The Effects of Web Deformation on the Torsion of I-Beams

1944 ◽  
Vol 11 (1) ◽  
pp. A35-A40
Author(s):  
J. N. Goodier ◽  
M. V. Barton
Keyword(s):  
Cross Section ◽  
Numerical Examples ◽  
End Conditions ◽  
Bending Stresses ◽  
Nonuniform Torsion ◽  
Stress And Deformation ◽  
The Web

Abstract An analysis of the I-beam in nonuniform torsion, as for instance, when a built-in end or section of symmetry is prevented from warping, is made which includes not only the bending of the flanges in their own planes (as considered previously by Timoshenko) but also a deformation of the web cross section. This extends the theory to thinner webs and permits the satisfaction of more general end conditions. Numerical examples worked out for three sections, differing in web thickness only, show that the stress and deformation are significantly modified by the web flexibility when the web is sufficiently thin, and that there are then bending stresses in the web which may be larger than the bending stresses in the flanges. Only the unbuckled state of the web is considered.

scholarly journals Detection of multiple cracks in a beam by means natural frequencies of transverse vibrations

2020 ◽  
pp. 19-26
Author(s):  
Иван Михайлович Лебедев ◽  
Ефим Ильич Шифрин
Keyword(s):  
Arbitrary Number ◽  
Natural Frequencies ◽  
Multiple Cracks ◽  
Transverse Cracks ◽  
Numerical Examples ◽  
Transverse Vibrations ◽  
End Conditions

Рассматривается задача обнаружения множественных, поперечных трещин в стержне с помощью собственных частот поперечных колебаний. В недавней статье авторов доказано, что любое количество трещин однозначно восстанавливается по трем спектрам, отвечающим трем различным типам краевых условий. В статье также предложен алгоритм идентификации повреждений, вносимых трещинами. Помимо этого, высказано предположение, что для однозначной идентификации трещиноподобных дефектов на самом деле достаточно знать два спектра. Для проверки этого предположения разработана модификация предложенного ранее численного алгоритма. Рассмотрены численные примеры. Полученные результаты дают основание полагать, что высказанное предположение справедливо. A problem of detection of multiple transverse cracks in a beam by means of natural frequencies of transverse vibrations is considered. It is proved in the recent paper of the authors that an arbitrary number of cracks can be uniquely determined by three spectra corresponding to three types of the end conditions. An algorithm of reconstruction the damages corresponding the cracks is also developed. In addition, it was assumed that the cracks can be detected using only two spectra. To verify this supposition a modification of the previously developed algorithm is proposed. Numerical examples are considered. The obtained results confirm the assumption.

scholarly journals The creation of a computational model of corrugated beams using the author’s program “GOPRO”

2018 ◽  
Vol 251 ◽  
pp. 04007 ◽  
Author(s):  
Vadim Alpatov ◽  
Alexey Lukin ◽  
Irina Laguta
Keyword(s):  
Finite Element ◽  
Computational Model ◽  
Cross Section ◽  
Geometrical Shape ◽  
File Format ◽  
Element Mesh ◽  
Automated Generation ◽  
Numerical Studies ◽  
Geometrical Scheme ◽  
The Web

The program «Gofro» is intended for the automated generation of data on the geometrical scheme of the beam with corrugated or plane web for further use in design complexes. The program has got a window interface, and it consists of one module for the input of feed da-ta, for calculation and for the display of its results in txt file format. The program offers a possibility to choose the outline of the structure, the profile of the web, the type of cross-section, and to set other parameters of the structure. When building up the model with the help of the author program «Gofro» and GMSH preprocessor for the automatic genera-tion of finite element mesh, the correctness of geometrical shape of elements is monitored by the algorithms that are input in the preprocessor. The author compares the time re-quired to create the models using the author program and GMSH preprocessor and using the standard resources of «Lira» software system. The authors performed numerical studies of various I-beams created in the program «GOPRO».

Inertial waves in a rotating spherical shell

1997 ◽  
Vol 341 ◽  
pp. 77-99 ◽  
Author(s):  
M. RIEUTORD ◽  
L. VALDETTARO
Keyword(s):  
Spherical Shell ◽  
Cross Section ◽  
Shear Layers ◽  
Inertial Waves ◽  
Ekman Number ◽  
Distribution Of Eigenvalues ◽  
Simple Rules ◽  
Meridional Cross Section ◽  
Zero Viscosity ◽  
The Web

The structure and spectrum of inertial waves of an incompressible viscous fluid inside a spherical shell are investigated numerically. These modes appear to be strongly featured by a web of rays which reflect on the boundaries. Kinetic energy and dissipation are indeed concentrated on thin conical sheets, the meridional cross-section of which forms the web of rays. The thickness of the rays is in general independent of the Ekman number E but a few cases show a scaling with E1/4 and statistical properties of eigenvalues indicate that high-wavenumber modes have rays of width O(E1/3). Such scalings are typical of Stewartson shear layers. It is also shown that the web of rays depends on the Ekman number and shows bifurcations as this number is decreased.This behaviour also implies that eigenvalues do not evolve smoothly with viscosity. We infer that only the statistical distribution of eigenvalues may follow some simple rules in the asymptotic limit of zero viscosity.

The Scattering Waves by Two Spheres in Solid

2013 ◽  
Vol 423-426 ◽  
pp. 1640-1643
Author(s):  
Yan Ru Zhang ◽  
Pei Jun Wei
Keyword(s):  
Wave Function ◽  
Cross Section ◽  
Spherical Wave ◽  
Addition Theorem ◽  
Wave Functions ◽  
Interface Condition ◽  
Elastic Sphere ◽  
Numerical Examples ◽  
Transmitted Waves ◽  
Expansion Coefficients

The scattering waves by two elastic spheres in solid are studied. The incident wave, the scattering waves in the host and the transmitted waves in the elastic spheres are all expanded in the series form of spherical wave functions. The total waves are obtained by addition of all scattered waves from individual elastic sphere. The addition theorem of spherical wave function is used to perform the coordinates transform for the scattering waves from different spheres. The expansion coefficients of scattering waves are determined by the interface condition between the elastic spheres and the solid host. The scattering cross section is computed as numerical examples.

