Combined Bending and Compression of a Pressurized Circular Cylindrical Membrane Column

1965 ◽  
Vol 87 (3) ◽  
pp. 372-378
Author(s):  
W. E. Jahsman
Keyword(s):  
Compressive Strength ◽  
Cross Section ◽  
Compressive Load ◽  
Circular Cross Section ◽  
Bending Moment ◽  
Maximum Load ◽  
Bending Moments ◽  
Lateral Deflection ◽  
The Cross

Load-lateral deflection curves are developed for a pressurized tube of circular cross section under combined bending and compression. The tube walls are assumed to have negligible compressive strength so that wrinkling develops if the stress tends to become negative. It is found that for a given bending moment, the load increases monotonically with deflection until a maximum is reached beyond which the load decreases with increasing deflection. An interaction curve of the maximum load versus bending moment shows that the presence of only a small amount of bending significantly decreases the maximum compressive load below the classical Euler load. Conversely, for bending moments which produce almost complete wrinkling of the cross section, only very small amounts of compressive load can be supported.

Shape Memory Elements in Bending: Influence of the Shape of their Cross-Section

2000 ◽  
Vol 11 (12) ◽  
pp. 977-984 ◽  
Author(s):  
Vratislav Kafka ◽  
David Vokoun
Keyword(s):  
Shape Memory ◽  
Cross Section ◽  
Elastic Limit ◽  
Rectangular Cross Section ◽  
Circular Cross Section ◽  
Bending Moment ◽  
Internal Variables ◽  
Memory Recovery ◽  
The Cross ◽  
The Mathematical Model

The effect of the shape of the cross-section of a bent prismatic bar on its shape memory recovery moment is investigated. The analysis is based on the mathematical model of the first author (Kafka, 1994a, 1994b, 2001). The area of the cross-section of the bar is assumed to be constant, the shape of the cross-section is varied. The investigated shapes are rectangles with various relations of their sides, and a circular cross-section. It is assumed that the rod is bent above elastic limit and unloaded at room temperature, which results in macroscopic residual stresses giving zero bending moment, and in residual internal variables descriptive of the change of the state of the material. Then, the resulting form is held fixed and temperature of the rod is raised. Due to the increase of temperature there arise recovery stresses resulting in recovery moments. These moments—depending on the shape of the cross-section—are calculated, and in this way the effectiveness of the shape of the cross-section is evaluated. In the case of a rectangular cross-section the effect of the relation of the sides is strongly non-linear, the effect of the circular cross-section is lower by 20% than that of a square cross-section.

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 Optimization of the parameters of truss beams with two posts

2021 ◽  
Vol 48 (3) ◽  
pp. 117-132
Author(s):  
A. K. Yusupov ◽  
H. M. Musеlеmov, ◽  
T. O. Ustarhanov
Keyword(s):  
Cross Section ◽  
Optimal Parameter ◽  
Bending Moment ◽  
Internal Force ◽  
Numerical Calculations ◽  
Design Parameters ◽  
Bending Moments ◽  
The Cross ◽  
Theoretical Results

Based on the theoretical results obtained in the article [17], here the analysis of the influence of various design parameters on the own weight and cost of metal of truss beams with two posts is carried out. An optimal parameter has been obtained that makes it possible to reduce the calculated bending moment in the cross section of a truss beam with two struts.Method. By equalizing the bending moments in various design sections of the truss beam, the internal force factors are reduced. The corresponding equation for optimizing the parameters of the beam has been drawn up and a formula has been obtained to determine the optimal parameter of the structure as a whole.Result. Using the example of numerical calculations, a decrease in the calculated bending moment by 14% compared to truss beams without optimization is shown.Conclusion. The proposed method and algorithm testify to the efficiency and rationality of the obtained optimal parameter of the structure as a whole.

