• Journal of the Korea institute for structural maintenance and inspection
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• v.9 no.1
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• pp.159-170
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• 2005

The grid structure is parallel main girders intersected with crossgirder. It distribute the loads to adjoining main girder through the crossgirder when a girder is subjected to a load. grillage girder bridge has high load-carrying capacity, it can save materials and become more economical type of bridge. In this paper, the grillage girder bridge analysis program developed by using the transfer matrix method deals with following problems: the comparision with Leonhardt, Szabo, FEM yang and jung in the analysis of grillage girder bridges, quality of straight and curved bridges with skew angle, forces of straight and curved bridges according to skew angle and bending stiffness/torsional stiffness ratio.

• Structural Engineering and Mechanics
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• v.90 no.3
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• pp.219-232
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• 2024

In current study, for the first time, Nonlinear Bending of a skew microplate made of a laminated composite strengthened with graphene nanosheets is investigated. A mixture of mechanical and thermal stresses is applied to the plate, and the reaction is analyzed using the First Shear Deformation Theory (FSDT). Since different percentages of graphene sheets are included in the multilayer structure of the composite, the characteristics of the composite are functionally graded throughout its thickness. Halpin-Tsai models are used to characterize mechanical qualities, whereas Schapery models are used to characterize thermal properties. The microplate's non-linear strain is first calculated by calculating the plate shear deformation and using the Green-Lagrange tensor and von Karman assumptions. Then the elements of the Couple and Cauchy stress tensors using the Modified Coupled Stress Theory (MCST) are derived. Next, using the Hamilton Principle, the microplate's governing equations and associated boundary conditions are calculated. The nonlinear differential equations are linearized by utilizing auxiliary variables in the nonlinear solution by applying the Frechet approach. The linearized equations are rectified via an iterative loop to precisely solve the problem. For this, the Differential Quadrature Method (DQM) is utilized, and the outcomes are shown for the basic support boundary condition. To ascertain the maximum values of microplate deflection for a range of circumstances-such as skew angles, volume fractions, configurations, temperatures, and length scales-a parametric analysis is carried out. To shed light on how the microplate behaves in these various circumstances, the resulting results are analyzed.

• Journal of the Korean Society of Industry Convergence
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• v.4 no.2
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• pp.157-166
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• 2001

The purpose of this study is to examine the accuracy of the code provisions on lateral load distribution factors of prestressed concrete girder bridges. Most designers in Korea use the lever method or lateral load distribution formula in the existing design codes. However, the methods do not account for the effect of bridge skew or direction of diaphragm. Therefore, this study analysed the prestressed concrete girder bridge with grillage model for various girder spacings, directions of diaphragms, span lengths, and skews, and compared the results with those of existing design code. It has been found that lateral load distribution factors were proportional to the girder spacing while they were not significantly affected by the change of span length, direction of diaphragm, and skew. For bending moments, lateral load distribution factors from the grillage analysis were 60%~68% of those from Korean bridge design code. Therefore, the code provisions result in very conservative design. For support reactions, however, lateral load distribution factors from the grillage analysis were slightly greater than those from Korean bridge design code. Therefore, the capacity of bearings of the bridge with a large skew should be determined by grillage analysis.

• Structural Engineering and Mechanics
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• v.7 no.3
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• pp.289-302
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• 1999

An approximate method for analyzing the bending problems of irregular-shaped plates is proposed. In this paper irregular-shaped plates are such plates as plate with opening, circular plate, semi-circular plate, elliptic plate, triangular plate, skew plate, rhombic plate, trapezoidal plate or the other polygonal plates which are not uniform rectangular plates. It is shown that these irregular-shaped plates can be considered finally as a kind of rectangular plates with non-uniform thickness. An opening in a plate can be considered as an extremely thin part of the plate, and a non-rectangular plate can be translated into a circumscribed rectangular plate whose additional parts are extremely thin or thick according to the boundary conditions of the original plate. Therefore any irregular-shaped plate can be replaced by the equivalent rectangular plate with non-uniform thickness. For various types of irregular-shaped plates the convergency and accuracy of numerical solution by proposed method are investigated.

• Structural Engineering and Mechanics
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• v.4 no.4
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• pp.415-424
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• 1996

This paper presents a newly suggested calculation method in which an arbitrary quadrilateral element with curved sides is transformed to a normal rectangular one by mapping of coordinates, then the two-dimensional spline is adopted to approach the displacement function of this element. Finally the solution can be obtained by the least-energy principle. Thereby, the application field of Spline Finite Element Method will be extended.

• Structural Engineering and Mechanics
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• v.71 no.5
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• pp.469-483
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• 2019

In this paper, an improved mathematical model is presented for the bending analysis of doubly curved functionally graded material (FGM) sandwich rhombic conoids. The mathematical model includes expansion of Taylor's series up to the third degree in thickness coordinate and normal curvatures in in-plane displacement fields. The condition of zero-transverse shear strain at upper and lower surface of rhombic conoids is implemented in the present model. The newly introduced feature in the present mathematical model is the simultaneous inclusion of normal curvatures in deformation field and twist curvature in strain-displacement equations. This unique introduction permits the new 2D mathematical model to solve problems of moderately thick and deep doubly curved FGM sandwich rhombic conoids. The distinguishing feature of present shell from the other shells is that maximum transverse deflection does not occur at its center. The proposed new mathematical model is implemented in finite element code written in FORTRAN. The obtained numerical results are compared with the results available in the literature. Once validated, the current model was employed to solve numerous bending problems by varying different parameters like volume fraction indices, skew angles, boundary conditions, thickness scheme, and several geometric parameters.