Stresses and deformations in overlapped diesel engine crankshafts, Part 2: Evaluation of results

1998 ◽  
Vol 212 (4) ◽  
pp. 255-270 ◽  
Author(s):  
I Bickley ◽  
V D'Olier ◽  
H Fessler ◽  
T. H. Hyde ◽  
N. A. Warrior
Keyword(s):  
Diesel Engine ◽  
Stress Concentration ◽  
Cross Sections ◽  
Shear Stresses ◽  
Previous Issue ◽  
Rectangular Section ◽  
Bending Stresses ◽  
Concentration Factors ◽  
Stress Concentration Factors ◽  
The Web

The extensive results presented in Part 1 (in the previous issue*) have been supplemented and analysed further. A large number of cross-sections which could be reasonably used to calculate nominal stresses has been listed and evaluated. An inclined (flat, rectangular) section through the web is shown to be the best to calculate nominal stresses due to torsion, pure radial bending and bending due to crankpin forces; its width is h (see Fig. 1), the length of the shortest line joining crankpin and journal fillets in the plane of symmetry. Stress concentration factors based on these nominal stresses show only modest scatter from single curves for crankpin and journal fillets for torsion and radial bending. Predictions using the most commonly used method underestimate shear stresses due to torsion and overestimate bending stresses.

Numerical Study of Cracked Titanium Shell under Compression

2011 ◽  
Vol 264-265 ◽  
pp. 490-495
Author(s):  
F. Ayari ◽  
Ali Zghal ◽  
E. Bayraktar
Keyword(s):  
Cylindrical Shell ◽  
Stress Intensity ◽  
Numerical Study ◽  
Applied Pressure ◽  
Economic Feasibility ◽  
Loading Conditions ◽  
Thin Cylindrical Shell ◽  
Bending Stresses ◽  
Stress And Deformation ◽  
Equivalent Loading

In many industrial conditions, light thin titanium shells are well used under various severe loading conditions. It is of interest to know the real conditions that govern the instability of a cracked panel subject to buckling loads in order to conserve as maximum as possible the strength of the structure. Several parameters can be varied in order to achieve this objective. The aim of this study is to determine the evolution of these parameters in order to achieve optimal crack propagation conditions while keeping these parameters within “reasonable” limits of physical and economic feasibility. For the purpose of the current study the considered structure can be regarded as thin cylindrical shell of radius r, thickness t with an initial through crack of length a. The titanium cylindrical shell is sealed on one edge and compression is applied on the other. An additional applied pressure can generates a stress and deformation field around the crack tip that has bending stresses and membrane stresses and appears as a bulge around the crack area. This paper give details of a simulation with FEA numerical analysis that determine governing instability conditions of a Titanium shell under particular loading conditions and to put in light the effect of bulging on the stress intensity factor at the crack tips. This bulging factor measures the severity of the stress intensity in the bulged crack compared to a plane shell subjected to equivalent loading conditions.

Rolling Force Research on Cogging Rolling of H-Beam

2010 ◽  
Vol 450 ◽  
pp. 87-90
Author(s):  
Qin Qin ◽  
Di Ping Wu ◽  
Jing Jing Li ◽  
Yong Zang
Keyword(s):  
Cross Section ◽  
Rolling Force ◽  
Three Dimensional ◽  
Reduction Rate ◽  
Rolling Process ◽  
Fem Model ◽  
Mechanical Coupling ◽  
Simulation Results ◽  
H Beam ◽  
The Web

Due to the complexity of H-beam’s cross section, it is difficult to calculate the rolling force and force torque accurately using classic formulas conveniently when H-beams of new size are developed. This paper describes an investigation into the reversing process of H-beam using MARC software and compares the results with rolling data from the production line. A FEM model involving in three-dimensional, elastic-plastic and thermo-mechanical coupling has been established successfully to predict multi-pass rolling process. The analysis produces outputs such as deformation rules, rolling force and the web thickening. The influence of rolling reduction, the reduction rate between the web and flange are also discussed. The indications are that there is much difference between the measurement of rolling force and the rolling force calculated by using classic formulas. The reason is that real reduction during rolling process is much more than the scheduled one. A new revised method was suggested to calculate the rolling force. The simulation results show that this new method for calculating rolling force is feasible.

Research Status of Local Stability in the Web of Castellated Components

2013 ◽  
Vol 291-294 ◽  
pp. 1117-1121
Author(s):  
Wen Qian Yin ◽  
Lian Guang Jia ◽  
Bo Shao
Keyword(s):  
Numerical Simulation ◽  
Cross Section ◽  
Stability Problem ◽  
Local Stability ◽  
Economic Benefit ◽  
Simulation Analysis ◽  
Theoretical Research ◽  
Web Openings ◽  
The Web ◽  
Section Form

Castellated components have many advantages such as high bearing capacity, better bending stiffness, reasonable cross-section form and significant economic benefit. Castellated components are weakened by the reason of web openings, so it is more prone to appear local stability problem. Therefore, the researches of local stability in castellated components play a very important role in the application of the castellated components. In this issue, scholars at home and abroad do a lot of researches, including theoretical research, numerical simulation analysis and experimental research. But the research of castellated bending components are still in groping stage .That has seriously hampered the application and promotion of castellated components in China. So it is necessary to study the local stability of castellated components.

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