scholarly journals Cross-Section Deformation and Bending Moment of a Steel Square Tubular Section

Materials ◽  
2020 ◽  
Vol 13 (22) ◽  
pp. 5170
Author(s):  
Stanisław Kut ◽  
Feliks Stachowicz
Keyword(s):  
Numerical Modeling ◽  
Cross Section ◽  
Circular Cross Section ◽  
Bending Moment ◽  
Experimental Tests ◽  
Cross Sectional ◽  
Cold Bending ◽  
Bending Process ◽  
The Cross ◽  
Sectional Shape

When bending thin-walled profiles, significant distortion of the cross-section occurs, which has a significant impact on the course of the bending moment characteristics and on the value of allowable bending curvatures. This paper presents the results of experimental and numerical modeling of the box profile bending process, which was carried out in order to determine the dependence of the cross-sectional shape and bending moment of bending curvature. Extensive numerical calculations were used to model the process of shaping a square pipe from a circular tube and to model the bending process, especially when taking into account the effects of such a deformation path. The pure bending moment characteristics and the deformation of the cross-section were performed for a 25 × 25 × 2 mm square tube made of S235JR structural steel. The innovative approach for determining the parameters of cold bending square tubes pertained to considering the stress state in the preserved material in individual areas of their cross-section. The results of numerical modeling—after considering the history of deformation (i.e., the process of forming a square pipe from a pipe with a circular cross-section)—gave a satisfactory agreement with the results of experimental tests, both in terms of the degree of pipe wall deflection and the characteristics of the bending moment.

scholarly journals Springback Prediction for Pure Moment Bending of Aluminum Alloy Square Tube

Materials ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 3814
Author(s):  
Stanisław Kut ◽  
Feliks Stachowicz ◽  
Grzegorz Pasowicz
Keyword(s):  
Aluminum Alloy ◽  
Cross Section ◽  
Bending Moment ◽  
Dimensional Accuracy ◽  
Experimental Tests ◽  
Cross Sectional ◽  
Cold Forming ◽  
The Cross ◽  
Springback Coefficient ◽  
Springback Prediction

The springback phenomenon occurring during cold forming is the main problem affecting the dimensional accuracy of bent products, especially when bending thin-walled profiles, where there are significant changes in the cross-section geometry. This article presents the results of the analysis of the springback phenomenon occurring during shaping with a pure bending moment of square tubes with the cross-sectional dimensions of 21.5 × 21.5 × 1.8 mm and 25 × 25 × 2.5 mm made of aluminum alloy 6060. The springback characteristics were determined by defining the dependence of the springback coefficient on the set bending radius of the band. The values of the springback coefficient were provided by means of analytical calculations and numerical modeling, which considered changes in the moment of inertia caused by deformation of the cross-section occurring during bending of the pipes. A good agreement of the calculation results with the results of experimental tests was obtained. In addition, the stress state and the state of deformation, as well as the springback characteristics of square-section pipes were compared with the results obtained during bending of a solid bar with the cross-sectional dimensions of 21.5 × 21.5 mm.

scholarly journals Optimization of the cross-sectional shape of the belts of trihedral lattice supports

2019 ◽  
Vol 7 (4) ◽  
pp. 5-8
Author(s):  
Linar Sabitov ◽  
Ilnar Baderddinov ◽  
Anton Chepurnenko
Keyword(s):  
Objective Function ◽  
Nonlinear Optimization ◽  
Cross Section ◽  
Optimization Methods ◽  
Cross Sectional ◽  
Maximum Value ◽  
Axial Moment ◽  
The Cross ◽  
Nonlinear Optimization Methods ◽  
Sectional Shape

The article considers the problem of optimizing the geometric parameters of the cross section of the belts of a trihedral lattice support in the shape of a pentagon. The axial moment of inertia is taken as the objective function. Relations are found between the dimensions of the pentagonal cross section at which the objective function takes the maximum value. We introduce restrictions on the constancy of the consumption of material, as well as the condition of equal stability. The solution is performed using nonlinear optimization methods in the Matlab environment.

