• Structural Engineering and Mechanics
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• v.67 no.5
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• pp.465-479
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• 2018

In a previous study, design charts where proposed to help the torsional design of axially restricted reinforced concrete (RC) beams with squared cross section. In this article, new design charts are proposed to cover RC beams with rectangular cross section. The influence of the height to width ratio of the cross section on the behavior of RC beams under torsion is firstly shown by using theoretical and experimental results. Next, the effective torsional strength of a reference RC beam is computed for several values and combinations of the study variables, namely: height to width ratio of the cross section, concrete compressive strength, torsional reinforcement ratio and level of the axial restraint. To compute the torsional strength, the modified Variable Angle Truss Model for axially restricted RC beams is used. Then, an extensive parametric analysis based on multivariable and nonlinear correlation analysis is performed to obtain nonlinear regression equations which allow to build the new design charts. These charts allow to correct the torsional strength in order to consider the favourable influence of the compressive axial stress that arises from the axial restraint.

• Journal of KSNVE
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• v.6 no.5
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• pp.587-594
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• 1996

The differential equation governing both the free vibrations and buckling loads of tapered beam-columns of regular polygon cross-section with constant volume were derived and solved numerically. The parabolic and sinusoidl tapers were chosen as the variable depth of cross-section for the tapered beam-column. In numerical examples, the clamped-clamped, hinged-clamped and hinged-hinged end constraints were considered. The variations of frequency parameters and first buckling load parameters with the non-dimensional system parameters are reported in figures, and typical vibrating mode shapes are presented. Also, the configurations of strongest columns were determined.

• Transactions of the Korean Society of Mechanical Engineers
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• v.13 no.5
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• pp.991-998
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• 1989

This investigation was carried out for the purpose of studying the turbulent flow and mixing characteristics after collision of two jets depending upon the cross angle variations. For effectuating this experimental study, a subsonic wind tunnel and a constant temperature type two channel hot-wire anemometer system have been utilized. The jets issuing from two nozzles have same Reynolds numbers and their cross angle was variable. After collision of two jets, the cross section of the mixing flow, mean and fluctuating velocities and Reynolds stresses have been measured, and analyzed comparing them with semi-empirical equations. It was found that the nondirectional contour of the cross section agreed well with an elliptic formula and the mean velocities along the centerline had a good similarity independent of cross angle variations. The distributions of U over bar-components measured in the Y direction have a good similarity and agree well with semi-empirical equations of Hinze and Gortler. The Reynolds stresses of u'v' over bar on the Y axis show a similar distributions and their agreement with the theoretical curve is remarkable but those of u'w' over bar measured along the Z axis are randomly scattered.

• International Journal of Aeronautical and Space Sciences
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• v.17 no.1
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• pp.29-36
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• 2016

Tensairity girder is a light weight inflatable fabric structural concept which can be used in road emergency transportation. It uses low pressure air to stabilize compression elements against buckling. With the purpose of obtaining the comprehensive target of minimum deflection and weight under ultimate load, the cross-section and the inner pressure of tensairity girder was optimized in this paper. The Variable Complexity Modeling (VCM) method was used in this paper combining the Kriging approximate method with the Finite Element Analysis (FEA) method, which was implemented by ABAQUS. In the Kriging method, the sample points of the surrogate model were outlined by Design of Experiment (DOE) technique based on Optimal Latin Hypercube. The optimization framework was constructed in iSIGHT with a global optimization method, Multi-Island Genetic Algorithm (MIGA), followed by a local optimization method, Sequential Quadratic Program (SQP). The result of the optimization gives a prominent conceptual design of the tensairity girder, which approves the solution architecture of VCM is feasible and efficient. Furthermore, a useful trend of sensitivity between optimization variables and responses was performed to guide future design. It was proved that the inner pressure is the key parameter to balance the maximum Von Mises stress and deflection on tensairity girder, and the parameters of cross section impact the mass of tensairity girder obviously.

