Stability Of Elastic Column Research Articles

Stability of elastic column with spring supports at both clamped ends

This paper analyzes the large deflections and stability of an elastic column. The column is supported by a spring at each of its clamped ends, and is also subject to a conservative compressive terminal force. The equilibrium equation is derived from the principle of the minimum total potential energy, and its solution is expressed using Jacobian elliptic functions. The stability is determined with the help of the Jacobi criterion, and the resulting bifurcation diagrams are also determined.

Elastic stability of columns with variable flexural rigidity under arbitrary axial load using the finite difference method

Elastic stability of columns with variable flexural rigidity under arbitrary axial load using the finite difference method

Critical load for buckling of non-prismatic columns under self-weight and tip force

The stability of elastic columns with variable cross-section under self-weight and concentrated end load is considered. A simple and easy-to-implement approach is suggested. Different end conditions are dealt with. The governing equation subject to associated boundary conditions for Euler–Bernoulli columns is transformed into an integral equation, and critical buckling load is then evaluated by seeking the lowest eigenvalue of the resulting integral equation. Numerical examples of the critical buckling load for prismatic and non-prismatic columns under self-weight and end force are given, and the effectiveness of this method for buckling analysis of tapered columns is validated. For several frequently encountered end supports, the influence of the taper ratio on the critical buckling load is discussed.

Elastic stability of columns on partial elastic foundations under subtangential loading

Divergence and flutter instability of a cantilevered beam on a partial elastic foundation subjected to a subtangential load at the free end are investigated. The dependence of divergence and flutter critical loads on the tangency coefficient is studied parametrically to illustrate the effects of the extent, position, and modulus of the partial foundation. Particular attention is paid to the stabilizing and destabilizing effects of the various parameters.

Buckling of stepped composite columns

The stability of elastic columns subjected to axial pressure is studied. An elastic multistepped column with rectangular cross sections are considered assuming that at the re-entrant corners of the column stable cracks are located. The influence of a crack on the loss of stability of the column is described by means of local flexibility and the function of compliance coupled with the stress intensity factor, which is known from the linear elastic fracture mechanics. A column with a single step is studied in more detail. The influence of crack location and length on the buckling load is assessed numerically.

Stability of elastic columns with periodic retarded follower forces

The objective of this work is to present a stability analysis for elastic columns under the influence of periodically varying follower forces whose orientation is retarded, i.e., depends on the position of the system at a previous time. One- and two-degree-of-freedom (dof) discretized systems under the simultaneous influence of both parametric excitation and time-delay, whose effects on such systems have previously been only considered separately, are studied. By employing an orthogonal polynomial approximation, the infinite-dimensional Floquet transition matrix associated with the time-periodic differential-delay system is approximated. The stability criteria that all the eigenvalues (Floquet multipliers) of this matrix must lie within the unit circle is then applied. The stability charts for different combinations of the remaining system parameters are shown, and the previously reported results for the special cases where either the parametric excitation or the time-delay vanishes are verified. Two cases, when the parametric forcing period is equal to or twice the delay period are taken into consideration in this work. For special cases of the single dof system, the numerical stability plots are verified by considering the analytical expressions for the corresponding stability boundaries for an analogous delayed Mathieu equation.

Stability chart for the delayed Mathieu equation

In the space of system parameters, the closedform stability chart is determined for the delayed Mathieu equation defined as (t)(cost)x(t) bx(t2). This stability chart makes the connection between t...

Story stability of semi-braced steel frames

This paper presents a practical method for the stability analysis of semi-braced steel frames with the effect of semi-rigid behaviour of beam-to-column connections being taken into account. The stability of a single column under different lateral restraining conditions is discussed first. Following the concept of story-based buckling, the stability equation for frames is then established. Lateral-bracing factors are introduced to characterize the effect of lateral bracing on the elastic stability of columns and frames. The procedure of evaluating column effective length factors for semi-braced steel frames is presented along with illustrated examples.

On the stability of an elastic column positioned on an elastic half space

Stability of a heavy elastic column loaded by a concentrated force at the top is analysed. It is assumed that the column is fixed to a rigid circular plate that is positioned on a homogeneous, isotropic, linearly elastic half-space. The constitutive equations for the column are assumed in the form that allows axial compressibility and takes into account the influence of shear stresses. It is shown that eigenvalues of the linearized equations determine the bifurcation points of the full non-linear system of equilibrium equations. Also, the type of bifurcation at the lowest eigenvalue is examined and shown that it could be both super-and sub-critical. The post-critical shape of the column is determined by numerical integration of the equilibrium equations.

Stability of columns subjected to an intermediate concentrated load with one end elastically restrained to move axially

The elastic stability of columns subjected to an intermediate concentrated load with one end elastically restrained to move axially is studied in this paper. The elastic axial restraint is represented by means of an axial spring. The finite element formulation including prebuckling load analysis and stability analysis is briefly described. Numerical results for several values of axial spring parameter and various positions of the intermediate concentrated load for four types of boundary conditions are obtained and are presented in the form of tables.

Vibration and stability of elastic columns under the combined action of uniformly distributed vertical and tangential forces

Vibration and stability of elastic columns subjected to uniformly distributed follower forces are investigated by means of the finite difference method for six typical cases of boundary conditions. A system of k finite difference equations is made of compact form by introducing the concept of a transfer matrix. The behavior of the eigenvalue curve is demonstrated in detail for various values of non-conservativeness parameter of the applied force. Precise stability maps are obtained from the eigen value analysis which determines the divergence and flutter limits.

Synthesis of two discrete vibratory systems using eigenvalue modification.

without an axial force. If the force P in each segment is specified, the analysis of either static or dynamic problems is straightforward. This is the case, for example, for beam-columns and for rotating beams. Problems in the elastic stability of columns can be handled by applying an arbitrary lateral force (or moment) and calculating the deflection with a series of successively greater axial forces. Southwell's method4 can then be applied to determine the buckling load. Incidentally, for a uniform column with any combination of end conditions, the exact expression for the elastic buckling load can be found directly from the stiffness matrix of the single beam segment. If the ends of the beam are restrained so as to prevent axial displacements, the axial force P is a nonlinear function of the lateral displacements. The customary assumption3 is that the deflection curve is a cubic. In this case, the axial force due to the stretching of the neutral axis of the beam segment shown in Fig. 3 is