20.11 : 具有单个对称平面的杆件的塑性变形

Consider a member experiencing plastic deformation due to bending and having one plane of symmetry. The stresses are uniformly distributed above and below the neutral axis, with stress being -σ_y above the neutral axis and +σ_y below the neutral axis.

Here, the neutral axis of the member does not coincide with the centroid of the member.

To locate the neutral axis, consider the resultant of the compressive forces above the neutral axis R₁ and the resultant of the tensile forces R₂ below the neutral axis.

The compressive and tensile resultant forces form a couple, which is equivalent to the couple applied to the member. This shows that the neutral axis divides the member into cross-sections of equal areas.

The line of action of the resultant compressive and tensile forces passes through the centroids of the two equal areas. 

If the distance between these two centroids is defined as d, then the plastic moment of the member is expressed as half of the product of the area of the cross-section, the magnitude of the stress, and d.