric about the y-axis and shaped like a segment of a circle centered at point C, is subjected to equal and opposite forces, its curvature and surface lengths change significantly. This alteration results in the shift of the curvature's center from C to C', indicating a tighter curve.
The important part of bending analysis for such a member is the concept of the neutral axis, a hypothetical line within the material whose length remains unchanged despite the bending. This axis does not experience tensile or compressive strain.
The strain at any point on the curved member is influenced by its distance from the neutral axis. The upper surface of the member shortens, and the lower surface elongates due to the bending.
Strain, which measures the deformation per unit length, varies across the member's thickness. This variation is due to the differential change in length between points above and below the neutral axis. Essentially, strain depends on how much more pronounced the curve becomes due to bending, reflecting a non-linear distribution from the neutral axis.
