Influence Of Warping Research Articles

Influence of Warping on Bearing Capacity of Steel I-Beam with Non-Fork Support

The European Standard 3 does not provide a direct answer about how to verify the bearing capacity of a beam with non-fork support. For a pinned beam it assumes, that there is no constraint on lateral bending and warping or full restraint. But in the most of design cases the constrainment is somewhere between them. There are some guidelines in scientific literature and computer programs that enhance the calculation of the value of a Critical Moment (which governs the Lateral-Torsional Buckling and as a result – the Bearing Capacity of Bending) for a flexible support. But there is no official information about which of method is the best for a certain case. To confine the variables only an influence of warping on a Lateral-Torsional Buckling was taken into the consideration. It was created by adding an endplate on one or both ends of a beam. Few approaches to calculate the Critical Moment were compared. A beam based on cross section of IS-300/150/10.7/7.1 with the length of 5.0m were taken into the consideration. The first method is the General Formula from pre-code of the European Standard 3 (1992) with the additional equations for calculating the stiffness of endplates according to Lindner (1994). The second approach bases on the General Formula, but with modification of C1 factor derived by Lopez, Yong and Serna (2006). The third method uses very similar equation to the G. F., but with other value of C1 factor. It was derived by Lindner (1994). Those approximated formulas were compared with Finite Element Method calculation. It was conducted using three different computer programs. In the first one, ABAQUS CAE, the spatial shell model of a beam was created. An influence of a type of a discretisation on results was validated. Secondly, LTBeamN, the dedicated program for calculating the value of Critical Moment written by CTICM, was used. Thirdly, computing was made using the RFEM – an application for civil engineers which allows to create models of beams with seven degrees of freedom in each node. The results show that an endplate’s influence on a value of a Critical Moment is significant. Even the thinnest plates can noticeably increase the bearing capacity of a cross-section. But over the certain value of plate’s thickness there is no further growth of the Critical Moment value. The results from equations based on the General Formula and calculations with the FEM are approximate for endplates below 4.0cm of thickness. It is very important to take few approaches to discretise the model of beam with endplates using ABAQUS, because there could be a major difference between them in outcomes.

Measurement and modelling of torsional warping free vibrations of beams with rectangular hollow cross-sections

This contribution contains the results of experimental measurements and modelling of torsional warping free vibrations of beams with rectangular hollow cross-sections. The experimental results are compared with results from a semi-analytical method, proposed by the authors, and from Finite Element (FE) computations by means of a standard commercial code. In these calculations, beam, solid, and shell elements are used. The semi-analytical calculations are based on the analogy between second-order beam theory, including consideration of the shear force deformation effect, and non-uniform torsion, considering the Secondary Torsion Moment Deformation Effect (STMDE). The influence of warping and of the STMDE on the torsional eigenfrequencies and eigenforms is evaluated. The difference between the measured and calculated eigenfrequencies is investigated and quantified.

Influence of Warping on Modal Parameters of Thin-walled Channel Section Steel Beam

In this study, free vibration analysis of thin-walled channel section beam including warping effects has been carried out using Finite element method (FEM) and compared with experimentally measured results. Results reveal that natural frequencies of the system decrease on exclusion of warping in the analysis. Also, it has been observed that the difference between higher mode shapes were significantly high when theoretically obtained mode shapes considering warping and without warping were compared. Thereafter, the Modal Assurance Criterion (MAC) plot is presented to show the difference between the mode shapes with and without consideration of warping stiffness.

Flexural-torsional buckling tests of cold-formed lipped channel beams under restrained boundary conditions

In this paper, tests on flexural buckling (Lateral-Torsional) of Cold-Formed Steel (CFS) lipped Channel beams under restrained boundary conditions are described Two point loading for flexural tests have been established for 3.0 m span to obtain uniform bending moment. The section sizes selected for testing are 100 × 50 × 10 mm, 100 × 50 × 15 mm and 100 × 50 × 20 mm with 1.6 mm and 2.0 mm thickness for the investigation. Carefully designed loading and support systems were used in the tests to apply gravity load through the web of the section and to ensure that simply supported ends were established. The test results are compared in the BS5950: Part 5 and IS code 801-1975. The influence of warping and torsional restraints on flexural capacity is presented. The influence of buckling length for different boundary conditions proposed by Rhodes was considered to calculate critical flexuraltorsional buckling moment.