An experimental investigation of a right-angled single unreinforced mitred-bend subjected to various bending moments

1966 ◽  
Vol 1 (3) ◽  
pp. 248-263 ◽  
Author(s):  
N Jones ◽  
R Kitching
Keyword(s):  
Cross Section ◽  
Circular Cross Section ◽  
Bending Moment ◽  
Straight Tube ◽  
Bending Moments ◽  
Curved Pipe ◽  
Design Procedures ◽  
Out Of Plane ◽  
Plane Bending ◽  
Comprehensive Study

It is well known that, upon the application of an in-plane bending moment, the initially circular cross-section of a curved pipe tends to flatten and become approximately elliptical in shape making it much more flexible than an equivalent straight tube. Mitred-bends exhibit similar properties though the behaviour is far more complex. A comprehensive study of a 90° single unreinforced mitred-bend having a radius/thickness ratio of 19 has been performed by means of a stress-probing method. In order to make the work more complete, results have been obtained for a similar bend when subjected to out-of-plane bending and twisting moments. Experimental measurements of stress and flexibility for each type of loading are discussed and certain modifications suggested to existing design procedures.

Determination of collapse moment of different angled pipe bends with initial geometric imperfection subjected to in-plane bending moments

2021 ◽  
pp. 095440622199640
Author(s):  
Manish Kumar ◽  
Pronab Roy ◽  
Kallol Khan
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Circular Cross Section ◽  
Initial Imperfection ◽  
Bend Angle ◽  
Bending Moments ◽  
Element Analysis ◽  
Geometric Imperfection ◽  
Initial Geometric Imperfection

From the recent literature, it is revealed that pipe bend geometry deviates from the circular cross-section due to pipe bending process for any bend angle, and this deviation in the cross-section is defined as the initial geometric imperfection. This paper focuses on the determination of collapse moment of different angled pipe bends incorporated with initial geometric imperfection subjected to in-plane closing and opening bending moments. The three-dimensional finite element analysis is accounted for geometric as well as material nonlinearities. Python scripting is implemented for modeling the pipe bends with initial geometry imperfection. The twice-elastic-slope method is adopted to determine the collapse moments. From the results, it is observed that initial imperfection has significant impact on the collapse moment of pipe bends. It can be concluded that the effect of initial imperfection decreases with the decrease in bend angle from 150∘ to 45∘. Based on the finite element results, a simple collapse moment equation is proposed to predict the collapse moment for more accurate cross-section of the different angled pipe bends.

scholarly journals Asymptotic Behavior of Stable Structures Made of Beams

2021 ◽  
Author(s):  
Georges Griso ◽  
Larysa Khilkova ◽  
Julia Orlik ◽  
Olena Sivak
Keyword(s):  
Asymptotic Behavior ◽  
Cross Section ◽  
Cross Sections ◽  
Linear Elasticity ◽  
Circular Cross Section ◽  
Linear Elasticity Theory ◽  
Linear Elastic ◽  
The Cross ◽  
Small Rotation ◽  
Stable Structures

AbstractIn this paper, we study the asymptotic behavior of an $\varepsilon $ ε -periodic 3D stable structure made of beams of circular cross-section of radius $r$ r when the periodicity parameter $\varepsilon $ ε and the ratio ${r/\varepsilon }$ r / ε simultaneously tend to 0. The analysis is performed within the frame of linear elasticity theory and it is based on the known decomposition of the beam displacements into a beam centerline displacement, a small rotation of the cross-sections and a warping (the deformation of the cross-sections). This decomposition allows to obtain Korn type inequalities. We introduce two unfolding operators, one for the homogenization of the set of beam centerlines and another for the dimension reduction of the beams. The limit homogenized problem is still a linear elastic, second order PDE.

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.

