• Earthquakes and Structures
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• 제22권6호
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• pp.571-584
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• 2022

The residual displacement ratio (RDRs) response spectra have been generally used as an important means to evaluate the post-earthquake repairability, and the ratios of residual to maximum inelastic displacement are considered to be more appropriate for development of the spectra. This methodology, however, assumes that the expected residual displacement can be computed as the product of the RDRs and maximum inelastic displacement, without considering the correlation between these two variables, which inevitably introduces potential systematic error. For providing an adequately accurate estimate of residual displacement, while accounting for the collapse resistance performance prior to the repairability evaluation, a probability-based procedure to estimate the residual displacement demands using the nonlinear static analysis (NSA) is developed for single-degree-of-freedom (SDOF) systems. To this end, the energy-based equivalent damping ratio used for NSA is revised to obtain the maximum displacement coincident with the nonlinear time history analysis (NTHA) results in the mean sense. Then, the possible systematic error resulted from RDRs spectra methodology is examined based on the NTHA results of SDOF systems. Finally, the statistical relation between the residual displacement and the NSA-based maximum displacement is established. The results indicate that the energy-based equivalent damping ratio will underestimate the damping for short period ranges, and overestimate the damping for longer period ranges. The RDRs spectra methodology generally leads to the results being non-conservative, depending on post-yield stiffness. The proposed approach emphasizes that the repairability evaluation should be based on the premise of no collapse, which matches with the current performance-based seismic assessment procedure.

• Smart Structures and Systems
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• 제8권3호
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• pp.239-252
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• 2011

In this study, the performances of a passive tuned mass damper (TMD) and a semi-active TMD (STMD) were evaluated in terms of seismic response control of elastic and inelastic structures under seismic loads. First, elastic displacement spectra were obtained for damped structures with a passive TMD and with a STMD proposed in this study. The displacement spectra confirmed that the STMD provided much better control performance than passive TMD and the STMD had less stroke requirement. Also, the robustness of the TMD was evaluated by off-tuning the frequency of the TMD to that of the structure. Finally, numerical analyses were conducted for an inelastic structure of hysteresis described by the Bouc-Wen model. The results indicated that the performance of the passive TMD whose design parameters were optimized for an elastic structure considerably deteriorated when the hysteretic portion of the structural responses increased, and that the STMD showed about 15-40% more response reduction than the TMD.

• Earthquakes and Structures
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• 제12권4호
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• pp.397-407
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• 2017

To estimate the structural seismic demand, some methods are based on an equivalent linear system such as the Capacity Spectrum Method, the N2 method and the Equivalent Linearization method. Another category, widely investigated, is based on displacement correction such as the Displacement Coefficient Method and the Coefficient Method. Its basic concept consists in converting the elastic linear displacement of an equivalent Single Degree of Freedom system (SDOF) into a corresponding inelastic displacement. It relies on adequate modifying or reduction coefficient such as the inelastic deformation ratio which is usually developed for systems with known ductility factors ($C_{\mu}$) and ($C_R$) for known yield-strength reduction factor. The present paper proposes a rational approach which estimates this inelastic deformation ratio for SDOF bilinear systems by rigorous nonlinear analysis. It proposes a new inelastic deformation ratio which unifies and combines both $C_{\mu}$ and $C_R$ effects. It is defined by the ratio between the inelastic and elastic maximum lateral displacement demands. Three options are investigated in order to express the inelastic response spectra in terms of: ductility demand, yield strength reduction factor, and inelastic deformation ratio which depends on the period, the post-to-preyield stiffness ratio, the yield strength and the peak ground acceleration. This new inelastic deformation ratio ($C_{\eta}$) is describes the response spectra and is related to the capacity curve (pushover curve): normalized yield strength coefficient (${\eta}$), post-to-preyield stiffness ratio (${\alpha}$), natural period (T), peak ductility factor (${\mu}$), and the yield strength reduction factor ($R_y$). For illustrative purposes, instantaneous ductility demand and yield strength reduction factor for a SDOF system subject to various recorded motions (El-Centro 1940 (N/S), Boumerdes: Algeria 2003). The method accuracy is investigated and compared to classical formulations, for various hysteretic models and values of the normalized yield strength coefficient (${\eta}$), post-to-preyield stiffness ratio (${\alpha}$), and natural period (T). Though the ductility demand and yield strength reduction factor differ greatly for some given T and ${\eta}$ ranges, they remain take close when ${\eta}>1$, whereas they are equal to 1 for periods $T{\geq}1s$.