Numerical study for the improvement of bead spreading architecture with modified nozzle geometries in additive manufacturing of polymers

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Easir Arafat Papon ◽  
Anwarul Haque ◽  
Muhammad Ali Rob Sharif
Keyword(s):  
Free Surface ◽  
Numerical Model ◽  
3D Printing ◽  
Cross Section ◽  
Nozzle Exit ◽  
Cross Sectional ◽  
Content Type ◽  
The Cross ◽  
Viscous Polymer ◽  
Sectional Shape

Purpose This paper aims to develop a numerical model of bead spreading architecture of a viscous polymer in fused filament fabrication (FFF) process with different nozzle geometry. This paper also focuses on the manufacturing feasibility of the nozzles and 3D printing of the molten beads using the developed nozzles. Design/methodology/approach The flow of a highly viscous polymer from a nozzle, the melt expansion in free space and the deposition of the melt on a moving platform are captured using the FLUENT volume of fluid (VOF) method based computational fluid dynamics code. The free surface motion of the material is captured in VOF, which is governed by the hydrodynamics of the two-phase flow. The phases involved in the numerical model are liquid polymer and air. A laminar, non-Newtonian and non-isothermal flow is assumed. Under such assumptions, the spreading characteristic of the polymer is simulated with different nozzle-exit geometries. The governing equations are solved on a regular stationary grid following a transient algorithm, where the boundary between the polymer and the air is tracked by piecewise linear interface construction (PLIC) to reconstruct the free surface. The prototype nozzles were also manufactured, and the deposition of the molten beads on a flatbed was performed using a commercial 3D printer. The deposited bead cross-sections were examined through optical microscopic examination, and the cross-sectional profiles were compared with those obtained in the numerical simulations. Findings The numerical model successfully predicted the spreading characteristics and the cross-sectional shape of the extruded bead. The cross-sectional shape of the bead varied from elliptical (with circular nozzle) to trapezoidal (with square and star nozzles) where the top and bottom surfaces are significantly flattened (which is desirable to reduce the void spaces in the cross-section). The numerical model yielded a good approximation of the bead cross-section, capturing most of the geometric features of the bead with a reasonable qualitative agreement compared to the experiment. The quantitative comparison of the cross-sectional profiles against experimental observation also indicated a favorable agreement. The significant improvement observed in the bead cross-section with the square and star nozzles is the flattening of the surfaces. Originality/value The developed numerical algorithm attempts to address the fundamental challenge of voids and bonding in the FFF process. It presents a new approach to increase the inter-bead bonding and reduce the inter-bead voids in 3D printing of polymers by modifying the bead cross-sectional shape through the modification of nozzle exit-geometry. The change in bead cross-sectional shape from elliptical (circular) to trapezoidal (square and star) cross-section is supposed to increase the contact surface area and inter-bead bonding while in contact with adjacent beads.

scholarly journals Analytical Model of a Multi-Step Straightening Process for Linear Guideways Considering Neutral Axis Deviation

Symmetry ◽  
2018 ◽  
Vol 10 (8) ◽  
pp. 316 ◽  
Author(s):  
Yongquan Zhang ◽  
Hong Lu ◽  
He Ling ◽  
Yang Lian ◽  
Mingtian Ma
Keyword(s):  
Analytical Model ◽  
Cross Section ◽  
Predictive Accuracy ◽  
Neutral Axis ◽  
Longitudinal Stress ◽  
Linear Superposition ◽  
Element Analysis ◽  
Cross Sectional ◽  
The Cross ◽  
Sectional Shape

The cross-sectional shape of a linear guideway has been processed before the straightening process. The cross-section features influence not only the position of the neutral axis, but also the applied and residual stresses along the longitudinal direction, especially in a multi-step straightening process. This paper aims to present an analytical model based on elasto-plastic theory and three-point reverse bending theory to predict straightening stroke and longitudinal stress distribution during the multi-step straightening process of linear guideways. The deviation of the neutral axis is first analyzed considering the asymmetrical features of the cross-section. Owing to the cyclic loading during the multi-step straightening process, the longitudinal stress curves are then calculated using the linear superposition of stresses. Based on the cross-section features and the superposition of stresses, the bending moment is corrected to improve the predictive accuracy of the multi-step straightening process. Finite element analysis, as well as straightening experiments, have been performed to verify the applicability of the analytical model. The proposed approach can be implemented in the multi-step straightening process of linear guideways with similar cross-sectional shape to improve the straightening accuracy.

Erythrocyte Sedimentation Rates in Inclined Vessels

1973 ◽  
Vol 51 (9) ◽  
pp. 685-690 ◽  
Author(s):  
R. N. O'Brien ◽  
M. B. Hocking ◽  
P. McOrmond ◽  
K. R. Thornton
Keyword(s):  
Cross Section ◽  
Sedimentation Rates ◽  
Settling Rate ◽  
Cross Sectional ◽  
Erythrocyte Sedimentation ◽  
The Cross ◽  
Sectional Shape ◽  
Erythrocyte Sedimentation Rates ◽  
Test Rack ◽  
Settling Rates

The rates of erythrocyte settling have been investigated in round and square cross-section tubes, vertically; and at nine different angles; and with the square tubes flat and on edge, to a minimum of 15° from the horizontal. Apparent settling rates increased as the angle from the horizontal decreased. Real settling rates (vertical settling rates) increased sharply on decreasing the angle from the horizontal, to a maximum at about 60°, and then decreased less abruptly for the shallower angles. The cross-sectional shape of the tube did not significantly affect the settling rates of erythrocytes. Settling in inclined tubes proceeds fast enough to permit clinical erythrocyte settling rate (E.S.R.) tests to be carried out in 10 min in place of the usual 60 min. If the standard E.S.R. test rack deviates as little as 5° from the vertical it can cause the observed settling rates to double relative to readings obtained on a vertical rack.

