Response and Stability of Square Tubes Under Bending

1997 ◽  
Vol 64 (3) ◽  
pp. 649-657 ◽  
Author(s):  
S. P. Vaze ◽  
E. Corona
Keyword(s):  
Analytical Model ◽  
Cross Section ◽  
Thickness Ratio ◽  
Pure Bending ◽  
Steel Tubes ◽  
Elastic Plastic ◽  
Plastic Steel

This paper addresses the response and stability of elastic-plastic steel tubes with square cross section under pure bending. An analytical model with sufficiently nonlinear kinematics to capture the development of ripples in the compression flange was developed. the results indicate that collapse of such tubes is imperfection sensitive for tubes with “high” height-to-thickness ratio (h/t), but the sensitivity decreases as h/t decreases. Experimentally, the tubes collapse due to a limit moment instability which is followed by the formation of a kink on the compression flange of the tubes. The limit moment and the development of the kink are captured well by the analytical model.

Pseudo-analytical model for calculation of flat circular inductors with rectangular cross-section

2018 ◽  
Vol 78 ◽  
pp. 46-53 ◽  
Author(s):  
Pedro Luis Ferrer Penalver ◽  
Carmen Leticia Crespillo Torriente ◽  
Edmundo da Silva Braga ◽  
Marco Antonio Robert Alves ◽  
Paulo Henrique Roesler ◽  
...  
Keyword(s):  
Analytical Model ◽  
Cross Section ◽  
Rectangular Cross Section

scholarly journals Validation of Welding Simulations Using Thermal Strains Measured with DIC

2011 ◽  
Vol 70 ◽  
pp. 129-134 ◽  
Author(s):  
Maarten De Strycker ◽  
Pascal Lava ◽  
Wim Van Paepegem ◽  
Luc Schueremans ◽  
Dimitri Debruyne
Keyword(s):  
Residual Stresses ◽  
Cross Section ◽  
Circular Cross Section ◽  
Welding Process ◽  
Weld Bead ◽  
Image Correlation ◽  
Steel Tubes ◽  
Element Analysis ◽  
Strain Evolution ◽  
The Cross

Residual stresses can affect the performance of steel tubes in many ways and as a result their magnitude and distribution is of particular interest to many applications. Residual stresses in cold-rolled steel tubes mainly originate from the rolling of a flat plate into a circular cross section (involving plastic deformations) and the weld bead that closes the cross section (involving non-uniform heating and cooling). Focus in this contribution is on the longitudinal weld bead that closes the cross section. To reveal the residual stresses in the tubes under consideration, a finite element analysis (FEA) of the welding step in the production process is made. The FEA of the welding process is validated with the temperature evolution of the thermal simulation and the strain evolution for the mechanical part of the analysis. Several methods for measuring the strain evolution are available and in this contribution it is investigated if the Digital Image Correlation (DIC) technique can record the strain evolution during welding. It is shown that the strain evolution obtained with DIC is in agreement with that found by electrical resistance strain gauges. The results of these experimental measuring methods are compared with numerical results from a FEA of the welding process.

An analytical model of a curved beam with a T shaped cross section

2018 ◽  
Vol 416 ◽  
pp. 29-54 ◽  
Author(s):  
Andrew J. Hull ◽  
Daniel Perez ◽  
Donald L. Cox
Keyword(s):  
Analytical Model ◽  
Cross Section ◽  
Curved Beam ◽  
Shaped Cross Section

Effect of Lu¨ders Bands on the Bending Capacity of Steel Tubes

2010 ◽  
Author(s):  
Julian F. Hallai ◽  
Stelios Kyriakides
Keyword(s):  
Limit State ◽  
Solution Procedure ◽  
Inhomogeneous Deformation ◽  
Pure Bending ◽  
Steel Tubes ◽  
Deformation Regime ◽  
Bending Capacity ◽  
The Moment ◽  
T Values ◽  
Structural Instabilities

