Chapter 12
Plastic Behavior of Structures
This chapter is devoted to the analysis of a structure, taking into account the plastic
properties of material. Such analysis allows the use of the reserves of strength of
material, which remains unused considering the material of structure as elastic.
Therefore, plastic analysis allows us to define the limit load on the structure and
to design a more economical structure. Fundamental idea of the plastic analysis is
discussed using the direct method. Kinematical and statical methods of calculation
of the limit loads are considered. Detailed plastic analysis of the beams and frames
are presented.
12.1 Idealized Stress–Strain Diagrams.....................................
In the previous chapters, we considered structures taking into account only elastic
properties of materials for all members of a structure. Analysis of a structure based
on elastic properties of material is called theelastic (or linear) analysis. Elastic anal-
ysis does not allow us to find out thereserveof strength of the structure beyond its
elastic limit. Also this analysis cannot answer the question: what would happen
with the structure, if the stresses in its members will be larger than the proportional
limit? Therefore, a problem concerning to the actual strength of a structure cannot
be solved using elastic analysis.
The typical stress–strain diagram for the specimen of structural steel is pre-
sented in Fig.12.1a. Elastic analysis corresponds tothe initial straight portion of
the"diagram. If a specimen is loaded into the proportional limit (or below)
and then released, then material will unload along the loading path back to the
origin (Fig.12.1a). So, there are no residual strains. This property of unloaded spec-
imen to return to its original dimensions is calledelasticity, and material in this
region is called thelinearly elastic. Within the elastic region, a relationship between
stress and strain obey to Hooke’s lawDE".
Let a specimen is loaded into the elastic limit. The stress at this point slightly
exceeds the proportional limit. From this point, the material unloads along the line
that is parallel to straight portion of the diagram and thus, the material has the very
smallresidualstrain (Fig.12.1a).
I.A. Karnovsky and O. Lebed,Advanced Methods of Structural Analysis,
DOI 10.1007/978-1-4419-1047-912,cSpringer Science+Business Media, LLC 2010
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