Semicrystalline Structure and Mechanical Properties of Polyolefin-Based Materials

2012 ◽  
Vol 441 ◽  
pp. 713-716
Author(s):  
Mizue Kuriyagawa ◽  
Koh Hei Nitta
Keyword(s):  
Mechanical Properties ◽  
Cross Section ◽  
Draw Ratio ◽  
Structural Model ◽  
Point Of View ◽  
Cross Sectional ◽  
Molecular Weights ◽  
The Cross ◽  
Sectional Shape ◽  
Structural Point

The mechanical yielding and necking behaviors of metallocene-catalyzed high density polyethylenes were investigated from a structural point of view. In particular the natural draw ratio was investigated with different crosshead speeds, molecular weights, and the cross-section shapes of sample specimens. We proposed a structural model for explaining the necking formation in addition to the molecular weight and the cross-sectional shape dependences of the natural draw ratio.

scholarly journals Cross-Sectional Analysis of the Resistance of Rc Members Subjected to Bending With/without Axial Force

2021 ◽  
Author(s):  
Marek Lechman
Keyword(s):  
Cross Section ◽  
Axial Force ◽  
Rectangular Cross Section ◽  
Bending Moment ◽  
Equilibrium Equations ◽  
Cross Sectional ◽  
Cross Sectional Analysis ◽  
Nonlinear Stress ◽  
The Cross ◽  
Sectional Analysis

The paper presents section models for analysis of the resistance of RC members subjected to bending moment with or without axial force. To determine the section resistance the nonlinear stress-strain relationship for concrete in compression is assumed, taking into account the concrete softening. It adequately describes the behavior of RC members up to failure. For the reinforcing steel linear elastic-ideal plastic model is applied. For the ring cross-section subjected to bending with axial force the normalized resistances are derived in the analytical form by integrating the cross-sectional equilibrium equations. They are presented in the form of interaction diagrams and compared with the results obtained by testing conducted on RC columns under eccentric compression. Furthermore, the ultimate normalized bending moment has been derived for the rectangular cross-section subjected to bending without axial force. It was applied in the cross-sectional analysis of steel and concrete composite beams, named BH beams, consisting of the RC rectangular core placed inside a reversed TT welded profile. The comparisons made indicated good agreements between the proposed section models and experimental results.

scholarly journals ЩОДО ПИТАННЯ ПРО РАЦІОНАЛЬНУ ФОРМУ ПРЕСОВАНОГО БУЛЬБОКОСИНЦЯ

2020 ◽  
pp. 165-172
Author(s):  
А. Г. Дибир ◽  
А. А. Кирпикин ◽  
Н. И. Пекельный
Keyword(s):  
Service Life ◽  
Residual Stresses ◽  
Cross Section ◽  
Transverse Load ◽  
Shear Stresses ◽  
Cross Sectional ◽  
The Cross ◽  
Sectional Shape ◽  
Aircraft Panels ◽  
Better Than

In airplane building and helicopter engineering a bulb angle bar  an angle bar with a bulb at the end of a wall are widespread. They are better than a simple angle bar, since they have higher critical stresses under compression more than the proportionality limit. They are better than T bar, as T bar are fastened with two rows of rivets, which impairs tightness. Bulb angle bar are better than Z bar. The latter are higher, which reduces the structural height of the cross section and increases the load on the panel and usually have an excess cross-sectional area. Bulb angle bars are widely used in the structure of metal fuselages of airplanes and helicopters, in the tail boom of helicopters, in the wing and tail unit of light aircraft, in flaps, ailerons and rudders. However, modern the bulb angle bar have a significant drawback.When a bulb angle bar is loaded by a transverse load from the skin in the wing structure, tail unit, fuselage, except of normal stresses from bending of the stringer with attached skin, supported by ribs or frames, additional normal and shear torsional stresses arise. This torsion is caused by the fact that the lateral load is not applied at the center of the bend. Additional stresses reduce the service life and tightness of the structure in this place. An altered cross-sectional shape of the bulb is proposed for use in light aircraft panels to increase their strength and service life. The change in shape had a significant impact on the location of the center of the bend in the cross section. The determination of the position of the center of the bend in the balloncube was carried out using the Wagner model with walls not working for shear stresses. The modified cross-sectional shape of the bulbogon allowed to reduce the level of residual stresses after the panels were assembled, to rationally transfer the load from the casing to the stringer and to improve the technology of their assembly in the panels. It is recommended to drill holes for rivets in the stringer in the middle of the entire width of its shelf, taking into account the wall.A modified cross-sectional shape of a corner with bulb is proposed for use in light aircraft panels. The change in shape had a significant impact on the location of the center of the bend in the cross section. This made it possible to reduce the level of residual stresses after the assembly of the panels, to rationally transfer the load from the casing to the stringer and to improve the technology of their assembly.

