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.

Light-framed wood structures generally have satisfied the life safety objective of the current seismic design approach. The main source of energy dissipation in such structures is the inelastic behavior of the connectors connecting framing and sheathing elements. Wood framed structures when subjected to strong ground excitations experience structural and non-structural damage which may incur large repair/replacement costs or may even render the structure out of service. Thus, it is very important to apply techniques to mitigate the seismic response of the light-framed structures and avoid large monetary losses. It is proposed to use commercially available permanent magnets, incorporated in the form of passive friction dampers, to dissipate a part of input energy induced due to strong ground motions, thereby reducing the inelastic energy dissipation demand of the lateral load resisting system. The force of attraction between the permanent magnet and ferromagnetic material like steel was utilized to produce the required friction resistance. A sliding wall configuration consisting of flexible permanent magnets and steel plates sandwiched between the plywood sheets was analyzed for its effectiveness in mitigating the response of a two story wood shear wall structure. The structural analysis program SAP2000 was used to perform nonlinear dynamic analysis of the finite element models generated using the meshing algorithms incorporated into 'WoodFrameMesh'. Nonlinear link elements available in SAP2000 were used to model the friction between the flexible magnet sheet and the steel plate. The effects of various modeling parameters on the solution of the nonlinear analysis were studied so as to arrive at appropriate values to represent the friction problem. Also the friction damped structure was analyzed to study its forced and free vibration characteristics. Further, the responses of the friction damped structure and the undamped structure were compared when subjected to different ground accelerations. The response of the friction damped structure was also compared to that of the structure in which the proposed friction dampers were replaced by normal shear walls. A huge reduction in the response of the friction damped structure was observed when compared to the response of the undamped structure. The friction damped structure was also analyzed for different values of modal damping ratios. Over all about 60-80% of the input energy was dissipated by friction damping in all the cases. The slip resistance of a flexible permanent magnet sheet was also verified in the laboratory. Above all the magnetic properties of commercially available permanent magnets and the effects of strong permanent magnets on human health were also studied. / Master of Science

The benefits of intentional friction damping to reduce the occurrence of wear and premature failure of turbomachinery bladed-disk assemblies are well known and many studies on this topic have focused on the analysis and prediction of the complicated nonlinear forced response exhibited by these structures. In this research, extensions of the recently introduced multi-harmonic Hybrid Frequency-Time method are proposed for the efficient analysis of the response of realistic structures featuring displacement-dependent nonlinearities, such as the friction and impact phenomena that may occur in the presence of friction dampers or when two parts of the same structure periodically contact each other. These theoretical extensions are adapted to the study of large scale, industrial bladed-disk structures that may feature cyclic symmetry or mistuning. Two analysis techniques are developed for the modeling of displacement-dependent nonlinearities. In the first technique friction dampers are modeled as nonlinear operators representing the contact forces acting on the blades, from the simple case of monodirectional friction with constant normal load to the more complex case of three dimensional contact with variable normal load. The analysis of the forced response of several nonlinear systems illustrates the capabilities of this approach as well as the complexity of the typical behavior exhibited by friction damped structures. The second technique introduced helps analyze structures experiencing intermittent contact or friction between two parts or sub-components of the same assembly. This method is applied to the study of the forced response of several simple systems and is used with great efficiency to predict the nonlinear behavior of a beam with a crack. This approach also allows the dampers to be modeled realistically as stand-alone components appended to the bladed disk assembly. In this case the bladed disk assembly as well as the friction dampers are modeled as independent structures that interact at their contacting interfaces. This allows the use of detailed finite element models of dampers rather than having to make simplifying assumptions regarding their geometry. These two methods are applied to the study of the nonlinear forced response a realistic bladed-disk assembly featuring a wedge damper model and a structure-like damper model.

In the last 35 years, several researchers have proposed, developed and tested different friction devices for seismic control of structures. Their research has demonstrated that such devices are simple, economical, practical, durable and very effective. However, research on passive friction dampers, except for few instances, has not been given appropriate attention lately. This has caused some of the results of old studies to become out-of-date, lose their validity in the context of today's design philosophies or to fall short on the expectations of this century's structural engineering. An analytical study on the behavior of friction devices and the effect they have on the structures into which they are incorporated has been undertaken to address the new design trends, codes, evaluation criteria and needs of today's society. The present study consists of around 7,000 structural analyses that are used to show the excellent seismic performance and economic advantages of Friction Damped Braced Frames. It serves, at the same time, to improve our understanding on their dynamic behavior. Finally, this thesis also sets the basis for future research on the application of this type of seismic energy dissipating systems.