• Journal of the Earthquake Engineering Society of Korea
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• v.15 no.3
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• pp.11-26
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• 2011

The inelastic displacement ratio is defined as the ratio of the peak inelastic displacement to the peak linear elastic displacement. The inelastic displacement ratio allows simple evaluation of the peak inelastic displacement directly from the peak elastic displacement without computation of the inelastic response. Existing research of the inelastic displacement ratio is limited to piece-wise linear systems such as bilinear or stiffness degrading systems. In this paper, the inelastic displacement ratio is investigated for smooth hysteretic behavior systems subjected to near- and far-fault earthquakes. A simple formula of the inelastic displacement ratio is proposed by using a two step procedure of regression analysis.

• Journal of the Earthquake Engineering Society of Korea
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• v.17 no.1
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• pp.1-10
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• 2013

In order to predict inelastic displacement response without nonlinear dynamic analysis, the equal displacement rule can be used for the structures with longer natural periods than the characteristic period, $T_g$, of earthquake record. In the period range longer than $T_g$, peak displacement responses of elastic systems are equal or larger than those of inelastic systems. In the period range shorter than $T_g$, opposite trend occurs. In the equal displacement rule, it is assumed that peak displacement of inelastic system with longer natural period than $T_g$ equals to that of elastic system with same natural period. The equal displacement rule is very useful for seismic design purpose of structures with longer natural period than $T_g$. In the period range shorter than $T_g$, the peak displacement of inelastic system can be simply evaluated from the peak displacement of elastic system by using the inelastic displacement ratio, which is defined as the ratio of the peak inelastic displacement to the peak elastic displacement. Smooth hysteretic behavior is more similar to actual response of real structural system than a piece-wise linear hysteretic behavior such as bilinear or stiffness degrading behaviors. In this paper, the inelastic displacement ratios of the smooth hysteretic behavior system are evaluated for far-fault and near-fault earthquakes. The simple formula of inelastic displacement ratio considering the effect of $T_g$ is proposed.

• Structural Engineering and Mechanics
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• v.48 no.5
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• pp.681-695
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• 2013

Performance-based seismic design allows a structure to develop inelastic response during earthquakes. This modern seismic design requires more clearly defined levels of inelastic response. The ultimate deformation of a structure without total collapse (target displacement) is used to obtain the inelastic deformation capacity (inelastic performance). The inelastic performance of a structure indicates its performance under excitation. In this study, a new energy-based method to obtain the target displacement for reinforced concrete frames under cyclic loading is proposed. Concrete structures were analyzed using nonlinear static (pushover) analysis and cyclic loading. Failure of structures under cyclic loading was controlled and the new method was tested to obtain target displacement. In this method, the capacity energy absorption of the structures for both pushover and cyclic analyses were considered to be equal. The results were compared with FEMA-356, which confirmed the accuracy of the proposed method.

• Structural Engineering and Mechanics
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• v.10 no.4
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• pp.405-426
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• 2000

Two approximate methods based on mechanism analysis suitable for seismic assessment/design of structural concrete are reviewed. The methods involve use of equal energy concept or equal displacement concept along with appropriate patterns of inelastic deformations to relate structure's maximum lateral displacement to member and plastic deformations. One of these methods (Clough's method), defined here as a ductility-based approach, is examined in detail and a modification for its improvement is suggested. The modification is based on estimation of maximum inelastic displacement using inelastic design response spectra (IDRS) as an alternative to using equal energy concept. The IDRS for demand displacement ductilities are developed for a single degree of freedom model subjected to several accelerograms as functions of response modification factor (R), damping ratios, and strain hardening. The suggested revised methodology involves estimation of R as the ratio of elastic strength demand to code level demand, and determination of design base shear using $R_{design}{\leq}R$ and maximum displacement, determination of plastic displacement using IDRS and subsequent local plastic deformations. The methodology is demonstrated for the case of a 10-story precast wall panel building.

• Smart Structures and Systems
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• v.8 no.3
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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.

• Journal of Industrial Technology
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• v.24 no.A
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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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• v.12 no.6
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• pp.573-594
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• 2001

A two-level displacement-based design procedure is developed. To obtain the displacement demands, elastic spectra for occasional earthquakes and inelastic spectra for rare earthquakes are used. Minimum global stiffness and strength to be supplied to the structure are based on specified maximum permissible drift limits and on the condition that the structure responds within the elastic range for occasional earthquakes. The performance of the structure may be assessed by an inelastic push-over analysis to the required displacement and the evaluation of damage indices. The approach is applied to the design of a five-story reinforced concrete coupled wall structure located in the most hazardous seismic region of Argentina. The inelastic dynamic response of the structure subjected to real and artificially generated acceleration time histories is also analyzed. Finally, advantages and limitations of the proposed procedure from the conceptual point of view and practical application are discussed.

• Journal of the Earthquake Engineering Society of Korea
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• v.14 no.1
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• pp.1-9
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• 2010

The actual hysteretic behavior of structural elements and systems is closer to smooth hysteretic behavior than piece-wise linear behavior. This paper presents a methodology for computing the constant-ductility inelastic response spectra for smooth hysteretic behaviors. The effect of the hysteretic smoothness on the inelastic response spectra for acceleration, displacement, and input energy is evaluated. The results indicate that increasing smoothness in the hysteretic behavior decreases the inelastic response spectra.

• Journal of the Earthquake Engineering Society of Korea
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• v.2 no.3
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• pp.61-71
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• 1998

A performance-based seismic design method for reinforced concrete building structures being developed in Japan is outlined. Technical and scientific background of the performance-based design philosophy as well as recently developed seismic design guidelines are is presented, in which maximum displacement response to design earthquake motion is used as the limit-state design criteria. A method of estimating dynamic response displacement of the structures based on static nonlinear analysis is described. A theoretical estimation of nonlinear dynamic response considering the characteristics of energy input to the system is described in detail, which may be used as the standard method in the new performance-based code. A desing philosophy not only satisfying the criteria but also evaluating seismic capacity of the structures is also introduced.

• Earthquakes and Structures
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• v.22 no.6
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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.