Search

A 7-story reinforced concrete building with a soft bottom story and plan-asymmetry in one horizontal direction was collapsed on a shake table by generation of bi-directional near-fault ground motions. The numerical model of the 7-story building is introduced and verified through a comparison with the experimental results. The hysteretic models of the verified numerical model are calibrated according to static cyclic component tests. To assume the condition that the static cyclic component tests are not available, the hysteretic models of some critical structural components are intentionally altered. Three additional numerical models of the building, which serve as the distorted numerical models, are obtained from the combinations of the altered hysteretic models. Incremental dynamic analyses (IDA) are applied to the four numerical models of the building (i.e., one verified model and three distorted models). Comparing the IDA results of the four numerical models helps to elucidate the effect of the hysteretic models on the full range of the seismic responses (i.e., from elastic response to total collapse) of the building.

Summary In this paper, an optimal energy dissipation control algorithm is applied into a semi-active suspension-type tuned mass damper (SA-STMD) to suppress excessive vibration by means of variable pendulum length. The SA-STMD mechanism consists of a mass block, a suspension rope, and a movable fulcrum that can be a short tube driven by a linear motor to vertically move along the suspension rope. As the fulcrum goes up, the pendulum length is extended, resulting in a smaller stiffness of the SA-STMD, and vice versa. Accordingly, the restoring force in the SA-STMD can be adjusted by varying the fulcrum positions. In the case where the energy dissipation ability by the original STMDs is insufficient, the movable fulcrum in the SA-STMD system can compensate the STMDs for stiffness according to the proposed optimal energy dissipation control algorithm to provide controllable restoring forces. The controllable restoring forces are designed to act as viscous dampers that can make up for the lack of energy dissipation capacity. The numerical results from the time domain and frequency domain analyses show that the proposed approach utilizing the optimal energy dissipation control algorithm to adjust the pendulum length can induce controllable restoring forces with a butterfly-shaped hysteresis loop, supplying a sufficient energy dissipation capacity to reduce responses to the unexpectedly large external vibration. Another potential benefit is cost reduction because of use of a less number of conventional viscous dampers in the STMD system. Copyright © 2016 John Wiley & Sons, Ltd.

SUMMARY Many significantly strong earthquakes have occurred over the years in Taiwan, which have caused tremendous damage to primary and middle school buildings; the 921 Chi-Chi earthquake was particularly devastating. According to statistics, 786 schools (1,958 classrooms) were damaged on September 21, 1999 during this earthquake event. The devastation showed that a lack of seismic performance is a common problem for existing school buildings in Taiwan. Therefore, the retrofit of existing school buildings has become an urgent issue in the prevention of possible damage in the future. The retrofit technique of adding sandwich columns to partition brick walls is proposed in this paper, and the feasibility of the proposed method was verified by in situ pushover tests of two real school buildings, one without and one with retrofit. The experimental and analytical results show that the sandwich column itself contributes significantly to the seismic capacity of the examined school building. Moreover, the analytical results yielded conservative capacity curves when compared with the experimental results. Copyright © 2013 John Wiley & Sons, Ltd.

An isolation system is not very effective when an inappropriate level of damping is used. This paper proposes a theoretical method which can be used to determine the optimal frictional coefficient of an isolation system. Only a one-dimensional isolation system and ground motion are considered. The frictional coefficient is optimized by minimizing the sum of squares of structural absolute accelerations, with the optimization results being validated graphically. Sensitivity studies were used to verify the feasibility of the optimal frictional coefficient, coupled with a practical example in Taipei under the conditions of the Hualien and El Centro earthquakes. Consequently, the feasibility and reliability of the proposed optimal design were verified.

The present study aims at proposing an innovative phase control methodology for semi-active tuned mass dampers (SA-TMDs) that intend to minimize the off-tuned problems associated with passive tuned mass dampers (P-TMDs). The phase control algorithm is first developed, the essential of which is to apply the variable friction force to slow down the mass block at specific moments when the phase lag of the SA-TMD with respect to the structure is different from 90°, resulting in the SA-TMD back to the desired phase lag, i.e., −90° phase deviation, so that the SA-TMD has the maximum power flow to reduce the structural vibration. The feasibility of the application of the phase control in SA-TMDs is verified by performing numerical analyses of a simplified Taipei 101 structure model with a SA-TMD subjected to sinusoidal loads and design level wind loads. The numerical simulation results show that the SA-TMD implemented with phase control can enable the mass block to vibrate in a manner with a phase lag close to the −90° when the structure model is under sinusoidal excitations with frequencies different from the structural fundamental mode. The SA-TMD with phase control not only exhibits better performance than the optimal P-TMD in terms of suppressing the structural vibration, but also enhances its robustness, particularly when the SA-TMD is off-tuned to the structure.

