• Proceedings of the Korea Concrete Institute Conference
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• 2002.10a
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• pp.161-166
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• 2002

The modification factor( k-factor) of equivalent damping ratio utilized in the current state-of-the-practice to account for the imperfection of reinforced concrete structures in hysteresis loop is investigated. From this, it is found that the current modification factor does not include the effect of cyclic loading, one of the important characteristic properties of earthquake loading. This could be taken into account by considering the energy absorption efficiency based on the cummulative plastic deformation. From the study, it is suggested that the current approach for the modification factor for the equivalent damping ratio should be reformed.

• Earthquakes and Structures
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• v.25 no.5
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• pp.325-342
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• 2023

The damping modification factor (DMF) is used to modify the 5%-damped response spectrum to produce spectral values that correspond to other necessary damping ratios for seismic design. The DMF has been the subject of numerous studies, and it has been discovered that seismological parameters like magnitude and distance can have an impact on it. However, DMF formulations incorporating these seismological parameters cannot be directly applied to seismic design because these parameters are not specified in the present seismic codes. The goal of this study is to develop a formulation for the DMF that can be directly applied in seismic design and that takes the effects of magnitude, distance, and site conditions into account. To achieve this goal, 16660 ground motions with magnitudes ranging from 4 to 9 and epicentral distances ranging from 10 to 200 km are used to systematically study the effects of magnitude, distance, and site conditions on the DMF. Furthermore, according to the knowledge that magnitude and distance affect the DMF primarily by changing the spectral shape, a spectral shape factor is adopted to reflect influences of magnitude and distance, and a new formulation for the DMF incorporating the spectral shape factor is developed. In comparison to the current formulations, the proposed formulation provides a more accurate prediction of the DMF and can be employed directly in seismic design.

• Earthquakes and Structures
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• v.26 no.3
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• pp.219-228
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• 2024

This study examines damping modification factors (DMFs) of elastic input energy spectra corresponding to a set of 116 earthquake ground motions. Mean input energy per mass spectra and mean DMFs are presented for both considered ground motion components. Damping ratios of 3%, 5%, 10%, 20%, and 30% are used and the 5% damping ratio is considered the benchmark for DMF computations. The geometric mean DMFs of the two horizontal components of each ground motion are computed and coefficients of variation are presented graphically. The results show that the input energy spectra-based DMFs exhibit a dependence on the damping ratio at very short periods and they tend to be nearly constant for larger periods. In addition, mean DMF variation is obtained graphically for also the damping ratio, and mathematical functions are fitted as a result of statistical analyses. A strong correlation between the computed DMFs and the ones from predicted equations is observed.

• Earthquakes and Structures
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• v.4 no.5
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• pp.489-508
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• 2013

Design spectra for damping ratios higher than 5% have several important applications in the design of earthquake-resistant structures. These highly damped spectra are usually derived from a 5%-damped reference pseudo-acceleration spectrum by using a damping modification factor. In cases of high damping, the absolute acceleration and the relative velocity spectra instead of the pseudo-acceleration and the pseudo-velocity spectra should be used. This paper elaborates on the recovery of spectral absolute acceleration and spectral relative velocity from their pseudo-spectral counterparts. This is accomplished with the aid of correction factors obtained through extensive parametric studies, which come out to be functions of period and damping ratio.

• Steel and Composite Structures
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• v.11 no.4
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• pp.273-290
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• 2011

In current ductility-based earthquake-resistant design, the estimation of design forces continues to be carried out with the application of response modification factors on elastic design spectra. It is well-known that the response modification factor (R) takes into account the force reduction, strength, redundancy, and damping of structural systems. The key components of the response modification factor (R) are force reduction ($R_{\mu}$) and strength ($R_S$) factors. However, the response modification and strength factors for structural systems presented in design codes were based on professional judgment and experiences. A numerical study has been accomplished to evaluate force reduction, strength, and response modification factors for special steel moment resisting frames. A total of 72 prototype steel frames were designed based on the recommendations given in the AISC Seismic Provisions and UBC Codes. Number of stories, soil profiles, seismic zone factors, framing systems, and failure mechanisms were considered as the design parameters that influence the response. The effects of the design parameters on force reduction ($R_{\mu}$), strength ($R_S$), and response modification (R) factors were studied. Based on the analysis results, these factors for special steel moment resisting frames are evaluated.

