• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.22 no.3
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• pp.223-233
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• 2012

This paper deals with free vibrations of the tapered Timoshenko beam with constant volume, in which both the rotatory inertia and shear deformation are included. The cross section of the tapered beam is chosen as the regular polygon cross section whose depth is varied with the parabolic function. The ordinary differential equations governing free vibrations of such beam are derived based on the Timoshenko beam theory by decomposing the displacements. Governing equations are solved for determining the natural frequencies corresponding with their mode shapes. In the numerical examples, three end constraints of the hinged-hinged, hinged-clamped and clamped-clamped ends are considered. The effects of various beam parameters on natural frequencies are extensively discussed. The mode shapes of both the deflections and stress resultants are presented, in which the composing rates due to bending rotation and shear deformation are determined.

• Geomechanics and Engineering
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• v.17 no.2
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• pp.133-143
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• 2019

An optimal hydraulic section is critical for irrigated water conservancy in seasonal frozen ground due to a large proportion of water leakage, as investigated by in-situ surveys. This is highly correlated with the frost heave of underlain soils in cold season. This paper firstly derived a practical model for frost heave of clayey soils, with temperature dependent thermal indexes incorporating phase change effect. A model test carried out on clay was used to verify the rationality of the model. A novel approach for optimizing the cross-section of irrigation canals in cold regions was suggested with live updated geometry characterized by three unique geometric constraints including slope of canal, ratio of practical flow section to the optimal and lining thickness. Allowable frost heave deformation and tensile stress in canal lining are utilized as standard in computation iterating with geometry updating while the construction cost per unit length is regarded as the eventual target in optimization. A typical section along the Jinghui irrigation canal was selected to be optimized with the above requirements satisfied. Results prove that the optimized hydraulic section exhibits smaller frost heave deformation, lower tensile stress and lower construction cost.

• International Journal of Korean Welding Society
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• v.3 no.2
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• pp.7-14
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• 2003

During the manufacture of a ship, longitudinal deformation is produced by fillet welding on the Built­Up beam used to improve the longitudinal strength of a ship. This deformation needs a correcting process separate from a manufacture process and decreases productivity and quality. This deformation is caused by welding moment, which is the value multiplied the shrinking force due to welding by the distance from the neutral axis on a cross section of Built­Up beam. This deformation can be offset by generating a moment which is the same magnitude with and is located in an opposite direction to the welding moment on web plate by induction heating. Accordingly, this study clarifies the creation mechanism of the longitudinal deformation on Built­Up beam with FEM analysis and presents the preventative method of this deformation by induction heating basing the mechanism and verifies its validity through analysis and experiments. The induction heating used here is performed by deciding its location and quantity with experiments and simple equations and by applying them to a real structure.

• 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.33 no.4
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• pp.447-484
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• 2009

The spatially coupled buckling, in-plane, and lateral bucking analyses of thin-walled Timoshenko curved beam with non-symmetric, double-, and mono-symmetric cross-sections resting on elastic foundation are performed based on series solutions. The stiffness matrices are derived rigorously using the homogeneous form of the simultaneous ordinary differential equations. The present beam formulation includes the mechanical characteristics such as the non-symmetric cross-section, the thickness-curvature effect, the shear effects due to bending and restrained warping, the second-order terms of semitangential rotation, the Wagner effect, and the foundation effects. The equilibrium equations and force-deformation relationships are derived from the energy principle and expressions for displacement parameters are derived based on power series expansions of displacement components. Finally the element stiffness matrix is determined using force-deformation relationships. In order to verify the accuracy and validity of this study, the numerical solutions by the proposed method are presented and compared with the finite element solutions using the classical isoparametric curved beam elements and other researchers' analytical solutions.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.26 no.4A
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• pp.577-585
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• 2006

In this research, nonlinear Timoshenko beam element that is able to capture nonlinear shear deformation is developed. The proposed model shows more reasonable prediction than Bernoulli beam theory in short columns or strong shear column due to the consideration of shear deformation. The cross-section is modeled as fiber approach. Since the model is based on the fiber approach for section discretization, the plastic progress of the section can be traced and the coupling effect of the axial and flexural response. The developed element is implemented into the finite element program to analysis general reinforced concrete structures. As parametric study, reinforced concrete columns are analyzed and compared with experimental results, analyzed the property of behavior for reinforced concrete columns.

• Journal of the Korea Concrete Institute
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• v.17 no.6 s.90
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• pp.911-922
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• 2005

A theoretical study was performed to investigate the behavioral chracteristics and shear strength of fiber reinforced concrete slender beams. In the fiber reinforced concrete beam, the shear force applied to a cross section of the beam was resisted by both compressive zone and tensile zone. The shear capacity of the compressive zone was defined addressing the interaction with the normal stresses developed by the flexural moment in the cross section. The shear capacity of the tensile zone was defined addressing the post-cracking tensile strength of fiber reinforced concrete. Since the magnitude and distribution of the normal stresses vary according to the flexural deformation of the beam, the shear capacity of the beam was defined as a function of the flexural deformation of the beam. The shear strength of the beam and the location of the critical section were determined at the intersection between the shear capacity and shear demand curves. The proposed method was developed as a unified shear design method which is applicable to conventional reinforced concrete as well as fiber reinforced concrete.

• 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.

• Journal of Institute of Control, Robotics and Systems
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• v.11 no.9
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• pp.768-773
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• 2005

A new approach for human foot modelling and last design based on the cross sectional method is presented in this paper. The proposed last design method utilizes the dynamic trimmed parametric patches for the foot 3D data and last 3D data. The cross section a surface of 3D foot for the 3D last, design modeling of free form geometric last shapes. The proposed last design scheme wraps the 3D last data surrounding the measured 3D foot data with the effect of deforming the last design rule The last design rule of the FFD is constructed on the FFD lattice based on foot-last shape analysis. In addition, the control points of FFD lattice are constructed with cross sectional data interpolation methods from the a finite set of 3D foot data. The deformed 3D last result obtained from the proposed FFD is saved as a 3D dxf foot data. The experimental results demonstrate that the last designed with the proposed scheme has good performance.

• Structural Engineering and Mechanics
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• v.11 no.4
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• pp.423-442
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• 2001

This paper presents a method of elastic-plastic analysis for planar steel frames that provides the accuracy of distributed plasticity methods with the computational efficiency that is greater than that of distributed plasticity methods but less than that of plastic-hinge based methods. This method accounts for the effect of spread of plasticity accurately without discretization through the cross-section of a beam-column element, which is achieved by the following procedures. First, nonlinear equations describing the relationships between generalized stresses and strains of the cross-section are derived analytically. Next, nonlinear force-deformation relationships for the beam-column element are obtained through lengthwise integration of the generalized strains. Elastic-plastic flexibility coefficients are then calculated by differentiating the above element force-deformation relationships. Finally, an elastic-plastic stiffness matrix is obtained by making use of the flexibility-stiffness transformation. Adding the conventional geometric stiffness matrix to the elastic-plastic stiffness matrix results in the tangent stiffness matrix, which can readily be used to evaluate the load carrying capacity of steel frames following standard nonlinear analysis procedures. The accuracy of the proposed method is verified by several examples that are sensitive to the effect of spread of plasticity.