• Structural Engineering and Mechanics
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• v.50 no.2
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• pp.163-180
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• 2014

Inaccurate predictions of effective stiffness for reinforced concrete (RC) columns having plain (undeformed) longitudinal rebars may lead to unsafe performance assessment and strengthening of existing deficient frames. Currently utilized effective stiffness models cover RC columns reinforced with deformed longitudinal rebars. A database of 47 RC columns (33 columns had continuous rebars and the remaining had spliced reinforcement) that were longitudinally reinforced with plain rebars was compiled from literature. The existing effective stiffness equations were found to overestimate the effective stiffness of columns with plain rebars for all levels of axial loads. A new approach that considers the contributions of flexure, shear and bond slip to column deflections prior to yielding was proposed. The new effective stiffness formulations were simplified without loss of generality for columns with and without lap-spliced plain rebars. In addition, the existing stiffness models for the columns with deformed rebars were improved while taking poor bond characteristics of plain rebars into account.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.4
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• pp.846-855
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• 1994

An effective stiffness, analogous to that of a wound spring, can be created by antagonistic redundant actuation of general closed-chain mechanisms. The qualitative and quantitative characteristics of the effective stiffness are investigated through a Four-bar mechanism, and a load distribution method is introduced which simultaneously guarantees the required system motion and the effective stiffness of the Four-bar mechanism. Furthermore, a simulation is performed to understand the inter-relationship among the effective stiffness, the Four-bar geometry, and the actuation effort. Based on this analysis, the Four-bar synthesis problem for effective stiffness generation is discussed.

• Proceedings of the Korea Concrete Institute Conference
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• 2001.05a
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• pp.833-838
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• 2001

The objectives of this study are to investigate effective stiffness of circular reinforced bridge columns and to provide reasonable effective stiffness equations for seismic design to the current Korean Bridge Design Standard. The material nonlinear analysis was conducted for 5184 columns of which variables were the concrete compressive stress, the steel yielding stress, the longitudinal steel location parameter, the longitudinal steel ratio, the axial load level, and the diameter of section. The current Korean Bridge Design Standard generally used the gross section stiffness because of unclear provision, it may be non-conservative because of being evaluated greater design seismic force and less design displacement than those of the abroad provision. Therefore, the proposed effective stiffness equations include three variables such as : the longitudinal steel location parameter, the longitudinal steel ratio, and the axial load ratio. Two equations of effective stiffness are proposed which may be used for earthquake force estimation and for earthquake displacement estimation, respectively.

• Computational Structural Engineering
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• v.8 no.4
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• pp.159-171
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• 1995

The parameters describing a complete hysteresis loop include pinch force, drift offset, effective stiffness, unloading and reloading trangential stiffness. Analytical equations proposed to quantify the nonlinear, inelastic behavior of reinforced shear walls can be used to predict these parameters as a function of axial load and drift ratio. For example, drift offset, effective stiffness, and first and second unloading and reloading tangential stiffness are calculated using equations obtained from test data for a desired drift ratio or ductility level. Pinch force can also be estimated for a given drift ratio and axial load. The effective virgin stiffness at the first yield and its post yield reduction can be estimated. The load deflection response of flexural reinforced concrete shear walls can now be estimated based on the effective wall stiffness that is a function of axial force and drift ratio.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.18 no.6
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• pp.521-526
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• 2005

Within wafer non-uniformity(WIWNU) improves as the stiffness of pad decrease. We designed the pad groove to study of pad stiffness on WIWNU in Chemical mechanical polishing(CMP) and measured the pad stiffness according to groove width. The groove influences effective pad stiffness although original mechanical properties of pad are unchanged by grooving. Also, it affects the flow of slurry that has an effect on the lubrication regime and polishing results. An Increase of the apparent contact area of pad by groove width results in decrease of effective pad stiffness. WIWNU and profile of removal tate improved as effective pad stiffness decreased. Because grooving the pad reduce its effective stiffness and it makes slurry distribution to be uniform. Futhermore, it ensures that pad conforms to wafer-scale flatness variability. By grooving the top pad, it is possible to reduce its stiffness and hence reduce WIWNU and edge effect.

• Proceedings of the Korea Concrete Institute Conference
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• 2001.11a
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• pp.941-946
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• 2001

The objectives of this study are to investigate effective stiffness of Rectangular reinforced concrete bridge columns. It is reasonable to use yielding effective stiffness of columns in seismic bridge design, especially in case that plastic hinges form at the bridge columns. In this study, the material nonlinear analysis was conducted for 3, 240 column sections of which variables were the concrete compressive stress, the steel yielding stress, the longitudinal steel location parameter, the longitudinal steel ratio, the axial load level, and the diameter of section. Based on the analytical results, an effective stiffness including two variables(longitudinal steel ratio and axial load ratio) was proposed by regression analyses, and it is compared with test results and the proposed equation for yielding effective stiffness of circular bridge columns.

