Today the lesson is divided in two parts.
Earthquake Excitation
After a visual introduction to the variety of different earthquake excitations, we define the response spectrum in terms of peak deformation as a function of SDOF characteristics.
Pseudo spectra (velocity and accelerations) simply replicate the information in the deformation response spectrum, but are convenient as they directly relate to different aspects of structural response.
From statistical analysis it is possible to infer some common characteristics of response spectra and develop an idealized model of a consistent set of response spectra in terms of simple parameters of the ground motion.
Design spectra are envelopes () of spectral response ordinates.
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.
Material available for the lesson:
- the slides for the first part and
- the slides for the second one
- a ready to print version of the slides (due to an excess of slides superposition, the ready to print pdf has some broken pages, please compare with the slides).