• Structural Engineering and Mechanics
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• v.13 no.4
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• pp.369-385
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• 2002

Ductility capacity is comprehensively studied for steel moment-resisting frames. Local, story and global ductility are being considered. An appropriate measure of global ductility is suggested. A time domain nonlinear seismic response algorithm is used to evaluate several definitions of ductility. It is observed that for one-story structures, resembling a single degree of freedom (SDOF) system, all definitions of global ductility seem to give reasonable values. However, for complex structures it may give unreasonable values. It indicates that using SDOF systems to estimate the ductility capacity may be a very crude approximation. For multi degree of freedom (MDOF) systems some definitions may not be appropriate, even though they are used in the profession. Results also indicate that the structural global ductility of 4, commonly used for moment-resisting steel frames, cannot be justified based on this study. The ductility of MDOF structural systems and the corresponding equivalent SDOF systems is studied. The global ductility values are very different for the two representations. The ductility reduction factor $F_{\mu}$ is also estimated. For a given frame, the values of the $F_{\mu}$ parameter significantly vary from one earthquake to another, even though the maximum deformation in terms of the interstory displacement is roughly the same for all earthquakes. This is because the $F_{\mu}$ values depend on the amount of dissipated energy, which in turn depends on the plastic mechanism, formed in the frames as well as on the loading, unloading and reloading process at plastic hinges. Based on the results of this study, the Newmark and Hall procedure to relate the ductility reduction factor and the ductility parameter cannot be justified. The reason for this is that SDOF systems were used to model real frames in these studies. Higher mode effects were neglected and energy dissipation was not explicitly considered. In addition, it is not possible to observe the formation of a collapse mechanism in the equivalent SDOF systems. Therefore, the ductility parameter and the force reduction factor should be estimated by using the MDOF representation.

• Earthquakes and Structures
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• v.4 no.1
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• pp.109-132
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• 2013

Current codes incorporate simplified methods for the prediction of acceleration demands on secondary structural and non-structural elements at different levels of a building. While the use of simple analysis methods should be advocated, damage to both secondary structural and non-structural elements in recent earthquakes have highlighted the need for improved design procedures for such elements. In order to take a step towards the formation of accurate but simplified methods of predicting floor spectra, this work examines the floor spectra on elastic and inelastic single-degree of freedom systems subject to accelerograms of varying seismic intensity. After identifying the factors that appear to affect the shape and intensity of acceleration demands on secondary structural and non-structural elements, a new series of calibrated equations are proposed to predict floor spectra on single degree of freedom supporting structures. The approach uses concepts of dynamics and inelasticity to define the shape and intensity of the floor spectra at different levels of damping. The results of non-linear time-history analyses of a series of single-degree of freedom supporting structures indicate that the new methodology is very promising. Future research will aim to extend the methodology to multi-degree of freedom supporting structures and run additional verification studies.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 2003.09a
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• pp.419-426
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• 2003

An efficient procedure using LQR method for determining optimal sliding surfaces appropriate for different controller types is provided. The parametric evaluation of the dynamic characteristics of sliding surfaces is peformed in terms of SMC controller performance of single-degree-of-freedom(SDOF) systems. The control force limit is considered in this procedure. Numerical simulations for multi-degree-of-freedom(MDOF) systems verify the effectiveness of proposed method.

• Journal of the Earthquake Engineering Society of Korea
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• v.12 no.3
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• pp.21-28
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• 2008

To evaluate the seismic performance of multi-degree of freedom(MDF) systems, repeated nonlinear response history analyses are often conducted, which require extensive computational efforts. To reduce the amount of computation required, equivalent single degree of freedom(SDF) systems representing complex multi-degree of freedom(MDF) systems have been developed. For the equivalent SDF systems, bilinear models and trilinear models have been most commonly used. In these models, the P-$\Delta$ effect due to gravity loads during earthquakes can be accounted for by assigning negative stiffness after elastic range. This study evaluates the adequacy of equivalent SDF systems having these hysteretic models to predict the actual response of steel moment resisting frames(SMRF). For this purpose, this study conducts cyclic pushover analysis, nonlinear time history analysis and incremental dynamic analysis(IDA) for SAC-Los Angeles 9-story buildings using nonlinear MDF models(exact) and equivalent SDF models(approximate). In addition, this study considers the strength limited model.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2003.04a
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• pp.19-26
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• 2003

In energy-based design, the structures are generally transformed into equivalent SDOF systems to obtain the input and the dissipated energy. In this study the energy demands in multi-story structures were compared with that of equivalent single degree of freedom systems to validate the transformation method. Three-, eight-, and twenty-story steel moment-resisting frames and buckling restrained braced frames are compared with those of equivalent single degree of freedom systems. Sixty earthquake ground motions recorded in different soil conditions were used to compute the input and hysteretic energy demands in model structures. According to the analysis results, in 3 and 8-story structures the hysteretic energy demands computed in the equivalent SDOF structures are compatible with those computed in the original MDOF structures, while in the 20-story structures the transformed equivalent structures underestimated the hysteretic energy demands.

