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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.

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.

In this paper, orthogonal collocation method (OCM) is applied to solve the free vibration of nonlocal Timoshenko beams with various boundary conditions by using piecewise cubic Hermite polynomials (CHPs). In the numerical implementation, approximation solution and its space derivatives over the interval are approximated by the combination of the CHPs and unknown parameters. Through the generalized eigen-value problem analysis, the vibration frequencies of beams can be determined precisely. Form numerical analysis by using OCM sufficiently indicate that it has excellent convergence rate, and very close to analytical solutions.

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.

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.

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.

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.

Applying the concept of minimum potential energy and the variational method proposed in this paper, one can derive the governing equation and transversality conditions for the critical slip surface of a cohesive land slope described by simplified Janbu's model where both horizontal and vertical inter-slice forces are neglected. The governing equation, transversality conditions and boundary conditions were solved by the boundary integral equation method, which is a one dimensional BIEM, so that the critical slip surface and its associated minimal factor of safety can be determined effectively. By comparison of the results gotten from the boundary integral equation method and other numerical methods, it can be concluded, that, for some simplified cases, by using the boundary integral equation method on slope stability analysis of a cohesive land slope, a more reasonable result can be obtained.

Applying the principle of virtual work, the slice element method, and the variational method proposed in this paper, one can derive the governing equation and transversality conditions for the rupture surface of a sliding mass of retaining wall and shallow foundation under several external conditions. The governing equation, transversality, and boundary conditions can be solved by the finite difference method (FDM) proposed in this paper, so that the rupture surface and its associated earth pressure acting on the retaining wall or the ultimate bearing capacity acting on the foundation can be determined effectively. By comparison of our results with those of some well known earth pressure and bearing capacity estimating methods, it can be concluded that determining the earth pressure on a retaining wall or the ultimate bearing capacity of a shallow foundation by using the variational method and FDM proposed in this paper, a logical and reasonable result can be obtained without the necessity of guessing the rupture surface.

The dynamic response of a homogeneous, isotropic and elastic circular plate on an elastic foundation subjected to axisymmetric time dependent loads is investigated both analytically and numerically in thisv paper. First, the Extended Finite Hankel Transform (EFHT) is derived. After applying the technique of the EFHT to the governing equation of the vibrating circular plate, the governing partial differential equation (PDE) is transformed into the governing ordinary differential equation (ODE). Therefore, the analytical solution of the plate problem can be found completely. Once the dynamic response of the plate is solved, the internal forces of the plate, including shear force, bending moment and torsion, can be obtained subsequently. Under the particular case that elastic springs do not exist under the foundation, the dynamic response of the circular plate by the method of EFHT matches exactly with that by the method of modal analysis. By comparing the methods of EFHT, Boundary Element Method (BEM) and Finite Element Method (FEM), the results indicate that the proposed method of EFHT is accurate, systematic and convenient.

In this paper, the application of the spline collocation method (SCM) to the analysis of rigid frame structures under various loading conditions is demonstrated originally and successfully. The derivation of the spline functions in the SCM is extended and simplified compactly through a finite difference approach that can be easily accepted by engineers. Without complicated calculation, the coefficient matrix for the weighting coefficients can be assembled simply by finding from the table the values of the quintic splines at knots. Since the coefficient matrix is invertible when the buckling problems of rigid frame are not considerered, the solution for the weighting coefficients always exists physically and uniquely. The feasibility of the proposed SCM formulation is first studied by the problem of the generalized beam analysis and excellent accuracy is achieved. The frame structure is considered to be the composition of beam elements approximately, then, the accuracy and efficiency of the SCM fo...

In this paper, spline collocation method (SCM) is successfully extended to solve the generalized problems of beam structures. The spline functions in SCM are re-formulated by finite difference method in a systematical way that is easily understood by engineers. The manipulation of SCM is further simplified by the introduction of quintic table so that the matrix-vector governing equation can be easily formulated to solve the weighting coefficients. SCM is first examined by the problems of a generalized single-span beam undergoing various types of loadings and boundary conditions, and it is then extended to the problems of continuous beam with multiple spans. By comparing with available analytical results, differential quadrature method (DQM), if any, excellent accuracy in deflection is achieved.

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.

Publisher Summary Direct absolute acceleration feedback control is considered to be unfeasible even though accelerometers are favorable sensors for measuring the dynamic structural responses from the viewpoint of measurement. Absolute acceleration feedback control becomes feasible when the feedback data is extended to cover the absolute accelerations of the previous time steps. 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 absolute acceleration information of the current and previous time steps multiplied by the pre-calculated optimal feedback gain matrix. The control effectiveness of the proposed control algorithm is verified through numerical simulation to be close to that of state feedback control algorithm. Simple on-line calculation and availability of accelerometers make the proposed control algorithm favorable to real-time control implementation.