20.14 : 非対称な曲げ

Unsymmetric bending occurs when the bending moment is not acting along the plane of the symmetry of the member or if the member does not possess any plane of symmetry.

An understanding of unsymmetric bending requires studying the conditions under which the neutral axis of a cross-section of an arbitrary shape coincides with the axis of the couple.

Consider an arbitrary shape, the neutral axis and the couple axis are along the z-axis. Here, the force along the x-axis and couple moments along the y and z-axis can be expressed in terms of stress and the cross-sectional area.

Within the proportional limit, the stress developed within the member can be expressed in terms of the maximum stress to calculate the y-component of the couple moment.

The integral is the product of inertia along the y and z-axis and will be zero if these are centroidal axes.

So, the neutral axis of the cross-section will coincide with the couple axis if and only if the couple axis is along one of the centroidal axes of the member.