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MCEER Technical Reports

MCEER technical reports are published to communicate specific research data and project results. Reports are written by MCEER- funded researchers, and provide information on a variety of fields of interest in earthquake engineering. The proceedings from conferences and workshops sponsored by MCEER are also published in this series. To request a complete list of titles and prices, contact MCEER publications. MCEER's web site offers a complete list of technical reports and their abstracts. The publications section allows users to search the report list by subject, title and author, and to place orders for these reports. Visit the site at .

Sensitivity Analysis of Dynamic Systems Subjected to Seismic Loads
by C. Roth and M. Grigoriu, 9/18/01, MCEER-01-0003, 240 pages, $35.00

This research provides analytical and numerical methods directed to the development of optimal strategies for improving the seismic performance of hospitals and other critical facilities. The sensitivity factors developed in this research provide the basis for a cost effective implementation of advanced technologies. 

This report investigates the parameters of both a seismic input and its effect on a dynamic system, such as a building. A quantitative measure of the sensitivity of the response to the seismic input or system parameter was developed, called the sensitivity factor. This factor is defined as the derivative of the response with respect to the parameter value. It can be used to identify critical parameters, estimate the effect of a small change in the parameter value, and select optimum values for the parameter. The direct differentiation method is proposed to calculate the sensitivity factors. By differentiating the governing equation of the system, the governing equation of the sensitivity factor is obtained. This equation can be solved numerically by a similar method to that used to calculate the system response. The errors in the numerical method were investigated and not found to be significant. The method was implemented in two computer programs: 

  1. An entire program to calculate both displacement and sensitivity factors was written using the MATLAB code, for a relatively simple, beam-element level of analysis; and 

  2. New subroutines were added to an existing finite element analysis program, DIANA, for more detailed analysis. 

An example is given illustrating applications of the sensitivity factors to a hospital in Buffalo, New York. Both the primary structural and a secondary piping system are considered. The sensitivity factors are used in identification of critical parameters, selection of retrofit strategies, and calculation of fragility curves. 

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