The Structure and Function of the Basement Membrane Muscle System in Amphiporus lactifloreus (Nemertea)

1952 ◽  
Vol s3-93 (21) ◽  
pp. 1-15
Author(s):  
J. B. COWEY
Keyword(s):  
Basement Membrane ◽  
Cross Section ◽  
Circular Cross Section ◽  
The Body ◽  
Minimum Length ◽  
Muscle Fibres ◽  
Body Volume ◽  
Cross Sectional ◽  
Elliptical Cross ◽  
Sectional Shape

The body wall of A. lactifloreus has the following structure from the outside inwards. (i) A basement membrane of five to six layers immediately underlying the epithelium. Each layer consists of right-hand and left-hand geodesic fibres making a lattice, whose constituent parallelograms have a side length of from 5 to 6µ. The fibres are attached to one another where they cross; so there can be no slipping relative to one another. (ii) A layer of circular muscle-fibres running round the animal containing two systems of argyrophil fibres--one of fibres at intervals of 10µ. running parallel to the muscle-fibres and the other of fibres running radially through the layer from the basement membrane to the myoseptum. (iii) A myoseptum which is identical in structure with a single layer of the basement membrane (iv) A layer of longitudinal muscle, whose fibres are arranged in layers on each side of a series of longitudinal radial membranes. Membranes identical in structure with the basement membrane invest the nerve cords, the gut, the gonads, and the proboscis. The interrelations of argyrophil and muscle-fibres in the muscle layers is described and their functioning discussed. The system of inextensible geodesic fibres is analysed from a functional standpoint. The maximum volume enclosed by a cylindrical element (cross-section circular), of such a length that the geodesic makes one complete turn round it, varies with the value of the angle θ between the fibres and the longitudinal axis. When θ is 0° the volume is zero; it increases to a maximum when θ is 54° 44' and decreases again to zero when θ is 90°. The length of the element under these conditions varies from zero when θ is 90° to a maximum (the length of one turn of the geodesic) when θ is 0°. The body-volume of the worm is constant. Thus it has a maximum and minimum length when its cross-section is circular, and at any length between these values its cross-section becomes more or less elliptical. It is maximally elliptical when θ is 54° 44', i.e. when the volume the system could contain, at circular cross-section, is maximal. From measurements of the ratio of major to minor axes of this maximally elliptical cross-section, the maximum and minimum lengths of the worm relative to the relaxed length and values of θ at maximum and minimum length are calculated. The worm is actually unable to contract till its cross-section is circular; but measurements of its cross-sectional shape at the minimum length it can attain, permit calculation of the theoretical length and value of θ for this cross-sectional shape. Calculated values of length and the angle 6 agree well with the directly observed values.

Bounds on the Maximum Thermoelastic Stress and Deflection in a Beam and Plate

1966 ◽  
Vol 33 (4) ◽  
pp. 881-887 ◽  
Author(s):  
Bruno A. Boley
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Practical Interest ◽  
Thermoelastic Stress ◽  
Cross Sectional ◽  
Special Cases ◽  
End Conditions ◽  
Instantaneous Temperature ◽  
The Cross ◽  
Sectional Shape

It is shown in this paper that the thermal stress in a beam or plate cannot exceed the value kαEΔT, where ΔT is the maximum instantaneous temperature excursion in a cross section, and k is a coefficient dependent on the shape of the cross section. A simple general formula for k is found, and results for several special cases of practical interest are given. For rectangular beams (suitably oriented) and for plates, for example, k = 4/3. For any section, k = 1 if the thermal moment is zero; simplifications also occur if the thermal force is zero. The corresponding results for beam deflections are also carried out: The maximum deflection cannot exceed the value kδ kδ′αLΔT, where kδ and kδ′ are coefficients depending respectively on the cross-sectional shape and on the end conditions. For example, for rectangular cross sections, kδ = 3/4; and for a simply supported beam, kδ′ = 1/8.

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