• Structural Engineering and Mechanics
• /
• v.24 no.2
• /
• pp.247-268
• /
• 2006

The parts of pile, above the soil and embedded in the soil are called the first region and second region, respectively. The forth order differential equations of both region for critical buckling load of partially embedded pile with shear deformation are obtained using the small-displacement theory and Winkler hypothesis. It is assumed that the behavior of material of the pile is linear-elastic and that axial force along the pile length and modulus of subgrade reaction for the second region to be constant. Shear effect is included in the differential equations by considering shear deformation in the second derivative of the elastic curve function. Critical buckling loads of the pile are calculated for by differential transform method (DTM) and analytical method, results are given in tables and variation of critical buckling loads corresponding to relative stiffness of the pile are presented in graphs.

• Structural Engineering and Mechanics
• /
• v.67 no.2
• /
• pp.185-206
• /
• 2018

This paper studies the non-axisymmetric 3D problem on the dynamics of the moving load acting in the interior of the hollow cylinder surrounded with elastic medium and this study is made by utilizing the exact equations of elastodynamics. It is assumed that in the interior of the cylinder the point located with respect to the cylinder axis moving forces act and the distribution of these forces is non-axisymmetric and is located within a certain central angle. The solution to the problem is based on employing the moving coordinate method, on the Fourier transform with respect to the spatial coordinate indicated by the distance of the point on the cylinder axis from the point at which the moving load acts, and on the Fourier series presentation of the Fourier transforms of the sought values. Numerical results on the critical moving velocity and on the distribution of the interface normal and shear stresses are presented and discussed. In particular, it is established that the non-axisymmetricity of the moving load can decrease significantly the values of the critical velocity.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2000.10a
• /
• pp.59-66
• /
• 2000

It is generally known that the lateral frequency( ω) of the vibration of a prismatic beam-column decreases according to the rele (equation omitted) (ω/sub 0/=natural frequency). In the cases of tapered members, the determination of P/ sub/ cr/(elastic critical load) and ω/ sub 0/ are not easy. Furthermore, the relationship between the compressive load and frequency can not be determined by the conventional analytical method. The axial force-frequency relationship of sinusolidally non-symmetrically tapered members with different shapes were investigated using the finite element method. To obtain the two eigenvalues, the axial thrust was increased step by step and the corresponding frequency was calculated. The result indicated that the axial thrust of the elastic critical load ratio and the square of the frequency ratio can be approximately represented in any case by a straight line. Finally, the linear relationship is also applicable to the sinusolidally non-symmetrically tapered member.

• Journal of KSNVE
• /
• v.8 no.2
• /
• pp.297-305
• /
• 1998

The finite element method is used for the study of the eigenvalue problems of partially fixed end beams with intermediate elastic supports. The elastic critical loads and natural frquencies of the beams are investigated by changing the numbers of elastic supports and their stiffness, and also by changing Kinney's fixity factor, $f_a$. The relationship between two eigenvalues is established by calculating the corresponding values of $(w/w_n)^2$ through changing $(P/P_{cr})$ values. The results of this study are as follows : (1) The elastic critical loads and natural frequencies of beams increase with increases in Kinney's fixity factor, $f_a$ and with the increased numbers of intermediate elastic supports. (2) The relationship between elastic critical loads and the natural frequencies of partially fixed end beams with intermediated elastic supports is $P/P_{cr} + (w/w_n)^2/ = 1$ without regard to Kinney's fixity factor, the stiffness of elastic supports, or the number of elastic supports.

• Structural Engineering and Mechanics
• /
• v.64 no.1
• /
• pp.1-10
• /
• 2017

The present paper deals with the free vibration and buckling problem with consideration of surface properties of circular nanobeams and nanoarches. The Gurtin-Murdach theory is used for investigating the surface effects parameters including surface tension, surface density and surface elasticity. Both linear and nonlinear elastic foundation effect are considered on the circular curved nanobeam. The analytically Navier solution is employed to solve the governing equations. It is obviously detected that the natural frequencies of a curved nanobeams is substantially influenced by the elastic foundations. Besides, it is revealed that by increasing the thickness of curved nanobeam, the influence of surface properties and elastic foundations reduce to vanished, and the natural frequency and critical buckling load turns into to the corresponding classical values.

