INDEPENDENT HARMONIC CONTROL FOR STRUCTURAL ENGINEERING

In a previous paper [Baratta and Corbi, 1999] one has defined a procedure allowing to identify a closed-ioop control algorithm with feedback based on the whole record of the response time-history rather than on instantaneous response parameters. The control force results from control of each harmonic component of the forcing function, simply integrated over the frequency domain. Every harmonic is controlled, independently of each other, by a classical linear control whose coefficients are calibrated in way to make the relevant response component a minimum compatibly with the control effort one wants to apply at the corresponding frequency. The distribution of this control intensity over the frequency range remains a arbitrary choice; such a choice however lends itself to be effectively assisted by intuition, much more than similar choices in other procedures (e.g.: the coefficients of the quadratic norms in the J-index optimization). The result is that every harmonic remains controlled by a different couple of optimal coefficients (corresponding to the proportional and to the derivative terms in the linear control law), and the overall control force for an arbitrary disturbance, after Fourier inverse transformation, is produced by feedback integration over the whole response time-history.

The procedure, tested with reference to simple and composed harmonic excitations incoming a s.d.o.f. structural system, has proved a good agreement of the numerical results with the theoretical treatment; furthermore it has shown that the main limit of such an approach consists of referring the dynamic equilibrium solution to a particular solution, that, neglecting the initial conditions, may introduce some unstable components in the oscillation. In the paper the effects induced in the controlled structural system response by the adoption of the proposed procedure are deepened and an improved strategy is presented, able to overcome the detrimental transient effects determined by the original algorithm. The final adopted control law is shown to achieve an improved time response, both in the transient and in the steady-state field, in comparison to a control strategy based on classical linear control minimizing the response norm conditioned by a bounded control.     

METHODOLOGY FOR THE PROBABILISTIC ASSESSMENT OF q FACTORS. A DAMAGE INDEX APPROACH

The objective of the present work is to present a methodology for the identification of relevant limit states, namely ultimate limit states leading to structural collapse, and for the assessment of design q factors (or force reduction factors) for reinforced concrete structures under seismic loading. It follows a probabilistic approach based on damage indices. The utilised nonlinear models, as well as the damage indices, which are those proposed by Miner and by Park and Ang, are.described. The methodology of analysis is presented emphasising its probabilistic characteristics. Some parametric studies are carried out, including the analysis of one regular plane frame reinforced concrete structure, designed for three different ductility classes (those proposed by Eurocode 8) and assuming different q factors in design. Results show how the chosen damage indices can be used as parameters to characterise the structural response and how the proposed methodology can be used to assess the design q factors. It is also shown that, for moderate seismic input, the three ductility classes are essentially equivalent in terms of maximum damage indices, but that for higher seismic levels the differences are evident, justifying the use of different q factors.     

ACTIVE/PASSIVE SEISMIC CONTROL OF STRUCTURES

In civil engineering, structural integrity and safety are of utmost importance as the consequences of failure are devastating. Maintaining the structural integrity becomes particularly important when the structures are subjected to severe earthquakes and strong wind-loading. Various passive and active control means have been considered to avoid catastrophic failure due to seismic or wind excitations. In this paper, a new class of hybrid actuators is presented which consists of a piezoelectric stack actuator combined with a viscoelastic damper to form a passive/active brace system (PAB). The actuator is used for mitigating structural dynamic responses of a three-storey structure subjected to simulated earthquakes loading. The proposed hybrid actuator is selected because it combines the attractive attributes of active and passive systems as well as because it has high stiffness-weight ratio, high frequency bandwidth, and low power consumption. The theoretical and experimental performance characteristics of the three-storey structure with the hybrid PAB actuator are presented. Comparisons are also included when the structure is controlled with conventional viscoeiastic dampers or conventional active control braces that operate without any viscoelastic damping. These comparisons emphasize the effectiveness of the hybrid actuator in damping out simulated seismic vibrations.     

