• Structural Engineering and Mechanics
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• 제77권5호
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• pp.691-703
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• 2021

Reinforced concrete (RC) beams can be subjected to a complex combination of shear forces (V), torsional moments (T), flexural moments (M) and axial loads (N). This paper proposes a unified approach for the analysis of these elements. An existing model for the analysis of orthogonally reinforced concrete membrane elements subjected to in-plane shear and normal stresses is generalized to apply to the case of beams subjected to the complex loading. The combination of V and T can be critical. Torsion is modelled using the hollow-tube analogy. A direct equation for the calculation of the thickness of the equivalent hollow tube is proposed, and the shear stresses caused by V and T are combined using a simple approach. The development and the evaluation of the model are described. The calculations of the model are compared to experimental data from 350 beams subjected to various combinations of stress-resultants and to the calculations of the ACI and the CSA codes. The proposed model provides the most favorable results. It is also shown that it can accurately model the interaction between V and T. The proposed model provides a unified treatment of shear in beams subjected to complex stress-resultants and in thin membrane elements subjected to in-plane stresses.

• 한국전산구조공학회논문집
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• 제22권6호
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• pp.597-605
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• 2009

본 연구에서는 철근 보강된 Engineered Cementitious Composite(ECC) 면내요소에 대한 2축응력 상태에서의 면내전단거동에 관한 예측 모델을 제시하였다. 기존의 철근콘크리트와 상이한 특성, 즉 ECC 요소의 복수미세균열 현상에 의한 높은 연성의 인장 거동, 일반 콘크리트에 비하여 연성적인 압축 연화 거동, 그리고 ECC 균열면에서의 전단전달 거동 특성 등을 모델에 반영하였다. 면내 순수전단거동에 대한 실험 및 해석결과를 통하여 개발된 R-ECC-MCFT 모델은 ECC 면내전단거동 예측에 효과적인 것으로 평가되었다. 또한 철근 보강된 ECC 면내요소는 철근콘크리트 면내요소에 비하여 최대전단강도 및 전단변형률이 증가하기 때문에 면내전단변형에서 높은 연성을 확보하는 것으로 평가되었다.

• Journal of Mechanical Science and Technology
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• 제19권12호
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• pp.2187-2196
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• 2005

In this paper, the stiffness and the mass matrices for the in-plane motion of a thin circular beam element are derived respectively from the strain energy and the kinetic energy by using the natural shape functions of the exact in-plane displacements which are obtained from an integration of the differential equations of a thin circular beam element in static equilibrium. The matrices are formulated in the local polar coordinate system and in the global Cartesian coordinate system with the effects of shear deformation and rotary inertia. Some numerical examples are performed to verify the element formulation and its analysis capability. The comparison of the FEM results with the theoretical ones shows that the element can describe quite efficiently and accurately the in-plane motion of thin circular beams. The stiffness and the mass matrices with respect to the coefficient vector of shape functions are presented in appendix to be utilized directly in applications without any numerical integration for their formulation.

• Journal of applied mathematics & informatics
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• 제41권2호
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• pp.363-372
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• 2023

We consider Kuo problem of hydrodynamic stability which deals with incompressible, inviscid, parallel shear flows in the 𝛽-plane. For this problem, we derived instability region without any approximations and which intersects with Howard semi-circle region under certain condition. Also, we derived upper bound for growth rate and amplification factor of an unstable mode and proved Howard's conjecture.

• Structural Engineering and Mechanics
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• 제60권5호
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• pp.781-794
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• 2016

Due to its relatively good safety performance and aesthetic benefits, laminated glass (LG) is increasingly being used as load-carrying members in modern buildings. This paper presents an experimental study into one applicational scenario of structural LG subjected to in-plane bending. The aim of the study is to reveal the in-plane behaviors of the LG beams made up of multi-layered glass sheets. The LG specimens respectively consisted of two, three and four plies of glass, bonded together by two prominent adhesives. A total of 26 tests were carried out. From these tests, the structural behaviors in terms of flexural stiffness, load resistance and post-breakage strength were studied in detail, whilst considering the influence of interlayer type, cross-sectional interlayer percentage and presence of shear forces. Based on the test results, analytical suggestions were made, failure modes were identified, corresponding failure mechanisms were discussed, and a rational engineering model was proposed to predict the post-breakage strength of the LG beams. The results obtained are expected to provide useful information for academic and engineering professionals in the analysis and design of LG beams bending in-plane.

• 대한화학회지
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• 제21권5호
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• pp.330-338
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• 1977

고체의 소성변형을 설명하기 위하여 다음과 같은 가정을 하였다. (1) 고체의 소성변형은 크게 두 가지 기구 즉 dislocation 운동과 grain boundary 운동에 의하여 일어난다. (2) Dislocation 운동에 있어서 유동 단위들은 역학적 모형으로 나타내면 다종의 Maxwell 단위들의 평행연결형으로 되고 grain boundary 유동단위들도 다종의 Maxwell 단위들의 평행연결로 표현된다. 이를 물리적으로 설명하면 같은 부류의 유동단위들은 모두 같은 shear plane에서 같은 shear rate로 흐름을 의미한다. (3) Grain boundary 유동단위들과 dislocation 유동단위들 같은 서로 직렬 연결되어 있다. 이는 물리적으로 고체내에서 stress는 균일하게 작용하나 shear rate는 shear plane 의 종류(dislocation 운동면과 grain boundary 운동면)에 따라 달리 나타남을 의미한다. (4) Dislocation 유동단위들과 grain boundary 운동단위들의 운동은 그들의 흐름을 방해하는 장애물 근방의 원자 또는 분자들이 확산해 나가므로써 가능하게 된다. 이러한 가정하에 반응속도론을 적용하여 shear rate와 shear stress를 구하는 일반식을 도출하였다. 본 연구에서는 실제로 중요한 네가지 경우에 대하여 상기 도출한 일반식을 고찰하였다.

