Design Displacement Spectrum

In this paper, a displacement response spectrum has been obtained through a deterministic procedure based on acceleration data for Iran earthquakes. These accelerograms were selected form more than 2000 records for different stations and earthquakes in Iran. The near field records were omitted and the accelerograms with medium to high magnitude (minimum 5 degrees in Richter scale) were selected. Using an Artificial Neural Network simulator (a committee neural simulator including competitive and back error propagating networks), prepared by the authors [17], the records were categorized according to their shapes (duration, sequence of peaks and their amplitude) by the competitive network to four categories. Each category represented a soil type thus the design displacement spectra for each soil type was obtained. The spectrum with 5 percent damping for soil type C (or II according to Iranian seismic code) has been presented in Fig. 1. A four-degree polynomial function has been matched to the data with a 0.98 standard deviation as shown in the figure. This equation was used to calculate the effective displacement in the numerical examples.

Definition of Effective Damping

Assuming a single displacement cycle based on the ultimate displacement the following well-known relationship between and the ductility demand ft for Elastic-Perfectly Plastic (EPP) behavior is

obtained (Equivalent Energy Method [16]),

where Eeiasiic stands for the damping of the elastic structure. The equivalent viscous damping for bilinear systems with strain hardening ratio a and ductility M may also be determined using the following equation [5],

,2 ((1 – a).(M-1) Ї + E

2 elastic

п у m – aM + aM )

The effective damping obtained above which is greater than the elastic viscous damping due to the hysteretic behavior is then used to get the effective period from the displacement spectrum. The presented spectrum shown in fig. 1 may be modified for other damping values using the EC8 [18]

spectrum and thus less base shear for the design.