Anisotropic intrasubband hole scattering by polar optical phonon modes in thin GaAs/AlxGa1−xAs quantum wells

A theoretical investigation of the hole – polar optical phonon scattering processes in thin GaAs/AlxGa1−xAs quantum wells is carried out at room temperature for both the confined and interface phonon modes within the dielectric continuum model framework. For high accuracy, the model for the hole dispersion uses the 6×6 Luttinger–Kohn Hamiltonian. Detailed and extensive calculations based on this model show that the rates for intra-subband scattering processes differ significantly from those of bulk GaAs because of quantization and reduced dimensionality. Moreover, the study of scattering as a function of hole energy shows that the trend of the scattering rates is governed mostly by (i) overlap integrals and (ii) the density of the final states to which the hole scatters. The influence of warping, in the hole energy dispersion, on the phonon scattering rates is also explored and found to be important when the initial hole energy is high. Our calculations show evidence of strong anisotropy in the scattering rates especially for processes involving the heavy hole subband, which anisotropy is in fact quite important and far from being negligible.

Nonlinear forced vibrations and static deformations of 3D beams with rectangular cross section: The influence of warping, shear deformation and longitudinal displacements

The geometrically nonlinear vibrations of beams with rectangular cross section, which may experience longitudinal, torsional and bending deformations, in any plane, are investigated by the p-version finite element method. Two main models are used: one of them is based on Bernoulli–Euler theory for beam bending and the other is based on Timoshenko theory; both models assume that the cross section rotates as a rigid body and is free to warp in longitudinal direction, as in Saint-Venants’s theory for torsion. The geometrical nonlinearity is taken into account by considering Green’s strain tensor and the importance of the longitudinal displacements of quadratic order, which are most often neglected in the strain–displacement relation, is here examined. Generalized Hooke’s law is used and the equation of motion is derived by the principle of virtual work. The importance of the warping function is analysed for different rectangular cross sections, and it is shown that its consideration can be fundamental to obtain correct results. Then, it is shown that the linearization of the trigonometric functions related with the twist angle, which is usually applied in the displacement field in models based on Saint-Venant’s hypothesis, should be done in the strain–displacement relations. Comparisons of the models for 3D beams based on Bernoulli–Euler’s and Timoshenko’s theories is presented. It is shown that if the rotations along the transverse axes are directly approximated by the respective derivatives of the transverse displacement functions, as is assumed in the model presented here that is based on Bernoulli–Euler’s theory, the additional shear stresses that appear when the bending and torsion motions are coupled, lead to wrong results. Finally, taking into account accuracy and simplicity, a model is chosen and employed to investigate the nonlinear forced vibrations of beams using direct integration of the equations of motion in the time domain. Examples of bending–torsion couplings due to the nonlinear terms are presented in dynamical problems.

1154 グリーンテープレーザ焼結チタン人工骨の形状精度と強度の向上

Recently, titanium is known as a hopeful material of the artificial bone. However, a cutting or casting procedure is difficult since its thermal and oxidizing activation are very high. In this research, the artificial bone made from titanium is fabricated by using Green Tape Laser Sintering method (GTLS). Any machining procedures are not needed to fabricate the titanium parts. In order to develop accuracy and strength of the artificial bone, we have examined the laser parameters in sintering procedure. Consequently the influence of warping has improved by changing the laser scanning path. The strength of a single layer can be increased by enlarging pulse width. During the laminating procedure, the warping influence can be reduced by alternating the laser sintering procedure by using low and high energy.