Modeling and evaluating the response of nonstructural equipment and contents is important for determining the overall economic losses associated with an earthquake event. The particular objectives of studies at UCI, which complement studies by researchers at UCB (Makris), are to characterize the seismic performance of bench and shelf-mounted equipment and contents within a biological/chemical building. In this case, the emphasis is on equipment and contents present in the UC Science building. Our approach, which contributes to the development of performance-based design methodologies, is to develop analytical seismic fragility curves describing the probability of exceedance of a limit state (damage measure DM) given an input (an engineering demand parameter EDP). Experimental data is being used to provide dynamic characterization of the supporting bench system and response information regarding the equipment-bench interface.

This project supports several aspects of the overall PEER vision. Analytical studies conducted provide continued use and development of the PEER OpenSees platform. Experimental studies will provide evaluation of these simple analytical models for performance evaluation of bench and shelf-mounted equipment. In addition, a unique experimental database has been developed on the full-scale response of bench-shelf systems and various types of equipment.

Our approach has combined experimental and analytical studies. Experimental studies include

1. component characterization (simple sliding tests) and
2. system characterization (mock-laboratory shake table tests and hammer/modal testing). The analytical portion includes the synthesis of the building and experimental equipment response data and the casting of this data into a probabilistic framework suitable for PBEE.

1. using calculated floor motions from the nonlinear time history analyses of the UC Science building by Lee and Mosalam (UCB),
2. determining the equivalent coefficient of kinetic friction mk (mean and standard deviation) from the experimental data (i.e., acceleration time history at bench level, equipment displacement time history, average coefficient of static friction ms),
3. determination of the equipment response using a basic sliding formulation and assuming uncertainties in different parameters involved, and
4. development of the fragility curve in the framework of basic probability theory [we are using the maximum likelihood method (Shinozuka et al. 2000)]. We can then consider a range of EDPs and DMs. Figure 2 shows an example of the seismic fragility curves developed based on this approach.

Experimental and analytical studies of heavy equipment within the UC Science building are being conducted by Professor Makris at UCB. Our work complements these studies, since our emphasis is on smaller equipment and contents mounted on shelves or benches. Our work also provides input information for the building loss modeling by Porter and Beck (CalTech).

Experimental studies on characterizing bench and shelf-mounted equipment subjected to earthquake motions have been conducted in the US and abroad. At the University of British Columbia, for example, researchers studied the seismic response of full and partially filled bookshelves. Restraint systems for these studies were largely proprietary and the focus was on creating a mock office environment, rather than a chemical/biological environment. Professor Soong of SUNY-Buffalo has also conducted extensive research on the response of nonstructural elements, including shake table studies investigating the response of sliding dominated equipment. Our work is different since we are considering different types of scientific equipment and elements mounted on a laboratory bench-shelf system. We are not aware of any experimental studies investigating the seismic response of integral laboratory bench-shelf systems.

In terms of analytical studies, much work has been done on the basic sliding formulation and the probabilistic theory allowing the development of seismic fragility curves for the equipment. Our work is different, however, since we must incorporate the bench-shelf dynamic characteristics and as well we are considering uncertainty in various parameters, including both the static and kinetic coefficients of friction. Previous analytical studies have assumed a constant, uniform distribution for and .

We propose three additional areas of consideration in this study

1. varying ratios of vertical to horizontal acceleration as input motions,
2. field hammer modal testing on various (in-structure) bench-shelf systems, and
3. expansion of the floor motions used for seismic input into the analytical fragilities and combined building-contents modeling.

The first idea we substantiated through preliminary numerical studies, which indicate that the fragility curve for sliding dominated equipment is sensitive to vertical ground motion input (this is well known and has also been substantiated by other researchers). To study this, we would like to conduct a series of shake table experiments, simply using the correct interface properties (i.e. equipment mounted directly on the laboratory bench top in turn mounted directly onto the shake table). We plan to begin these experiments during the end of year 6.

Since the sliding of unrestrained rigid equipment is initiated when the acceleration of the supporting bench overcomes the resistance due to friction between the two surfaces of contact, considering the acceleration amplification due to the bench in the fragility curve development is very important (idea 2). In both our analytical and experimental studies, we find the bench amplification plays a major role in the response of small, rigid bench-top mounted equipment. Experimental data from the first three configurations indicates that the dominant frequency of bench and shelf system is between 10 and 15 Hz while the damping ratio of this mode varies between 10% and 12%. While we have captured the dynamic characteristics of the configurations we have modeled in our laboratory, we feel that field studies are warranted using low amplitude hammer testing on-site to determine a broader range of shelf-bench system characteristics.

The final idea is related to the input motions selected for development of the fragility curves. Currently, we have used over 200 input floor motions, based on the input motions provided by Sommerville and the analyses results of the UC Science building modeling performed by Lee and Mosalam. Lee and Mosalam are currently updating their model to 3-dimensions and are performing sensitivity studies on the model parameters. We would like to expand our database of input motions to evaluate the sensitivity of the fragility of the contents due to the model structure uncertainty.

We are unaware of instances were our results have been directly adopted in practice, although we have engaged practicing structural engineer, Mr. Richard Hess in our studies. Richard is a member of the nonstructural components committee responsible for developing FEMA-273 and FEMA-274 and through this relationship our work has an indirect influence. Mr. Hess visited UCI twice during year 5 one of these meetings involved observing our shake table testing. We have also discussed with Bob Bachman our desire to participate in the development of the newly funded ATC-58 initiative.

We are currently focusing on analyzing and synthesizing our data from our final series of mock-laboratory experiments, configuration four, conducted in mid-March. We plan to prepare a data report summarizing these experimental results. By May, we will prepare an experimental plan for considering both horizontal and vertical input shaking applied to the various equipment types mounted on the benchtop surface. In late Summer 2003 we plan to begin conducting these experiments. By the end of year 6, we will complete a PEER report synthesizing the shake table experimental results (under uniaxial loading) and the complementary analytical studies, also considering uniaxial loading.

During year 6, our work will result in the following deliverables:

1. contributions to the UC Science test bed report, including fragility curve input for the loss modelers (Beck and Porter),
2. data report summarizing the bench and shelf mock laboratory experiments, and
3. a year 6 PEER technical report.