A Beginner's Guide to Structural Mechanics/Analysis Continuous Beam Analysis (c) 2007, 2008 T. Bartlett Quimby
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Section CB.3

Plastic Analysis

Last Revised: 08/01/2008

Another method of indeterminate analysis is known as "plastic analysis".  This method is particularly applicable to steel structures when flexural strength is frequently limited by the yielding limit state.

The basic premise is that a plastic hinge forms in the member when the plastic strength of the member is achieved.  This will occur at locations of maximum moment.  A hinge is a location of known moment, so, with the formation of each hinge a statically indeterminate problem becomes less indeterminate by a degree of one for each hinge that is formed.  A structure becomes unstable when too many hinges are formed.  The series of hinges that will make a structure unstable is referred to as a collapse mechanism.

The plastic analysis method is used to determine the capacity of a structure for a given loading system.  The method becomes cumbersome for highly indeterminate structures subjected to multiple load sources.  Plastic analysis has not become common in the design of structures, though it is viable and easier to apply that elastic methods for simple cases.

There are many good references that discuss the application and theory of plastic analysis.  It is not covered here.