• Journal of the Earthquake Engineering Society of Korea
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• v.14 no.4
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• pp.49-60
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• 2010

The actual hysteretic behavior of structural elements and systems is smooth. Smooth hysteretic behavior is more representative of actual behavior than bi-linear or piece-wise linear stiffness degrading models. The strength reduction factor in seismic design is used to reduce the elastic strength demand to design levels. In this study, the effect of smoothness on the strength reduction factor is evaluated for several smooth hysteretic systems subjected to near-fault and far-fault earthquakes. For design purposes, a simple expression of the strength reduction factor considering hysteretic smoothness and earthquake characteristics, represented as near-fault and far-fault earthquakes, is proposed. The strength reduction factors calculated by the proposed simple formulation are more similar to the factors directly obtained from inelastic response spectrum analyses than those calculated by several existing formulas.

• 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 $T{\geq}1s$.

• Structural Engineering and Mechanics
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• v.12 no.3
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• pp.249-266
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• 2001

Current seismic design provisions allow structures to deform into inelastic range during design level earthquakes since the chance to meet such event is quite rare. For this purpose, design base shear is defined in current seismic design provisions as the value of elastic seismic shear force divided by strength reduction factor, R (${\geq}1$). Strength reduction factor generally consists of four different factors, which can account for ductility capacity, overstrength, damping, and redundancy inherent in structures respectively. In this study, R factor is assumed to account for only the ductility rather than overstrength, damping, and redundancy. The R factor considering ductility is called "ductility factor" ($R_{\mu}$). This study proposes ductility factor with correction factor, C, which can account for dynamic P-${\Delta}$ effect. Correction factor, C is established as the functional form since it requires computational efforts and time for calculating this factor. From the statistical study using the results of nonlinear dynamic analysis for 40 earthquake ground motions (EQGM) it is shown that the dependence of C factor on structural period is weak, whereas C factor is strongly dependant on the change of ductility ratio and stability coefficient. To propose the functional form of C factor statistical study is carried out using 79,920 nonlinear dynamic analysis results for different combination of parameters and 40 EQGM.

• Steel and Composite Structures
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• v.23 no.3
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• pp.363-383
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• 2017

In cold-formed stainless steel lipped channel-sections, use of web openings for service purposes are becoming increasingly popular. Web openings, however, result in the sections becoming more susceptible to web crippling. This paper presents a finite element investigation into the web crippling strength of cold-formed stainless steel lipped channel-sections with circular web openings under the interior-two-flange (ITF) loading condition. The cases of web openings located centred and offset to the bearing plates are considered in this study. In order to take into account the influence of the circular web openings, a parametric study involving 2,220 finite element analyses was performed, covering duplex EN1.4462, austenitic EN1.4404 and ferritic EN1.4003 stainless steel grades. From the results of the parametric study, strength reduction factor equations are proposed. The strengths obtained from reduction factor equations are first compared to the strengths calculated from the equations recently proposed for cold-formed carbon steel lipped channel-sections. It is demonstrated that the strength reduction factor equations proposed for cold-formed carbon steel are unconservative for the stainless steel grades by up to 17%. New coefficients for web crippling strength reduction factor equations are then proposed that can be applied to all three stainless steel grades.

• 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).

• Journal of the Korea institute for structural maintenance and inspection
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• v.15 no.5
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• pp.101-112
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• 2011

This paper shows a study carried out on the estimation of nominal flexural strength for CFRP-plated RC beams failed by intermediate crack debonding. A strength reduction factor is proposed to consider the effect of the intermediate crack debonding for the determination of nominal flexural strength. The proposed factor is derived from experimental data and utilizes the ratio of effective stress(or strain) in the CFRP plate to its ultimate strength(or strain) which is called effective strain model. An analytical equation for the estimation of the nominal flexural strength is formulated as a function of strength reduction factor. The validity, accuracy and efficiency of the proposed factor are established by comparing the analytical results with the experimental data, and the major design codes, as well as a number of factors given by researchers. The analytical results presented in this paper indicate that the proposed factor can effectively estimate the flexural nominal strength of CFRP-plated reinforced concrete beams failed by intermediate crack debonding.