Seismic resistance of elementary and high school buildings is of great concern due to high earthquake risk in Taiwan. Existing school buildings are often built of similar configurations, and designed based on previous building codes, which are not in compliance with current codes in seismic performance objective. The use of current code procedures on seismic performance assessment of existing typical school buildings may not be applicable in predicting their structural behavior during earthquakes. This paper describes a full-size two-story, three-bay frame structure test of typical school building design in Taiwan, and examines the performance and failure mechanism of the frame structure with current building codes. Results from loading test show good agreement with the code-defined procedures in identifying soft story, weak story, and failure modes of columns, but show different failure mechanism in beam–column joint region, i.e. strong-column–weak-beam is expected by building code procedures, whereas the test specimen exhibits weak-column–strong-beam behavior. Although the joint shear check following current code procedures gives satisfactory results, i.e. is consistent with the experiment, the check on its own is not a reasonable one. Revisions of current checking procedures for failure mechanism in beam column joint and for joint shear are also proposed in this paper for existing non-ductile reinforced concrete school buildings. The revised procedures incorporate the effects of both weak story and weak-column–strong-beam behavior. After adopting the proposed procedures, the predicted structural behavior and failure modes are consistent with those observed from the full-size frame test.

SUMMARY Tuned mass dampers with viscous damping and isolation systems with friction pendulums have been proposed and widely applied over the past several decades. By combining these two ideas, a friction pendulum tuned mass damper (FPTMD) is proposed in this study. Because the restoring and friction forces are provided by the spherical surface of the FPTMD, springs and dampers are not needed. Moreover, suspension is not necessary and the installation space is greatly reduced. The optimal design of the FPTMD with varying friction coefficients for wind-excited high-rise structures is investigated. The optimization procedures are demonstrated by the FPTMD implemented on Taipei 101 under white-noise wind force, and the optimization results are validated by three-dimensional graphs. From the results of the sensitivity study, the effectiveness of the FPTMD with two different patterns of friction coefficients is sensitive to the tuning frequency ratio but not very sensitive to the friction parameters. Moreover, an FPTMD with a friction coefficient that linearly varies with displacement is even less sensitive to the friction parameters and the amplitude of excitation. The feasibility of the FPTMD with two different patterns of friction coefficient is illustrated by Taipei 101 subjected to the design wind force with a return period of 50 years. Following design optimization and numerical verification, the effect of vibration reduction for Taipei 101 is demonstrated. Copyright © 2012 John Wiley & Sons, Ltd.

A variable-stiffness isolation system, whose isolation stiffness can be altered instantaneously in response to the seismic load, is able to provide better seismic protection for vibration-sensitive equipment or facilities than a conventional isolation system with a fixed stiffness. To determine its time-variant isolation stiffness, this system usually requires an effective on-line control law. In this study, a control strategy called the least input energy control (LIEC) is proposed for a general variable-stiffness isolation system. With the feedback of the ground velocity, at each time step the LIEC is able to determine the optimal isolation stiffness that minimizes the input seismic energy transmitted onto the isolated object. In order to evaluate its control performance, the LIEC was physically implemented on a leverage-type variable-stiffness isolation system, and tested in a seismic simulation test. The experimental response of the LIEC was then compared to the uncontrolled response, as well as the simulated responses of two semi-active control laws derived from the widely used LQR control and modal control. A comparison of the results demonstrates that, among all the control cases considered, the LIEC transmits the least seismic input energy to the isolated system, and thus has the best isolation performance. In addition, the test data also show that the LIEC requires the least control force and control energy. This indicates that the LIEC is also a very efficient control method for variable-stiffness isolation systems.