Estimation of the Displacement of Viscously Damped Pinching Hysteretic Structures Subjected to Near-fault Ground Motions

To fulfill a displacement-based design or response prediction for nonlinear structures, the concept of equivalent linearization is usually applied, and the key issue is to derive the equivalent parameters considering the characteristics of hysteretic model, ductility level, and input ground motions. Pinching hysteretic structures subjected to dynamic loading exhibit hysteresis with degraded stiffness and strength and thus reduced energy dissipation. In case of excitation of near-fault earthquake ground motions, the energy dissipation is further limited due to the short duration of vibration. In order to improve the energy dissipation capability, viscous-type dampers have been advantageously incorporated into these types of structures. Against the viscously damped pinching hysteretic structure under the excitation of near-fault ground motions, this study aims to develop a seismic response estimation method using an equivalent linearization technique. The energy dissipation of various hysteretic cycles, including stationary hysteretic cycle, amplitude expansion cycle, and amplitude reduction cycle, is investigated, and empirical formulas for the equivalent damping ratio is proposed. A damping modification factor that accounts for the near-fault effect is introduced and expanded to ensure its applicability to structures with damping ratios less than 5%. An approach for estimating the maximum displacement of a viscously damped pinching hysteretic structure, in which the pinching hysteretic effect of a structure and the near-fault effect of ground motions are considered, is developed. A time history analysis of an extensive range of structural parameters is performed. The results confirm that the proposed approach can be applied to estimate the maximum displacement of a viscously damped pinching hysteretic structure that is subjected to near-fault ground motions.     

Modeling and Control of the CSCEC Multi-Function Testing System

In order to promote the research and development on evaluating the seismic performance of structures, China State Construction Engineering Corporation (CSCEC) planned to construct a large-scale loading testing facility, the Multi-Function Testing System (MFTS). This facility can perform full-scale, real-time, 6-degree-of-freedom static and dynamic testing of rubber bearings and many types of structural components including long columns, shear walls and cross shape joints. The basic performances of the MFTS are a clearance of 9.1 m × 6.6 m × 10 m for specimen installation, maximum x-directional displacement 1500 mm, maximum y-directional velocity 1570 mm/s and maximum z-directional compressive load 108 MN. The system configuration and performance specifications of the MFTS are presented in this paper. The inverse kinematics model and the nonlinear model of the hydraulic servosystem of the MFTS are built. A modified feedback forward kinematics algorithm is developed for real-time control of the MFTS. Internal force characteristics of the loading system are analyzed. The internal force control method based on real-time solution of basis of internal force space is proposed for the system with large motion ranges. The motion controller combining position control loop and internal force control loop is developed. To meet the requirement of simultaneously imposing vertical compressive load and horizontal displacement, a mixed load and displacement controller is designed, where a direct force control loop is used to improve the response speed of the force control and reduce spatial dynamic coupling effects. Finally, a dynamic bearing testing is performed. The test results demonstrate that the system using the proposed controller has good abilities on position tracking, force balance, and load following.     

Capacity Design of Coupled RC Walls

Capacity design aims to ensure controlled ductile response of structures when subjected to earthquakes. This article investigates the performance of existing capacity design equations for reinforced concrete coupled walls and then proposes a new simplified capacity design method based on state-of-the-art knowledge. The new method is verified through a case study in which a set of 15 coupled walls are subject to nonlinear time-history analyses. The article includes examination of the maximum shear force in individual walls in relation to the total maximum shear force in the coupled wall system, and subsequently provides recommendations for design.     

Robust Design of a Single Tuned Mass Damper for Controlling Torsional Response of Asymmetric-Plan Systems

A new robust design methodology to control the seismic performance of asymmetric structures equipped with a Single Tuned Mass Damper (STMD) is presented in this article. This design approach aims to control the seismic response of such systems by reducing both flexible-and stiff-edge maximum displacement. The dynamic problem has been investigated in the state space representation showing that the TMD works as a closed-loop feedback control action. A synthetic index to estimate the seismic performance of the main system has been defined by using H_∞ norm. Wide-ranging parametric numerical experimentation has been carried out to obtain design formulae for the STMD in order to minimize such a performance index. These formulae allow for a simple design of STMD position and stiffness to optimally control both translational and rotational motion components, whereas two mass devices are generally considered to improve the seismic performance of asymmetric structural systems The effectiveness and efficiency of the obtained design formulae have been tested by investigating the dynamic behavior of the asymmetric structure after being subjected to different recorded seismic inputs.     

