• Structural Engineering and Mechanics
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• 제24권1호
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• pp.51-62
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• 2006

Differential transform method (DTM) for free vibration analysis of both ends simply supported beam resting on elastic foundation is suggested. The fourth order partial differential equation for free vibration of the beam resting on elastic foundation subjected to bending moment, shear and axial compressive load is obtained by using Winkler hypothesis and small displacement theory. It is assumed that the material is linear-elastic, and that axial load and modulus of subgrade reaction to be constant. In the analysis, shear and axial load effects are considered. The frequency factors of the beam are calculated by using DTM due to the values of relative stiffness; the results are presented in graphs and tables.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1996년도 가을 학술발표회 논문집
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• pp.221-229
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• 1996

An analytical method based on the nonlinear layered finite element method is used to simulate the load-deflection behavior of strengthened beam. Beams considered in this study are the ones strengthened either with external steel plate or Carbon Fiber Reinforced Plastic (CFRP) sheets bonded to the overlay soffit or with reinforcing rebars in the overlay. The theoretically obtained load-deflections and strains of the strengthened beam are compared to the corresponding experimental values. Comparing the approximate measures on the cumulative slips, efficiencies of the repairing techniques are evaluated. Parametric studies are, then, peformed using the developed model to investigate the effects of design variables on the overal flexural behavior of the strengthened beam. Simply supported beams under monotonically increasing symmetrical loads are considered exclusively.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2003년도 추계학술대회논문집
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• pp.958-963
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• 2003

In this paper a dynamic behavior of simply supported cracked pipe conveying fluid with the moving mass is presented. Based on the Timoshenko beam theory, the equation of motion can be constructed by using the Lagrange's equation. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments i.e. the crack is modelled as a rotational spring. This flexibility matrix defines the relationship between the displacements and forces across the crack section and is derived by applying fundamental fracture mechanics theory. And the crack is assumed to be in th first mode of fracture. As the depth of the crack and velocity of fluid are increased the mid-span deflection of the pipe conveying fluid with the moving mass is increased. As depth of the crack is increased, the effect that the velocity of the fluid on the mid-span deflection appears more greatly.

• Structural Engineering and Mechanics
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• 제15권6호
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• pp.705-716
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• 2003

Gradient elastic flexural beams are dynamically analysed by analytic means. The governing equation of flexural beam motion is obtained by combining the Bernoulli-Euler beam theory and the simple gradient elasticity theory due to Aifantis. All possible boundary conditions (classical and non-classical or gradient type) are obtained with the aid of a variational statement. A wave propagation analysis reveals the existence of wave dispersion in gradient elastic beams. Free vibrations of gradient elastic beams are analysed and natural frequencies and modal shapes are obtained. Forced vibrations of these beams are also analysed with the aid of the Laplace transform with respect to time and their response to loads with any time variation is obtained. Numerical examples are presented for both free and forced vibrations of a simply supported and a cantilever beam, respectively, in order to assess the gradient effect on the natural frequencies, modal shapes and beam response.

• International Journal of Concrete Structures and Materials
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• 제11권1호
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• pp.1-16
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• 2017

The compression or tension-controlled failure mode of concrete beams prestressed with unbonded FRP tendons is governed by the relative amount of prestressing tendon to the balanced one. Explicit assessment to determine the balanced reinforcement ratio of a beam with unbonded tendons (${\rho}^U_{pfb}$) is difficult because it requires a priori knowledge of the deformed beam geometry in order to evaluate the unbonded tendon strain. In this study, a theoretical evaluation of ${\rho}^U_{pfb}$ is presented based on a concept of three equivalent rectangular curvature blocks for simply supported concrete beams internally prestressed with unbonded carbon-fiber-reinforced polymer (CFRP) tendons. The equivalent curvature blocks were iteratively refined to closely simulate beam rotations at the supports, mid-span beam deflection, and member-dependent strain of the unbonded tendon at the ultimate state. The model was verified by comparing its predictions with the test results. Parametric studies were performed to examine the effects of various parameters on ${\rho}^U_{pfb}$.

• Steel and Composite Structures
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• 제27권6호
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• pp.777-788
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• 2018

An investigation on the thermal buckling resistance of simply supported FGM beams having parabolic-concave thickness variation and temperature dependent material properties is presented in this paper. An analytical formulation based on the first order beam theory is derived and the governing differential equation of thermal stability is solved numerically using finite difference method. a function of thickness variation is introduced which controls the parabolic variation intensity of the beam thickness without changing its original material volume. The results showed the high importance of taking into account the temperature-dependent material properties in the thermal buckling analysis of such critical beam sections. Different Influencing parametric on the thermal stability are studied which may help in design guidelines of such complex structures.

• Structural Engineering and Mechanics
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• 제55권4호
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• pp.871-884
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• 2015

In the present study, separate and combined effects of rotary inertia, shear deformation and material non-homogeneity (MNH) on the values of natural frequencies of the simply supported beam are examined. MNH is characterized considering the parabolic variations of the Young's modulus and density along the thickness direction of the beam, while the value of Poisson's ratio is assumed to remain constant. At first, the equation of the motion including the effects of the rotary inertia, shear deformation and MNH is provided. Then the solutions including frequencies of the first three modes for various combinations of the parameters of the MNH, depth to length ratios, and shear corrections factors are reported. To show the accuracy of the present results, two comparisons are carried out and good agreements are found.

• Advances in nano research
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• 제5권2호
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• pp.113-126
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• 2017

This paper proposes a new nonlocal higher-order hyperbolic shear deformation beam theory (HSBT) for the static bending and vibration of nanoscale-beams. Eringen's nonlocal elasticity theory is incorporated, in order to capture small size effects. In the present model, the transverse shear stresses account for a hyperbolic distribution and satisfy the free-traction boundary conditions on the upper and bottom surfaces of the nanobeams without using shear correction factor. Employing Hamilton's principle, the nonlocal equations of motion are derived. The governing equations are solved analytically for the edges of the beam are simply supported, and the obtained results are compared, as possible, with the available solutions found in the literature. Furthermore, the influences of nonlocal coefficient, slenderness ratio on the static bending and dynamic responses of the nanobeam are examined.

• Structural Engineering and Mechanics
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• 제76권3호
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• pp.413-420
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• 2020

Considering inverse cotangential shear strain function, the present paper studies nonlinear stability of nonlocal higher-order refined beams made of metal foams based on Chebyshev-Ritz method. Based on inverse cotangential beam model, it is feasible to incorporate shear deformations needless of shear correction factor. Metal foam is supposed to contain different distributions of pores across the beam thickness. Also, presented Chebyshev-Ritz method can provide a unified solution for considering various boundary conditions based on simply-supported and clamped edges. Nonlinear effects have been included based upon von-karman's assumption and nonlinear elastic foundation. The buckling curves are shown to be affected by pore distribution, geometric imperfection of the beam, nonlocal scale factor, foundation and geometrical factors.

• Structural Engineering and Mechanics
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• 제72권2호
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• pp.257-273
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• 2019

In this paper, the mechanical behaviour of functionally graded material beams is studied using the 3D Saint-Venant's theory, in which the section is free to warp in and out of its plane (Poisson's effects and out-of-plane warpings). The material properties of the FGM beam are distributed continuously through the thickness by several distributions, such as power-law distribution, exponential distribution, Mori-Tanaka schema and sigmoid distribution. The proposed method has been applied to study a simply supported FGM beam. The numerical results obtained are compared to other models in the literature, which show a high performance of the 3D exact theory used to describe the stress and strain fields in FGM beams.