Plastic bending

Plastic bending is a nonlinear behaviour particular to members made of ductile materials that frequently achieve much greater ultimate bending strength than indicated by a linear elastic bending analysis. In both the plastic and elastic bending analyses of a straight beam, it is assumed that the strain distribution is linear about the neutral axis (plane sections remain plane). In an elastic analysis this assumption leads to a linear stress distribution but in a plastic analysis the resulting stress distribution is nonlinear and is dependent on the beam’s material.

The limiting plastic bending strength $M_{r}$ $M_{r}$ (see Plastic moment)can generally be thought of as an upper limit to a beam’s load–carrying capability as it only represents the strength at a particular cross–section and not the load–carrying capability of the overall beam. A beam may fail due to global or local instability before $M_{r}$ $M_{r}$ is reached at any point on its length. Therefore, beams should also be checked for local buckling, local crippling, and global lateral–torsional buckling modes of failure.

Note that the deflections necessary to develop the stresses indicated in a plastic analysis are generally excessive, frequently to the point of incompatibility with the function of the structure. Therefore, separate analysis may be required to ensure design deflection limits are not exceeded. Also, since working materials into the plastic range can lead to permanent deformation of the structure, additional analyses may be required at limit load to ensure no detrimental permanent deformations occur. The large deflections and stiffness changes usually associated with plastic bending can significantly change the internal load distribution, particularly in statically indeterminate beams. The internal load distribution associated with the deformed shape and stiffness should be used for calculations.

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