• Computers and Concrete
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• v.19 no.1
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• pp.1-6
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• 2017

Prestressed concrete I-girders are subject to different load types at their construction stages. At the time of strand release, i.e., detensioning, prestressed concrete girders are under the effect of dead and prestressing loads. At this stage, the camber, total net upward deflection, of prestressed girder is summation of the upward deflection due to the prestressing force and the downward deflection due to dead loads. For the calculation of the upward deflection, it is generally considered that prestressed concrete I-girder behaves linear-elastic. However, the field measurements on total net upward deflection of prestressed I-girder after detensioning show contradictory results. In this paper, camber calculations with the linear-elastic beam and elastic-stability theories are presented. One of a typical precast I-girder with 120 cm height and 31.5 m effective span length is selected as a case study. 3D finite element model (FEM) of the girder is developed by SAP2000 software, and the deflections of girder are obtained from linear and nonlinear-static analyses. Only geometric nonlinearity is taken into account. The material test and field measurement of this study are performed at prestressing girder plant. The results of the linear-elastic beam and elastic-stability theories are compared with FEM results and field measurements. It is seen that the camber predicted by elastic-stability theory gives acceptable results than the linear-elastic beam theory while strand releasing.

• Structural Engineering and Mechanics
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• v.19 no.4
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• pp.401-411
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• 2005

The influence of cracks on the elastic deflection and ultimate bearing capacity of eccentric thin-walled columns with both ends pinned was studied in this paper. First, a method was developed and applied to determine the elastic deflection of the eccentric thin-walled columns containing some model-I cracks. A trigonometric series solution of the elastic deflection equation was obtained by the Rayleigh-Ritz energy method. Compared with the solution presented in Okamura (1981), this solution meets the needs of compatibility of deformation and is useful for thin-walled columns. Second, a two-criteria approach to determine the stability factor ${\varphi}$ has been suggested and its analytical formula has been derived. Finally, as an example, box columns with a center through-wall crack were analyzed and calculated. The effects of cracks on both the maximum deflection and the stability coefficient ${\varphi}$ for various crack lengths or eccentricities were illustrated and discussed. The analytical and numerical results of tests on the columns show that the deflection increment caused by the cracks increases with increased crack length or eccentricity, and the critical transition crack length from yielding failure to fracture failure ${\xi}_c$ is found to decrease with an increase of the slenderness ratio or eccentricity.

• Bulletin of the Society of Naval Architects of Korea
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• v.25 no.1
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• pp.33-46
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• 1988

This paper describes a simplified method for estimation of the ultimate compressive strength of actual ship panels with initial deflection of complex shape. The proposed method consists of the elastic analysis using the large deflection theory and the rigid-plastic analysis based on the collapse mechanism which also includes the large deformation effect. In order to reduce the computing time for the elastic large deflection theory and the rigid-plastic analysis based on the collapse mechanism which also includes the large deformation effect. In order to reduce the computing time for the elastic large deflection analysis, only one term of Fourier series for the plate deflection is considered. The results of the proposed method are in good agreement with those calculated by the elasto-plastic large deflection analysis using F.E.M. and the computing time of the proposed method is extremely short compared with that of F.E.M.

• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1225-1240
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• 2015

We provide a complete proof that there are no eigenvalues of the integral operator ${\mathcal{K}}_l$ outside the interval (0, 1/k). ${\mathcal{K}}_l$ arises naturally from the deflection problem of a beam with length 2l resting horizontally on an elastic foundation with spring constant k, while some vertical load is applied to the beam.

• International Journal of Safety
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• v.2 no.1
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• pp.39-44
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• 2003

The present study deals with an approximate integral equation approach to finite deflection of elastic plates with arbitrary plane form. An integral formulation leads to a system of boundary integral equations involving values of deflection, slope, bending moment and transverse shear force along the edge. The basic principles of the development of boundary element technique are reviewed. A computer program for solving for stresses and deflections in a isotropic, homogeneous, linear and elastic bending plate is developed. The fundamental solution of deflection and moment is employed in this program. The deflections and moments are assumed constant within the quadrilateral element. Numerical solutions for sample problems, obtained by the direct boundary element method, are presented and results are compared with known solutions.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2005.06a
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• pp.1695-1698
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• 2005

In this paper we investigate characteristics of deflection for circular plate with the non-symmetric boundary condition that is the boundary condition partly supported along the width direction of plate according to the length change of supporting end. For two boundary conditions such as simple supported and completely clamped boundary conditions, this study derives the maximum deflection formula of the circular plate using differential equation of elastic curve, assuming that a circular plate is a beam with the change of width and thickness along the longitudinal direction. The deflection formula of circular plate is verified by carrying out finite element analysis with regard to the ratio of length of supporting end to radius of circular plate.

