20.15 : 非対称曲げ: 中立軸の角度

Consider a member with a vertical plane of symmetry subjected to bending couples in a plane at an angle θ with respect to the vertical axis of the member, causing an unsymmetric bending.

Resolving one of the bending couple vectors along the principle centroidal axes of the member and writing the expression for the stress due to each component, the distribution of the stresses due to the bending couple is calculated using the superposition method.

The distribution of the stress due to bending couples is linear. The magnitude of the stress will be zero for the neutral axis of the section.

Solving the equation for the neutral axis and rewriting the components of bending vectors in terms of θ gives the equation of a straight line.

Here, the slope of the equation gives the angle ϕ of the neutral axis with respect to the z-axis.

Here, the angle ϕ will be greater than the angle θ when the moment of inertia along the z-axis is greater than the moment of inertia along the y-axis.