In several offshore applications hot-finished pipe that often exhibits Lu¨ders bands is bent to strains of 2–3%. Lu¨ders banding is a material instability that leads to inhomogeneous plastic deformation in the range of 1–4%. It can precipitate structural instabilities and collapse of the pipe. Experiments and analysis are used to study the interaction of the prevalent structural instabilities under bending with Lu¨ders banding, with the objective of providing guidance to the designer. Pure bending experiments on tubes of various D/t values reveal that Lu¨ders bands result in the development of inhomogeneous deformation in the structure, in the form of coexistence of two curvature regimes. Under rotation controlled bending, the higher curvature zone(s) gradually spreads while the moment remains essentially unchanged. For relatively low D/t tubes with relatively smaller Lu¨ders strain, the whole tube eventually is deformed to the higher curvature, subsequently entering the usual hardening regime where it continues to deform uniformly until the expected limit state is reached. For higher D/t tubes and/or for materials with longer Lu¨ders strain, the structure collapses during the inhomogeneous deformation regime. This class of problems is analyzed using 3D finite elements and an elastic-plastic constitutive model with an up-down-up material response. It will be demonstrated that the solution procedure followed can simulate the experiments with consistency.

scholarly journals Structure of the Balmer jump

2018 ◽  
Vol 613 ◽  
pp. A55
Author(s):  
F. Calvo ◽  
L. Belluzzi ◽  
O. Steiner
Keyword(s):  
Hydrogen Atom ◽  
Absorption Coefficient ◽  
Total Cross Section ◽  
Analytical Model ◽  
Cross Section ◽  
Quantum Structure ◽  
Balmer Series ◽  
Polarization Phenomena ◽  
Definition Of ◽  
Rapid Drop

Context.The spectrum of the hydrogen atom was explained by Bohr more than one century ago. We revisit here some of the aspects of the underlying quantum structure, with a modern formalism, focusing on the limit of the Balmer series.Aims.We investigate the behaviour of the absorption coefficient of the isolated hydrogen atom in the neighbourhood of the Balmer limit.Methods.We analytically computed the total cross-section arising from bound-bound and bound-free transitions in the isolated hydrogen atom at the Balmer limit, and established a simplified semi-analytical model for the surroundings of that limit. We worked within the framework of the formalism of Landi Degl’Innocenti & Landolfi (2004, Astrophys. Space Sci. Lib., 307), which permits an almost straight-forward generalization of our results to other atoms and molecules, and which is perfectly suitable for including polarization phenomena in the problem.Results.We analytically show that there is no discontinuity at the Balmer limit, even though the concept of a “Balmer jump” is still meaningful. Furthermore, we give a possible definition of the location of the Balmer jump, and we check that this location is dependent on the broadening mechanisms. At the Balmer limit, we compute the cross-section in a fully analytical way.Conclusions.The Balmer jump is produced by a rapid drop of the total Balmer cross-section, yet this variation is smooth and continuous when both bound-bound and bound-free processes are taken into account, and its shape and location is dependent on the broadening mechanisms.

scholarly journals Rate of deformation in the cross section of a spatially curved rod with various assumptions

2021 ◽  
Vol 18 (3) ◽  
pp. 76-83
Author(s):  
Yu. L. Rutman ◽  
◽  
V. A. Meleshko ◽  
Keyword(s):  
Cross Section ◽  
Deformation Rate ◽  
Kinematic Parameters ◽  
Elastic Plastic ◽  
Tangential Stiffness ◽  
The Cross ◽  
Curved Rod

The article considers incremental relations connecting the changes in the kinematic parameters of the rod cross section with the deformation rate. These relations allow assessing the deformation rate on the elemental areas of a spatially curved rod, as well as considering the distortion of cross-section in its plane due to shear and torsion. Assessment of such relations between deformation rates and the rates of kinematic parameters allows developing the method of nonlinear calculation of rod systems based on integral expressions. Subsequently, these relations will be used for assessing the tangential stiffness of the rod element cross-section subjected to elastic-plastic calculation.

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