• Earthquakes and Structures
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• v.9 no.3
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• pp.481-501
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• 2015

Current design codes and technical recommendations often provide rough indications on how to assess effective stiffness of Reinforced Concrete (R/C) frames subjected to seismic loads, which is a key factor when a linear analysis is performed. The Italian design code (NTC-2008), Eurocode 8 and ACI 318 do not take into account all the structural parameters affecting the effective stiffness and this may not be on the safe side when second-order $P-{\Delta}$ effects may occur. This paper presents a study on the factors influencing the effective stiffness of R/C beams, columns and walls under seismic forces. Five different approaches are adopted and analyzed in order to evaluate the effective stiffness of R/C members, in accordance with the scientific literature and the international design codes. Furthermore, the paper discusses the outcomes of a parametric analysis performed on an actual R/C building and analyses the main variables, namely reinforcement ratio, axial load ratio, concrete compressive strength, and type of shallow beams. The second-order effects are investigated and the resulting displacements related to the Damage Limit State (DLS) under seismic loads are discussed. Although the effective stiffness increases with steel ratio, the analytical results show that the limit of 50% of the initial stiffness turns out to be the upper bound for small values of axial-load ratio, rather than a lower bound as indicated by both Italian NTC-2008 and EC8. As a result, in some cases the current Italian and European provisions tend to underestimate second-order $P-{\Delta}$ effects, when the DLS is investigated under seismic loading.

• Nuclear Engineering and Technology
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• v.31 no.6
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• pp.586-594
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• 1999

To limit both the large displacement and acceleration response of the structure efficiently, the relationships between acceleration and displacement responses of the structure under several earthquakes are investigated for various horizontal stiffness of the base isolation system to determine the effective stiffness of the base isolation system in this paper. An example structure is a five-storey steel frame building as the primary structure and the secondary structures are assumed to be located on the fifth floor of the primary structure. Input motions used in the structural analysis are El Centre 1940, Taft 1952, Mexico 1985, San Fernando 1971 Pacoima Dam, and artificially generated earthquakes. The relationships of the absolute peak acceleration and the displacement at the top of the structure are calculated for various natural periods of base isolators under various earthquakes. The peak acceleration response of the fifth floor in the base isolated structure is significantly reduced by a factor of 2.1 through 6.25. Also, the relative displacement response of the floor to the base of the superstructure is very small. The results of this study can be utilized to determine the effective stiffness of the base isolation system.

• Proceedings of the Korea Concrete Institute Conference
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• 2006.11a
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• pp.129-132
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• 2006

It is generally reported that most of RC beams strengthened with simply bonded FRP composite is failed by FRP debonding. Also, the flexural performance of RC member strengthened with FRP composite can be calculated using the effective strain of FRP. The effective strain as a result of the debonding failure depends on many variables, such as FRP stiffness including the thickness($t_f$) and modulus of elasticity($E_f$), the amount of FRP but the FRP stiffness is reportedly the most influential. The purpose of this paper, therefore, is to examine effects of FRP stiffness on the flexural strengthening of RC beams. 4 different stiffness of CFRP composite including CFRP sheet and laminae were selected. From the tests, it was found that the flexural performance of RC beams strengthened with CFRP composite can be calculated based on the effective strain of the CFRP composite and the effective strain is inversely proportional to the CFRP stiffness.

• Structural Engineering and Mechanics
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• v.89 no.4
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• pp.411-420
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• 2024

The purpose of this research was to investigate the cyclic behavior of the D-shaped dampers (DSD). Similarly, at first, the numerical model was calibrated using the experimental sample. Then, parametric studies were conducted in order to investigate the effect of the radius and thickness of the damper on energy dissipation, effective and elastic stiffness, ultimate strength, and equivalent viscous damping ratio (EVDR). An analytical equation for the elastic stiffness of the DSD was also proposed, which showed good agreement with experimental results. Additionally, approximate equations were introduced to calculate the elastic and effective stiffness, ultimate strength, and energy dissipation. These equations were presented according to the curve fitting technique and based on numerical results. The results indicated that reducing the radius and increasing the thickness led to increased energy dissipation, effective stiffness, and ultimate strength of the damper. On the other hand, increasing the radius and thickness resulted in an increase in EVDR. Moreover, the ratio of effective stiffness to elastic stiffness also played a crucial role in increasing the EVDR. The thickness and radius of the damper were evaluated as the most effective dimensions for reducing energy dissipation and EVDR.