• Journal for History of Mathematics
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• v.24 no.3
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• pp.23-35
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• 2011

The sphere theorem is one of the main streams in modern Riemannian geometry. In this article, we survey developments of pinching theorems from the classical one to the recent differentiable pinching theorem. Also we include sphere theorems of metric invariants such as diameter and radius with historical view point.

• Journal of the Korea Concrete Institute
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• v.19 no.6
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• pp.685-692
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• 2007

When the shear force governs the response of an RC element, as in the case of a low-rise shear wall, the effect of shear on the element's response is thought to be responsible for the 'pinching effect' in the hysteretic loops. However, it was recently shown that this undesirable pinching effect can be eliminated in the hysteretic load-deformation curves of a shear-dominant element if the steel grid orientation is properly aligned in the direction of the applied principal stresses. In this paper, the presence and absence of the pinching mechanism in the hysteretic loops of the shear stress-strain curves of RC elements was explained rationally using a compatibility aided truss model. The analytical results indicate that the pinching effect of the RC elements is strongly related to the direction of the steel arrangement. The area of the energy dissertation does not increase proportionally to the difference between the direction of the principal compressive stress and the direction of the steel arrangement.

• Journal of Korean Society of Steel Construction
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• v.30 no.1
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• pp.37-48
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• 2018

Cyclic loading tests for shear dominant hybrid steel link beams with circular web openings were performed to evaluate the seismic performance. Four half-scaled specimens with bolted connections were tested. The test parameter is a diameter of the web opening, i.e., shear strength ratio ($V_{pw}/V_p$) of the link beam and presence of top-seat angles. Using test results, adequate design shear strength of link beam was finally suggested. Test results showed that when the shear capacity is less than half of the plastic shear strength, seismic performance was improved due to mitigation of pinching under reversed cyclic inelastic deformations.

• Journal of the Korea Concrete Institute
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• v.15 no.4
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• pp.594-605
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• 2003

Pinching is an important property of reinforced concrete member which characterizes its cyclic behavior. In the present study, numerical studies were performed to investigate the characteristics of pinching behavior and the energy dissipation capacity of flexure-dominated reinforced concrete members. By investigating existing experiments and numerical results, it was found that flexural pinching which has no relation with shear action appears in RC members subject to axial compression force. However, members with specific arrangement and amount of re-bars, have the same energy dissipation capacity regardless of the magnitude of the axial force applied even though the shape of the cyclic curve varies due to the effect of the axial force. This indicates that concrete as a brittle material does not significantly contribute to the energy dissipation capacity though its effect on the behavior increases as the axial force increases, and that energy dissipation occurs primarily by re-bars. Therefore, the energy dissipation capacity of flexure-dominated member can be calculated by the analysis on the cross-section subject to pure bending, regardless of the actual compressive force applied. Based on the findings, a practical method and the related design equations for estimating energy dissipation capacity and damping modification factor was developed, and their validity was verified by the comparisons with existing experiments. The proposed method can be conveniently used in design practice because it accurately estimates energy dissipation capacity with general design parameters.

• Journal of the Earthquake Engineering Society of Korea
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• v.8 no.5 s.39
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• pp.45-54
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• 2004

Since existing hysteretic models for R/C members focused on presenting the degrading stiffness using empirical equations based on experiments, they cannot accurately predict the energy dissipation capacity during cyclic loading. Recently, design equations which can evaluate the energy dissipation capacity of R/C members were developed. Based on those equations, in the present study, an energy-based hysteretic model for flexure-dominated R/C members was developed. The proposed model was devised to dissipate the same energy as the actual one dissipated during a complete load cycle. The proposed model represents the hysteretic behaviors of R/C members accompanied by stiffness degradation and pinching using primary and cyclic curves and six unloading/reloading rules. The proposed model was verified by comparisons with various experimental results. The energy-based hysteretic model can be used to develop computer programs for static and dynamic analysis/design because it is simple and easily applicable to numerical analysis.

