The Earthquake Engineering Online Archive

Sensitivity analysis for hysteretic dynamic systems: application to earthquake engineering

Ray, Debabrata

UCB/EERC-74/05, Earthquake Engineering Research Center, University of California, Berkeley, 1974-04, 88 pages (530/R29/1974)

The sensitivity analysis part of the total problem of optimum system synthesis, utilizing methods based on gradient search techniques, is developed. Two general theorems for sensitivity analysis with respect to a time-invariant parameter vector for a nonlinear (hysteretic), spatially discretized structural system subjected to dynamic excitation are hypothesized and proved; a generalized Gronwall-type lemma is also proved. The applicability of the first theorem with the parameter vector consisting of moments of inertia of column sections of each story of a multistory building frame subjected to earthquake ground motion is established by numerical experimentation. In the context of system synthesis, the concept of complete analysis, i.e., dynamic analysis and sensitivity analysis, is developed. The concept of a complementary pair is introduced for computational efficiency, and a numerical scheme is developed for the solution of the basic (analysis) and derived (sensitivity analysis) equations of motion. Results of numerical experimentation on four 8-story shear-type building frames are presented to demonstrate effectiveness of the theory and numerical analysis developed. A discussion of results and their implication to the development of methods for determining optimum earthquake-resistant designs of multistory buildings concludes the study.

Available online: http://nisee.berkeley.edu/documents/EERC/EERC-74-05.pdf (5 MB)