Matthew R. Eatherton

Residual Drifts of Self-Centering Systems Including Effects of Ambient Building Resistance

There has been widespread interest in the development and use of self-centering (SC) lateral resisting systems that eliminate residual drifts after large earthquakes. SC systems often include a restoring force component and a component that dissipates seismic energy. Typically, it is assumed that the criterion for self-centering is satisfied if the restoring force is proportioned to be greater than the force required to yield the energy dissipating component. A parametric SDOF study was conducted using time-history analyses on several prototype buildings to quantify the effect of varying system parameters on structural response including residual drifts. The ambient resistance of the rest of the building was considered, as well as proportioning the system with less restoring force than the yield capacity of the dissipative component. In addition, the probabilistic mechanism that creates a propensity for reducing residual drifts in systems with little or no restoring force is explored and quantified. It was found that a restoring force that is at least one-half of the force required to yield the dissipative component will still reliably eliminate residual drifts in a non-softening system.

Design Concepts for Controlled Rocking of Self-Centering Steel-Braced Frames

AbstractThe self-centering rocking steel-braced frame is a high-performance system that can prevent major structural damage and minimize residual drifts during large earthquakes. It consists of braced steel frames that are designed to remain elastic and allowed to rock off their foundation. Overturning resistance is provided by elastic post-tensioning, which provides a reliable self-centering restoring force, and replaceable structural fuses that dissipate energy. The design concepts of this system are examined and contrasted with other conventional and self-centering seismic force resisting systems. Equations to predict the load-deformation behavior of the rocking system are developed. Key limit states are investigated including desired sequence of limit states and methods to help ensure reliable performance. Generalized design methods for controlling the limit states are developed. The design concepts are then applied to a six-story prototype structure to illustrate application of the rocking steel fram...

Seismic Design and Behavior of Steel Frames with Controlled Rocking—Part I: Concepts and Quasi-Static Subassembly Testing

Research and experience of past earthquakes suggest the need for buildings that are less vulnerable to damage and easier to repair after a major earthquake. Our research aims to develop a new structural system that employs controlled frame rocking action and replaceable structural fuses to provide safe and cost effective resistance to earthquakes. The system combines desirable aspects of conventional steel-braced frame systems with energy dissipating shear fuses that are mobilized through rocking action. Vertical posttensioning is provided to increase overturning resistance and enhance the self-centering characteristics to reduce residual drifts. This is the first of two companion papers to present research findings from a NSF-NEES Small Group Project on this topic. This paper examines the behavior of controlled rocking systems through large (1/2) scale rocking-frame subassembly tests conducted at the University of Illinois. Conducted using quasi-static cyclic and hybrid simulation techniques, the tests demonstrate the viability of the controlled rocking system and provide the basis for establishing design criteria to ensure an appropriate balance of overturning resistance, self-centering capacity, and energy dissipation.

Seismic Design and Behavior of Steel Frames with Controlled Rocking - Part II: Large Scale Shake Table Testing and System Collapse Analysis

This is the second of two companion papers that investigate the design and behavior of steel braced frames that resist earthquake effects through controlled rocking. By employing vertical post-tensioning and energy dissipating fuses, the controlled rocking systems can sustain large earthquake ground motions with minimal damage and without residual drift. This paper describes a series of large (two-thirds) scale dynamic shaking table tests, conducted at the E-Defense facility in Japan, to validate the system behavior for ground motions with intensities up to and beyond those of the maximum considered earthquake (MCE) level. The tests investigate response with alternative fuse designs and variable post-tensioning. Results of nonlinear dynamic analyses are shown to compare well with the shake table tests, which can be extended to assess the collapse performance of the controlled rocking frames, using procedures outlined in the FEMA P695 methodology to evaluate provisions for seismic design.

Self-Centering Beams with Resilient Seismic Performance

Although several self-centering seismic systems have been developed, their use in practice has been relatively limited. Complicated or unusual field construction, perceived initial cost premiums, and deformation incompatibility with the gravity framing may be some of the factors restricting their use. A self-centering beam moment frame (SCB-MF) has been developed that mitigates several of these issues. The self-centering beam (SCB) can be shop fabricated with self-contained restoring force which eliminates deformation incompatibility and allows conventional field construction methods. The strength and stiffness of the SCB are decoupled resulting in a cost-effective system that may be competitive with conventional moment frames. This paper describes the SCB-MF concepts, construction and modeling. An upcoming experimental program on two-thirds scale test specimens will also be presented. Computational simulations of the SCB-MF are presented and the results are analyzed.