SLIDING MODE CONTROL OF BUILDING FRAMES UNDER RANDOM GROUND MOTION

A sliding mode control theory is presented to control the response of building frames to predominant frequency components of the random ground motions. The control algorithm is derived based on a sliding surface which is a function of a state vector containing the structural displacements and velocities and variables that dictate the predominant frequency components of the excitation. Three control mechanisms are employed to control the response of the building frame namely, (1) active mass damper (AMD) placed at the top storey of the building, (2) an actuator placed at a storey level and, (3) an actuator placed at a storey level along with a tuned mass damper (TMD) situated at the top storey level. Responses obtained by the proposed control strategy are compared with those obtained by the linear feedback and feedforward-feedback control strategies (conventional control strategies). Also, they are compared with those obtained by the sliding mode control strategy that considers in its state vector only structural displacements and velocities. It is shown that the proposed control strategy generally performs better than other control strategies in the higher range of control forces. For the lower range of control forces, conventional control strategies are more effective.     

Rapid Diagnosis of Crack Patterns of Masonry Buildings Subjected to Landslide-Induced Settlements by Using the Load Path Method

One of the main difficulties, when dealing with landslide structural vulnerability, is the diagnosis of the causes of the crack pattern. This is also due to the excessive complexity of models based on classical structural mechanics that makes them inappropriate especially when there is the necessity to perform a rapid vulnerability assessment at the territorial scale. This is why in this article a new approach for the rapid diagnosis of crack patterns of masonry buildings subjected to landslide-induced settlements is proposed. This approach is based on the Load Path Method, recently applied to the interpretation of the behavior of masonry buildings subjected to landslide-induced settlements.     

A FIBRE FINITE BEAM ELEMENT WITH SECTION SHEAR MODELLING FOR SEISMIC ANALYSIS OF RC STRUCTURES

The paper describes the formulation of a non-linear, two-dimensional beam finite element with bending, shear and axial force interaction for the static and dynamic analysis of reinforced concrete structures. The hysteretic behaviour of “squat” reinforced concrete members, in which the interaction between shear and flexural deformation and capacity is relevant for the overall structural performance, is emphasised. The element is of the distributed inelasticity type; section axial-flexural and shear behaviours are integrated numerically along the element length using a new equilibrium-based approach. At section level a “hybrid” formulation is proposed: the axial-flexural behaviour is obtained using the classic fibre discretisation and the plane sections remaining plane hypothesis, the shear response instead is identified with a non-linear truss model and described with a hysteretic stress-strain relationship. The latter contains a damage parameter, dependent on flexural ductility, that provides interaction between the two deformation mechanisms. The element has been implemented into a general-purpose finite element code, and is particularly suitable for seismic time history analyses of frame structures. Analytical results obtained with the model are compared with recent experimental data.     

DEVELOPMENT AND VERIFICATION OF A DISPLACEMENT-BASED ADAPTIVE PUSHOVER PROCEDURE

In this paper, an innovative displacement-based adaptive pushover procedure, whereby a set of laterally applied displacements, rather than forces, is monotonically applied to the structure, is presented. The integrity of the analysis algorithm is verified through an extensive comparative study involving static and dynamic nonlinear analysis of 12 rein-forced concrete buildings subjected to four diverse acceleration records. It is shown that the new approach manages to provide much improved response predictions, throughout the entire deformation range, in comparison to those obtained by force-based methods. In addition, the proposed algorithm proved to be numerically stable, even in the highly inelastic region, whereas the additional modelling and computational effort, with respect to conventional pushover procedures, is negligible. This novel adaptive pushover method is therefore shown to constitute an appealing displacement-based tool for structural assessment, fully in line with the recently introduced deformation- and performance-oriented trends in the field of earthquake engineering.     

SEISMIC ENERGY DEMAND IN STEEL MOMENT FRAMES

The present paper investigates the seismic energy demand in steel moment-resisting frames. The frames, with 3, 6 and 10 storeys, and 4 and 8 spans, are designed according to current seismic code provisions. The energy response (energy quantities and their distributions) in the frames subjected to an ensemble of six earthquake ground motions recorded on different soil conditions, is investigated by nonlinear time history analysis. The study concludes that (1) the results of energy response can be developed into a rational method of seismic evaluation and design for steel moment-resisting frames; (2) the energy concept based on the single-degree-of-freedom has limitations when extended to the realistic structural system for design purposes; and (3) it is necessary to develop the energy-based approach for seismic evaluation and design based on the seismic response of a realistic multi-degree-of-freedom structural system.     

