Linear modal combination procedure for structural dynamics

Tanışer, Sadun
Earthquake engineering practice utilizes different analysis procedures in the estimation of seismic demands on structures. These procedures are mainly divided into two groups as static and dynamic procedures. Dynamic procedures are more accurate than the static procedures since they include the entire history of any response parameter during the ground motion. Nevertheless, there are also approximate but much simpler static analysis procedures that overcome high computational demands and inherent difficulties of dynamic analysis such as tedious post-processing, and stability and convergence issues especially when the behavior is nonlinear. A deterministic linear modal combination procedure is developed in this thesis as an alternative analysis tool to determine the maximum values of seismic response parameters of structures under earthquake ground motions. The proposed procedure is based on the linear combination of maximum modal responses which are obtained from single-degree-of-freedom modal analyses. In this procedure, modal scaling coefficients are determined when interstory drift ratio at each story attains its maximum value during dynamic response. Each maximum modal response is scaled with these coefficients and combined linearly. The modal scaling coefficients hold the directional information of each mode inside; thereby the direction of total maximum response is preserved. Alternative procedures combine the maximum modal responses with some statistical rules such as SRSS or CQC, which lead to the loss of accuracy and loss of directionality of response. Since the contribution of each mode is linearly combined in the proposed procedure, it overcomes the major drawbacks of statistical combination rules. The suggested procedure is tested on four different structures under three different ground motions. It has been shown that the procedure yields almost exact results for linear elastic response as compared to the statistical CQC method and it is a suitable analysis tool.
Citation Formats
S. Tanışer, “Linear modal combination procedure for structural dynamics,” M.S. - Master of Science, Middle East Technical University, 2013.