Recently, the benefit of nonlinear isolation systems under resonance or near-fault earthquake has been investigated. In this paper, an eccentric rolling isolation system (ERIS) with additional friction damping is proposed. The isolation object is eccentrically pinned on a set of circular isolators so that the restoring force is nonlinear. To investigate the advantage of the ERIS, a corresponding isolation system with linear restoring force is also considered for comparison. The friction parameters of the two systems with linear and nonlinear restoring force are designed under the far-field El Centro earthquake. The performances of the two isolation systems are inspected under excitations other than the design one. In free vibration, the response of the ERIS decays faster than the corresponding linear system. In resonance sinusoidal excitation, the responses are divergent for the linear system but convergent for the ERIS. The linear system is ineffective but the ERIS is effective due to the nonlinearity under the near-fault Chi-Chi earthquake with various peak ground accelerations.

SUMMARY Optimal design for tuned mass dampers (TMDs) with linear or nonlinear viscous damping is formulated in order for design practitioners to directly compute the optimal parameters of a TMD in a damped structure subjected to wind excitations. The optimal TMD tuning frequency ratio and damping coefficient for a viscous TMD system installed in a damped structure under 10 white noise excitations are determined by using the time-domain optimization procedure, which minimizes the structural response. By applying a sequence of curve-fitting schemes to the obtained optimal values, design formulas for optimal TMDs are then derived. These are expressed as a function of the mass ratio and damping power-law exponent of the TMD as well as the damping ratio of the structure. The feasibility of the proposed optimal design formulas is verified in terms of formulary accuracy and of comparisons with existing formulas from previous research works. In addition, one numerical example of the Taipei 101 building with a nonlinear TMD, which is redesigned according to the proposed optimal formulas, is illustrated in effort to describe the use of the formulas in the TMD design procedure and to investigate the effectiveness of the optimal TMD. The results indicate that the proposed optimal design formulas provide a convenient and effective approach for designing a viscous TMD installed in a wind-excited damped structure. Copyright © 2011 John Wiley & Sons, Ltd.

Thousands of buildings were damaged by the devastating Chi-Chi earthquake on September 21, 1999. Of all the public buildings, school buildings are the most vulnerable to earthquake damage, and the retrofitting of existing school buildings becomes a stringent issue. In addition to cost effectiveness, the impact of retrofitting methods on the functions of the school buildings needs to be considered. This paper therefore proposes the retrofitting of school buildings by adding sandwich columns onto partition brick walls. The sandwich column is divided into two parts and is added to the two sides of the partition brick wall held with pairs of U-shaped bars. The retrofit does not require the removal of windows or doors in the longitudinal direction making the proposed method cost effective and minimizes the impact on the function of the school buildings. Five full-scale specimens without and with retrofitting were designed and fabricated for testing based on the partition brick wall frames of the existing school buildings. The specimens were subjected to cyclic loading in the out-of-plane direction through a loading frame so that the columns deformed with double curvatures. The experimental results verified the feasibility of the proposed retrofit method. The data showed that the lateral strength of the retrofitted specimen doubled that which was not and that the residual strength of the retrofitted specimen was just as high as the ultimate strength of the specimen without retrofitting. The analytical results in lateral strength yielded conservative figures compared with experimental measurements. Copyright © 2011 John Wiley & Sons, Ltd.

The algorithm of modified predictive control (MPC) is derived with the partial-state concept of direct output feedback (DOF) to reduce the number of sensors for real implementation. The feasibility of using modified predictive control with direct output feedback (MPCwDOF) is verified through numerical and experimental study. According to the MPCwDOF algorithm, the online control forces are simply generated from the actual output measurements that are multiplied by a prescribed constant output feedback gain matrix. An off-line numerical method is introduced to find the feedback gain systematically and efficiently. Numerical examples of two control systems with respect to single-controller and multiple-controller systems are illustrated for validating the feasibility of using the MPCwDOF algorithm and the application of the decentralized control strategy to the MPCwDOF algorithm. An experiment of a large-scale 5-story structural model with an MPCwDOF-controlled active mass damper on the roof is also performed. Results indicate that the controlled structures achieve good performance under environmental excitations. Simple online calculations and a small number of sensors make the proposed control algorithm more favorable to real implementation. Copyright © 2010 John Wiley & Sons, Ltd.

