2011-06-21

Inelastic Response to Earthquake Excitation

Structures designed to remain elastic during a large earthquake are antieconomical, it is custumary to design for reduced lateral forces, accepting a controlled level of damage during a large earthquake.

A commonly used idealization of complex force-displacement relationships is the elastic-perfectly plastic model.

For a given excitation we compute the ductility ratio (e-p peak displacement over yield displacement) as a function of the normalized yield force: the ductility is a measure of the structure excursion into plastic range, and indirectly of structural damage.

Reversing the reasoning and the line of flow of the computation, we need to know the normalized yield force that give rise to a ductility demand that is deemed acceptable for a particular class of structures.

From the normalized yield force we derive the yield displacement (simply dividing by k) and repeating the procedure for different levels of ductility demand it is possible to construct a yield displacement response spectrum.

Finally it is possible to introduce an inelastic design spectrum using a mean value of the rduction factor, different for different vibration period ranges.

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Giacomo Boffi