• 한국구조물진단유지관리공학회 논문집
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• 제28권4호
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• pp.13-20
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• 2024

이 연구에서는 전단벽과 같은 면내 전단을 받는 경우에 대해, 종방향 보강근비를 2.96%로 일정하게 하고, 횡방향 보강근비를 0.30에서 2.98%까지 변화시켰을 때, CFRP 보강근을 사용한 콘크리트 부재의 거동특성을 MCFT 이론에 기반하여 평가하고, 철근을 사용한 콘크리트 부재의 경우와 비교하여 분석하고자 하였다. 보강근비 0.30에서 1.19% 사이에서는 CFRP 보강근을 사용한 경우가 철근을 사용한 경우보다 높은 전단강도를 보였으며, 그 이상의 1.79% 및 2.98%에서는 상대적으로 낮은 전단강도를 나타내었다. 최대전단변형률은 낮은 보강근비에서 철근을 사용한 경우가 더 크게 나타났으며, 0.97% 이상에서는 CFRP 보강근을 사용한 경우에 더 크게 나타났으며 보강근비가 커질수록 철근 대비 전단변형률 증가율이 더 크게 나타났다. 철근 및 CFRP 보강근의 기계적 성질 차이로 인해 발생하는 보강근에서의 변형률 차이 및 요소에서의 주변형률 차이 분석을 통해 보강근비 변화에 따른 철근 및 CFRP 보강근을 사용한 경우의 전단강도 및 전단변형률 변화를 비교하여 분석할 수 있었다.

• Structural Engineering and Mechanics
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• 제48권4호
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• pp.547-567
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• 2013

Nonlinear behavior of functionally graded material (FGM) plates under thermal loads is investigated here using an efficient sinusoidal shear deformation theory. The displacement field is chosen based on assumptions that the in-plane and transverse displacements consist of bending and shear components, and the shear components of in-plane displacements give rise to the sinusoidal distribution of transverse shear stress through the thickness in such a way that shear stresses vanish on the plate surfaces. Therefore, there is no need to use shear correction factor. Unlike the conventional sinusoidal shear deformation theory, the proposed efficient sinusoidal shear deformation theory contains only four unknowns. The material is graded in the thickness direction and a simple power law based on the rule of mixture is used to estimate the effective material properties. The neutral surface position for such FGM plates is determined and the sinusoidal shear deformation theory based on exact neutral surface position is employed here. There is no stretching-bending coupling effect in the neutral surface-based formulation, and consequently, the governing equations and boundary conditions of functionally graded plates based on neutral surface have the simple forms as those of isotropic plates. The non-linear strain-displacement relations are also taken into consideration. The thermal loads are assumed as uniform, linear and non-linear temperature rises across the thickness direction. Closed-form solutions are presented to calculate the critical buckling temperature, which are useful for engineers in design. Numerical results are presented for the present efficient sinusoidal shear deformation theory, demonstrating its importance and accuracy in comparison to other theories.

• International Journal of Aerospace System Engineering
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• 제3권1호
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• pp.10-16
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• 2016

A trigonometric Layerwise higher order shear deformation theory (TLHSDT) is developed and implemented for free vibration and buckling analysis of laminated composite and sandwich plates by analytical and finite element formulation. The present model assumes parabolic variation of out-plane stresses through the depth of the plate and also accomplish the zero transverse shear stresses over the surface of the plate. Thus a need of shear correction factor is obviated. The present zigzag model able to meet the transverse shear stress continuity and zigzag form of in-plane displacement continuity at the plate interfaces. Hence, botheration of shear correction coefficient is neglected. In the case of analytical method, the governing differential equation and boundary conditions are obtained from the principle of virtual work. For the finite element formulation, an efficient eight noded $C^0$ continuous isoparametric serendipity element is established and employed to examine the dynamic analysis. Like FSDT, the considered mathematical model possesses similar number of variables and which decides the present models computationally more effective. Several numerical predictions are carried out and results are compared with those of other existing numerical approaches.

• Earthquakes and Structures
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• 제7권5호
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• pp.667-689
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• 2014

Structural walls (also known as shear walls) are one of the common lateral load resisting elements in reinforced concrete (RC) buildings in seismic regions. The performance of RC structural walls in recent earthquakes has exposed some problems with the existing design of RC structural walls. The main issues lie around the buckling of bars, out-of plane deformation of the wall (especially the zone deteriorated in compression), reinforcement getting snapped beneath a solitary thin crack etc. This study compares performance of a typical wall designed by different standards. For this purpose, a case study RC shear wall is taken from the Hotel Grand Chancellor in Christchurch which was designed according to the 1982 version of the New Zealand concrete structures standard (NZS3101:1982). The wall is redesigned in this study to comply with the detailing requirements of three standards; ACI-318-11, NZS3101:2006 and Eurocode 8 in such a way that they provide the same flexural and shear capacity. Based on section analysis and pushover analysis, nonlinear responses of the walls are compared in terms of their lateral load capacity and curvature as well as displacement ductilities, and the effect of the code limitations on nonlinear responses of the different walls are evaluated. A parametric study is also carried out to further investigate the effect of confinement length and axial load ratio on the lateral response of shear walls.