| A typical problem in earthquake engineering consists of a dynamic system, such as a building, subjected to a seismic ground motion input. In practical problems, the parameters of both the input and the system are not well known. This thesis investigates a quantitative measure of the sensitivity of the response to an input or system parameter. The measure, termed the sensitivity 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. 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. |