Investigation of Smooth Pipe Bends Under the Effect of In-Plane Bending

2017 ◽  
Author(s):  
Diana Abdulhameed ◽  
Michael Martens ◽  
J. J. Roger Cheng ◽  
Samer Adeeb
Keyword(s):  
High Stress ◽  
Circular Cross Section ◽  
Bending Moment ◽  
Bend Angle ◽  
Bending Moments ◽  
Bend Radius ◽  
Pipe Bend ◽  
Cross Sectional ◽  
Smooth Pipe ◽  
Plane Bending

Pipe bends are frequently used to change the direction in pipeline systems and they are considered one of the critical components as well. Bending moments acting on the pipe bends result from the surrounding environment, such as thermal expansions, soil deformations, and external loads. As a result of these bending moments, the initially circular cross-section of the pipe bend deforms into an oval shape. This consequently changes the pipe bend’s flexibility leading to higher stresses compared to straight pipes. Past studies considered the case of a closing in-plane bending moment on 90-degree pipe bends and proposed factors that account for the increased flexibility and high-stress levels. These factors are currently presented in the design codes and known as the flexibility and stress intensification factors (SIF). This paper covers the behaviour of an initially circular cross-sectional smooth pipe bend of uniform thickness subjected to in-plane opening/closing bending moment. ABAQUS FEA software is used in this study to model pipe bends with different nominal pipe sizes, bend angles, and various bend radius to cross-sectional pipe radius ratios. A comparison between the CSA-Z662 code and the FEA results is conducted to investigate the applicability of the currently used SIF factor presented in the design code for different loading cases. The study showed that the in-plane bending moment direction acting on the pipe has a significant effect on the stress distribution and the flexibility of the pipe bend. The variation of bend angle and bend radius showed that it affects the maximum stress drastically and should be considered as a parameter in the flexibility and SIF factors. Moreover, the CSA results are found to be un-conservative in some cases depending on the bend angle and direction of the applied bending moment.

Biaxial bending of cold-formed angle members

1984 ◽  
Vol 11 (4) ◽  
pp. 933-942 ◽  
Author(s):  
Murty K. S. Madugula ◽  
Sujit K. Ray
Keyword(s):  
Exact Solution ◽  
Compressive Strength ◽  
Computer Program ◽  
Cross Section ◽  
Simultaneous Equations ◽  
Biaxial Bending ◽  
Total Stress ◽  
The Cross ◽  
The Galerkin Method ◽  
Shear Centre

Theoretical load–deflection relationships for cold-formed angles under biaxial bending using the Galerkin method are presented. The computational difficulties encountered in the exact solution of differential equations of equilibrium involving 12 unknown constants in 12 simultaneous equations are pointed out. A computer program for pinned-end boundary conditions was developed to estimate the deflection components of the shear centre, to calculate the total stress at various points in the cross section, and to predict the ultimate strength of the cold-formed angle sections connected by one leg. Failure is assumed to have occurred when the total stress at any point on the cross section reaches the value of yield stress, compressive or tensile, or when there is a change of sign for at least one of the deflection components. A table giving the ultimate compressive strength of two commonly used cold-formed angles for various gauge distances is included. The theoretical load–deflection curves are compared with experimental results and typical curves for three test specimens are also presented.

Bearing Capacity of Structures Made of Materials with Different Tensile and Compression Strengths

2019 ◽  
Vol 968 ◽  
pp. 200-208
Author(s):  
Mykola Soroka
Keyword(s):  
Cross Section ◽  
Rectangular Cross Section ◽  
Limit State ◽  
Analytical Calculation ◽  
Bending Moment ◽  
Maximum Load ◽  
Longitudinal Force ◽  
Plastic State ◽  
Limiting State ◽  
Tension And Compression

The paper considers the problem of the ultimate load finding for structures made of a material with different limits of tensile strength and compression. The modulus of elasticity under tension and compression is the same. It is assumed that upon reaching the ultimate strength, the material is deformed indefinitely. The calculations use a simplified material deformation diagram — Prandtl diagrams. The limiting state of a solid rectangular section under the action of a longitudinal force and a bending moment is considered. The dependences describing the boundary of the strength of a rectangular cross section are obtained. Formulas allowing the calculation of the values of the limit forces and under the action of which the cross section passes into the plastic state are derived. Examples of the analytical calculation of the maximum load for the frame and two-hinged arch are given. An algorithm is proposed and a program for calculating arbitrary flat rod systems according to the limit state using the finite element method is compiled. The proposed algorithm does not involve the use of iterative processes, which leads to an exact calculation of the maximum load within the accepted assumptions.

Sign in / Sign up

Export Citation Format

Share Document