The fast interpretation on the stress of the cylindrical shell under the bending moment

2020 ◽  
Author(s):  
Feng Shouyi ◽  
Liu Ping
Keyword(s):  
Cylindrical Shell ◽  
Bending Moment

A Theoretical Study of the Elastic Behavior of Two Normally Intersecting Cylindrical Shells

1969 ◽  
Vol 91 (3) ◽  
pp. 563-572 ◽  
Author(s):  
J. W. Hansberry ◽  
N. Jones
Keyword(s):  
Cylindrical Shell ◽  
Theoretical Study ◽  
Circular Cylindrical Shell ◽  
Cylindrical Shells ◽  
Bending Moment ◽  
Pressure Vessels ◽  
Numerical Results ◽  
Elastic Behavior ◽  
Cylinder Diameter ◽  
Plane Transverse

A theoretical study has been made into the elastic behavior of a joint formed by the normal intersection of a right circular cylindrical shell with another of larger diameter. The wall of the larger cylinder is assumed to remain open inside the joint in order to give an arrangement which is encountered frequently in pressure vessels or pipeline intersections. An external bending moment which acts in the plane of the joint is applied to the nozzle cylinder and is equilibriated by moments of half this magnitude applied to either end of the parent cylinder. A solution for this loading has been obtained by assuming antisymmetric distributions of certain stresses across a plane transverse to the joint. The analysis presented is believed to be valid for nozzle to cylinder diameter ratios of less than 1:3. Numerical results are given for a number of cases having radius ratios of 1:10 and 1:4.

Simplified Methods for Calculation of Redundant Moments and Forces at the Discontinuities in Pressure Vessels—Part II: Hemisphere—Shell and Shells of Different Thicknesses

1994 ◽  
Vol 116 (2) ◽  
pp. 204-206 ◽  
Author(s):  
H. Chen ◽  
K. Zhou
Keyword(s):  
Cylindrical Shell ◽  
Good Accuracy ◽  
Cylindrical Shells ◽  
Bending Moment ◽  
Pressure Vessels ◽  
Shearing Force ◽  
Mean Diameter ◽  
Similar Idea

Following a similar idea as described in Part I of this paper, the redundant bending moment and the redundant shearing force at the junctures of hemispherical/cylindrical shells and of cylindrical shells of different thicknesses are shown to be unique functions of λ (ratio of the thickness of the joint members) and η (ratio of the thickness of the cylindrical shell to its mean diameter). Thereby, simplification of the calculation for the redundant moment and the redundant force is proposed and demonstrated to possess a good accuracy.

Stress Concentration in Nonlinear Creep of a Simple Shell

1966 ◽  
Vol 33 (2) ◽  
pp. 322-326 ◽  
Author(s):  
C. R. Calladine
Keyword(s):  
Cylindrical Shell ◽  
Stress Concentration ◽  
Strain Rate ◽  
Circular Cylindrical Shell ◽  
Bending Moment ◽  
Elastic Problem ◽  
Nonlinear Creep ◽  
Linear Elastic ◽  
Perfectly Plastic ◽  
Plastic Analysis

A long, thin circular cylindrical shell is loaded at one edge by symmetrical radial shear Qx and bending moment Mx. (No interior pressure.) The shell is made of material which under applied stress creeps with a strain rate which is proportional to the rth power of the stress. Previous results are used to derive, approximately, the greatest stress in the shell for any Qx, Mx, and r. It is shown that for any load the greatest stress decreases as r increases, and is approximately a linear function of 1/r. The case r = 1 is exactly analogous to a linear elastic problem, and the case r → = ∞ corresponds exactly to a perfectly plastic problem. Results for any exponent r may thus be found approximately by simple interpolation between results obtained in linearelastic analysis and perfectly plastic analysis.

scholarly journals Application of the Line-Spring Model to a Cylindrical Shell Containing a Circumferential or Axial Part-Through Crack

1982 ◽  
Vol 49 (1) ◽  
pp. 97-102 ◽  
Author(s):  
F. Delale ◽  
F. Erdogan
Keyword(s):  
Cylindrical Shell ◽  
Stress Intensity ◽  
Surface Crack ◽  
Crack Depth ◽  
Crack Problem ◽  
Bending Moment ◽  
Circular Ring ◽  
Spring Model ◽  
Axial Part ◽  
Line Spring Model

In this paper the line-spring model developed by Rice and Levy is used to obtain an approximate solution for a cylindrical shell containing a part-through surface crack. It is assumed that the shell contains a circumferential or axial semi-elliptic internal or external surface crack and is subjected to a uniform membrane loading or a uniform bending moment away from the crack region. To formulate the shell problem, a Reissner type theory is used to account for the effects of the transverse shear deformations. The stress intensity factor at the deepest penetration point of the crack is tabulated for bending and membrane loading by varying three-dimensionless length parameters of the problem formed from the shell radius, the shell thickness, the crack length, and the crack depth. The upper bounds of the stress intensity factors are provided by the results of the elasticity solution obtained from the axisymmetric crack problem for the circumferential crack, and that were found from the plane strain problem for a circular ring having a radial crack for the axial crack. Qualitatively the line-spring model gives the expected results in comparison with the elasticity solutions. The results also compare well with the existing finite element solution of the pressurized cylinder containing an internal semi-elliptic surface crack.

