• Journal of the Korea institute for structural maintenance and inspection
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• v.15 no.6
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• pp.219-225
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• 2011

Advanced composite structures are too difficult for such design engineers for construction and some simple but accurate enough methods are necessary. The simply supported laminated plates are analyzed by the specially orthotropic laminates theory. This method, however, may be too difficult for some practising engineers. In this paper, the result of analysis for such plate by means of the beam theory with unit width is reported. The plate aspect ratio considered is from 1 : 1 to 1 : 5. Most of the bridge and building slabs on girders have large aspect ratios. For such cases further simplification is possible by neglecting the effect of the longitudinal moment terms($M_x$) on the relevant partial differential equations of equilibrium. In this paper. the influence of the aspect ratio on the natural frequency of the specially orthotropic laminated plates is studied and it is concluded that the method used is sufficiently accurate for engineering purposes. The result of this paper can be used for simply supported laminated plates analysis.

• Journal of Korean Society of Steel Construction
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• v.18 no.1
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• pp.93-100
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• 2006

A simple but precise method of calculating the natural vibration frequencies of composite laminated plates with all-simple support and under axial loadings is presented herein. This method uses deflection influence surfaces, which can be obtained by any method for vibration analysis and member due to the inertia force under resonance condition. Beginning with an initially guessed mode shape, the exact mode shape is obtained by the process similar to iteration. In this paper, equations are given for the case of special orthotropic laminates. The same equations, however, can be used for any laminate as long as ${B_1_6}$, ${B_2_6}$, ${D_1_6}$, and ${D_2_6}$ are negligible as the number of plies increases. Some laminates that possess such properties are presented in the paper.

• Journal of the Korean Society for Advanced Composite Structures
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• v.1 no.3
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• pp.35-40
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• 2010

The specially orthotropic plate theory is used for analysis of panels made of girders and cross-beams. The cross-sections of both girders and cross-beams are H-types. The results of application of this method to rolled beam bridge by using specially orthotropic plate theory is presented. The result is compared with that of the beam theory. Finite difference method is used for this purpose. The influence of the $D_{22}$ stiffness on the natural frequency is rigorously investigated. According to numerical examination given in this paper, the result by the plate theory is 2.43 times stiffer than that of beam theory.

• Journal of the Korean Society for Advanced Composite Structures
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• v.2 no.2
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• pp.20-25
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• 2011

In this paper, two dimensional concrete slabs for a railroad bridge were analyzed by the specially orthotropic laminates theory. Both the geometrical and material property of the cross section of the slab was considered symmetrically with respect to the neutral surface so that the bending extension coupling stiffness, $B_{ij}$ = 0, and $D_{16}=D_{26}=0$ Bridge deck behaves as specially orthotropic plates. In general, the analytical solution for such complex systems is very difficult to obtain. Thus, finite difference method was used for analysis of the problem. In this paper, the finite difference method and the beam theory were used for analysis.

• Journal of Korean Society of Steel Construction
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• v.14 no.1
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• pp.23-29
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• 2002

Many of the bridge systems, including the girders and cross-beams, and concrete decks behave as the special orthotropic plates. Such systems with boundary conditions other than Navier or Levy solution types, or with irregular cross sections, analytical solution is very difficult to obtain. Numerical method for eigenvalue problems are also very much involved in seeking such a solution. A method of calculating the natural frequency corresponding to the first mode of vibration of beam and tower structures with irregular cross-sections was developed and reported by Kim in 1974. Recently, this method was extended to two dimensional problems including composite laminates, and has been applied to composite plates with shear deformation effects. In this paper, application of this method to the specially orthotropic laminated plates with various boundary condition is accomplished and the result of analysis is presented.

• Journal of Korean Society of Steel Construction
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• v.14 no.1
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• pp.105-111
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• 2002

A post-tensioned slab bridge is analyzed by the specially orthotropic laminates theory. Both the geometry and the material of the cross section of the slab are considered symmetrical with respect to the mid-surface so that the bending extension coupling stiffness, $B_{ij}=0$, and $D_{16}=D_{26}=0$. Each longitudinal and transverse steel layer is regarded as a lamina, and material constants of each lamina is calculated by the use of rule of mixture. This bridge with simple support is under uniformly distributed vertical and axial loads. In this paper, the finite difference method and the beam theory are used for analysis. The result of beam analysis is modified to obtain the solution of the plate analysis. The result of this paper can be used for post-tensioned slab bridge analysis by the engineers with undergraduate study in near future.

