An Assessment to Benchmark the Seismic Performance of a Code-Conforming Reinforced-Concrete Moment-Frame Building

This report describes a state-of-the-art performance-based earthquake engineering methodology that is used to assess the seismic performance of a four-story reinforced concrete (RC) office building that is generally representative of low-rise office buildings constructed in highly seismic regions of California. This “benchmark” building is considered to be located at a site in the Los Angeles basin, and it was designed with a ductile RC special moment-resisting frame as its seismic lateral system that was designed according to modern building codes and standards. The building’s performance is quantified in terms of structural behavior up to collapse, structural and nonstructural damage and associated repair costs, and the risk of fatalities and their associated economic costs. To account for different building configurations that may be designed in practice to meet requirements of building size and use, eight structural design alternatives are used in the performance assessments. Our performance assessments account for important sources of uncertainty in the ground motion hazard, the structural response, structural and nonstructural damage, repair costs, and life-safety risk. The ground motion hazard characterization employs a site-specific probabilistic seismic hazard analysis and the evaluation of controlling seismic sources (through disaggregation) at seven ground motion levels (encompassing return periods ranging from 7 to 2475 years). Innovative procedures for ground motion selection and scaling are used to develop acceleration time history suites corresponding to each of the seven ground motion levels. Structural modeling utilizes both “fiber” models and “plastic hinge” models. Structural modeling uncertainties are investigated through comparison of these two modeling approaches, and through variations in structural component modeling parameters (stiffness, deformation capacity, degradation, etc.). Structural and nonstructural damage (fragility) models are based on a combination of test data, observations from post-earthquake reconnaissance, and expert opinion. Structural damage and repair costs are modeled for the RC beams, columns, and slabcolumn connections. Damage and associated repair costs are considered for some nonstructural building components, including wallboard partitions, interior paint, exterior glazing, ceilings, sprinkler systems, and elevators. The risk of casualties and the associated economic costs are evaluated based on the risk of structural collapse, combined with recent models on earthquake fatalities in collapsed buildings and accepted economic modeling guidelines for the value of human life in loss and cost-benefit studies. The principal results of this work pertain to the building collapse risk, damage and repair cost, and life-safety risk. These are discussed successively as follows. When accounting for uncertainties in structural modeling and record-to-record variability (i.e., conditional on a specified ground shaking intensity), the structural collapse probabilities of the various designs range from 2% to 7% for earthquake ground motions that have a 2% probability of exceedance in 50 years (2475 years return period). When integrated with the ground motion hazard for the southern California site, the collapse probabilities result in mean annual frequencies of collapse in the range of [0.4 to 1.4]x10 -4 for the various benchmark building designs. In the development of these results, we made the following observations that are expected to be broadly applicable: (1) The ground motions selected for performance simulations must consider spectral shape (e.g., through use of the epsilon parameter) and should appropriately account for correlations between motions in both horizontal directions; (2) Lower-bound component models, which are commonly used in performance-based assessment procedures such as FEMA 356, can significantly bias collapse analysis results; it is more appropriate to use median component behavior, including all aspects of the component model (strength, stiffness, deformation capacity, cyclic deterioration, etc.); (3) Structural modeling uncertainties related to component deformation capacity and post-peak degrading stiffness can impact the variability of calculated collapse probabilities and mean annual rates to a similar degree as record-to-record variability of ground motions. Therefore, including the effects of such structural modeling uncertainties significantly increases the mean annual collapse rates. We found this increase to be roughly four to eight times relative to rates evaluated for the median structural model; (4) Nonlinear response analyses revealed at least six distinct collapse mechanisms, the most common of which was a story mechanism in the third story (differing from the multi-story mechanism predicted by nonlinear static pushover analysis); (5) Soil-foundation-structure interaction effects did not significantly affect the structural response, which was expected given the relatively flexible superstructure and stiff soils. The potential for financial loss is considerable. Overall, the calculated expected annual losses (EAL) are in the range of $52,000 to$97,000 for the various code-conforming benchmark building designs, or roughly 1% of the replacement cost of the building ($8.8M). These losses are dominated by the expected repair costs of the wallboard partitions (including interior paint) and by the structural members. Loss estimates are sensitive to details of the structural models, especially the initial stiffness of the structural elements. Losses are also found to be sensitive to structural modeling choices, such as ignoring the tensile strength of the concrete (40 EAL) or the contribution of the gravity frames to overall building stiffness and strength (15 change in EAL). Although there are a number of factors identified in the literature as likely to affect the risk of human injury during seismic events, the casualty modeling in this study focuses on those factors (building collapse, building occupancy, and spatial location of building occupants) that directly inform the building design process. The expected annual number of fatalities is calculated for the benchmark building, assuming that an earthquake can occur at any time of any day with equal probability and using fatality probabilities conditioned on structural collapse and based on empirical data. The expected annual number of fatalities for the code-conforming buildings ranges between 0.05*10 -2 and 0.21*10 -2 , and is equal to 2.30*10 -2 for a non-code conforming design. The expected loss of life during a seismic event is perhaps the decision variable that owners and policy makers will be most interested in mitigating. The fatality estimation carried out for the benchmark building provides a methodology for comparing this important value for various building designs, and enables informed decision making during the design process. The expected annual loss associated with fatalities caused by building earthquake damage is estimated by converting the expected annual number of fatalities into economic terms. Assuming the value of a human life is$3.5M, the fatality rate translates to an EAL due to fatalities of $3,500 to$5,600 for the code-conforming designs, and $79,800 for the non-code conforming design. Compared to the EAL due to repair costs of the code-conforming designs, which are on the order of$66,000, the monetary value associated with life loss is small, suggesting that the governing factor in this respect will be the maximum permissible life-safety risk deemed by the public (or its representative government) to be appropriate for buildings. Although the focus of this report is on one specific building, it can be used as a reference for other types of structures. This report is organized in such a way that the individual core chapters (4, 5, and 6) can be read independently. Chapter 1 provides background on the performance-based earthquake engineering (PBEE) approach. Chapter 2 presents the implementation of the PBEE methodology of the PEER framework, as applied to the benchmark building. Chapter 3 sets the stage for the choices of location and basic structural design. The subsequent core chapters focus on the hazard analysis (Chapter 4), the structural analysis (Chapter 5), and the damage and loss analyses (Chapter 6). Although the report is self-contained, readers interested in additional details can find them in the appendices

