• Communications of the Korean Mathematical Society
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• v.20 no.2
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• pp.195-207
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• 2005

리만 기하학에서 중요한 문제중의 하나는 주어진 곡률부호를 가지는 다양체를 분류하는 것이다. 그렇게 하기 위해서는 곡률과 위상과의 상호 관계를 밝히는 것이 중요하다. 특히 양의 곡률을 가지는 공간을 분류하는 것은 어려운 문제로 알려져 있으며 위상적 성질에 대해서도 알려진 것은 매우 적다. 본 논문에서는 지금까지 알려진 양의 곡률을 가지는 공간들을 살펴 보고 그들 공간들에 대한 일반적인 정리들과 호프의 문제를 소개하고자 한다.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.14 no.12
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• pp.6542-6549
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• 2013

In highly elevated piers and long span beams, a hollow section is often used to reduce the self-weight and increase the flexural rigidity of members. Numerical analysis was conducted to obtain the moment-curvature curves and curvature ductility factor for the RC hollow section beams under a range of hollow portion sizes and reinforcement conditions in the upper flange and web. The curvature ductility factor was constantly maintained until the hollow portion size($b_i/b_o/h_i/h_o$) was less than or equal to 0.5. The curvature ductility factor decreased sharply if ($b_i/b_o/h_i/h_o$) was 0.7 or more. The curvature ductility factor of the beam decreased if reinforcement was provided in the web of the RC hollow section beam. To obtain the same level of the ductility factor as the singly reinforced section, the reinforcement should be provided in the upper flange as much as the web reinforcement.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.34 no.6
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• pp.393-401
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• 2021

In this paper, we proposed a numerical model based on moment-curvature, to evaluate the resistance of reinforced concrete (RC) members subjected to blast loading. To consider the direct shear failure mode, we introduced a dimensionless spring element based on the empirical direct shear stress-slip relation. Based on the dynamic increase factor equations for materials, new dynamic increase factor equations were constructed in terms of the curvature rate for the section which could be directly applied to the moment-curvature relation. Additionally, equivalent bending stiffness was introduced in the plastic hinge region to consider the effect of bond-slip. To verify the validity of the proposed model, a comparative study was conducted against the experimental results, and the superiority of this numerical model was confirmed through comparison with the analytical results of the single-degree of freedom model. Pressure-impulse (P-I) diagrams were produced to evaluate the resistance of members against bending failure and direct shear failure, and additional parametric studies were conducted.

• 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 Korean Society of Steel Construction
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• v.11 no.2 s.39
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• pp.143-151
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• 1999

An analytical study on the behavior of composite beams, which are composed of cold-formed profiled steel sheeting and normal strength concrete, is described. An analytical method to trace the nonlinear behavior of a composite beam is developed to include the nonlinear material properties of steel sheeting, reinforcing steel bar and concrete. A simple Power Model has also been proposed for the nonlinear moment-curvature relation of the composite beam. The model, which has been originally used to predict the flexural capacity of the beam to column connections, is adapted to the composite beams. The load-deflection behavior of the beams has been simulated by the step-by-step numerical integration using the moment-curvature relation obtained by the Power Model. The results have been compared with test results.

• Journal of the Korea Concrete Institute
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• v.22 no.6
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• pp.761-768
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• 2010

When cracks occur in reinforced concrete structures, a steel carries all tensile force at crack section, while the concrete between cracks carries a part of the tensile force due to bond, so that the steel is less elongated. This is called the tension-stiffening effect, that plays an important role in verification of a serviceability limit state. But it is a complicated work to use a complex strain distribution between cracks, therefore an average strain is used to calculate deflection and crack width. In Eurocode 2, tension-stiffening effect expressed in the first order form or the second order form is used in calculating an average curvature for deflection. In this study for a flexural member deflection and crack width are calculated using various models for the tension-stiffening effect and the results are compared with the values of Eurocode 2 and KCI provisions. As results, the predicted values using the second order form are appeared to be well agreed with the experimental values and it could secure more analytical consistency.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.23 no.1
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• pp.95-110
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• 2010

A numerical model to simulate bond-slip behavior of composite beam bridges is introduced in this paper. Assuming a linear bond stress-slip relation along the interface between the slab and girder, the slip behavior is implemented into a finite element formulation. Adopting the introduced model, the slip behavior can be taken account even in a beam element which is composed of both end nodes only. Governing equation of the slip behavior, based on the linear partial interaction theory, can be determined from the force equilibrium and a constant curvature distribution across the section of a composite beam. Since the governing equation for the slip behavior requires the moment values at both end nodes, the piecewise linear distribution of the constant bending moment in an element is assumed. Analysis results by the model are compared with numerical results and experimental values, and load-displacement relations of composite beams were then evaluated to verify the validity of the proposed model.