• Proceedings of the Korean Society For Composite Materials Conference
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• 1999.11a
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• pp.22-27
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• 1999

고급복합재료(advanced composite material)는 여러 가지 훌륭한 장점에도 불구하고 건설기술자에게는 그 이론이 너무 복잡하여 건설구조에 대한 응용이 지연되고 있다. [$\alpha/\beta/\beta/\gamma/\alpha/\alpha/\beta$]r, $\alpha$=-$\beta$, $\gamma$=0$^{\circ}$ 또는 90$^{\circ}$ 와 같은 몇 가지 배향각을 갖은 적층판은, r이 증가함에 따라, $B_{i,j}$강성이 0으로 접근한다(1995). 건설구조물은 그 치수가 커서 r이 증가해도 지간 대 두께비가 충분히 커서, 횡방향 변형율(${\varepsilon}_{xz}$,${\varepsilon}_{yz}$)의 영향이 무시될 수 있다. 이 경우 판의 지배방정식은 간단한 특별직교이방성판의 식으로 변화된다. 김덕현은 토목구조물에 흔히 적용될 수 있는 이러한 배향각을 가진 적층판의 지배방정식을 취급이 간단한 특별직교 이방성 판의 경우로 변경시킨 다음 해석을 더 간단히 진행할 수 있도록 기술자들이 유사 등방성 상수(quasi-isotropic constant)를 사용하여 낮익은 등방성판의 방정식을 사용하여 답을 구한 다음 그가 개발한 "수정계수(correction factor)"를 사용하여 "정확한"해를 구하는 방법을 발표한바 있다(1991).는 방법을 발표한바 있다(1991).

• Composites Research
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• v.12 no.4
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• pp.33-41
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• 1999

In this paper, a simple but accurate method of vibration analysis of structural elements with or without attached mass/masses is presented. The method used has been developed by D.H., Kim since 1974. This method is very effective for the plates with arbitrary conditions and irregular sections. This method is applied to the special orthotropic plate with two opposite edges simply supported and the other two opposite edges free. Such plate represents the most of the simply supported bridges/decks, including concrete and girders-cross beam systems. Detailed illustration is given for beams and plates for easy understanding. Some laminate orientation for which the special orthotropic equations can be applied are identified.

• Composites Research
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• v.12 no.4
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• pp.25-32
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• 1999

A method of calculating the natural frequency corresponding to the first mode of vibration of beams and tower structures, with irregular cross sections and with arbitrary boundary conditions was developed and reported by Kim, D. H. in 1974. In this paper, the result of application of this method to the special orthotropic plates on elastic foundation with free boundaries is presented. Such plates represent the concrete highway slab and hybrid composite pavement on bridges. Any method may be used to obtain the deflection influence surfaces needed for this vibration analysis. Finite difference method is used for this purpose, in this paper. The influence of the modulus of the foundation and the aspect ratio of the plate on the natural frequency is thoroughly studied. The effect of neglecting the mass of the plates on the natural frequency, as the ratio of the point mass/masses to the plate mass increases, is also studied, in deep.

• Composites Research
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• v.22 no.5
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• pp.24-29
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• 2009

In this paper, a post-tensioned reinforced concrete slab was analyzed by the specially orthotropic laminates theory. Both the geometrical and material property of the cross section of the slab was considered symmetrically with respect to the neutral surface so that the bending extension coupling stiffness, $B_{ij}=0$, and $D_{16}=D_{26}=0$. Reinforced concrete slab behave as specially orthotropic plates. In general, the analytical solution for such complex systems is very difficult to obtain. Thus, finite difference method was used for analysis of the problem. In this paper, the finite difference method and the beam theory were used for analysis. The result of beam analysis was modified to obtain the solution of the plate analysis.