INTEGRATED PASSIVE-ACTIVE SYSTEM FOR SEISMIC PROTECTION OF A CABLE-STAYED BRIDGE

This paper presents an integrated passive-active (i.e. hybrid) system for seismic response control of a cable-stayed bridge. Since multiple control devices are operating, a hybrid control system could alleviate some of the restrictions and limitations that exist when each system is acting alone. Lead rubber bearings are used as passive control devices to reduce the earthquake-induced forces in the bridge and hydraulic actuators are used as active control devices to further reduce the bridge responses, especially deck displacements. In the proposed hybrid control system, a linear quadratic Gaussian control algorithm is adopted as a primary controller. In addition, a secondary bang-bang type (i.e. on-off type) controller according to the responses of lead rubber bearings is considered to increase the controller robustness. Numerical simulation results show that control performances of the integrated passive-active control system are superior to those of the passive control system and are slightly better than those of the fully active control system. Furthermore, it is verified that the hybrid control system with a bang-bang type controller is more robust for stiffness perturbation than the active controller with a μ-synthesis method, and there are no signs of instability in the over-all system whereas the active control system with linear quadratic Gaussian algorithm shows instabilities in the perturbed system. Therefore, the proposed hybrid protective system could effectively be used for seismically excited cable-stayed bridges.     

NONLINEAR SHAKE TABLE IDENTIFICATION AND CONTROL FOR NEAR-FIELD EARTHQUAKE TESTING

The primary focus of a structural shake table system is the accurate reproduction of acceleration records for testing. However, many systems deliver variable and less than optimal performance, particularly when reproducing large near-field seismic events that require extreme table performance. Improved identification and control methods are developed for large hydraulic servo-actuated shake table systems that can exhibit unacceptable tracking response for large, near-field seismic testing. The research is presented in the context of a 5-tonne shake table facility at the University of Canterbury that is of typical design. The system is identified using a frequency response approach that accounts for the actual magnitudes and frequencies of motion encountered in seismic testing. The models and methods developed are experimentally verified and the impact of different feedback variables such as acceleration, velocity and displacement are examined.

The methods show that shake table control in testing large near-field seismic events is often a trade off between accurate tracking and nonlinear velocity saturation of the hydraulic valves that can result in severe acceleration spikes. Control methods are developed to improve performance and include both acceleration and displacement feedback to reduce the acceleration spikes, and record modification, where the reference signal is modified to conform to the shake table's operational parameters. Results show record modification gives exact tracking for near-field ground motions, and optimal system response for reference signals with velocity components greater then the system capabilities. Overall, the research presents a methodology for simple effective identification, modelling, diagnosis and control of structural shake table systems that can be readily generalised and applied to any similar facility.     

Direct Acceleration Feedback Control of Shake Tables with Force Stabilization

This study presents a new strategy for shake table control that uses direct acceleration feedback without need for displacement feedback. To ensure stability against table drift, force feedback is incorporated. The proposed control strategy was experimentally validated using the shake table at the Johns Hopkins University. Experimental results showed that the proposed control strategy produced more accurate acceleration tracking than conventional displacement-controlled strategies. This article provides the control architecture, details of the controller design, and experimental results. Furthermore, the impact of input errors in shake table testing on the structural response is also discussed.     

The Influence of Masonry Infill Walls in the Framework of the Performance-Based Design

In this article, a performance-based seismic design (PBD) methodology is proposed for the design of reinforced concrete buildings, taking into account the influence of infill walls. Two variants of the PBD framework are examined: The first is based on the non-linear static analysis procedure (NSP) while the second relies on the non-linear dynamic analysis procedure (NDP). Both design approaches are compared in the context of structural optimization with reference to the best possible design achieved for each case examined. Life-cycle cost analysis is considered a reliable tool for assessing the performance of structural systems and it is employed in this study for assessing the optimum designs obtained. The optimization part of the problem is performed with an Evolutionary Algorithm while three performance objectives are implemented in all formulations of the design procedures. The two most important findings can be summarized as follows: (i) if structural realization follows the design assumptions, then total expected life-cycle cost of the three type of structures, bare, fully infilled and open ground story, is almost the same and (ii) if an open ground story building is designed as bare or as fully infilled frame, real performance will be much worse than anticipated at the design stage.     