Vibration-based damage detection in an aircraft wing scaled model using principal component analysis and pattern recognition

This study deals with vibration-based fault detection in structures and suggests a viable methodology based on principal component analysis (PCA) and a simple pattern recognition (PR) method. The frequency response functions (FRFs) of the healthy and the damaged structure are used as initial data. A PR procedure based on the nearest neighbour principle is applied to recognise between the categories of the damaged and the healthy wing data. A modified PCA method is suggested here, which not only reduces the dimensionality of the FRFs but in addition makes the PCA transformed data from the two categories more differentiable. It is applied to selected frequency bands of FRFs which permits the reduction of the PCA transformed FRFs to two new variables, which are used as damage features. In this study, the methodology is developed and demonstrated using the vibration response of a scaled aircraft wing simulated by a finite element (FE) model. The suggested damage detection methodology is based purely on the analysis of the vibration response of the structure. This makes it quite generic and permits its potential development and application for measured vibration data from real aircraft wings as well as for other real and complex structures

PEER Testbed Study on a Laboratory Building: Exercising Seismic Performance Assessment

From 2002 to 2004 (years five and six of a ten-year funding cycle), the PEER Center organized the majority of its research around six testbeds. Two buildings and two bridges, a campus, and a transportation network were selected as case studies to “exercise” the PEER performance-based earthquake engineering methodology. All projects involved interdisciplinary teams of researchers, each producing data to be used by other colleagues in their research. The testbeds demonstrated that it is possible to create the data necessary to populate the PEER performancebased framing equation, linking the hazard analysis, the structural analysis, the development of damage measures, loss analysis, and decision variables. This report describes one of the building testbeds—the UC Science Building. The project was chosen to focus attention on the consequences of losses of laboratory contents, particularly downtime. The UC Science testbed evaluated the earthquake hazard and the structural performance of a well-designed recently built reinforced concrete laboratory building using the OpenSees platform. Researchers conducted shake table tests on samples of critical laboratory contents in order to develop fragility curves used to analyze the probability of losses based on equipment failure. The UC Science testbed undertook an extreme case in performance assessment—linking performance of contents to operational failure. The research shows the interdependence of building structure, systems, and contents in performance assessment, and highlights where further research is needed. The Executive Summary provides a short description of the overall testbed research program, while the main body of the report includes summary chapters from individual researchers. More extensive research reports are cited in the reference section of each chapter

Small-Signal Modelling and Analysis of Doubly-Fed Induction Generators in Wind Power Applications

The worldwide demand for more diverse and greener energy supply has had a significant impact on the development of wind energy in the last decades. From 2 GW in 1990, the global installed capacity has now reached about 100 GW and is estimated to grow to 1000 GW by 2025. As wind power penetration increases, it is important to investigate its effect on the power system. Among the various technologies available for wind energy conversion, the doubly-fed induction generator (DFIG) is one of the preferred solutions because it offers the advantages of reduced mechanical stress and optimised power capture thanks to variable speed operation. This work presents the small-signal modelling and analysis of the DFIG for power system stability studies. This thesis starts by reviewing the mathematical models of wind turbines with DFIG convenient for power system studies. Different approaches proposed in the literature for the modelling of the turbine, drive-train, generator, rotor converter and external power system are discussed. It is shown that the flexibility of the drive train should be represented by a two-mass model in the presence of a gearbox. In the analysis part, the steady-state behaviour of the DFIG is examined. Comparison is made with the conventional synchronous generators (SG) and squirrel-cage induction generators to highlight the differences between the machines. The initialisation of the DFIG dynamic variables and other operating quantities is then discussed. Various methods are briefly reviewed and a step-by-step procedure is suggested to avoid the iterative computations in initial condition mentioned in the literature. The dynamical behaviour of the DFIG is studied with eigenvalue analysis. Modal analysis is performed for both open-loop and closed-loop situations. The effect of parameters and operating point variations on small signal stability is observed. For the open-loop DFIG, conditions on machine parameters are obtained to ensure stability of the system. For the closed-loop DFIG, it is shown that the generator electrical transients may be neglected once the converter controls are properly tuned. A tuning procedure is proposed and conditions on proportional gains are obtained for stable electrical dynamics. Finally, small-signal analysis of a multi-machine system with both SG and DFIG is performed. It is shown that there is no common mode to the two types of generators. The result confirms that the DFIG does not introduce negative damping to the system, however it is also shown that the overall effect of the DFIG on the power system stability depends on several structural factors and a general statement as to whether it improves or detriorates the oscillatory stability of a system can not be made

