Report - PEER - University of California, Berkeley

interaction between the bench and the equipment in the same way as it neglects theinteraction between the bench and floor. Such an assumption is reasonable for mostinstalled bench systems, since the frequency of the bench system is much higher thanthat of the building structure and the mass of the bench is negligible compared withthe buildings’ mass. Dynamic characteristics regarding representative bench systemsrequired to solve equation (5) were determined using shake table and low amplitudemodal (hammer) experiments applied to full-scale specimens (Hutchinson and RayChaudhuri, 2003). Through the dynamic testing, the natural frequency and associateddamping were determined to range from f n= 10 to 15 Hz and ζ = 3 to 12% fornsystems arranged in the transverse and longitudinal directions.3. SYSTEM AND PARAMETERS CONSIDERED FOR FRAGILITY CURVEDEVELOPMENTFragility curves are developed for bench-mounted rigid equipment consideringdifferent: (i) types and magnitudes of damage measures (displacement and velocity),(ii) coefficients of static and kinetic friction, and (iii) support characteristics (benchand building). In addition, the overall uncertainty due to the range of excitations(provided by the different structures and at the ground level) is considered. Thefollowing sections describe the system parameters selected as well as the probabilisticformulation adopted for constructing these curves.3.1 Ground MotionsIn this study, 22 measured ground motions are scaled to different hazard levels of 50,10, and 2% in 50 years, resulting in a total of 32 input motions (Sommerville 2002).Hazard level scale factors are determined by matching site-specific spectral ordinatesat the fundamental period of a numerical building model (discussed in the followingsection). The ground motions are derived from actual ground motion recordsconsidering their magnitude and distance of fault from site at which records arecollected. The list of the ground motions used along with their different peakparameters is provided in Sommerville (2002). The resulting range of peak groundaccelerations (PGA) encompasses the coefficient of friction for the equipment ofinterest, with PGA = 0.26 – 2.5g. The range of peak ground velocity (PGV) for thesemotions is PGV = 14 – 352.4 cm/sec, and the range of peak ground displacements(PGD) for these motions is PGD = 1.2 – 141.2 cm.3.2 Numerical Model of a Representative Science BuildingFor this study, a numerical model of a representative science building where suchequipment would be found is constructed. The influence of other building types isalso considered and described in subsequent sections. However, the first building ofconsideration, herein termed the RC building, is a seven-story reinforced concrete201