Difference between elastic and inleastic response spectra?

As far as I know inelastic response spectra is supposed to consider the geometric distribution, in plan and height and also the importance, nonetheless this concept is a little vague and I could not really find a explicit statement about it.

1 Answer

Inelastic response, spectra are the response spectra after the structure yields. So the restoring force is nonlinear.

Very briefly, eg, in an SDF elastic vibration of a cantilever column subject to ground vibration, the restoring force is $$-kx$$.

But in an inelastic vibration, the restoring force is a combination of past yield restoring force for part of the movement beyond the elastic range and the regular elastic restoring force for the beginning and end of the motion cycle.

For the column above, vibrating with a magnitude beyond its elastic range, once it yields, the restoring force is constant (section plastic moment remains steady regardless of the amount of bending) till the column cycles back to the elastic range with permanent deformation! see figure.

This is interesting for designing the structures so that they give occupants the opportunity to vacate even with earthquakes above design stress and even when the structure is damaged beyond repair.

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