• Earthquakes and Structures
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• v.1 no.2
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• pp.147-162
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• 2010

The ground acceleration measured at a point on the earth's surface is composed of several waves that have different phase velocities, arrival times, amplitudes, and frequency contents. For instance, body waves contain primary and secondary waves that have high frequency content and reach the site first. Surface waves are composed of Rayleigh and Love waves that have lower phase velocity, lower frequency content and reach the site next. Some of these waves could be of more damage to the structure depending on their frequency content and associated amplitude. This paper models critical earthquake loads for single-degree-of-freedom (SDOF) inelastic structures considering evolution of the seismic waves in time and frequency. The ground acceleration is represented as combination of seismic waves with different characteristics. Each seismic wave represents the energy of the ground motion in certain frequency band and time interval. The amplitudes and phase angles of these waves are optimized to produce the highest damage in the structure subject to explicit constraints on the energy and the peak ground acceleration and implicit constraints on the frequency content and the arrival time of the seismic waves. The material nonlinearity is modeled using bilinear inelastic law. The study explores also the influence of the properties of the seismic waves on the energy demand and damage state of the structure. Numerical illustrations on modeling critical earthquake excitations for one-storey inelastic frame structures are provided.

• Earthquakes and Structures
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• v.8 no.6
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• pp.1325-1348
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• 2015

Real-time hybrid testing (RTHT) involves virtual splitting of the structure into two parts: physical substructure that contains the key region of interest which is tested in a laboratory and numerical substructure that contains the remaining part of the structure in the form of a numerical model. This paper numerically assesses four step-by-step integration methods (Central difference method (CDM), Operator splitting method (OSM), Rosenbrock based method (RBM) and CR-integration method (CR)) which are widely used in RTHT. The methods have been assessed in terms of stability and accuracy for various realistic damping ratios of the physical substructure. The stability is assessed in terms of the spectral radii of the amplification matrix while the accuracy in terms of numerical damping and period distortion. In order to evaluate the performance of the methods, five carefully chosen examples have been studied - undamped SDOF, damped SDOF, instantaneous softening, instantaneous hardening and hysteretic system. The performance of the methods is measured in terms of a non-dimensional error index for displacement and velocity. Based on the error indices, it is observed that OSM and RBM are robust and performs fairly well in all the cases. CDM performed well for undamped SDOF system. CR method can be used for the system showing softening behaviour. The error indices indicate that accuracy of OSM is more than other method in case of hysteretic system. The accuracy of the results obtained through time integration methods for different damping ratios of the physical substructure is addressed in the present study. In the presence of a number of integration methods, it is preferable to have criteria for the selection of the time integration scheme. As such criteria are not available presently, this paper attempts to fill this gap by numerically assessing the four commonly used step-by-step methods.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 1998.04a
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• pp.212-219
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• 1998

Dynamic analyses are performed for the wood structure modeled as a SDOF hysteretic system. The hysteresis model presented is a modified version of Takeda model. The comparison between the results of numerical simulation and the experimental results show good agreements in overall tendencies. The response of wood structure subjected to artificially generated earthquakes considering site effects is studied. It appears that the response is very strongly influenced by the intensity and the frequency contents of the ground motion.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2011.10a
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• pp.59-63
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• 2011

Friction damping is one of the attractive vibration control technique for space structures due to its simplicity and large damping capacity. However, passive approaches for friction damping have a limitation because energy is no longer dissipated at sticking. In order to overcome this problem, semi-active control methods to adjust normal force at frictional interface have been studied in previous researches. In this paper, two semi-active friction control method is compared by simulating SDOF model of truss structure. The first approach is on-off control to maximize rate of energy dissipation, whereas the second concept is variable friction force control to minimize amplitude ratio for each half period. The maximum friction force, control variable in on-off control method, is obtained to minimize 1% settling time, and is different from optimal friction force in passive control. Simulation results show that performance of on-off control is better than that of variable friction force control in terms of settling time and controlled friction force.

• Structural Engineering and Mechanics
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• v.29 no.2
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• pp.187-201
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• 2008

Earthquake induced hysteretic energy demand for a structure can be used as a limiting value of a certain performance level in seismic design of structures. In cases where it is larger than the hysteretic energy dissipation capacity of the structure, failure will occur. To be able to select the limiting value of hysteretic energy for a particular earthquake hazard level, it is required to define the variation of hysteretic energy in terms of probabilistic terms. This study focuses on the probabilistic evaluation of earthquake induced worst failure probability and approximate confidence intervals for inelastic single-degree-of-freedom (SDOF) systems with a typical steel moment connection based on hysteretic energy. For this purpose, hysteretic energy demand is predicted for a set of SDOF systems subject to an ensemble of moderate and severe EQGMs, while the hysteretic energy dissipation capacity is evaluated through the previously published cyclic test data on full-scale steel beam-to-column connections. The failure probability corresponding to the worst possible case is determined based on the hysteretic energy demand and dissipation capacity. The results show that as the capacity to demand ratio increases, the failure probability decreases dramatically. If this ratio is too small, then the failure is inevitable.

