Seismic Analysis of Structures: Improvements Due to Probabilistic Concepts - Dynamic Behavior of Concrete and Seismic Engineering - page 304

8.8. Seismic analysis of non-linear behavior structures
8.8.1. Introduction
Generally speaking, the dynamic study of non-linear systems is a mathematics
topic that is quite extensive and complex with many remaining gray areas. Unlike
linear cases with which we have been occupied so far, there is no theoretical frame
strong enough to allow us to draw predictive methods engineers could use in an
acceptable way. It is not surprising, as the non-linear feature does not correspond to
the general case, whereas the linear feature corresponds to quite specific properties.
As a consequence, we will be able to propose valid predictive methods only if
the problem becomes particular, i.e. if we can precisely know the nature of the non-
linearities encountered, and those of the stimulation sources, as losing the linearity
property forbids characterization of the structure as a “responsive system”
independently of the source.
Let us note that the type of result we are interested in, regarding the response
(here essentially the maxima), also plays an important part.
In this section we are not dealing with developing theories about non-linear
systems but, after clarifying the main types of non-linearities commonly used in
practice, with illustrating the associated dynamic (seismic) behaviors and describing
the simplified methods used by engineers for direct prediction or interpretation and
thus for a reasonable use of time digital simulations.
8.8.2. Main non-linearities of seismically-loaded structures
Non-linear behaviors can be generated by:
- geometry due to the important displacements of the structure (bridge stay-
cables or high-voltage cables, for instance) or due to limit conditions (the impact of
two neighboring structures like pipework with its supports, for example, or sliding at
the level of anti-seismic bearing devices); or
- behavior laws of materials (for example, the plastic behavior of steel or of
reinforced or pre-stressed concrete extensively illustrated in this topic).
In dynamics, it is important to distinguish non-linearities leading to great energy
dissipation (like plastic or visco-plastic behaviors, or friction) from those implying