20.17 : 曲線部材の曲げ: ひずみ解析

Consider a curved member having a transverse section symmetric with the y-axis. Its upper and lower surfaces intersect with xy-planes along arcs of circles having a center at point C.

If two equal and opposite couples act on a member in the plane of symmetry, then the curvature of the arcs of the section increases, with the new center C'.

The applied couples also result in the reduction of the length of the upper surface and an increase in the length of the lower surface of the member, implying that there exists a surface of unchanged length known as the neutral axis.

The deformation of the arc V' W' that is situated at a distance y from the neutral surface is expressed as a change in the length of the arc.

Using geometry, the deformation can be rewritten in terms of the radius of the curvature of the neutral surface.

The strain is given by dividing deformation by its original length, which shows that the strain varies non-linearly with distance y from the neutral surface.