• Structural Engineering and Mechanics
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• 제70권1호
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• pp.113-123
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• 2019

In the classical stability investigation of rectangular plates the classical thin plate theory (CPT) is often employed, so omitting the transverse shear deformation effect. It seems quite clear that this procedure is not totally appropriate for the investigation of moderately thick plates, so that in the following the first shear deformation theory proposed by Meksi et al. (2015), that permits to consider the transverse shear deformation influences, is used for the stability investigation of simply supported isotropic rectangular plates subjected to uni-axial and bi-axial compression loading. The obtained results are compared with those of CPT and, for rectangular plates under uniaxial compression, a novel direct formula, similar to the conventional Bryan's expression, is found for the Euler stability stress. The accuracy of the present model is also ascertained by comparing it, with model proposed by Piscopo (2010).

• Structural Engineering and Mechanics
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• 제77권1호
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• pp.1-17
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• 2021

The influence of prestress force on the fundamental frequency and static deflection shape of uncracked Prestressed Concrete (PC) beams with a parabolic bonded tendon was examined in this paper. Due to the conflicts among existing theories, the analytical solutions for properly considering the dynamic and static behavior of these members is not straightforward. A series of experiments were conducted for a total period of approximately 2.5 months on a PC beam made with high strength concrete, subsequently and closely to the 28 days of age of concrete. Specifically, the simply supported PC member was short term subjected to free transverse vibration and three-point bending tests during its early-age. Subsequently, the experimental data were compared with a model that describes the dynamic behavior of PC girders as a combination of two substructures interconnected, i.e., a compressed Euler-Bernoulli beam and a tensioned parabolic cable. It was established that the fundamental frequency of uncracked PC beams with a parabolic bonded tendon is sensitive to the variation of the initial elastic modulus of concrete in the early-age curing. Furthermore, the small variation in experimental frequency with time makes doubtful its use in inverse problem identifications. Conversely, the relationship between prestress force and static deflection shape is well described by the magnification factor formula of the "compression-softening" theory by assuming the variation of the chord elastic modulus of concrete with time.

• Advances in materials Research
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• 제11권1호
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• pp.59-73
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• 2022

In the construction industry, thin-walled frame elements with very slender open cross-sections and low torsional stiffness are often subjected to a complex loading condition where axial, bending, shear and torsional stresses are present simultaneously. Hence, these often fail in instability even before the yield capacity is reached. One of the most common instability conditions associated with thin-walled structures is Lateral Torsional Buckling (LTB). In this study, a first order Generalized Beam Theory (GBT) formulation and numerical analysis of cold-formed steel lipped channel beams (C80×40×10×1, C90×40×10×1, C100×40×10×1, C80×40×10×1.6, C90×40×10×1.6 and C100×40×10×1.6) subjected to uniform moment is carried out to predict pure Lateral Torsional Buckling (LTB). These results are compared with the Finite Element Analysis of the beams modelled with shell elements using ABAQUS and analytical results based on Euler's buckling formula. The mode wise deformed shape and modal participation factors are obtained for comparison of the responses along with the effect of varying the length of the beam from 2.5 m to 10 m. The deformed shapes of the beam for different modes and GBTUL plots are analyzed for comparative conclusions.

• 천문학회지
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• 제56권2호
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• pp.287-292
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• 2023

This paper investigates the number of scatterings a photon undergoes in random walks before escaping from a medium. The number of scatterings in random walk processes is commonly approximated as τ + τ² in the literature, where τ is the optical thickness measured from the center of the medium. However, it is found that this formula is not accurate. In this study, analytical solutions in sphere and slab geometries are derived for both optically thin and optically thick limits, assuming isotropic scattering. These solutions are verified using Monte Carlo simulations. In the optically thick limit, the number of scatterings is found to be 0.5 τ² and 1.5 τ² in a sphere and slab, respectively. In the optically thin limit, the number of scatterings is ≈ τ in a sphere and ≈ τ (1 - γ - ln τ + τ) in a slab, where γ ≃ 0.57722 is the Euler-Mascheroni constant. Additionally, we present approximate formulas that reasonably reproduce the simulation results well in intermediate optical depths. These results are applicable to scattering processes that exhibit forward and backward symmetry, including both isotropic and Thomson scattering.

• 대한환경공학회지
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• 제33권7호
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• pp.536-543
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• 2011

다목적 여과저류지에 하상여과를 적용하기 위한 인공하천의 최적설계를 찾기 위해서 하천수의 에너지경사와 Manning의 평균유속공식을 이용하여 물 흐름에 대한 수학적 모델을 수립하였고, Euler의 방법을 이용한 수치해법으로 해석하였다. 모델을 이용하여 다양한 시나리오에 대한 모사를 수행함으로써 하상여과용 인공하천의 여러 설계요소를 검토하였다. 검토결과 면적이 100 ha인 강변저류지의 경우, 인공하천의 종단경사는 2/10,000, 하상에서의 침투율은 $2.5m^3/m^2-day$가 적당한 것을 알 수 있었다. 이 경우 수심은 1 m 이내이고 하상에서의 Manning의 조도계수는 0.026 정도로 예측되었으며, 인공하천의 길이가 길수록 유리함을 알 수 있었다. 한편, 인공하천에 빠른 유속을 발생시킴으로써 하상여과에 수반하는 하상의 폐색을 방지하는 방법은 효율적이지 않음을 알 수 있었고, 낙차가 큰 보의 주변에서 본 설비의 효율이 더 좋아짐을 알 수 있었다.