• Journal of the Korea Concrete Institute
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• v.26 no.2
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• pp.125-133
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• 2014

In this study, experimental research was carried out to investigate the seismic and structural performance of precast concrete exterior beam-column joints using bolt type connection and prestressing method. A total of five full-scale exterior beam-column joints were constructed and tested under reversed cyclic loading, controlled by displacement. Results of the test are as follows: Energy dissipation capacity and pinching phenomenon of PC beam-column joints showed disadvantageous behavior compared to RC beam-column joints. However, drift capacity of the PC joint was excellent. Also, yield mechanism concentrated on embedded nuts was suitable as an exterior beam-column joint of lateral load resistance frame. Additional application of prestressing method was also very effective to control excessive pinching and cracking in the joint region, and thus improved an overall seismic performance of the PC joint.

• Proceedings of the Korea Concrete Institute Conference
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• 2006.05a
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• pp.482-485
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• 2006

The response of a reinforced concrete element under cyclic shear is characterized by the hysteretic loops of the shear stress-strain curves. These hysteretic loops can exhibit strength deterioration, stiffness degradation, and a pinched shape. Recent tests have shown that the orientation of steel grids in RC shear elements has a strong effect on the "pinching effect" in the post-yield hysteretic loops. When the steel grid was set at a 45 degree angle to the shear plane, there was no pinching effect and no strength deterioration. However, when the steel grid was set parallel to the shear plane, there was a severe pinching effect and severe strength deterioration with increasing shear strain magnitude. In this paper, two RC elements subjected to revered cyclic shear stresses are considered to study the effect of the steel grid orientation. The presence and absence of the pinching mechanism in the post-yield shear hysteretic loops is studied using the Rotating Angle Softened Truss Model (RA-STM) theory.

• Journal of the Korea Concrete Institute
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• v.20 no.2
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• pp.203-212
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• 2008

The cyclic behavior and energy dissipation mechanism of short coupling beams with various reinforcement layouts were studied. For numerical analysis of coupling beams, nonlinear truss model was used. The results of numerical analysis showed that the coupling beams with conventional reinforcement layout showed pinched cyclic behavior without significant energy dissipation, whereas the coupling beams with diagonal reinforcement exhibited stable cyclic behavior without pinching. The energy dissipation of the coupling beams was developed mainly by diagonal reinforcing bars developing large plastic strains rather than concrete which is a brittle material Based on this result, simplified equations for evaluating the energy dissipation of coupling beams were developed. For verification, the predicted energy dissipation was compared with the test results. The results showed that the simplified equations can predict the energy dissipation of short coupling beams with shear span-to-depth ratio less than 1.25 with reasonable precision, addressing various design parameters such as reinforcement layout, shear span-to-depth ratio, and the magnitude of inelastic displacement. The proposed energy equations can be easily applied to performance-based seismic evaluation and design of reinforced concrete structures and members.

• Journal of Korean Society of Steel Construction
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• v.9 no.2 s.31
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• pp.277-285
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• 1997

To investigate the shear strength and hysteretic behavior of SRC column to H steel beam joints, seven cruciform specimens were fabricated and tested. The test specimens showed stable hysteresis behavior with a little pinching. The strength decreased with increase in deflection after the speciemens reached at the maximum strength. The shear strength of panel zones increased with increased in the concrete amount of SRC column sections. The shear strength may conservatively be estimated by the sum of shear yielding strength of steel column web, plastic bending strength of steel column flange and ultimate shear strength of concrete in the panel zone.

• Computational Structural Engineering
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• v.8 no.4
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• pp.117-127
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• 1995

The objective of this research is to investigate the effectiveness of rotating orthotropic axes model in analyzing reinforced concrete planar members under cyclic as well as monotonic loading. The structural members to be addressed are moderately reinforced beams, columns, beam-column joints, and shear walls, whose failure occurs due to compressive crushing after extensive crack propagation, The rotating orthotropic axes model which is usually used for monotonic loading is developed for cyclic loading. With the existing cyclic material models of reinforcing steel and bond-slip, this material model is used for the finite element analysis. For monotonic loading, the analytical results of the rotating orthotropic axes model are compared with reinforced concrete beams which have brittle failure. For Shear wall members under cyclic loading, the analyses are compared with the experiments for the ultimate load capacity, nonlinear deformation, and pinching effect due to crack opening and closing.