Behavior Of Thin-walled Beams Research Articles

Effect of local stiffeners and warping constraints on the buckling of symmetric open thin-walled beams with high warping stiffness

Local stiffeners affect the behaviour of thin-walled beams (TWBs). An in-house code based on a one-dimensional model proved effective in several instances of compressive buckling of TWBs but gave counterintuitive results for locally stiffened TWBs. To clarify the matter, we investigated TWBs with multi-symmetric double I cross-section, widely used in practical applications where high bending stiffness is required. Several samples were manufactured and stiffened on purpose, closing them over a small portion of the axis at different places. The samples were tested with end constraints accounting for various warping conditions. The experimental and numerical outputs from a commercial FEM code gave a key to overcome the unexpected results by the in-house code, paving the way for further studies.

Simulating Twisting Behavior of Thin-Walled Beams Using Simplified Finite Element Models

This paper develops simplified finite element (FE) models for simulating twisting behavior of thin-walled beams with box and hexagonal cross-sections. The twisting behavior of the thin-walled beam models under large plastic rotation is investigated and existing plastic deformation theories are applied in developing the simplified FE models. The developed simplified models are composed of beam elements and a nonlinear rotational spring element, which simulates the twisting behavior and stores the energy during the large plastic rotation. Accuracy and efficiency of the simplified models are validated through numerical analyses and the results correlate to those obtained from detailed models. The analyses and comparisons verify that the simplified models correctly reflect the thin-walled beam's twisting buckling as the detailed models did.

Large torsion finite element model for thin-walled beams

Behaviour of thin-walled beams with open section in presence of large torsion is investigated in this work. The equilibrium equations are derived in the case of elastic behaviour without any assumption on torsion angle amplitude. This model is extended to finite element formulation in the same circumstances where 3D beams with two nodes and seven degrees of freedom per node are considered. Due to large torsion assumption and flexural–torsional coupling, new matrices are obtained in both geometric and initial stress parts of the tangent stiffness matrix. Incremental-iterative Newton–Raphson method is adopted in the solution of the nonlinear equations. Many applications are presented concerning the nonlinear and post-buckling behaviour of beams under torsion and bending loads. The proposed beam element is efficient and accurate in predicting bifurcations and nonlinear behaviour of beams with asymmetric sections. It is proved that the bifurcation points are in accordance with nonlinear stability solutions. The convenience of the model is outlined and the limit of models developed in linear stability is discussed.

Experiments on chaotic vibrations of a post-buckled beam with an axial elastic constraint

To clarify chaotic behavior of thin walled beams, detailed experimental results are presented on chaotic vibrations of a post-buckled beam subjected to periodic lateral acceleration. A thin steel beam of thickness 0.198 mm, breadth 12.7 mm and length 106 mm is used as a test beam. Both ends of the beam are clamped for deflection. One end of the beam is elastically constrained by an axial spring. The beam is compressed to the post-buckled configuration by the axial spring. First, characteristics of restoring force and natural frequency of the beam are obtained. Dynamic nonlinear responses of the beam are measured under periodic acceleration. In specific frequency regions, chaotic responses are generated. The chaotic responses are examined carefully with the Poincaré maps, the Fourier spectra, the maximum Lyapunov exponents and the principal component analysis.The post-buckled beam shows the soften-and-hardening characteristics of restoring force. The dominant chaotic responses of the beam are bifurcated from the sub-harmonic resonances of 1 2 and 1 3 orders with the lowest mode of vibration. Changing the exciting frequency gradually, dynamical transition behaviors from these steady-state sub-harmonic response to the chaotic responses are precisely inspected by the Poincaré projection. The maximum Lyapunov exponent of the former chaotic response of 1 2 order is larger than that of the latter chaotic response of 1 3 order. The principal component analysis predicts that the contribution of the lowest mode of vibration to the chaos is dominant among other contributions of multiple vibration modes.

Non-uniform torsional behavior and stability of thin-walled elastic beams with arbitrary cross sections

In this paper, the analysis of the behavior of thin-wa lled beams, derived from Prokić’s work, is carried out by using beam theory with a single warping function valid for arbitrary form of cross sections, without any distinction between open and closed profiles and without using sectorial coordinates. The finite element method is used and numerical examples show the accuracy of the solution by comparison with other numerical or analytical results. For the stability analysis, analytical and numerical calculations of critical loads are given for beams submitted to bending moment and centrally applied forces. Equilibrium equations are established from the principle of virtual work. Critical loads are calculated by considering that a structure already in equilibrium reaches instability if there is one or more than one equilibrium position for the same loading. Results with this formulation are compared to those obtained with classical warping functions.

The influence of the in-plane warping on the behavior of thin-walled beams

The paper presents a theoretical study of the importance of the in-plane deformation on the structural behavior of thin-walled isotropic and composite beams which are subjected to bending and torsional moments. To separate the effects of the out-of-plane warping and the in-plane warping, the overall solution methodology is based on a generic combination of two complementary “inner” and “outer” solutions. The inner model is based on numerical optimization tools which are employed to determine the in-plane deformation that will ensure a stationary (minimum) state of the total potential energy. The outer model performs global solution for cross-sections that are rigid in their own plane but includes the out-of-plane warping. The overall solution is capable of determining the influence of the in-plane warping on any existing approximate numerical scheme that do not include this deformation component. The results correlate well with known analytic solutions for isotropic tubes under pure bending. A parametric study of the relative importance of the in-plane warping as a function of the geometry and the loading parameters in rectangular thin-walled isotropic and composite beams is also presented along with some buckling considerations.

VIBRATIONS OF BEAMS PRESTRESSED BY INTERNAL FRICTIONLESS CABLES

A greased cable is positioned along a generic curve in the interior of a beam and is anchored to the beam at its extreme points. The absence of friction permits a relative slipping between the cable and beam at intermediate points and this makes the cable strain dependent on the global deformation of the beam. Such a system permits controlling the beam state of stress and strain by assigning a predetermined traction force on the cable. This paper proposes a formulation of the system dynamics by defining the balance conditions describing the infinitesimal motions in the neighbourhood of a known balanced static configuration in order to evaluate the effect due to the presence of the stretched cable on the motion and free vibrations of the system. The kinematical model adopted for the beam permits a sufficiently accurate description of the behavior of thin walled beams and the cable strain is obtained as a functional of global deformation. Some qualitative aspects concerning the problem formulation and the dynamical behavior are stated. An applicative example referring to a case of interest shows that the state of stress obtained by stretching the cable notably influences only a reduced set of vibration modes, determined by the path geometry and cable force. Such aspects of the problem can be of interest in structural identification.

Numerical analysis of thin walled beams with internal unbonded cables by the Ritz method

The authors analyze the behavior of thin walled beams crossed by internal stretched cables anchored at their ends but free to slip without friction along their path, by using a previously presented model. The guidelines for the numerical solution of the linear elastic problem and the stability analysis are presented in general form and applied to a class of problems of technical interest. The numerical analysis examines the case of simply supported beam with symmetric open cross section, crossed by a cable placed on rectilinear or parabolic paths lying in the symmetry plane, assuming as problem variables the beam stiffness, the parameters describing the cable path and the cable traction force. This permitted evidencing some aspects of the problem of interest in structural engineering, by showing the relations between stress increments of beam and cable under external force and the complex relations arising between beam bending, torsional and shear stiffness, cable path, cable traction force and external load in the stability analysis.