• Journal of the Korean Geosynthetics Society
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• v.23 no.1
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• pp.9-16
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• 2024

In order to evaluate the relationship between the ground confining pressure and the shear characteristics of the pile-soil interface, this study described the comparative results of the existing experimental results and the FEA results using the strength reduction factor. The strength reduction factor was applied to simulate the shear behavior of the pile-soil interface in finite element analysis(FEA). The analysis results showed that the maximum pullout resistance decreased due to the influence of low confining pressure, as the fines content increased. This trend was similar to the previous experimental research, and this FEA model simulated with the interface strength reduction factor was evaluated as reasonable. The analysis results of the variation in the interface strength reduction factor clearly showed that the interface strength reduction factor clearly increased at a high fines content when the confining pressure was 50kPa. However, it was found that the increase rate was low when the confining pressure was 100kPa and 150kPa. Therefore, confining pressure and fines content need to be considered in FEA to evaluate the shear behavior of the pile-soil interface.

• Steel and Composite Structures
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• v.21 no.3
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• pp.629-659
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• 2016

In cold-formed stainless steel lipped channel-sections, web openings are becoming increasingly popular. Such openings, however, result in the sections becoming more susceptible to web crippling, especially under concentrated loads applied near the web opening. This paper presents the results of a finite element parametric study into the effect of circular web openings on the web crippling strength of cold-formed stainless steel lipped channel-sections for the interior-one-flange (IOF) loading condition. This involves a bearing load applied to the top flange of a length of member, away from the end supports. The cases of web openings located centred beneath the bearing load (i.e. beneath the bearing plate delivering the load) and offset to the bearing plate, are considered. Three grades of stainless steel are considered: duplex EN1.4462, austenitic EN1.4404 and ferretic EN1.4003. In total, 2218 finite element models were analyzed. From the results of the parametric study, strength reduction factors for load bearing capacity are determined, where these reduction factors are applied to the bearing capacity calculated for a web without openings, to take account the influence of the web openings. The strength reduction factors are first compared to equations recently proposed for cold-formed carbon steel lipped channel-sections. It is shown that for the case of the duplex grade, the strength reduction factor equations for cold-formed carbon steel are conservative but only by 2%. However, for the cases of the austentic and ferritic grades, the cold-formed carbon steel equations are around 9% conservative. New strength reduction factor equations are proposed for all three stainless steel grades.

• The Journal of Engineering Geology
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• v.27 no.1
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• pp.31-40
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• 2017

The slope stability analysis by the limit equilibrium method has the disadvantage that it can be applied only when the analysis is performed by setting the critical plane after analyzing the active surface many times and the soil is uniform and only the safety factor can be calculated. However, the analysis using the strength reduction analysis method has advantages that the engineer can judge various aspects and calculate the safety factor. In this study, the safety factor according to the change of slope and shear strength was compared and analyzed using limit equilibrium analysis and strength reduction method. It is suggested that it is desirable to use the strength reduction method which can synthetically review the stress, displacement, and strain in the soil.

• Journal of the Korea Concrete Institute
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• v.22 no.4
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• pp.451-460
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• 2010

There are many types of remodeling, however, engineers and architectures preferred to merge two or more separate units to one very spacious unit. Performing this type of remodeling, in the case of wall dominant apartments, requires partial removal of structural wall causing a concern of structural integrity. However, there are insufficient studies about partial removal, that is, openings. Presently, ACI standard have no clear way to evaluate the effect of opening on the structural wall. AIJ has the provision about strength reduction factor '$\gamma$'. However, this reduction factor cannot exactly evaluate the reduction effect of openings because this factor '$\gamma$' was determined through the elastic analysis. Therefore, in this study, 2 structural wall specimens were tested and many test results from previous studies were collected. Using these data, this study performed statistical analysis about strength of structural wall which have the opening in wall panel. And this study performed parametric study verifying shear strength reducing effect by opening area. In the results of statistical study, previous reduction factor show very conservative results because this equation did not consider other factors, reinforcement ratio and aspect ratio of openings, which was affect the shear strength of shear walls. Therefore we performed parametric study based on the test data and suggest new equation for shear strength reduction factor '$\gamma$'.