Optimal design theory for linear tuned mass dampers (TMD) has been thoroughly investigated, but is still under development for nonlinear TMDs. In this paper, optimization procedures in the time domain are proposed for design of a TMD with nonlinear viscous damping. A dynamic analysis of a structure implemented with a nonlinear TMD is conducted first. Optimum design parameters for the nonlinear TMD are searched using an optimization method to minimize the performance index. The feasibility of the proposed optimization method is illustrated numerically by using the Taipei 101 structure implemented with TMD. The sensitivity analysis shows that the performance index is less sensitive to the damping coefficient than to the frequency ratio. Time history analysis is conducted using the Taipei 101 structure implemented with different TMDs under wind excitation. For both linear and nonlinear TMDs, the comfort requirements for building occupants are satisfied as long as the TMD is properly designed. It was found that as the damping exponent increases, the relative displacement of the TMD decreases but the damping force increases.

The linear isolator has fixed vibration frequency. When structures with these linear isolators are located near a fault, it may cause resonance and large displacement response. Hence, nonlinear isolation may avoid this situation. In this study, an eccentric nonlinear rolling isolator with a parameter, which is the eccentricity of the pin connection of the mass block (facility) to the circular isolator, is investigated. If the eccentricity is not equal to zero, the dynamic response is nonlinear rolling behavior. The equation of motion of the isolation system is derived. The frequency of the isolator increases with the eccentricity under the same initial angle. The influence of the eccentricity to the effect of isolation is scrutinized. Finally, the feasibility of the proposed isolation device is verified numerically. If the proposed isolator is designed properly, it is effective for far-field earthquake (El Centro earthquake). Even though the linearized frequency of the proposed isolator falls into the dominant frequency range of near-fault earthquake (Chi-Chi earthquake), resonance can be avoided due to nonlinearity. Copyright © 2008 John Wiley & Sons, Ltd.

Many experiments have been studied for bolted beam–column connections for past years to prevent the demerit of welding at the site. Wing plates welded at beam ends of bolted beam–column connections in CFT structures have been studied experimentally by authors to ensure that plastic hinges are away from the welding. This paper studies the effect of wing plates numerically by simulating H-beams in bolted beam–column connections as cantilever beams using ABAQUS. Through convergence and cyclic loading analyses, simulation agrees well with the experimental results. The brittle failure due to developed crack can be predicted once equivalent plastic strain exceeds the maximum plastic strain. From numerical results, the effect of wing plates is verified. Furthermore, suitable formulas for the width of wing plates are derived to prevent the brittle failure of beams. Consequently, it is suggested that the length and the width of wing plates in application should be designed by using the suggested design process proposed in this paper.

An optimal discrete-time direct output-feedback control algorithm is developed with the consideration of sampling period and appropriate time delay in its control force action. Optimal-delayed output-feedback gains are derived through a variation process and will be complementarily arranged with respect to the applied delay time by either altering their magnitude or phases to assure the efficacy and stability of the delayed direct digital control system. Parametric studies of single-degree-of-freedom (SDOF) systems with different feedback types demonstrate the relationships of the delayed gains and the modal properties corresponding to the sampling period used and the intentionally delay time added. The maximum allowable delay time defined at the onset of instability of controlled system can be the optimal delay time that reaches the optimal control performance if the delay time is considered in the delayed feedback gains. The inclusion of sampling period and delay time in the optimization process for discrete-time control illustrates the beneficial effect under the same delay time. Numerical simulation results of proposed direct digital control principles on a three-degree-of-freedom (3DOF) shaking table structure model show that the efficacy of the collocated control cases with optimal delay time to reduce the dynamic responses subjected to earthquake excitations is assured. Copyright © 2007 John Wiley & Sons, Ltd.

This research investigates the seismic performance of four steel beams to concrete filled steel tube (CFT) column connections with floor slabs, including two interior and two exterior joints. The objective of this research is to evaluate firstly the composite effect of the steel beam and floor slab commonly used in Taiwan in practice. Secondly, the seismic behavior of new connection details such as the taper flange or larger shear tab in the beam-end is investigated to prevent complete joint penetration welds (CJP) of the girder flanges from the unexpected brittle failure found in the latter after the Northridge earthquake. In addition to the experimental investigation, the development and validation of analytical models for the assessment of the force–deformation behavior of the joint components are also conducted. The slab effect on the shear transfer in the panel zone is investigated as well.

