# WP6

### Analysis of Retrofitted Structures

### Retrofitting Existing Buildings

The seismic response of isolated structures supported on seismic isolation bearings with bilinear and trilinear behavior was revisited with dimensional analysis in an effort to better understand the relative significance of the various parameters that control the mechanical behavior of isolation systems. An isolation system that consists of lead rubber bearings or of single concave spherical sliding bearings exhibits bilinear behavior ; whereas, when a double concave configuration is used the behavior is trilinear. For the case of bilinear behavior it is well known that the value of the normalized yield displacement is immaterial to the response of the isolated superstructure–or, in mathematical terms, that the response of the bilinear oscillator exhibits a complete similarity in the dimensionless yield displacement. Similarly, for the case of trilinear behavior the paper shows that the presence of the intermediate slope is immaterial to the peak response of most isolated structures–a finding that shows that the response of the trilinear oscillator exhibits a complete similarity in the difference between the coefficients of friction along the two sliding surfaces as well as in the ratio of the intermediate to the final slope. This finding implies that even when the coefficient of friction of the two sliding surfaces are different, the response of isolated structures for most practical configurations can be computed with confidence by replacing the double concave spherical bearings with single concave spherical bearings with an effective radius of curvature and an effective coefficient of friction.

**Relevant Publications:** A16 [Makris & Vassiliou, 2010].