• Journal of Mechanical Science and Technology
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• 제18권6호
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• pp.955-960
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• 2004

Some characteristics of the eigenvalue sensitivities have been found for beams in the paper. For cantilever beams and simply supported beams, the sensitivities of the eigenvalues to the stiffness correction factor of one element are equal and opposite to the sensitivities to the mass correction factor of the symmetrically positioned element. For beams with other boundary conditions, however, the relationship does not hold. The relationship has been proven analytically for simply supported beams.

• Structural Engineering and Mechanics
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• 제68권6호
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• pp.713-720
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• 2018

In this paper a new numerical method to determine the elastic curve of the simply supported beams of variable cross-section is demonstrated. In general case it needs to solve linear or small nonlinear second order differential equations with prescribed boundary conditions. For numerical solution the initial values of the slope and the deflection of the end cross-section of the beam is necessary. For obtaining the initial values a lively procedure is developed: it is a special application of the shooting method because boundary value problems can be transformed into initial value problems. As a result of these transformations the initial values of the differential equations are obtained with high accuracy. Procedure is applied for calculating of elastic curve of a simply supported beam of variable cross-section. Results of these numerical procedures, analytical solution of the linearized version and finite element method are compared. It is proved that the suggested procedure yields technically accurate results.

• 한국농공학회지
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• 제41권1호
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• pp.106-114
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• 1999

This paper explores the geometrical non-linear behavior of the simply supported tapered beams subject to the trapezoidal distributed load and end moments. In order to apply the Bernoulli -Euler beam theory to this tapered beam, the bending moment equation on any point of the elastical is obtained by the redistribution of trapezoidal distributed load. On the basis of the bending moment equation and the BErnoulli-Euler beam theory, the differential equations governging the elastical of such beams are derived and solved numerically by using the Runge-Jutta method and the trial and error method. The three kinds of tapered beams (i.e. width, depth and square tapers) are analyzed in this study. The numerical results of non-linear behavior obtained in this study from the simply supported tapered beams are appeared to be quite well according to the results from the reference . As the numerical results, the elastica, the stress resultants and the load-displacement curves are given in the figures.

• 대한기계학회논문집A
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• 제28권2호
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• pp.143-148
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• 2004

This paper discussed on the stability of elastic material subjected to dry friction force for low boundary conditions: clamped free, clamped-simply supported, simply supported-simply supported, clamped-clamped. It is assumed in this paper that the dry frictional force between a tool stand and an elastic material can be modeled as a distributed follower force. The friction material is modeled for simplicity into a Winkler-type elastic foundation. The stability of beams on the elastic foundation subjected to distribute follower force is formulated by using finite element method to have a standard eigenvalue problem. It is found that the clamped-free beam loses its stability in the flutter type instability, the simply supported-simply supported beam loses its stability in the divergence type instability and the other two boundary conditions the beams lose their stability in the divergence-flutter type instability.

• Structural Engineering and Mechanics
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• 제72권5호
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• pp.631-642
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• 2019

The objective of the present study is to examine the flexural behavior of two-span post-tensioned lightweight aggregate concrete (LWAC) beams using unbonded tendons and the reliability of the design provisions of ACI 318-14 for such beams. The parameters investigated were the effective prestress and loading type, including the symmetrical top one-point, two third-point, and analogous uniform loading systems. The unbonded prestressing three-wire strands were arranged with a harped profile of variable eccentricity. The total length of the beam, measured between both strand anchorages, was 11000 mm. The test results were compared with those compiled from simply supported LWAC one-way members, wherever possible. The ultimate load capacity of the present beam specimens was evaluated by the collapse mechanism of the plasticity theorem and the nominal section moment strength calculated following the provision of the ACI 318-14. The test results showed that the two-span post-tensioned LWAC beams had lower stress increase (Δf_ps) in the unbonded tendons than the simply supported LWAC beams with a similar reinforcement index. The effect of the loading type on Δf_ps and displacement ductility was less significant for two-span beams than for the comparable simply supported beams. The design equations for Δf_ps and Δf_ps proposed by ACI 318-14 and Harajli are conservative for the present two-span post-tensioned LWAC beams, although the safety decreases for the two-span beam, compared to the ratios between experiments and predictions obtained from simply supported beams.