Concrete-filled tubes (CFTs) have the advantages of both steel tubes and concrete. For that the confinement of the steel tube on the concrete would enhance the stiffness, strength and ductility of the concrete; also, the filled concrete can decrease the possibility of inward buckling of the steel. In this paper, bidirectional bolted beam-to-column connections for CFTs are proposed. A mechanical model is established to derive theoretical equations for calculating the stiffness, the yielding shear strength and ultimate shear strength of the panel zone. Also, a series of cyclic loading experiments has been conducted to verify it. The experimental results demonstrate that the bidirectional bolted connections have superior earthquake resistance in stiffness, strength, ductility and energy dissipation mechanism. These results indicate that the seismic resistance exceeds those specified in the seismic design codes of Taiwan and the US. Therefore, the bidirectional bolted beam-to-column connection has excellent seismic resistance, and this structural system can perform well as expected and be put into practice.

The seismic response of a structural system equipped with friction-type energy dissipation devices is generally nonlinear. The main reason for this nonlinearity is the friction mechanism that possesses two possible motion states, referred to as stick and slip states. The essential force and kinematic conditions of a friction damper, in these two states, are different. In this paper, by employing a state-space formulation and a linear integration scheme, the discrete-time solution of dynamic response of a structural system equipped with multiple friction devices, which can be in either a stick or slip state, was derived in a single and unified form. The nonlinear friction forces, in each time step of analysis, were solved by satisfying both the force and kinematic conditions of certain motion states. Based on a derived discrete-time solution, a numerical analysis procedure was proposed, which allows the time interval of analysis to remain constant, even at the transition of stick and slip states; thus, it is a systematic and efficient method for numerical implementation. The solution of the method was compared with the analytical free-vibration response of a single DOF system, and also with the harmonic and seismic responses simulated by other conventional numerical methods. These examples demonstrate the accuracy and stability of the proposed method.

An optimal design theory for structures implemented with tuned mass dampers (TMDs) is proposed in this paper. Full states of the dynamic system of multiple-degree-of-freedom (MDOF) structures, multiple TMDs (MTMDs) installed at different stories of the building, and the power spectral density (PSD) function of environmental disturbances are taken into account. This proposed method allows for a more extensive application and successfully releases the limitations based on simplified models. The optimal design parameters of TMDs in terms of the damping coefficients and spring constants corresponding to each TMD are determined through minimizing a performance index of structural responses defined in the frequency domain. Moreover, a numerical method is also proposed for searching for the optimal design parameters of MTMDs in a systematic fashion such that the numerical solutions converge monotonically and effectively toward the exact solutions as the number of iterations increases. The feasibility of the proposed optimal design theory is verified by using a SDOF structure with a single TMD (STMD), a five-DOF structure with two TMDs, and a ten-DOF structure with a STMD.

Concrete-filled steel tubes (CFT) have the advantage of high strength, high stiffness and being constructed quickly. However, because the behavior of the beam-to-column connection for CFT is complicated and its design has not been sufficiently verified, their use has been limited. In this paper, a new design of bolted beam-to-column connections for CFT is proposed. A mechanical model is established in order to derive theoretical equations for calculating the stiffness, the yielding shear strength and the ultimate shear strength of the panel zone. Also, a series of cyclic loading experiments have been conducted. The experimental results and theoretical results are very close, which demonstrates that the bolted connections have superior seismic resistance in stiffness, strength, ductility and energy dissipation mechanisms. From the laboratory studies, even though the story angular drift reaches 7% and the plastic angular displacement reaches 5%, the structure still stands. Those results indicate that the seismic resistance exceeds those specified in Taiwan and the US.

Although there are many well-established control methods for vibration mitigation of seismic structures with active devices, their direct application for structures with semi-active control devices are limited. This limitation is primarily contributed by the fact that a semi-active device can only provide a resistant (passive) force to the controlled structure. In this paper, a general method for semi-active feedback control of seismic structures with variable friction dampers (VFD) is proposed. In order to overcome the force limitation of friction dampers, the method forms a semi-active feedback gain by multiplying an active gain with Heaviside functions. Based on this method, two newly developed control laws, i.e., semi-active modal control and semi-active optimal control were numerically investigated. A multiple DOF structural system with various sensor deployments, for either full-state or direct-output feedbacks was considered in the numerical study. The performances of both semi-active control laws for seismic vibration mitigation were compared with those of passive and active controls. The numerical results showed that both semi-active controls resulted in better acceleration reductions than the passive case and were able to closely imitate the performance of their active control counterparts.