• Computers and Concrete
• /
• v.26 no.1
• /
• pp.53-62
• /
• 2020

Concrete is the most widely used substance in construction industry, so it's been required to improve its quality using new technologies. Nowadays, nanotechnology offers new frontiers for improving construction materials. In this paper, we study the stability analysis of the Single Walled Carbon Nanotubes (SWCNT) reinforced concrete cylindrical shell embedded in elastic foundation using the Donnell cylindrical shell theory. In this regard, we propose a new explicit analytical formula of the critical buckling load which takes into account the distribution of SWCNT reinforcement through the thickness of the concrete shell using the U, X, O and V forms and the elastic foundation using Winkler and Pasternak models. The rule of mixture is used to calculate the effective properties of the reinforced concrete cylindrical shell. The influence of diverse parameters on the stability behavior of the reinforced concrete shell is also discussed.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 1999.04a
• /
• pp.252-259
• /
• 1999

One of the most important factors for a proper design of a slender compression member may be the exact determination of the elastic critical load of that member. In the cases of non-prismatic compression member, however, there are times when the exact critical load becomes impossible to determinate if one relies on the neutral equilibrium method or energy principle. Here in this paper, the approximate critical loads of symmetrically or non-symmetrically tapered members are computed by finite element method. The two parameters considered in this numerical analysis are the taper parameter, $\alpha$ and the sectional property parameters, m. The computed results for each sectional property parameter, m are presented in an algebraic equation which agrees with those by F.E.M The algebraic equation can be easily used by structural engineers, who are engaged in structural analysis and design of non-prismatic compression member.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 1999.10a
• /
• pp.421-428
• /
• 1999

The elastic critical load of a slender compression member plays an important role when the proper design of that member is required. For the tapered compression members, however, there are cases when the conventional neutral equililbrium or energy method can't be applied to the determination of critical loads of those members. In this paper, finite element method is applied to the approximate determination of the symmetrically tapered bars. Here in this paper, the bars are assumed to take sinusoidally changing shapes along their axes. The parameters considered in this study are taper parameter, $\alpha$ and the sectional property parameter, m. The computed results by finite element method are represented in the forms of algebraic equations. Regression technique is employed to determine the coefficients of algebraic equations. The critical loads estimated by the proposed algebraic equations coincide fairly well with those of finite element method.

• Structural Engineering and Mechanics
• /
• v.85 no.6
• /
• pp.825-835
• /
• 2023

The effective buckling length factor is an important parameter in the elastic buckling analysis of steel structures. The present article aims at developing a new method that allows the determination of the buckling factor values for frames. The novelty of the method is that it considers the interaction between the bracing and the elastic supports for asymmetrical frames in particular. The approach consists in isolating a critical column within the frame and evaluating the rotational and translational stiffness of its restraints to obtain the critical buckling load. This can be achieved by introducing, through a dimensionless parameter 𝜙_i, the effects of coupling between the axial loading and bending stiffness of the columns, on the classical stability functions. Subsequently, comparative, and parametric studies conducted on several frames are presented for assessing the influence of geometry, loading, bracing, and support conditions of the frame columns on the value of the effective buckling length factor K. The results show that the formulas recommended by different approaches can give rather inaccurate values of K, especially in the case of asymmetric frames. The expressions used refer solely to local stiffness distributions, and not to the overall behavior of the structure.

• Structural Engineering and Mechanics
• /
• v.13 no.3
• /
• pp.329-343
• /
• 2002

In this research, the dynamic stability of an orthotropic elastic conical shell, with elasticity moduli and density varying in the thickness direction, subject to a uniform external pressure which is a power function of time, has been studied. After giving the fundamental relations, the dynamic stability and compatibility equations of a nonhomogeneous elastic orthotropic conical shell, subject to a uniform external pressure, have been derived. Applying Galerkin's method, these equations have been transformed to a pair of time dependent differential equations with variable coefficients. These differential equations are solved using the method given by Sachenkov and Baktieva (1978). Thus, general formulas have been obtained for the dynamic and static critical external pressures and the pertinent wave numbers, critical time, critical pressure impulse and dynamic factor. Finally, carrying out some computations, the effects of the nonhomogeneity, the loading speed, the variation of the semi-vertex angle and the power of time in the external pressure expression on the critical parameters have been studied.