• Earthquakes and Structures
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• v.12 no.4
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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 $T{\geq}1s$.

• Journal of the Earthquake Engineering Society of Korea
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• v.6 no.3
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• pp.87-93
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• 2002

A procedure for figuring out proper amount of additional viscous damping required to keep the inelastic deformation of a plan-wise asymmetric structure within a given target performance point was developed. To this end the behavior of an asymmetric nonlinear structure after yielding is investigated. Then a formula for the required amount of equivalent damping was derived based on the ductility demand of the structure. The procedure was applied to a five-story asymmetric structure subjected to an earthquake load. According to the comparison with the results from the dynamic time-history analysis, the structure with viscous dampers installed in accordance with the proposed procedure showed satisfactory seismic performance in both the stiff and the flexible edges.

• Journal of the Korea Concrete Institute
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• v.24 no.6
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• pp.705-714
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• 2012

Precast reinforced concrete bridge columns with hollow rectangular section were tested under cyclic lateral load with constant axial force to investigate its seismic performance. After all the precast column segments were erected, longitudinal reinforcement was inserted in the sheath prefabricated in the segments, which were then mortar grouted. Main variables of the test series were column aspect ratio, longitudinal reinforcement ratio, amount of lateral reinforcement, and location of segment joints. The aspect ratios were 4.5 and 2.5, and the longitudinal steel ratios were 1.15% and 3.07%. The amount of lateral reinforcement were 95%, 55%, 50%, and 27% of the minimum amount for full ductility design requirements in the Korean Bridge Design Code. The locations of segment joints in plastic hinge region were 0.5 and 1.0 times of the section depth from the bottom column end. The test results of cracking and failure mode, axial-flexural strength, lateral load-displacement relationship, and displacement ductility are presented. Then, safety of the ductility demand based seismic design in the Korean Bridge Design Code is discussed. The column specimens showed larger ductility than expected, because buckling of longitudinal reinforcing bar was prevented due to confinement developed not only by transverse steel but also by sheath and infilling mortar.

• Earthquakes and Structures
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• v.3 no.1
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• pp.59-81
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• 2012

A ductility inverse-mapping method for SDOF systems including passive dampers is proposed which enables one to find the maximum acceleration of ground motion for the prescribed maximum response deformation. In the conventional capacity spectrum method, the maximum response deformation is computed through iterative procedures for the prescribed maximum acceleration of ground motion. This is because the equivalent linear model for response evaluation is described in terms of unknown maximum deformation. While successive calculations are needed, no numerically unstable iterative procedure is required in the proposed method. This ductility inverse-mapping method is applied to an SDOF model of bilinear hysteresis. The SDOF models without and with passive dampers (viscous, viscoelastic and hysteretic dampers) are taken into account to investigate the effectiveness of passive dampers for seismic retrofitting of building structures. Since the maximum response deformation is the principal parameter and specified sequentially, the proposed ductility inverse-mapping method is suitable for the implementation of the performance-based design.

• Earthquakes and Structures
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• v.20 no.2
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• pp.133-148
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• 2021

The paper presents a simplified force-based seismic design procedure for the preliminary design of steel haunch retrofitting for the seismic upgrade of deficient RC frames. The procedure involved constructing a site-specific seismic design spectrum for the site, which is transformed into seismic base shear coefficient demand, using an applicable response modification factor, that defines base shear force for seismic analysis of the structure. Recent experimental campaign; involving shake table testing of ten (10), and quasi-static cyclic testing of two (02), 1:3 reduced scale RC frame models, carried out for the seismic performance assessment of both deficient and retrofitted structures has provided the basis to calculate retrofit-specific response modification factor Rretrofitted. The haunch retrofitting technique enhanced the structural stiffness, strength, and ductility, hence, increased the structural response modification factor, which is mainly dependent on the applied retrofit scheme. An additional retrofit effectiveness factor (ΩR) is proposed for the deficient structure's response modification factor Rdeficient, representing the retrofit effectiveness (ΩR=Rretrofitted /Rdeficient), to calculate components' moment and shear demands for the retrofitted structure. The experimental campaign revealed that regardless of the deficient structures' characteristics, the ΩR factor remains fairly the unchanged, which is encouraging to generalize the design procedure. Haunch configuration is finalized that avoid brittle hinging of beam-column joints and ensure ductile beam yielding. Example case study for the seismic retrofit designs of RC frames are presented, which were validated through equivalent lateral load analysis using elastic model and response history analysis of finite-element based inelastic model, showing reasonable performance of the proposed design procedure. The proposed design has the advantage to provide a seismic zone-specific design solution, and also, to suggest if any additional measure is required to enhance the strength/deformability of beams and columns.

• Journal of the Earthquake Engineering Society of Korea
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• v.3 no.2
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• pp.29-40
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• 1999

This study presents a simplifled calculation method for required ductility of coupling beams in precast coupled shear walls at preliminary seismic design stages. Deflection of precast coupled shear walls based on a continuum approach is combined with inelastic gap opening of horizontal connection of panels to provide a relationship between the system-level ductility and the element-level ductility in a precast coupled shear wall. The equation proposed herein for ductility requirement for coupling beams shows that higher stiffness and lower strength of coupling beams result in high ductility reuqirement. The equation also shows that the ductility requirement is proportional to the degree of gap opening of the story in question. However, the coupling beam ductility in higher stories are not affected by gap openings of horizontal connections of panel.