• Journal of the Korea institute for structural maintenance and inspection
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• v.16 no.4
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• pp.34-43
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• 2012

The behaviors of the curved bridges which has been constructed in the RAMP or Interchange are very complicate and different than orthogonal bridges according to the variations of radius of curvature, skew angle and spacing of shoes. Occasionally, the camber of girder and negative reactions can be occurred due to bending and torsional moment. In this study, the effects on the negative reaction in the curved bridge were investigated on the basis of design variables such as radius of curvature, skew angle, and spacing of shoes. For this study, the twin-steel box girder curved bridge with single span which is applicable for the RAMP bridges with span length(L) of 50.0m and width of 9.0m was chosen and the structural analysis to calculate the reactions was conducted using 3-dimensional equivalent grillage system. The value of negative reaction in curved bridges depends on the plan structures of bridges, the formations of structural systems, and the boundary conditions of bearing, so, radius of curvature, skew angle, and spacing of shoes among of design variables were chosen as the parameter and the load combination according to the design standard were considered. According to the results of numerical analysis, the negative reaction in curved bridge increased with an decrease of radius of curvature, skew angle, and spacing of shoes, respectively. Also, in case of skew angle of $60^{\circ}$ the negative reaction has been always occurred without regard to ${\theta}/B$, and in case of skew angle of $75^{\circ}$ the negative reaction hasn't been occurred in ${\theta}/B$ below 0.27 with the radius of curvature of 180m and in ${\theta}/B$ below 0.32 with the radius of curvature of 250m, and in case of skew angle of $90^{\circ}$ the negative reaction hasn't been occurred in the radius of curvature over 180m and in ${\theta}/B$ below 0.38 with the radius of curvature of 130m, The results from this study indicated that occurrence of negative reaction was related to design variables such as radius of curvature, skew angle, and spacing of shoes, and the problems with the stability including negative reaction will be expected to be solved as taken into consideration of the proper combinations of design variables in design of curved bridge.

• Journal of the Korea institute for structural maintenance and inspection
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• v.8 no.2
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• pp.147-158
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• 2004

For stiffened plates composed of composite materials, many researchers have used a finite element method which connected isoparametric plate elements and beam elements. However, the finite element method is difficult to reflect local behavior of stiffener because beam elements are transferred stiffness for nodal point of plate elements, especially the application is limited in case of laminated composite structures. In this paper, for analysis of laminated composite stiffened plates, 3D shell elements for stiffener and plate are employed. Reissner-Mindlin's first order shear deformation theory is considered in this study. But when thickness will be thin, isoparamatric plate bending element based on the theory of Reissner-Mindlin is generated by transverse shear locking. To eliminate the shear locking and virtual zero energy mode, the substitute shear strain field is used. A deflection distribution is investigated for simple supported rectangular and skew stiffened laminated composite plates with arbitrary orientation stiffener as not only variation of slenderness and aspect ratio of the plate but also variation of skew angle of skew stiffened plates.

• Journal of Korean Society of Steel Construction
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• v.12 no.3 s.46
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• pp.291-302
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• 2000

In recent years the development of high modulus, high strength and low density boron and graphite fibers bonded together has brought renewed interestes in structural elements. When a plate with arbitrarily oriented layers and clamped boundary conditions is subjected to uniform loading, it is difficult to analyze and apply, compared with isotropic and orthotropic cases. Therefore the numerical methods, such as finite difference method or finite element method, should be emloyed to analyse such problems. In this study the finite difference technique is used to formulate the bending analysis of symmetric composite laminated skew plates. When this technique is used to solve the problem, it is desirable to reduce the order of the derivatives in order to minimize the number of the pivotal points involved in each equation. The 4th order partial differential equations of laminated skew plates are converted to an equivalent three of 2nd order partial differential equations with three dependant variables.

• Transactions of the Korean Society of Mechanical Engineers
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• v.14 no.5
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• pp.1129-1137
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• 1990

Based on the formulation which incorporates large deformation and anisotropy, an elastic-plastic finite element code is developed with membrane element to include the contact treatment. For the analysis of the general sheet metal forming process with contact condition, the treatment of contact is considered by employing the successive skew coordinate system. Three kinds of sheet metal forming processes with contact conditions are analyzed; stretching of a square diaphragm with a hemispherical punch, deep drawing of a circular cup and deep drawing of a square cup. Then the computational results are compared with the experiment. The computed loads and the distribution of the thickness strain are in good agreement with the experiment for all cases. However, the computational results of the thickness strain show the effect of bending can not be ignored in the deep drawing process whereas the effect of bending is negligible in stretching.