Stationary Creep Stresses for Elliptical Cross-Sectional Pipe Bends Subject to In-Plane Bending

1974 ◽  
Vol 96 (3) ◽  
pp. 162-170 ◽  
Author(s):  
J. Spence
Keyword(s):  
Elastic Beam ◽  
Constitutive Law ◽  
Constant Thickness ◽  
Straight Tube ◽  
Cross Sectional ◽  
Elliptical Cross ◽  
Curved Pipe ◽  
Linear Elastic ◽  
Plane Bending ◽  
Stationary Creep

A theoretical analysis is presented which allows the determination of the stationary creep stresses acting in a smooth curved pipe of initially elliptical cross section when subject to in-plane bending. The bend is assumed to be of constant thickness and “thin” compared with its cross-sectional axes. The analysis is based on an energy approach and uses a simple power-type creep constitutive law. Results are presented in nondimensional fashion in terms of the maximum linear elastic beam bending stress in a straight tube. A large range of possible geometries is covered.

Type 1 energy analysis for the creep of smooth circular pipe bends under combined in-plane bending and internal pressure

1977 ◽  
Vol 12 (1) ◽  
pp. 1-7 ◽  
Author(s):  
J Spence
Keyword(s):  
Internal Pressure ◽  
Creep Behaviour ◽  
Constitutive Relationship ◽  
Constant Thickness ◽  
Pipe Bend ◽  
Curved Pipe ◽  
Linear Elastic ◽  
Special Cases ◽  
Plane Bending

Many pipeline systems, in addition to catering for thermal expansion conditions, have to carry internal pressure loading. An approximate theoretical analysis is given for the pure creep of a smooth curved pipe bend under fixed ratios of combined pressure and in-plane bending. The bend is circular in cross-section and of constant thickness. An energy method designated type 1, coupled with a simple n-power constitutive relationship, is used and implemented by direct minimization techniques. Selected deformation and stress results are presented as possible design factors for a number of the geometric and material parameters. For part of the geometric spectrum, large displacement effects are significant and lead to non-steady creep behaviour. Consequently there is not a direct analogy with elasticity, although linear elastic results can nevertheless be identified. Other special cases of loading or geometry are reducible from the general case.

Creep Analysis of Smooth Curved Pipes under in-plane Bending

1973 ◽  
Vol 15 (4) ◽  
pp. 252-265 ◽  
Author(s):  
J. Spence
Keyword(s):  
Circular Cross Section ◽  
Approximate Solutions ◽  
Constitutive Relationship ◽  
Constant Thickness ◽  
Stationary Condition ◽  
Curved Pipe ◽  
Curved Pipes ◽  
Plane Bending ◽  
Stationary Creep ◽  
Stress Concentration Factors

Theoretical analyses are presented for the behaviour of a smooth circular cross-section thin-walled curved pipe of constant thickness when loaded by in-plane bending moments under isothermal creep conditions. Twin energy analyses, designated type 1 and type 2 respectively, are used in conjunction with an n-power stationary creep constitutive relationship. Approximate solutions are obtained by direct minimization techniques on a computer. Deformation results and stress-concentration factors relevant to the stationary condition based on straight-pipe values are reported for all practical geometries of pipe bends. The influence of the results on design and matters of total deformation and stress redistribution are briefly mentioned.

Maximum Stresses and Flexibility Factors of Smooth Pipe Bends With Tangent Pipe Terminations Under In-Plane Bending

1983 ◽  
Vol 105 (4) ◽  
pp. 329-336 ◽  
Author(s):  
G. Thomson ◽  
J. Spence
Keyword(s):  
Elastic Behavior ◽  
Constant Thickness ◽  
Recent Experimental Data ◽  
Cross Sectional ◽  
Linear Elastic ◽  
Total Potential ◽  
Wide Range ◽  
Theoretical Predictions ◽  
Plane Bending ◽  
Minimum Total Potential Energy

A theoretical solution is presented for the in-plane bending, linear elastic behavior of smooth, circular cross-sectional constant thickness pipe bends with connected tangent pipes of similar section. The analytical method employs the theorem of minimum total potential energy with suitable kinematically admissible displacements. Integration and minimization is performed numerically. Results are given for bend flexibilities and peak stresses covering a wide range of practical geometries. These are compared with other theoretical predictions and finite element results as well as with some recent experimental data.