• Structural Engineering and Mechanics
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• v.86 no.5
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• pp.589-605
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• 2023

This paper investigates the ductility demands of steel frames equipped with self-centring fuses under near-fault earthquake motions considering multiple yielding stages. The study is commenced by verifying a trilinear self-centring hysteretic model accounting for multiple yielding stages of steel frames equipped with self-centring fuses. Then, the seismic response of single-degree-of-freedom (SDOF) systems following the validated trilinear self-centring hysteretic law is examined by a parametric study using a near-fault earthquake ground motion database composed of 200 earthquake records as input excitations. Based on a statistical investigation of more than fifty-two (52) million inelastic spectral analyses, the effect of the post-yield stiffness ratios, energy dissipation coefficient and yielding displacement ratio on the mean ductility demand of the system is examined in detail. The analysis results indicate that the increase of post-yield stiffness ratios, energy dissipation coefficient and yielding displacement ratio reduces the ductility demands of the self-centring oscillators responding in multiple yielding stages. A set of empirical expressions for quantifying the ductility demands of trilinear self-centring hysteretic oscillators are developed using nonlinear regression analysis of the analysis result database. The proposed regression model may offer a practical tool for designers to estimate the ductility demand of a low-to-medium rise self-centring steel frame equipped with self-centring fuses progressing in the ultimate stage under near-fault earthquake motions in design and evaluation.

• Earthquakes and Structures
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• v.3 no.2
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• pp.141-168
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• 2012

The Retrofit Yield Spectrum (RYS) is a new spectrum-based device that relates seismic demand of a retrofitted structure with the fundamental design parameters of the retrofit. This is obtained from superposition of Yield Point Spectra with design charts that summarize in pertinent spectrum-compatible coordinates the attributes of a number of alternative retrofit scenarios. Therefore, once the requirements for upgrading a given structure have been determined, the RYS enable direct insight of the sensitivity of the seismic response of the upgraded structure to the preliminary design decisions made while establishing the retrofit plan. By virtue of their spectrum-based origin, RYS are derived with reference to a single mode of structural vibration; a primary objective is to control the contribution of this mode in the retrofit design so as to produce a desirable distribution of damage at the ultimate limit state by removing soft storey formations and engaging the maximum number of structural members in deformation, in response to the input motion. Calculations are performed with reference to the yield-point, where secant stiffness is proportional to the flexural strength of reinforced concrete members. Derivation and use of the Retrofit Yield Spectra (RYS) refers to the seismic demand expressed either in terms of spectral acceleration, spectral displacement or interstory drift, at yield of the first storey. A reinforced concrete building that has been tested in full scale to a sequence of simulated earthquake excitations is used in the paper as a demonstration case study to examine the effectiveness of the proposed methodology.

• Journal of the Earthquake Engineering Society of Korea
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• v.6 no.5
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• pp.53-58
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• 2002

A recent development, a concrete-filled steel(CFS) pier is an alternative to a reinforced concrete bridge pier in an urban area, because of its fast construction and excellent ductility against earthquakes. The capacity of CFS piers has not been used to a practical design, because there is no guide of a seismic design for CFS piers. Therefore, the guide of a seismic design value is derived from tests of CFS piers in order to apply it to a practical seismic design. Steel piers and concrete-filled steel piers are tested with constant axial load using quasi-static cyclic lateral load to check ductile capacity and using the real Kobe ground motion of pseudo-dynamic test to verify seismic performance. The results prove that CFS piers have more satisfactory ductility and strength than steel piers and relatively large hysteretic damping in dynamic behaviors. The seismic performance of steel and CFS piers is quantified on the basis of the test results. These results are evaluated through comparison of both the response modification factor method by elastic response spectrum and the performance-based design method by capacity spectrum and demand spectrum using effective viscous damping. The response modification factor of CFS piers is presented to apply in seismic design on a basis of this evaluation for a seismic performance.

• Journal of the Korea Concrete Institute
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• v.15 no.6
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• pp.877-887
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• 2003

For a performance-based design of structural walls, it is necessary to develop a rational design method for determining the length and detail of boundary confinement so as to satisfy the given ductility demand. In the present study, the curvature capacity of a structural wall with boundary confinement was estimated considering the effects of various design parameters. The curvature demand of the plastic hinge corresponding to the given design displacement was also determined. By equalizing the curvature capacity to the demand, a design method for determining the length of boundary confinement, was developed. According to the design method, the length of boundary confinement increases as axial compressive load and design displacement increase, and as concrete strength, wall thickness, amount of lateral reinforcement and aspect ratio decrease. A study was performed on details for effective lateral confinement of walls with rectangular cross-section. Based on the findings, design guidelines on spacings of ties and cross-ties were proposed.