Robust Period-Independent Ground Motion Selection and Scaling for Effective Seismic Design and Assessment

A period-independent approach for the selection and scaling of ground motion records aimed at reducing demand variability is proposed for seismic response history analysis. The same set of scaled records can be used to study various structures at the same site regardless of their dynamic characteristics. The statistical robustness of the proposed and current approaches is compared through nonlinear inelastic dynamic analyses performed on single-degree-of-freedom systems and multi-story braced frames. The proposed approach leads to consistent response predictions with a limited number of records. This is advantageous for day-to-day structural design or assessment against code hazard-based seismic demand levels.     

FATIGUE ANALYSIS OF MOMENT RESISTING STEEL FRAMES

A procedure for the fatigue assessment of steel building structures subjected to earthquakes is presented. The procedure constitutes an extension of the present, high-cycle, fatigue assessment to cases of low-cycle fatigue. It may serve as a basis for the introduction of a fatigue limit state in the earthquake design of steel structures. It may be also used for the damage assessment of existing steel buildings subjected to past earthquakes. By means of parametric studies, the effects of various parameters on the fatigue susceptibility of several moment resisting steel frames are studied. The influence of a number of parameters such as the type of ground motion, type of structural typology, local fatigue behaviour, overall frame design and semi-rigidity of joints on the susceptibility to damage are investigated.     

TORSIONAL EFFECTS IN THE PUSHOVER-BASED SEISMIC ANALYSIS OF BUILDINGS

The general trends of the inelastic behaviour of plan-asymmetric structures have been studied. Systems with structural elements in both orthogonal directions and bi-axial eccentricity were subjected to bi-directional excitation. Test examples include idealised single-storey and multi-storey models, and a three-storey building, for which test results are available. The response in terms of displacements was determined by nonlinear dynamic analyses. The main findings, limited to fairly regular and simple investigated buildings, are: (a) The amplification of displacements determined by elastic dynamic analysis can be used as a rough, and in the majority of cases conservative estimate in the inelastic range, (b) Any favourable torsional effect on the stiff side, which may arise from elastic analysis, may disappear in the inelastic range. These findings can be utilised in the approximate pushover-based seismic analysis of asymmetric buildings, e.g. in the N2 method. It is proposed that the results obtained by pushover analysis of a 3D structural model be combined with the results of a linear dynamic (spectral) analysis. The former results control the target displacements and the distribution of deformations along the height of the building, whereas the latter results define the torsional amplifications. The proposed approach is partly illustrated and evaluated by test examples.     

A New Proposed Passive Mega-Sub Controlled Structure and Response Control

It is still a serious challenge for structural engineers to effectively reduce the seismic responses of tall and super tall buildings to further improve these structural safeties. In order to solve this problem, in this article a new kind of structural configuration, named passive mega-sub controlled structure (PMSCS), is presented, which is constructed by applying the structural control principle into structural configuration itself, to form a new structure with obvious response self-control ability, instead of employing the conventional method. In the analysis of PMSCS the equations of motion of the seismically excited system are developed, based on a realistic analytical model of the complete mega-structural system. Expressions of the displacement and acceleration response of the structure, resulting from simulated earthquake ground motions represented by stationary and nonstationary random processes, are derived. These responses are then determined for both the PMSCS and its conventional mega-sub structure (MSS) counterpart, whose configuration was modeled after the traditional mega-frame that was used in the construction of the Tokyo City Hall. A parametric study of the structural characteristics that influence the response control effectiveness of the PMSCS is presented and discussed. The region over which these structural characteristics yield the optimum seismic response control of the PMSCS is identified and serves as a very useful design tool for practitioners. The study illustrates that the proposed PMSCS offers an effective means of controlling the seismic displacement and acceleration response of tall/super-tall mega-systems. It also overcomes shortcomings exhibited in earlier proposed mega-sub controlled structural configurations.