• Structural Engineering and Mechanics
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• v.65 no.1
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• pp.9-17
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• 2018

This study concerns about calculating exact natural frequencies of frames using a single variable shear deformation theory (SVSDT) which considers the parabolic shear stress distribution across the cross section. Free vibration analyses are performed for multi-bay, multi-storey and multi-bay multi-storey type frame structures. Dynamic stiffness formulations are derived and used to obtain first five natural frequencies of frames. Different beam and column cross sections are considered to reveal their effects on free vibration analysis. The calculated natural frequencies are tabulated with the results obtained using Euler-Bernoulli Beam Theory (EBT) and Timoshenko Beam Theory (TBT). Moreover, the effects of inner and outer columns on natural frequencies are compared for multi-bay frames. Several mode shapes are plotted.

• Structural Engineering and Mechanics
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• v.22 no.2
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• pp.131-150
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• 2006

Exact analytical solutions for in-plane static problems of planar curved beams with variable curvatures and variable cross-sections are derived by using the initial value method. The governing equations include the axial extension and shear deformation effects. The fundamental matrix required by the initial value method is obtained analytically. Then, the displacements, slopes and stress resultants are found analytically along the beam axis by using the fundamental matrix. The results are given in analytical forms. In order to show the advantages of the method, some examples are solved and the results are compared with the existing results in the literature. One of the advantages of the proposed method is that the high degree of statically indeterminacy adds no extra difficulty to the solution. For some examples, the deformed shape along the beam axis is determined and plotted and also the slope and stress resultants are given in tables.

• Computational Structural Engineering
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• v.9 no.3
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• pp.135-143
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• 1996

The differential equations governing both the free vibrations and buckling loads of tapered beam-columns of circular cross-section with constant volume are derived and solved numerically. The effects of axial load are included in the differential equations. The parabolic equation is chosen as the variable radius of circular cross-section for the tapered beam-column. In numerical examples, the clamped-clamped, clamped-hinged and hinged-hinged end constraints are considered. The variations of the frequency parameters and buckling load parameters with the non-dimensional system parameters are presented in figures and the configurations of strongest columns are obtained.

• Structural Engineering and Mechanics
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• v.75 no.6
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• pp.737-746
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• 2020

This paper attempts to investigate the free vibration of functionally graded material beams with nonuniform width based on the nonlocal elasticity theory. The theoretical formulations are established following the Euler-Bernoulli beam theory, and the governing equations of motion of the system are derived from the minimum total potential energy principle using the nonlocal elasticity theory. In addition, the Differential Quadrature Method (DQM) is applied, along with the Chebyshev-Gauss-Lobatto polynomials, in order to determine the weighting coefficient matrices. Furthermore, the effects of the nonlocal parameter, cross-section area of the functionally graded material (FGM) beam and various boundary conditions on the natural frequencies are examined. It is observed that the nonlocal parameter and boundary conditions significantly influence the natural frequencies of the functionally graded material beam cross-section. The results obtained, using the Differential Quadrature Method (DQM) under various boundary conditions, are found in good agreement with analytical and numerical results available in the literature.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 1997.10a
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• pp.114-119
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• 1997

Natural vibration of the rotor system having multi-step cross-sections is analyzed. The rotary inertia and the shear deformation are considered. Torque is also included in order to simulate the power transmission system. The complex displacement and the variable separation are introduced. The exact solutions in uniform cross-section segment and the boundary conditions are used. Natural frequencies and mode shapes are obtained, especially the mode shapes are countinuous.

• The Journal of Korean Physical Therapy
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• v.22 no.5
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• pp.39-47
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• 2010

Purpose: The purpose of this study was to characterize changes in back muscles in patients with chronic back pain. Accordingly, we studied 154 patients with chronic low back pain with regard to area, aspect and triggering position of the pain. We also determined muscle atrophy in painful areas. Methods: Subjects were questioned about pain and a pain provoking test was done. On Magnetic Resonance Imaging (MRI), we measured cross sections of the multifidus, erector spinae, iliopsoas and quadratus lumborum muscles at each spinal level. Results: Muscles in painful regions (multifidus and erector spinae muscles) decreased in area significantly more than nonpainful regions, and showed a significant difference (p<0.05) at levels L3, L4, and L5. Painful regions of the iliopsoas and quadratus lumborum did not change significantly more than non-painful regionsexcept at L5 (p<0.05). The group that had unilateral low back pain showed a significant decrease in cross section compared to the group that had central or bilateral pain (p<0.05). Conclusion: Chronic low back pain causes variable decreases in cross-sectional areas of some but not all back muscles, and at some but not all spinal levels.