Non-Classical Damping Properties and Modal Correlation Coefficient for Dynamic Analysis of Structures

Abstract

The seismic response of secondary systems depends, in addition to their uncoupled dynamic characteristics, on the interaction with primary structures supporting them. This dissertation presents a verification study of the formulations to evaluate the seismic response of non-classically damped building-piping systems by modal synthesis approach. The existing studies consider only simple representative primary-secondary systems. No real-life like coupled system such as building-piping was used in these studies. Further, the majority of simple systems considered in these studies do not represent realistic coupled systems with significant effect of non-classical damping as they have either high values of mass ratios or systems with detuned modes.In this dissertation, different configurations of simple representative systems as well as real-life like building-piping systems are considered. Responses obtained from modal superposition time history analyses as well as response spectrum analyses are compared with the corresponding responses obtained by Brookhaven National Laboratory from the direct integration time history analyses. Modal superposition time history analyses results and direct integration time history analyses results are almost identical. The mean and standard deviation of responses from response spectrum analyses are close to the corresponding values evaluated using direct integration time history analysis. In addition to the verification results, a detailed discussion is also presented on the significance of non-classical damping. It is shown that the effect of non-classical damping is significant in systems that have nearly tuned modes and sufficiently small values of modal mass ratios. It is also illustrated that composite modal damping is an alternate form of classical damping that can result in incorrect responses in non-classically damped systems. Possible reasons for numerical and modeling differences that can occur in real-life like building-piping system are identified and their effect on the dynamic characteristics of the coupled system is illustrated.In the response spectrum method, the maximum modal responses are combined using an appropriate formulation for the modal correlation coefficient. This dissertation presents a new formulation which is based on the observation that the response spectrum method is a design method such that the statistical values of responses evaluated from multiple time history analyses should be close to the corresponding values obtained from the response spectrum method. Results from a numerical study using several real earthquake records are used to develop the new formulation. Different expressions are proposed for combining modal responses that have same algebraic sign and for those that have opposite algebraic signs.