• Journal of the Korean Society for Precision Engineering
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• v.21 no.3
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• pp.109-116
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• 2004

This paper investigates the characteristics of deflection for circular plate that has same supporting boundary condition along the width direction of plate according to the length change of supporting end. For two boundary conditions such as simple supporting and clamping on both ends, this study derives maximum deflection formula of circular plate using differential equation of elastic curve, assuming that a circular plate is a beam with different widths along the longitudinal direction. The deflection formula of circular plate is verified by carrying out finite element analysis with regard to the ratio of length of supporting end to radius of circular plate.

• The korean journal of orthodontics
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• v.16 no.1
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• pp.133-144
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• 1986

This study was conducted to evaluate the effects of loop formation and heat treatment upon the elastic properties of orthodontic wires. The specimens selected were .016', .018', .016x.022', and .018x.022' sized stainless steel (standard) and cobalt-chromium-nickel wires, and were divided into 7 groups as; 1. straight non-heat treated 2. U looped non-heat treated 3. L looped non-heat treated 4. Circle looped non-heat treated 5. U looped heat treated 6. L looped heat treated 7. Circle looped heat treated Heat treatment was performed in Big Jane furnace at 850' F for 3 minutes. The elastic limit and the elastic range of each specimen were determined by bending test, and load deflection rate was computed from those values. The findings were as follows; 1. The formation of loop resulted in increased load-deflection rate for both stainless steel and cobalt-chromium-nickel wires. 2. The heat treated group showed higher load-deflection rate than non-heat treated group, which was more apparent in cobalt-chromiumnickel wire than in stainless steel wire. 3. L loop had the highest load-deflection rate among 3 types of loops, followed by U loop and circle loop. 4. The specimens with greater diameter displayed the more increase in load-deflection rate by looping and heat treatment.

• Journal of the Korean Society for Precision Engineering
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• v.20 no.3
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• pp.172-177
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• 2003

This paper investigates the effect of reinforced plate on the deflection of the rectangular plate, when the rectangular plate is reinforced with rectangular rigid body at the centroid of the plate. For two boundary conditions such as simple supported and clamped boundary This study derives deflection formula of reinforced plates with three kinds of the aspect ratio of a rectangular plate with respect to the elastic modulus ratio and the length ratio of rigid body using the least square method. The results are as follows: 1. As the elastic modulus ratio r$_{e}$$\geq$ 1000, the maximum deflection with respect to the length ratio r$_{1}$ converges into constant value. 2. Deflection formula with respect to the length ratio r$_{1}$ is derived as the third order polynomial.l.

• Earthquakes and Structures
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• v.26 no.4
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• pp.251-259
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• 2024

In this paper, the thermal post-buckling behavior of graphene platelets reinforced metal foams (GPLRMFs) plate with initial geometric imperfections on nonlinear elastic foundations are studied. First, the governing equation is derived based on the first-order shear deformation theory (FSDT) of plate. To obtain a single equation that only contains deflection, the Galerkin principle is employed to solve the governing equation. Subsequently, a comparative analysis was conducted with existing literature, thereby verifying the correctness and reliability of this paper. Finally, considering three GPLs distribution types (GPL-A, GPL-B, and GPL-C) of plates, the effects of initial geometric imperfections, foam distribution types, foam coefficients, GPLs weight fraction, temperature changes, and elastic foundation stiffness on the thermal post-buckling characteristics of the plates were investigated. The results show that the GPL-A distribution pattern exhibits the best buckling resistance. And with the foam coefficient (GPLs weight fraction, elastic foundation stiffness) increases, the deflection change of the plate under thermal load becomes smaller. On the contrary, when the initial geometric imperfection (temperature change) increases, the thermal buckling deflection increases. According to the current research situation, the results of this article can play an important role in the thermal stability analysis of GPLRMFs plates.