• Proceedings of the Korea Concrete Institute Conference
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• 2001.05a
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• pp.859-864
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• 2001

For earthquake resistance design, a response modification factor is used to reduce the design strength and it reflects ductility, reserve strength, redundancy and damping effect. But this factor has not theoretical basis. In this study, two response modification factors are compared and analyzed for shear wall apartment building.; the one is introduced by ATC-19 Procedures, the other is suggested FEMA-273 and ATC-40 through nonlinear static analysis. For the results, ATC-19 procedure gives a reasonable estimation to R factor. But $R_{u}$ by using FEAM-273 and ATC-40 methods is estimated so small in case of a minor or moderate earthquake region. Due to this fact, response modification factor is smaller than suggested load criterion 3.0. So, it needs to decrease wall volume and reduce the global strength and system stiffness for proper ductile behavior matching to domestic load criterion.

• Structural Engineering and Mechanics
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• v.63 no.1
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• pp.23-35
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• 2017

A nonlinear static procedure considering work-energy principle and global failure mechanism to estimate base shears of reinforced concrete (RC) frame-type structures is presented. The relative energy equation comprising of elastic vibrational energy, plastic strain energy and seismic input energy is obtained. The input energy is modified with a factor depending on damping ratio and ductility, and the energy that contributes to damage is obtained. The plastic energy is decreased with a factor to consider the reduced hysteretic behavior of RC members. Given the pre-selected failure mechanism, the modified energy balance equality is written using various approximations for modification factors of input energy and plastic energy in scientific literature. External work done by the design lateral forces distributed to story levels in accordance with Turkish Seismic Design Code is calculated considering the target plastic drift. Equating the plastic energy obtained from energy balance to external work done by the equivalent inertia forces considering, a total of 16 energy-based base shears for each frame are derived considering different combinations of modification factors. Ductility related parameters of modification factors are determined from pushover analysis. Relative input energy of multi degree of freedom (MDOF) system is approximated by using the modal-energy-decomposition approach. Energy-based design base shears are compared with those obtained from nonlinear time history (NLTH) analysis using recorded accelerograms. It is found that some of the energy-based base shears are in reasonable agreement with the mean base shear obtained from NLTH analysis.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 2002.09a
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• pp.189-196
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• 2002

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.

• Earthquakes and Structures
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• v.5 no.1
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• pp.23-48
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• 2013

In this study, the effect of flexibility of superstructures and nonlinear characteristics of LRB (Lead Rubber Bearing) isolator on inelastic response of base isolated structures is investigated. To demonstrate the intensity of damage in superstructures, demand response modification factor without the consideration of damping reduction factor, demand RI, is used and the N2 method is applied to compute this factor. To evaluate the influence of superstructure flexibility on inelastic response of base isolated structures, different steel intermediate moment resisting frames with different heights have been investigated. In lead rubber bearing, the rubber provides flexibility and the lead is the source of damping; variations of aforementioned characteristics are also investigated on inelastic response of superstructures. It is observed that an increase in height of superstructure leads to higher value of demand RI till 4-story frame but afterward this factor remains constant; in other words, an increase in height until 4-story frame causes more damage in the superstructure but after that superstructure's damage is equal to the 4-story frame's. The results demonstrate that the low value of second stiffness (rubber stiffness in LRBs) tends to show a significant decrease in demand RI. Increase in value of characteristic strength (yield strength of the lead in LRBs) leads to decrease in the demand RI.

• Proceedings of the Korea Concrete Institute Conference
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• 1998.04b
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• pp.433-438
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• 1998

Design lateral strength calculated by current seismic design code is prescribed to be much lower than the force level required for a structure to respond elastically during design level earthquake ground motion. Present procedures for calculating seismic design forces are based on the use of elastic spectra reduced by a strength reduction factor known as "response modification factor, R". This factor accounts for the inherent ductility, overstrength, redundancy, and damping of a structural system. This study considers ductility and overstrength of the wall-type structure for investigating R factor. This means that R factor is determined from the product of "ductility-based R factor($R_$\mu$$) and overstrength factor($R_s$). $R_$\mu$$ factor is calibrated to attain the targer ductility ratio (system ductility capacity) and produced in the from of $R_$\mu$$ spectra considering the influence of target ductility, natural period, and hysteretic model. On the other hand, $R_s$ is more difficult to quantify, since it depends on both material and system-dependent uncertain parameters. In this study Rs factor was determined from the result of push-over analysis.-over analysis.