Behavior of Post-Tensioning Strand Systems Subjected to Inelastic Cyclic Loading

Post-tensioning (PT) strand systems have been employed in a number of self-centering seismic systems as part of their restoring force mechanism to eliminate residual building drifts following seismic loading. Because of their large elastic deformation capability, PT strand systems have been shown to be effective in these applications. Although typically designed to stay elastic during design basis earthquake events, PT strands can be subjected to inelastic strains during extreme seismic events. Furthermore, the yielding and fracture behaviors of PT strand systems are central to understanding and predicting the collapse behavior of self-centering systems. The loading conditions associated with prestressed/post-tensioned concrete applications are vastly different, and only limited research has explored the behavior of PT strand systems as subjected to inelastic cyclic loading. To better characterize the behavior of PT strand systems subjected to inelastic cyclic loading, a testing program was conducted to investigate important parameters related to self-centering system applications. The testing program consisted of both monotonic and cyclic tests of PT strand systems to failure. Variations in the test configuration included strand obtained from two manufactures, two types of multiple use anchorage systems, and several levels of initial post-tensioning strand stress. Characteristics of the response that were investigated included seating losses, deformation capacity prior to initial wire fracture, additional deformation capacity after initial fracture, and the overall load-deformation behavior. An equation was developed that provides the reduction in PT strand force due to seating losses. Other practical information is also summarized, including suggested strain limits to prevent PT wire fracture.

Self-Centering Beams for Seismically Resilient Moment Frames

Self-centering beam moment frames (SCB-MFs) have been developed with the capability of resilient performance during large earthquakes by virtually eliminating residual drifts and concentrating structural damage in replaceable fuses. The self-centering beams (SCBs) can be shop-fabricated with the self-centering mechanism built into the beam unit, thus eliminating deformation incompatibility with the surrounding gravity framing that is associated with some other self-centering systems. Furthermore, the SCB-MFs allow for conventional field construction methods, making them more accessible to the construction industry. A parametric study was performed on single self-centering beam units to investigate the sensitivity of the SCBs to a variety of design variables. The results of this study show that these units can be implemented in a wide variety of configurations for various beam depths and moment capacities. Additionally, the ability of the system to dissipate seismic energy while minimizing residual drift was demonstrated. Ultimately, this study has shown that SCB-MFs are a viable seismic force resisting system for reducing structural damage due to large earthquakes and have the potential to limit the cost and time required to make a building operational following a strong ground motion.

Steel-Framed Rocking Structural Systems for Moderate Seismic Zones

Incorporating a rocking mechanism into steel frames, concrete shear walls, or masonry piers has been shown to reduce the amount of seismic base shear that a lateral resisting system is required to resist. Rocking structural systems have therefore been developed primarily for high seismic regions. The benefits provided by allowing rocking are, however, also advantageous in moderate seismic zones. This paper summarizes previous research on the seismic behavior of steel-framed rocking systems and examines the application of the rocking mechanism to steel frames in moderate seismic zones by analyzing an example braced frame with and without allowing column uplift.

Axial Hysteretic Modeling of Cold-Formed Steel Members for Computationally Efficient Seismic Simulation

Analysis and design of cold-formed steel (CFS) structures subjected to seismic forces usually focuses on the behavior of systems such as strapped/sheathed shear walls. Experimental data from tests on these systems offers limited information concerning the seismic performance of the individual CFS components or other configurations of shear walls. Buckling and cross-sectional deformations (unique to thin-walled steel sections) highly influence the response under cyclic loading of CFS members and the associated systems. Therefore, accurate and computationally efficient hysteretic models are required to predict the seismic performance of individual CFS components and CFS buildings. Experimental data from twenty-four axial tests is utilized to calibrate a hysteretic model that represents the axial cyclic response of cold-formed steel C-section structural framing members. The model includes strength degradation, unloading stiffness degradation and pinching behavior of the observed experimental response. Model parameters and damage rules are calibrated for local, distortional and global buckling based on the hysteretic energy dissipated. The calibrated parameters can be utilized to develop a toolbox of nonlinear hysteretic springs to represent framing axial members in CFS structures for seismic analysis and facilitate performance based earthquake engineering of CFS structures.

Time-Domain Spectral Matching of Earthquake Ground Motions using Broyden Updating

Time-domain spectral matching of an earthquake ground motion consists of iteratively adding sets of wavelets to an acceleration history until the resulting response spectrum sufficiently matches a target spectrum. The spectral matching procedure is at its core a nonlinear problem because the addition of a wavelet often causes shifting in the time of peak response or creation of a larger second peak at a different time. A modification to existing time-domain spectral matching algorithms is proposed using Broyden updating for solving the set of nonlinear equations. Three wavelet bases are evaluated and the corrected tapered cosine wavelet is selected. The proposed algorithm is then tested and compared with other methods that are commonly used for spectral matching. The results show that the proposed algorithm is able to match the target spectrum while reasonably preserving the spectral nonstationarity, energy development, and the frequency content of the original time histories.