Laboratory observations of slow earthquakes and the spectrum of tectonic fault slip modes

Slow earthquakes represent an important conundrum in earthquake physics. While regular earthquakes are catastrophic events with rupture velocities governed by elastic wave speed, the processes that underlie slow fault slip phenomena, including recent discoveries of tremor, slow-slip and low-frequency earthquakes, are less understood. Theoretical models and sparse laboratory observations have provided insights, but the physics of slow fault rupture remain enigmatic. Here we report on laboratory observations that illuminate the mechanics of slow-slip phenomena. We show that a spectrum of slow-slip behaviours arises near the threshold between stable and unstable failure, and is governed by frictional dynamics via the interplay of fault frictional properties, effective normal stress and the elastic stiffness of the surrounding material. This generalizable frictional mechanism may act in concert with other hypothesized processes that damp dynamic ruptures, and is consistent with the broad range of geologic environments where slow earthquakes are observed

Design and fabrication of a long-life Stirling cycle cooler for space application. Phase 3: Prototype model

A second-generation, Stirling-cycle cryocooler (cryogenic refrigerator) for space applications, with a cooling capacity of 5 watts at 65 K, was recently completed. The refrigerator, called the Prototype Model, was designed with a goal of 5 year life with no degradation in cooling performance. The free displacer and free piston of the refrigerator are driven directly by moving-magnet linear motors with the moving elements supported by active magnetic bearings. The use of clearance seals and the absence of outgassing material in the working volume of the refrigerator enable long-life operation with no deterioration in performance. Fiber-optic sensors detect the radial position of the shafts and provide a control signal for the magnetic bearings. The frequency, phase, stroke, and offset of the compressor and expander are controlled by signals from precision linear position sensors (LVDTs). The vibration generated by the compressor and expander is cancelled by an active counter balance which also uses a moving-magnet linear motor and magnetic bearings. The driving signal for the counter balance is derived from the compressor and expander position sensors which have wide bandwidth for suppression of harmonic vibrations. The efficiency of the three active members, which operate in a resonant mode, is enhanced by a magnetic spring in the expander and by gas springs in the compressor and counterbalance. The cooling was achieved with a total motor input power of 139 watts. The magnetic-bearing stiffness was significantly increased from the first-generation cooler to accommodate shuttle launch vibrations

The physics of earthquakes

Earthquakes occur as a result of global plate motion. However, this simple picture is far from complete. Some plate boundaries glide past each other smoothly, while others are punctuated by catastrophic failures. Some earthquakes stop after only a few hundred metres while others continue rupturing for a thousand kilometres. Earthquakes are sometimes triggered by other large earthquakes thousands of kilometres away. We address these questions by dissecting the observable phenomena and separating out the quantifiable features for comparison across events. We begin with a discussion of stress in the crust followed by an overview of earthquake phenomenology, focusing on the parameters that are readily measured by current seismic techniques. We briefly discuss how these parameters are related to the amplitude and frequencies of the elastic waves measured by seismometers as well as direct geodetic measurements of the Earth's deformation. We then review the major processes thought to be active during the rupture and discuss their relation to the observable parameters. We then take a longer range view by discussing how earthquakes interact as a complex system. Finally, we combine subjects to approach the key issue of earthquake initiation. This concluding discussion will require using the processes introduced in the study of rupture as well as some novel mechanisms. As our observational database improves, our computational ability accelerates and our laboratories become more refined, the next few decades promise to bring more insights on earthquakes and perhaps some answers

Application of a Combined Active Control and Fault Detection Scheme to an Active Composite Flexible Structure.

In this paper, the problem of increasing reliability of active control procedure is considered. Indeed, a design method of rejection perturbation in presence of potentially faults, on a flexible structure with integrated piezo-ceramics, is presented. The piezo-ceramics are used as actuators and sensors. A single unit based solution, which handles both control action and fault diagnosis is proposed. The algorithm uses H∞ optimization techniques. A full order model of the structure is first obtained via both finite-element (FE) approach and identification procedure. This model is then reduced in order to be used in our robust approach. By a suitable choice of weightings functions, the provided method is able to reject disturbance robustly and to estimate occurred faults. The case of sensors and actuators faults is discussed. The choice of weightings for diagnosis and control systems is also tackled. Finally, the effectiveness of this integrated method is confirmed by both simulation and experimental results