• Journal of the Earthquake Engineering Society of Korea
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• v.7 no.6
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• pp.71-80
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• 2003

Though a nonlinear time history analysis may be provided to estimate more exactly the seismic performance of building structure, approximation methods are still needed in the aspect of practicality and simplicity, In converting a multi-story structure to an equivalent SDOF system, the mode vectors of the multi-story structure are assumed as the mode shape in elastic state regardless of elastic or elastic-plastic state. However, the characteristics of displacement mode are also changed after the yielding made in the structural elements, because the structure becomes inelastic in each incremental load step. In this research, a method of converting MDOF system to ESDOF system is presented by using nonlinear displacement mode considering the mode change of structures after the yielding. Also, the accuracy and efficiency of the method of the nonlinear displacement mode method of the estimate of seismic response of Mixed Building Structures were examined by comparing the displacements of the roof level of the multi-story building structures estimated from this converted displacement response of ESDOF with the displacement of the roof level through the nonlinear dynamic analysis of the multi-story building structures subjected to an actual earthquake excitation.

• Earthquakes and Structures
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• v.19 no.4
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• pp.243-259
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• 2020

This study aims to optimize, design, and predict the MTMDs performance in SDOF systems using spectral analysis, and then apply their results to MDOF structures. Given the importance of spectral analysis in the design of new engineering structures, achieving a method for designing TMDs based on this theory can be of great importance for structural designers. In this study, several convenient combinations of MTMDs in an SDOF system are first considered to minimize the maximum displacement. For calculating the frequency ratios of dampers, an innovative technique is adopted in which the values of different modal responses obtained from the spectral analysis are approached together. This procedure is done using a harmony search (HS) algorithm. Also, using the random vibration theory, the damping ratio of the dampers is obtained. Then, an equation is presented for predicting the performance of MTMDs. For evaluating this equation, three structures with different stories are designed. Some of the presented combinations of dampers are added to them. The time history analyses are employed to analyze the structures under 30 different accelerograms. The findings indicated that the proposed equation could efficiently predict the performance of the MTMDs. Furthermore, four different patterns of damper distribution along the height of the structures are defined. The effect of them on the maximum deformation of the structures in time history analyses is discussed, and an equation is presented to estimate this effect. The results indicated that the average and maximum error percentages of the proposed equations are about three and seven percent, respectively, compared to the time history analyses results, which are negligible values.

• Journal of the Earthquake Engineering Society of Korea
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• v.10 no.1 s.47
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• pp.51-62
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• 2006

To dale, lots of types of tuned mass dampers are developed and investigated to reduce dynamic responses of a structure due to various causes. In this study, control performance of semi-active tuned mass damper(STMD), that can change the damping of tuned mass damper in real time based on structural responses, was investigated with respect to various types of excitation employing numerical simulation. Skyhook control algorithm was used to appropriately modulate the damping ratio of semi-active damper that composes STMD. The control effectiveness of a STMD under harmonic and random excitation were evaluated using a single-degree-of-freedom (SDOF) structure in comparison with a conventional passive tuned mass damper (TMD). The robustness of a STMD and a passive TMD were compared along with the variation of the mass of a SDOF structure. The control performance of STMD using magnetorheological (MR) damper was also investigated in this study. Based on the numerical studios, it was shown that the control effectiveness of the STMD was significantly superior to that of a passive TMD with respect to harmonic and random excitation.

• Structural Engineering and Mechanics
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• v.39 no.5
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• pp.683-701
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• 2011

In this study, inelastic displacement ratios and ductility demands are investigated for SDOF systems with period range of 0.1-3.0 s. with elastoplastic behavior considering soil structure interaction. Earthquake motions recorded on different site conditions such as rock, stiff soil, soft soil and very soft soil are used in analyses. Soil structure interacting systems are modeled with effective period, effective damping and effective ductility values differing from fixed-base case. For inelastic time history analyses, Newmark method for step by step time integration was adapted in an in-house computer program. Results are compared with those calculated for fixed-base case. A new equation is proposed for inelastic displacement ratio of interacting system ($\tilde{C}_R$) as a function of structural period of interacting system ($\tilde{T}$), strength reduction factor (R) and period lengthening ratio ($\tilde{T}/T$). The proposed equation for $\tilde{C}_R$ which takes the soil-structure interaction into account should be useful in estimating the inelastic deformation of existing structures with known lateral strength.

• Structural Engineering and Mechanics
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• v.41 no.3
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• pp.365-378
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• 2012

In this study, strength reduction factors are investigated for SDOF systems with period range of 0.1-3.0 s with elastoplastic behavior considering soil structure interaction for 64 different earthquake motions recorded on different site conditions such as rock, stiff soil, soft soil and very soft soil. Soil structure interacting systems are modeled and analyzed with effective period, effective damping and effective ductility values differing from fixed-base case. For inelastic time history analyses, Newmark method for step by step time integration was adapted in an in-house computer program. Results are compared with those calculated for fixed-base case. A new equation is proposed for strength reduction factor of interacting system as a function of structural period of system (T), ductility ratio (${\mu}$) and period lengthening ratio (T/T). It is concluded that soil structure interaction reduces the strength reduction factors for soft soils, therefore, using the fixed-base strength reduction factors for interacting systems lead to non-conservative design forces.