Stresses and Deformations in a Cylindrical Shell Lying on a Continuous Rigid Support

1974 ◽  
Vol 41 (4) ◽  
pp. 969-973 ◽  
Author(s):  
R. Vinet ◽  
R. Dore´
Keyword(s):  
Cylindrical Shell ◽  
Internal Pressure ◽  
Pressure Vessel ◽  
Bending Moment ◽  
Upper Bounds ◽  
Circumferential Direction ◽  
Geometrical Parameters ◽  
Rigid Support ◽  
Radial Displacements ◽  
Different Types

This paper develops a theoretical tool to predict rigorously the different types of contact between a cylindrical shell and a continuous rigid support for the complete range of pressure, vessel, and support parameters. The technique consists in comparing the actual angle of opening of the support with two limiting angles. These angles represent the upper bounds of the support for contact to take place on two lines only at the tips of the support or on three lines at the tips and at the center of the support. Using Flu¨gge’s equations and considering variations in the circumferential direction, it is shown that the type of contact depends on the internal pressure of the fluid, the geometrical parameters of the shell, and on the angle of opening of the support. The analysis also indicates that separation between the shell and the support is always to be expected in the circumferential direction. Results for the limiting angles of the support are presented graphically. The radial displacements and the circumferential bending moment are given for a specific example.

The Application of Long and Short Cylindrical Shell Solutions for Stress and Flexibility Determination in a Single Mitred Bend

2016 ◽  
Author(s):  
Igor Orynyak ◽  
Andrii Bogdan ◽  
Iryna Selivestrova
Keyword(s):  
Cylindrical Shell ◽  
Shell Theory ◽  
Bending Moment ◽  
Axial Direction ◽  
Piping System ◽  
Structural Elements ◽  
Thin Cylindrical Shell ◽  
Straight Pipe ◽  
Pipe Bend ◽  
Short Shell

The continuous pipe bend behavior is well elaborated in literature. It is characterized by local ovalization of each cross section during bending which results in enhanced flexibility of it as compared to straight pipe. When pipe bend approaches some other structural elements of a piping system the end effect take place which can be described by so called long shell solution. This long solution is, in fact, a semi-membrane Vlasov’s solution when the derivative of any geometrical or force function in axial direction is much smaller than in the circumferential one [1]. Mitred bend is formed by conjunction by welding of two oblique sections of initially straight pipes. Its behavior during loading by pressure or bending moment is not evident and poorly described in standards. The goal of this paper is to give a set of general functions within a thin cylindrical shell theory which will give the opportunity to consider the mitred bend as an element of a piping system. Here we additionally introduce the so called short solution when the derivative of any parameter in axial direction is much bigger than that in circumferential one. Its main goal is to give the local behavior of stress in the vicinity of the oblique weld. Each of these two solutions satisfy by differential equations of forth order. The complete theoretical solution for a particular mitred bend is compared with a) existing analytical solutions and formulas; b) numerical results obtained by FEM with distinction of the zones of influence of a long as well as short shell solution; c) experimental data on real mitred bends given in the literature.

scholarly journals Analysis of Limit Setting Force of Casing Inside Slips Based on Cylindrical Shell Theory

2014 ◽  
Vol 8 (1) ◽  
pp. 234-237
Author(s):  
Yinping Cao ◽  
Shaokai Tong ◽  
Yihua Dou
Keyword(s):  
Cylindrical Shell ◽  
Hoop Stress ◽  
Shell Theory ◽  
Bending Moment ◽  
Thick Wall ◽  
Outer Diameter ◽  
Thin Wall ◽  
Moment Theory ◽  
Limit Setting ◽  
Dangerous Section

Casing will be damaged in a well because of the setting force, and may even be broken when the force is too large. To clearly demonstrate the interaction of the mechanism of packer and casing, a mechanical model of casing as thin-wall cylinder was established with the consideration of the axial force and additional bending moment induced by the bending of casing near the slips of packer. And, the equation of limit setting force on the casing exerted by slips was deduced by bending moment theory of cylindrical shell. The relationships of the limit setting force of N80, P110, TP140 casing and thickness were analyzed. It was found that the bending stress and the hoop stress were the biggest near the bottom of the slips, and that position was the dangerous section. The limit setting force of casing exerted by slips increased with the thickness of casing, when the packer and the outer diameter of casing remained the same. And the limit setting force was higher in high grade casing. The limit setting force calculated in this paper was decreased by 5 % to 14 % than by thick-wall theory, and it is deduced to be safer. The method proposed in the paper can be used to evaluate the limit setting force and provide the basis for the choice of hanging load.

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