• 한국강구조학회 논문집
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• 제28권5호
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• pp.355-363
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• 2016

본 논문은 절곡 제작된 U형 단면 거더의 상부플랜지를 구성하는 자유돌출판의 좌굴거동 특성에 논하고자 한다. 절곡된 판 부재는 둥근 모서리를 가지므로 단면의 유효폭-두께비가 불명확하고 이에 따라 공칭 압축강도를 산정하는 데 모호한 면이 있다. 냉간성형에 의해 둥근 모서리를 갖는 자유돌출판의 등가유효폭을 평가하기 위해 3차원 유한요소해석을 수행하였다. 절곡에 따른 재료특성과 기하하적 특성을 반영하였다. 본 변수 해석적 연구로부터 각진 모서리를 갖는 일반적인 자유돌출판의 좌굴강도와 비교 분석하여 등가유효폭-두께비를 추정하였다. 국내 설계기준의 공칭 좌굴강도식이 근거하고 있는 이론식과의 비교를 통해 기준공식의 적용 방안에 대해 검토하였다.

• 한국항공우주학회지
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• 제37권1호
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• pp.36-41
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• 2009

임무를 수행하는데 있어 정확한 자세 정보는 필수적이다. 두 개 또는 그 이상의 관측벡터를 이용하는 자세 결정 알고리듬에는 크게 두 가지가 널리 알려져 있다. 하나는 결정적인 방법인 TRIAD 알고리듬이며, 다른 하나는 최적의 해를 찾는 방법인 QUEST 알고리듬이다. 본 논문은 TRIAD 알고리듬의 성능 향상과 서로 다른 정확도를 가진 센서의 조합을 이용한 자세 결정 방법을 제안하였다. 첫째, 보다 정확한 자세 행렬을 구하기 위하여 직교화 방법을 이용하는 대신 방향 여현 행렬을 오일러 각으로 바꾸고, 분산 대신 공분산행렬을 고려하여 편향되지 않은 최소 공분산 기법을 적용하였다. 또한, 세 개 이상의 측정값이 주어졌을 경우 TRIAD 알고리듬을 적용할 수 있는 방법을 제안하였다. 제안된 평균 TRIAD 알고리듬의 성능은 서로 다른 센서의 조합을 가정하여 표준편차와 확률적 측면에서의 수치 시뮬레이션을 통해 분석되었다.

• Structural Engineering and Mechanics
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• 제17권2호
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• pp.167-186
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• 2004

The design load-carrying capacities of wooden shores depend on factors, such as the wood species and properties, and construction methods. This paper focuses on the construction methods, including an upright single shore, group of upright shores, group of inclined shores, butt connections and lap connections. This paper reports experiments to obtain critical loads and then developed an empirical equation based on Euler' formula for the critical loads and design load-carrying capacities. The test results show that the critical loads for an upright single wooden shore are greater than the average values for a group of upright shores, and the latter are greater than the average values for a group of inclined shores. Test results also show that the critical loads become smaller when butt or lap connections are used, butt connections possessing greater critical loads than lap connections. Groups of inclined shores are very popular at work sites because they have some practical advantages even though they actually possess inferior critical loads. This paper presents an improved setup for constructing groups of inclined shores. With this method, the inclined shores have larger critical loads than upright shores. The design load-carrying capacities were obtained by multiplying the average critical loads by a resistance factor (or strength reduction factor, ${\phi}$) that were all smaller than 1. This article preliminarily suggests ${\phi}$ factors based on the test results for the reference of engineers or specification committees.

• 대한조선학회논문집
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• 제50권2호
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• pp.79-87
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• 2013

In this paper, an Euler equation solver based on a Cartesian-grid method and non-uniform staggered grid system is applied to predict the ship motion response and added resistance in waves. Water, air, and solid domains are identified by a volume-fraction function for each phase and in each cell. For capturing the interface between air and water, the tangent of hyperbola for interface capturing (THINC) scheme is used with a weighed line interface calculation (WLIC) method. The volume fraction of solid body embedded in a Cartesian-grid system is calculated by a level-set based algorithm, and the body boundary condition is imposed by volume weighted formula. Added resistance is calculated by direct pressure integration on the ship surface. Numerical simulations for a Wigley III hull and an S175 containership in regular waves have been carried out to validate the newly developed code, and the ship motion responses and added resistances are compared with experimental data. For S175 containership, grid convergence test has been conducted to investigate the sensitivity of grid spacing on the motion responses and added resistances.

• 국제강구조저널
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• 제18권4호
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• pp.1440-1463
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• 2018

The Wagner coefficient is a key parameter used to describe the inelastic lateral-torsional buckling (LTB) behaviour of the I-beam, since even for a doubly-symmetric I-section with residual stress, it becomes a monosymmetric I-section due to the characteristics of the non-symmetrical distribution of plastic regions. However, so far no theoretical derivation on the energy equation and Wagner's coefficient have been presented due to the limitation of Vlasov's buckling theory. In order to simplify the nonlinear analysis and calculation, this paper presents a simplified mechanical model and an analytical solution for doubly-symmetric I-beams under pure bending, in which residual stresses and yielding are taken into account. According to the plate-beam theory proposed by the lead author, the energy equation for the inelastic LTB of an I-beam is derived in detail, using only the Euler-Bernoulli beam model and the Kirchhoff-plate model. In this derivation, the concept of the instantaneous shear centre is used and its position can be determined naturally by the condition that the coefficient of the cross-term in the strain energy should be zero; formulae for both the critical moment and the corresponding critical beam length are proposed based upon the analytical buckling equation. An analytical formula of the Wagner coefficient is obtained and the validity of Wagner hypothesis is reconfirmed. Finally, the accuracy of the analytical solution is verified by a FEM solution based upon a bi-modulus model of I-beams. It is found that the critical moments given by the analytical solution almost is identical to those given by Trahair's formulae, and hence the analytical solution can be used as a benchmark to verify the results obtained by other numerical algorithms for inelastic LTB behaviour.