• 산업기술연구
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• 제24권A호
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• pp.195-204
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• 2004

To evaluate inelastic seismic responses of multi-span bridge structures, the capacity spectrum method(CSM) incorporating the equivalent single-degree-of freedom(ESDOF) method is presented. Application of the CSM incorporating the ESDOF method is illustrated by example analysis for symmetric and asymmetric bridge structures. To investigate an accuracy of the CSM, the maximum displacements estimated by the CSM are compared to those by inelastic time history analysis for several artificial earthquakes. The results show that the CSM provided conservative estimates of the maximum displacements for the symmetric and asymmetric bridge structures, and the trend of conservative estimates of the asymmetric bridge structures was significantly larger than that of the symmetric bridge structure.

• Structural Engineering and Mechanics
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• 제13권2호
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• pp.135-154
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• 2002

This paper presents the convected material frame approach to study the nonlinear behavior of inelastic frame structures. The convected material frame approach is a modification of the co-rotational approximation by incorporating an adaptive convected material frame in the basic definition of the displacement vector and strain tensor. In the formulation, each discrete element is associated with a local coordinate system that rotates and translates with the element. For each load increment, the corresponding strain-displacement and nodal force-stress relationships are defined in the updated local coordinates, and based on the updated element geometry. The rigid body motion and deformation displacements are decoupled for each increment. This modified approach incorporates the geometrical nonlinearities through the continuous updating of the material frame geometry. A generalized nonlinear function is used to derive the inelastic constitutive relation and the kinematic hardening is considered. The equation of motion is integrated by an explicit procedure and it involves only vector assemblage and vector storage in the analysis by assuming a lumped mass matrix of diagonal form. Several numerical examples are demonstrated in close agreement with the solutions obtained by the ANSYS code. Numerical studies show that the proposed approach is capable of investigating large deflection of inelastic planar structures and providing an excellent numerical performance.

• Earthquakes and Structures
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• 제9권3호
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• pp.673-698
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• 2015

This paper investigates inelastic seismic demands of the normal component of near-fault pulse-like ground motions, which differ considerably from those of far-fault ground motions and also parallel component of near-fault ones. The results are utilized to improve the nonlinear static procedure (NSP) called Displacement Coefficient Method (DCM). 96 near-fault and 20 far-fault ground motions and the responses of various single degree of freedom (SDOF) systems constitute the dataset. Nonlinear Dynamic Analysis (NDA) is utilized as the benchmark for comparison with nonlinear static analysis results. Considerable influences of different faulting mechanisms are observed on inelastic seismic demands. The demands are functions of the strength ratio and also the pulse period to structural period ratio. Simple mathematical expressions are developed to consider the effects of near-fault motion and fault type on nonlinear responses. Modifications are presented for the DCM by introducing a near-fault modification factor, $C_N$. In locations, where the fault type is known, the modifications proposed in this paper help to obtain a more precise estimate of seismic demands in structures.

• Structural Engineering and Mechanics
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• 제71권5호
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• pp.545-552
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• 2019

The analysis and design of complex structures like sandwich-panel elements are difficult; the use of finite element method for the analysis is complicated and time consuming when non-linear effects are considered. On the other hand, artificial neural network (ANN) models can capture the non-linear effects and its application requires lesser computational demand. Two ANN models were trained, tested and validated to compute the force for a given displacement of a sandwich-type roof element; 2555 force and element deformation pairs were used for training the ANN models. For the models trained without considering the damping effect, there were two values in the input layer: maximum displacement and current displacement, and for the model considering damping, displacement from the previous step was used as an additional input. Totally, 400 ANN models were trained. Results show that there is a good agreement between the experimental and simulated data, and the models showed a good performance with a mean square error value of 4548.85. Both the ANN models could simulate the inelastic behaviour, loss of rigidity, and evolution of permanent displacements. The models could also interpolate and extrapolate, which enables them to be used as an analysis and design tool for such complex elements.