• Smart Structures and Systems
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• v.5 no.3
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• pp.279-290
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• 2009

Two degrees of freedom resonant systems are employed to improve the resonant property of resonant sensor, as compared to a single degree of freedom resonant system. This paper presents design, development and testing of two degrees of freedom resonant sensor. To measure absolute mass, cantilever shaped two different masses (smaller/absorber mass and bigger/drive mass) with identical resonant frequency are mechanically linked to form 2 - Degree-of-Freedom (DOF) resonator which exhibits higher amplitude of displacement at the smaller mass. The same concept is extended for measuring differential quantity, by having two bigger mass and one smaller mass. The main features of this work are the 3 - DOF resonator for differential detection and the microcontroller based closed loop electronics for resonant sensor with piezoelectric sensing and excitation. The advantage of using microcontroller is that the method can be easily extended for any range of measurand.

• Smart Structures and Systems
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• v.23 no.3
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• pp.243-261
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• 2019

This paper introduces an appropriate technique to estimate the weighting matrices used in the linear quadratic regulator (LQR) method for active structural control. For this purpose, a parameter is defined to regulate the relationship between the structural energy and control force. The optimum value of the regulating parameter, is determined for single degree of freedom (SDOF) systems under seismic excitations. In addition, the suggested technique is generalized for multiple degrees of freedom (MDOF) active control systems. Numerical examples demonstrate the robustness of the proposed method for controlled buildings under a wide range of seismic excitations.

• 한국방재학회:학술대회논문집
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• 2008.02a
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• pp.257-259
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• 2008

Acceleration time history (ATH) used in the seismic analysis should envelop a target power spectral density (PSD) function in addition to the design response spectrum in order to have sufficient energy at each frequency for the purpose of ensuring adequate load. Even though design regulations require the ATH used in seismic analysis to meet a target PSD function, the reason that ATHs meet to a target PSD function is not described. Thus, artificial ATHs for high PSD function and artificial ATHs for low PSD function are generated. And then elastic and inelastic single-degree-of-freedom (SDOF) systems are loaded with these artificial time histories as the earthquake load. As a result, linear response and inelastic response of SDOF systems are affected by PSD function.

• Journal of the Korean Society for Precision Engineering
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• v.10 no.3
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• pp.41-46
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• 1993

The transitional characterisics of oscillations and rotational speeds from the starting to the stationary states in damped single degree of freedom systems acted upon the rotor unbalance forces are studied. Angular travel is assumed to vary with time. The theoretical analysis is obtained by using Laplace transform method. Integration involved in the theoretical results is carried out by the numerical analysis program of continuous-time linear systems to arbitrary inputs. It is evident that the transitional charcterixtics of a machine are affected remarkably by damping ratios, stationary angular velocity time and frequency ratios.

• Earthquakes and Structures
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• v.7 no.1
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• pp.17-38
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• 2014

As the desire for high performance buildings increases, it is increasingly evident that engineers require reliable methods for the estimation of seismic demands on both structural and non-structural components. To this extent, improved tools for the prediction of floor spectra would assist in the assessment of acceleration sensitive non-structural and secondary components. Recently, a new procedure was successfully developed and tested for the simplified construction of floor spectra, at various levels of elastic damping, atop single-degree-of-freedom structures. This paper extends the methodology to multi-degree-of-freedom (MDOF) supporting systems responding in the elastic range, proposing a simplified modal combination approach for floor spectra over upper storeys and accounting for the limited filtering of the ground motion input that occurs over lower storeys. The procedure is tested numerically by comparing predictions with floor spectra obtained from time-history analyses of RC wall structures of 2- to 20-storeys in height. Results demonstrate that the method performs well for MDOF systems responding in the elastic range. Future research should further develop the approach to permit the prediction of floor spectra in MDOF systems that respond in the inelastic range.