Plastic Structural Behavior

Plastic Structural Behavior

Yield and collapse will occur simultaneously only for structural shapes that carry constant stress fields (uniform distribution of tension, compression, or shear). In a general structure such as our standard blob (Figure 10.3), only a certain point or points reach yield and the load can be increased beyond that threshold. As the load increases beyond “first yield,” the load-deformation response of the structure becomes nonlinear as plastic regions grow until a full “collapse mechanism” is formed. At this point, if there is no strain hardening or “geometric strengthening,” the structure or parts of it become dynamic either suddenly (and violently, sometimes killing peo-ple) or gradually so there is time to get out of the way.

The plastic behavior of a structure must be clearly differentiated conceptu-ally from the plastic behavior of the material from which it is made. For our EPS material, the stress�'strain curve is made up of two straight lines and is, in that sense, piecewise linear. The load deformation structural response beyond first yield is generally not linear and is therefore much more difficult to deter-mine than its behavior in the elastic range.

In fact only a handful of complete, formal, closed-form, plasticity solutions have ever been found. These solutions are all based on a strategy where the deformations are calculated from elastic strains in those portions of the struc-ture that remain linear while the plastic zones spread with increasing load to generate the limit condition at collapse. Moreover, most of these are limited to two-dimensional problems with σ_z= σ₂ intermediate between σ₁ and σ₃ in the x, y, or r,  plane.*