• Structural Engineering and Mechanics
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• 제34권5호
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• pp.549-561
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• 2010

In this paper, free vibration analyses of a parallel placed twin pipe system simulated by simply supported-simply supported and fixed-fixed Euler-Bernoulli beams resting on Winkler elastic soil are presented. The motion of the system is described by a homogenous set of two partial differential equations, which is solved by a simulation method called the Differential Transform Method (DTM). Free vibrations of an elastically connected twin pipe system are realized by synchronous and asynchronous deflections. The results of the presented theoretical analyses for simply supported Euler-Bernoulli beams are compared with existing ones in open literature and very good agreement is demonstrated.

• Structural Engineering and Mechanics
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• 제60권1호
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• pp.21-30
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• 2016

In this paper two procedures for determination of the elastic curve of the simply and multiple supported beams are developed. Determination of the elastic curve is complex as it requires to solve a strong nonlinear differential equation with given boundary conditions. For numerical solution the initial guess of the slope at the end of the beam is necessary. Two procedures for obtaining of the initial guess are developed: one, based on transformation of the supported beam into a clamped-free one, and second, on the linearization of the problem. Procedures are applied for calculating of elastic curve of a simply supported beam and a beam with three supports. Obtained results are compared. Advantages and disadvantages of both methods are discussed. It is proved that both suggested procedures give us technically accurate results.

• 콘크리트학회논문집
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• 제12권2호
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• pp.71-78
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• 2000

This paper presents a study on the flexural rigidity of reinforced high strength concrete beams. Thirty six beams with different compressive strength of concrete, tensile reinforcement ratio, compressive reinforcement ratio, and pattern of loadings(1 point loading and 2 points loading) were tested to evaluate the effective moment of inertia. According to the experimental results, the eqation(1) proposed by ACI code for the effective moment of inertia overestimated that of simply supported reinforced high strength concrete beams. Thus, in this paper, an empirical equation(3) is proposed as a lower bound of 90% confidence limit to estimate the effective moment of inertia of simply supported reinforced high strength concrete beams.

• Structural Engineering and Mechanics
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• 제32권6호
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• pp.811-833
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• 2009

In the present article bending, buckling and vibration analyses of tapered beams using Eringen non-local elasticity theory are being carried out. The associated governing differential equations are solved employing Rayleigh-Ritz method. Both Euler-Bernoulli and Timoshenko beam theories are considered in the analyses. Present results are in good agreement with those reported in literature. Beam material is considered to be made up of functionally graded materials (fgms). Non-local analyses for tapered beam with simply supported - simply supported, clamped - simply supported and clamped - free boundary conditions are carried out and discussed. Further, effect of length to height ratio on maximum deflections, vibration frequencies and critical buckling loads are studied.

• Structural Engineering and Mechanics
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• 제66권2호
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• pp.229-235
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• 2018

This study investigated the behaviour of the simply supported hollow steel tube (HST) beams, either concrete filled or unfilled when strengthened with carbon fibre reinforced polymer (CFRP) sheets. Eight specimens with varied tubes thickness (sections classification 1 and 3) were all tested experimentally under static flexural loading, four out of eight were filled with normal concrete (CFST beams). Particularly, the partial CFRP strengthening scheme was used, which wrapped the bottom-half of the beams cross-section (U-shaped wrapping), in order to use the efficiency of high tensile strength of CFRP sheets at the tension stress only of simply supported beams. In general, the results showed that the CFRP sheets significantly improved the ultimate strength and energy absorption capacities of the CFST beams with very limited improvement on the related HST beams. For example, the load and energy absorption capacities for the CFST beams (tube section class 1) were increased about 20% and 32.6%, respectively, when partially strengthened with two CFRP layers, and these improvements had increased more (62% and 38%) for the same CFST beams using tube class 3. However, these capacities recorded no much improvement on the related unfilled HST beams when the same CFRP strengthening scheme was adopted.