• 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.

• Journal of the Earthquake Engineering Society of Korea
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• v.11 no.6
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• pp.53-61
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• 2007

This study investigates the effect of site class, post-yield stiffness ratio, damping ratio, yield-strength reduction factor, and natural period on inelastic displacement ratio of bilinear SDF systems located at the sites classified as NEHRP site class B,C,D. The previous studies developed inelastic displacement ratio using equal displacement rule in the intermediate and long period range. But, this approximation overestimates the inelastic displacement ratio. Furthermore, inelastic displacement ratio has not been developed for the systems having a damping ratio less than 5%. This study conducts nonlinear regression analysis for proposing equations for calculating median and deviation of the inelastic displacement ratio of the bilinear SDOF system having damping ratios ranging from 0 to 20%. Using median and deviation of the inelastic displacement ratio, probabilistic inelastic displacement ratio is estimated, which can be used for performance-based seismic evaluation.

• Structural Engineering and Mechanics
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• v.45 no.5
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• pp.655-676
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• 2013

In this study, strength reduction factors and inelastic displacement ratios are investigated for SDOF systems with period range of 0.1-3.0 s considering soil structure interaction for earthquake motions recorded on soft soil. The effect of stiffness degradation on strength reduction factors and inelastic displacement ratios is investigated. The modified-Clough model is used to represent structures that exhibit significant stiffness degradation when subjected to reverse cyclic loading and the elastoplastic model is used to represent non-degrading structures. The effect of negative strain - hardening on the inelastic displacement and strength of structures is also investigated. 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. New equations are proposed for strength reduction factor and inelastic displacement ratio of interacting system as a function of structural period($\tilde{T}$, T) ductility (${\mu}$) and period lengthening ratio ($\tilde{T}$/T).

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2007.04a
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• pp.777-782
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• 2007

Displacement amplification factor can be used to estimate inelastic displacement demands from elastic displacement demands, The simple formula for displacement amplification factor considering hysteretic behavior of structural system and earthquake characteristics is proposed. And the effects of several parameters such as displacement ductility, strain hardening ratio, period, characteristics of earthquakes and hysteretic models for the displacement amplification factor are evaluated. Accuracy of the proposed formula is evaluated by comparing the displacement amplification factors estimated by existing and proposed formula with those calculated from inelastic time history analysis. The displacement amplification factors by proposed formulas provide a good agreement with those calculated by inelastic time history analysis.

• 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.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.45 no.6
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• pp.741-758
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• 2013

In this study, inelastic displacement ratios are investigated for existing systems with known lateral strength considering soil structure interaction. For this purpose, SDOF systems for period range of 0.1-3.0 s with different hysteretic behaviors are considered for a number of 18 earthquake motions recorded on soft soil. The effect of stiffness degradation on inelastic displacement ratios is investigated. The Modified Clough model is used to represent structures that exhibit significant stiffness degradation when subjected to reverse cyclic loading and the elastoplastic model is used to represent non-degrading structures. Soil structure interaction analyses are conducted by means of equivalent fixed base model 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. A new equation is proposed for inelastic displacement ratio of system with SSI with elastoplastic or degrading behavior as a function of structural period ($\tilde{T}$), 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.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.

• 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.