Deformations in a Transverse Cross Section

When a material is subjected to uniaxial stress, the material undergoes elongation or contraction in the direction of the applied stress.

At the same time, deformation occurs in the transverse direction to the applied stress, governed by Poisson's ratio.

The deformation in the transverse direction will result either in expansion or contraction above and below the neutral surface.

The expansion and contraction in the vertical transverse direction compensate each other and vanish.

For the horizontal transverse direction, expansion and contraction will result in various horizontal lines of the section, which are bent into circular arcs.

The radius of the curvature of the neutral surface can be expressed as the ratio of the radius of curvature due to bending to the Poisson's ratio of the material.

This radius of curvature corresponds to the circle whose center is situated on the other side of the radius of curvature due to bending.

The reciprocal of the radius of curvature of the neutral surface represents the curvature of the transverse section and is known as the anticlastic curvature.