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.

The Effect of Thickness Variations on the Behavior of Smooth Curved Pipes Under External Bending

1980 ◽  
Vol 102 (1) ◽  
pp. 45-48 ◽  
Author(s):  
J. Spence ◽  
G. E. Findlay
Keyword(s):  
Cross Sections ◽  
Theoretical Work ◽  
Small Displacement ◽  
Constant Thickness ◽  
Elliptical Cross ◽  
Classical Energy ◽  
Curved Pipes ◽  
Bending Stresses ◽  
Plane Bending ◽  
Thickness Variations

By various manufacturing techniques straight pipes with initially circular cross sections can be processed into smooth bends but usually with noncircular cross sections and with variations in thickness. These changes from the ideal are normally referred to as “ovality” and “thinning”; their influence on the subsequent behaviour of curved pipes is not yet fully understood. Here theoretical work on constant thickness circular and elliptical cross sections has been extended to cope with typical variations in thickness. The theory which is based on a classical energy approach is outlined for in-plane bending loading and is easily extended to cover out-of-plane bending. Linear elastic small displacement limitations apply. It is concluded that normally accepted values of thinning have virtually no effect on the flexibility due to bending of smooth pipe bends with or without initial ovality. Similarly, the peak meridional bending stresses were found to be insensitive to thickness variations.

Strain-Rate Effect on the Tensile Behaviour of High Strength Alloys

2011 ◽  
Vol 82 ◽  
pp. 124-129 ◽  
Author(s):  
Ezio Cadoni ◽  
Matteo Dotta ◽  
Daniele Forni ◽  
Stefano Bianchi
Keyword(s):  
Strain Rate ◽  
Rate Sensitivity ◽  
High Strength ◽  
Constitutive Law ◽  
Tensile Behaviour ◽  
Strain Rates ◽  
Cross Sectional ◽  
Split Hopkinson Tensile Bar ◽  
Wide Range ◽  
First Results

In this paper the first results of the mechanical characterization in tension of two high strength alloys in a wide range of strain rates are presented. Different experimental techniques were used for different strain rates: a universal machine, a Hydro-Pneumatic Machine and a JRC-Split Hopkinson Tensile Bar. The experimental research was developed in the DynaMat laboratory of the University of Applied Sciences of Southern Switzerland. An increase of the stress at a given strain increasing the strain-rate from 10-3 to 103 s-1, a moderate strain-rate sensitivity of the uniform and fracture strain, a poor reduction of the cross-sectional area at fracture with increasing the strain-rate were shown. Based on these experimental results the parameters required by the Johnson-Cook constitutive law were determined.

scholarly journals Analysis of dynamics of a vertical cantilever in rotary coupling to the moving frame with movement limiters

2018 ◽  
Vol 241 ◽  
pp. 01021
Author(s):  
Piotr Wolszczak ◽  
Grzegorz Litak ◽  
Krystian Lygas
Keyword(s):  
Mechanical Energy ◽  
Elastic Beam ◽  
Beam Deflection ◽  
Moving Frame ◽  
Nonlinear Phenomena ◽  
Horizontal Distance ◽  
Energy Effect ◽  
Cross Sectional ◽  
Excitation Beam ◽  
Analysis Of Dynamics

The efficiency of the mechanical energy harvesting with the use of vibrating elements can be improved by synchronizing stimulation vibrations and own linear frequencies of systems as well as super or sub harmonics induced by non-linear phenomena. The article presents numerical cross-sectional study of the mechanical system. The system consists of an elastic beam set vertically, which the lower end is fixed in the rotary support, and is stimulated to move in the horizontal axis. The upper end of the beam is free but below its level there are bumpers limiting the free rotation of the beam. Numerical studies took into account the variability of the frequency and amplitude of the excitation beam movement, and horizontal distance between bumpers. Beam deflection was observed, on the basis of which the amount of energy generated by the piezo element was estimated. Nonlinear phenomena and analysis of frequency synchronization of vibrations improving the energy effect of an energy generator are presented.

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.

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