A Comparative Study on Seismic Analysis Methods and the Response of Systems with Classical and Nonclassical Damping
Abstract
This thesis investigated the application of seismic analysis methods and the response of idealized shear frames subjected to seismic loading. To complete this research, a Design Basis Earthquake (DBE) for a project site in San Luis Obispo, CA, and five past earthquake records were considered. The DBE was produced per the American Society of Civil Engineers’ Minimum Design Loads for Buildings and Other Structures (ASCE 7-10) and used for application of the Equivalent Lateral Force Procedure (ELFP) and Response Spectrum Analysis (RSA). When applying RSA, the modal peak responses were combined using the Absolute Sum (ABS), Square-Root-of-the-Sum-of-Squares (SRSS), and Complete Quadratic Combination (CQC) method.
MATLAB scripts were developed to produce several displacement, velocity, and acceleration spectrums for each earthquake. Moreover, MATLAB scripts were written to yield both analytical and numerical solutions for each system through application of Linear Time History Analysis (THA). To obtain analytical solutions, two implicit forms of the Newmark-beta Method were employed: the Average Acceleration Method and the Linear Acceleration Method.
To generate a comparison, the ELFP, RSA, and THA methods were applied to shear frames up to ten stories in height. The system parameters that impacted the accuracy of each method and the response of the systems were analyzed, including the effects of classical damping and nonclassical damping models. In addition to varying levels of Rayleigh damping, non-linear hysteric friction spring dampers (FSDs) were implemented into the systems. The design of the FSDs was based on target stiffness values, which were defined as portions of the system’s lateral stiffness. To perform the required Nonlinear Time History Analysis (NTHA), a SAP2000 model was developed. The efficiencies of the FSDs at each target stiffness, with and without the addition of low levels of viscous modal damping are analyzed.
It was concluded that the ELFP should be supplemented by RSA when performing seismic response analysis. Regardless of system parameters, the ELFP yielded system responses 30% to 50% higher than RSA when combing responses with the SRSS or CQC method. When applying RSA, the ABS method produced inconsistent and inaccurate results, whereas the SRSS and CQC results were similar for regular, symmetric systems. Generally, the SRSS and CQC results were within 5% of the analytical solution yielded through THA. On the contrary, for irregular structures, the SRSS method significantly underestimated the response, and the CQC method was four to five times more accurate. Additionally, both the Average Acceleration Method and Linear Acceleration Method yielded numerical solutions with errors typically below 1% when compared with the analytical solution.
When implemented into the systems, the FSDs proved to be most efficient when designed to have stiffnesses that were 50% of the lateral stiffness of each story. The addition of 1% modal damping to the FSDs resulted in quicker energy dissipation without significantly reducing the peak response of the system. At a stiffness of 50%, the FSDs reduced the displacement response by 40% to 60% when compared with 5% modal damping. Additionally, the FSDs at low stiffnesses exhibited the effects of negative lateral stiffness due to P-delta effects when the earthquake ground motions were too weak to induce sliding in the ring assemblies.