Narrow Rectangular Beam Research Articles

Lateral torsional buckling of rectangular beams using variational iteration method

Lateral torsional buckling is the main failure mode that controls the design of “slender” beams; that is, the beams which have greater major axis bending stiffness than minor axis bending stiffness or the beams which have considerably large laterally unsupported lengths. Since the buckling equations for beams are usually much more complex than those for columns, most of the analytical studies in literature on beam buckling are concentrated on simple cases. This paper shows that complex beam buckling problems, such as lateral torsional buckling of narrow rectangular cantilever beams whose minor axis flexural and torsional rigidities vary exponentially along their lengths, can successfully be solved using variational iteration method (VIM). The paper also investigates the effectiveness of three VIM algorithms, two of which have been proposed very recently in solving lateral torsional buckling equations. Analysis results show that all iteration algorithms yield exactly the same results in all studied problems. As far as the computation times and spaces are concerned, however, one of these algorithms, called variational iteration algorithm II, is found to be superior than the others especially in lateral torsional buckling problems where the beam rigidities vary along the beam length. Key words: Lateral torsional buckling, narrow rectangular beam, tapered beam, variable rigidity, variational iteration algorithms, variational iteration method.

Nonlinear Elastic Nonuniform Torsion

This paper is concerned with large twist rotations of elastic thin-walled open section beams that induce additional longitudinal stresses, which exert nonlinear “Wagner” stiffening torques. The nonlinear behavior of a narrow rectangular beam is first analyzed and then extended to elastic beams of general cross section. Expressions are derived for the nonlinear Wagner section constants for narrow rectangular sections, doubly symmetric I sections, and monosymmetric equal angle sections. A general finite element method of analyzing nonlinear torsion is described, and used to develop a computer program FENLT. This program can analyze a beam of general cross section under any combination of concentrated and distributed torques and concentrated bimoments, and which may be prevented from twisting or warping at points along its length. The program is validated by comparison with closed form or numerical solutions for a number of simple examples.

Lateral buckling of narrow rectangular beams containing openings

The paper deals with the critical lateral buckling load of deep slender rectangular beams containing openings along the centre-lines of the beams. The numerical method proposed to predict the critical load is outlined in detail; cantilever beams and simply supported beams are considered. The critical loads evaluated numerically using the energy approach are compared with those values obtained experimentally. The study shows good agreement between the values obtained numerically and experimentally.

Optimal design of tapered beams for maximum buckling strength

This paper is concerned with the determination of the optimal linear taper of a narrow rectangular beam that will maximize the critical buckling load subject to a volume constraint. The beam considered is either cantilevered or simply supported and is under a uniformly distributed load or a point load. The solution to the problem is obtained by two independent approaches. Whilst one of the approaches is based on the Timoshenko energy technique, the other is based on a Lagrange multiplier and the gradient expression of problem.

Post-Buckling of Redundant I-Beams

It is shown that while redundant I-beams have similar potential post-buckling reserves of strength to those possessed by redundant rectangular beams, their decreased section slendernesses requires great post-buckling deformations to take place before these reserves of strength can be realized. It is concluded that redundant I-beams are less likely to achieve their potential post-buckling strengths than narrow rectangular beams because of premature yielding, and that the elastic post- buckling behavior of steel I-beams will rarely be important, except when the member and section slendernesses and the yield strength are high and large deformations are acceptable. The reliability of Southwell Plot methods of predicting the experimental critical loads of redundant I-beams is investigated and the methods are shown to be adequate provided that the deflections are only small to moderate.

Analysis of strain in fibre-reinforced materials

Techniques such as birefringent coatings, moiré, brittle lacquers, strain gauge, and holography can all be used on composites since they enable surface strains to be measured. However, a correct and accurate interpretation of results obtained by these methods is essential. The significance of this is demonstrated by observing the effect of the differences between the directions of principal stresses and strains. In addition the suitability of the birefringent-coating technique for application to fibre-composite materials is examined by considering the three-point flexure of a narrow rectangular beam of span/depth ratio 6 in some detail. Within the framework of the assumptions that stresses will be distributed in accordance with elementary bending theory and that the appropriate stress-strain relations for orthotropic materials are applicable, isochromatic and isoclinic patterns are predicted and compared with experimental results. A more precise solution is also obtained by employing the finite-element displacement method. From a qualitative standpoint the comparison is found to be good although more research is required before the birefringent-coating technique can be used in situations demanding a reliable quantitative appreciation.

On the Lateral Buckling of a Tapered Narrow Rectangular Beam

On the Lateral Buckling of a Tapered Narrow Rectangular Beam