A nonlinear force-deformation model to simulate shear transfer behavior in the panel zone of CFT (Concrete-Filled Steel Tube) beam-column connections is proposed. In this model, influence of axial load on the shear transfer behavior is accounted for. To validate the proposed theory, five circular CFT beam-column connections were constructed and tested. Test results showed that all specimens failed by the welding fracture while entering nonlinear stage. It is found that the higher the axial load was applied, the better the ductility of connections was obtained. Comparison of analytical and experimental results shows that the proposed prediction for panel shear falls in a reasonable range for higher axial load tests, but tends to be conservative for lower axial load tests.

In conventional methods of modal control, the number of controllable structural modes is usually restrained by the number of sensors that feedback the structural signals. In this paper a modal control scheme where the feedback gain is formulated in an augmented state space is proposed. The advantage of the proposed method is that it increases the number of the controllable modes without adding extra sensors. The method is verified experimentally by an earthquake simulation test with a full-scale building model. The proposed modal control was also compared with the conventional ones in the test. For the building model tested, the performance of the proposed control with only one feedback signal can be as efficient as that of modal control with full state feedback. Copyright © 2001 John Wiley & Sons, Ltd.

A modified predictive control algorithm for the active control of structures is developed in the discrete-time formulation. Before the control algorithm is modified, the predictive control forces are kept constant throughout the predictive time-steps in the predictive control algorithm so that dynamic instability is induced to the control systems for certain numbers of predictive time-steps. After the control algorithm is modified, the predictive control forces are assigned to be linearly related with the predictive structural states so that dynamic stability of the control systems is guaranteed. In addition to the dynamic stability of the control systems, the control performance of the modified control algorithm is also superior to that of the original one. The feasibility of the modified control algorithm is verified through eigenvalue analysis, frequency-domain analysis and time-domain analysis. The tendon control systems of a single-degree-of freedom structure and a three-degree-of-freedom structure are illustrated to demonstrate the control effectiveness of the modified predictive control algorithm.

This paper aims to investigate the possible use of a control system that combines the concept of active members and a direct output feedback method to mitigate the seismic vibration of civil engineering structural systems. An active member, according to the definition used in this paper, is an added structural member in which an actuator, a sensor and a simple controller are highly integrated. By integrating these fundamental control devices together, the active members will be less vulnerable to environmental influence; moreover, each active member can be used as an independent control mechanism. In this study, an output feedback control algorithm called the Modal Truncated Output Feedback (MTOF), suitable for the active member control, is adopted. With this algorithm, the failure or malfunction of one active member will not impair the entire control system. A numerical example of the shear building type is used to demonstrate the proposed control system. It is shown that the concept of active members and the MTOF control algorithm together form a very stable, effective, and reliable control system for vibration control of seismic structures.

SUMMARY A systematic method is developed for the dynamic analysis of the structures with sliding isolation which is a highly non-linear dynamic problem. According to the proposed method, a unified motion equation can be adapted for both stick and slip modes of the system. Unlike the traditional methods by which the integration interval has to be chopped into infinitesimal pieces during the transition of sliding and non-sliding modes, the integration interval remains constant throughout the whole process of the dynamic analysis by the proposed method so that accuracy and eƒciency in the analysis of the non-linear system can be enhanced to a large extent. Moreover, the proposed method is general enough to be adapted for the analysis of the structures with multiple sliding isolators undergoing independent motion conditions simultaneously. The superiority of the proposed method for the analysis of sliding supported structures is verified by a three-span continuous bridge subjected to harmonic motions and real earthquakes. In addition, the side e⁄ect of excessive displacement of the superstructure induced by the sliding isolation is eliminated by replacing one of the roller supports on the abutments with hinge support. Therefore, both reductions in the forces of the substructure and the displacements of the superstructure can be achieved simultaneously. ( 1998 John Wiley & Sons, Ltd.

The essential feedback signals for direct output feedback control are limited to velocities and direct acceleration feedback control is found to be unfeasible even though accelerometers are favorable sensors from the viewpoint of measurement. In this paper, acceleration feedback control becomes feasible when the feedback data is extended to cover accelerations of the previous time-steps. A multi-step acceleration feedback control algorithm is derived through an optimization process such that a certain prescribed quadratic performance index is minimized. Control forces are simply generated from acceleration information of the current and previous time-steps. The feasibility of the proposed control algorithm is verified numerically by the tendon control of structures subjected to real earthquake excitation. The control effectiveness of the proposed control algorithm is close to that of state feedback control algorithm. Simple on-line calculation and availability of accelerometers make the proposed control algorithm favorable to realtime control implementation.