• 한국구조물진단유지관리공학회 논문집
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• 제6권3호
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• pp.91-96
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• 2002

There are many methods for analyzing underground box structures. One is the method of Iterative removal of tensional spring. The other is the method of modeling of ground to 8-node elastic-plastic planar element. In this study, We use inelastic soil spring element for analyzing underground box structures. First, if N-value is over 50, the results of inelastic soil spring method is the same as the method of 8-node planar element in last stage. Second, as N is increasing, element forces in two methods are generally decreasing. Third, as N-value is increasing, element forces in two method are generally decreasing and displacement has decreasing incline. This is the same as the force-displacement curve of general underground structures.

• Earthquakes and Structures
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• 제13권1호
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• pp.59-66
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• 2017

Modern seismic codes rely on performance-based seismic design methodology which requires that the structures withstand inelastic deformation. Many studies have focused on the inelastic deformation ratio evaluation (ratio between the inelastic and elastic maximum lateral displacement demands) for various inelastic spectra. This paper investigates the inelastic response spectra through the ductility demand ${\mu}$, the yield strength reduction factor $R_y$, and the inelastic deformation ratio. They depend on the vibration period T, the post-to-preyield stiffness ratio ${\alpha}$, the peak ground acceleration (PGA), and the normalized yield strength coefficient ${\eta}$ (ratio of yield strength coefficient divided by the PGA). A new inelastic deformation ratio $C_{\eta}$ is defined; it is related to the capacity curve (pushover curve) through the coefficient (${\eta}$) and the ratio (${\alpha}$) that are used as control parameters. A set of 140 real ground motions is selected. The structures are bilinear inelastic single degree of freedom systems (SDOF). The sensitivity of the resulting inelastic deformation ratio mean values is discussed for different levels of normalized yield strength coefficient. The influence of vibration period T, post-to-preyield stiffness ratio ${\alpha}$, normalized yield strength coefficient ${\eta}$, earthquake magnitude, ruptures distance (i.e., to fault rupture) and site conditions is also investigated. A regression analysis leads to simplified expressions of this inelastic deformation ratio. These simplified equations estimate the inelastic deformation ratio for structures, which is a key parameter for design or evaluation. The results show that, for a given level of normalized yield strength coefficient, these inelastic displacement ratios become non sensitive to none of the rupture distance, the earthquake magnitude or the site class. Furthermore, they show that the post-to-preyield stiffness has a negligible effect on the inelastic deformation ratio if the normalized yield strength coefficient is greater than unity.

• 한국지진공학회논문집
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• 제14권4호
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• pp.23-28
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• 2010

본 연구는 철골 모멘트 골조의 이력거동을 잘 나타내는 강도한계 이선형 단자유도 시스템에 대하여 지반조건, 후탄성 기울기, 감쇠비, 항복강도 저감계수, 고유주기 등의 변화가 비탄성변위비에 미치는 영향을 분석하였다. NEHRP의 기준에 따라 B(보통암지반), C(매우 조밀한 토사지반), D(단단한 토사지반)의 지반조건에 해당하는 총 240개의 지진 가속도에 대하여 비선형 시간이력 해석을 수행하였다. 본 연구에서는 비탄성 거동 하에서 P-$\Delta$ 효과를 반영할 수 있도록 음강성비를 -0.1 에서 -0.5까지 고려하였다. 비선형 회귀분석을 통하여 감쇠비 2%, 5%, 10%, 20%에 대한 강도한계 이선형 모델의 비탄성 변위비와 로그표준편차식을 제안하였다.