analyzing stresses in pipe joints

7/31/2019 Analyzing Stresses in Pipe Joints

1/6

Calculations are presented on the state of strain in pipe joints to equipment and pressure vessels used in the

chemical and oil industries. Various model approaches are considered for calculating reinforced pipe joints.

Calculated results are given for a pipe joint as a welded joint between three cylindrical shells (body, ring,

and pipe). A complete solution is presented for the three-dimension contact problem and a two-dimensional

solution obtained with the SAIS program.

There are usually pipe joints (PJ) in the apparatus and vessels used in the chemical industry, petrochemical indus-

try, oil refining, and adjacent areas of industry, in which the main load comes from the internal excess pressure. A local state

of stress arises in the PJ, which is characterized by a high stress level.

A pipe joint is usually welded, and the highest stresses in the body and pipe arise near the weld. The stress concen-

tration here is the cause of microplastic strain, which in the presence of cyclic loading may lead to crack initiation and fail-

ure. Research on stress concentration effects in PJ regions is thus important in the general strength analysis of such structures.

At present, GOST 24755-89 deals with the standards and calculation methods for PJ on cylindrical and conical shells

and on elliptical and spherical base plates and other such vessels made in Russia. In foreign practice, the most familiar standards

are the American ASME Code and the British standard BS 5500, which contain rules and recommendations for choosing the

basic geometrical parameters and other such information. However, such documentation cannot reflect all practical aspects of

structures of this type, particularly as there are wide ranges of variation in the geometrical parameters of pipes and bodies.The body of the apparatus and the pipe are shells of rotation, which are often thin-walled (particularly the body of the

apparatus or vessel), so usually the PJ is considered as the joining of intersecting shells differing in geometrical form. The stress

state in the shells in the region of their intersection is inhomogeneous. The stresses vary considerably in the direction of the

intersection between the shell surfaces (outside or inside) and also along the intersection line. The character of the maximal

stresses in the shells (predominance of membrane or bending components) is extremely important for strength evaluation.

To reduce the maximal stresses in a PJ, it is best to use various types of local reinforcement: monolithic (integral)

mounting; fitted ring; transitional section (rim or toroidal insert); and lining tubes.

There are possible forms of combined local PJ reinforcement, e.g., a pipe with locally thickened wall (monolithic

reinforcement) and a welded ring attached to the body.

One chooses the local reinforcement method on the basis of the performance (reduction in the maximal stresses in

the shells), with allowance for the object (body or pipe), the soundness of the reinforcement, and so on. Local reinforcementis also favorable from the viewpoint of PJ metal content.

One can analyze a PJ as the junction of intersecting shells, but this is a difficult task, even with the existing means

of numerical analysis: the finite-element method FEM and computing programs based for example on ANSYS, NASTRAN,

FEPipe, ASTRA-NOVA [1], KAPRIS-DINAMIKA [2], and so on. The difficulty is determined by factors such as the inho-

Chemical and Petroleum Engineering, Vol. 43, Nos. 78, 2007

ANALYZING STRESSES IN PIPE JOINTS

TO VESSELS WITH REINFORCING RINGS

V. N. Skopinskii, N. A. Berkov,

and O. A. Rusanov

Moscow State Industrial University. Translated from Khimicheskoe i Neftegazovoe Mashinostroenie, No. 8, pp. 1519,

August, 2007.

0009-2355/07/0708-0445 2007 Springer Science+Business Media, Inc. 445


2/6

mogeneity of the joints, the variability of the state of stress, and the high gradients in the stresses near the intersection.

Practical interest attaches to analysis of PJ stresses in the presence of local reinforcement.

Here we consider PJ states of stress on a cylindrical body reinforced by a superimposed ring.

Methods. One can analyze the state of stress for an object of intersecting shell type in various formulations: as a

two-dimensional solution based on shell theory [3] or as a three-dimensional solution that gives the fullest picture of the stress

state in the intersection region [4]. However, three-dimensional simulation and PJ calculation are much more laborious than

two-dimensional solutions from shell theory, so it is difficult to use three-dimensional analysis in considering the set of cases

for such units or in calculations to optimize geometrical parameters or in express analysis. On the other hand, such refine-

ment is best used to provide sound shell calculation schemes and models.

Consider the determination of stresses in the junction (welding zone) of a radial pipe on a cylindrical shell. The hole

in the cylindrical shell is additionally reinforced by a superimposed ring welded at the edge (Fig. 1, welded joint not shown).

The joint is loaded by the excess internal pressurep. The calculation incorporates also the axial load transmitted to the shells

by the internal pressure at the bottom of the apparatus and in the pipe to the cover. That is, we consider locally reinforced

radial joints for intersecting cylindrical shells [3] with relative geometrical parameters of the joint and reinforcement

d/D, h/H, D/H, Hr/H, Lr/D, (1)

in whichD and dare the diameters of the median surfaces of the main shell (cylindrical shell) and pipe.

A pipe joint on a shell is a linkage of three cylindrical shells: pipe, body, and reinforcement. The main shell and the

reinforcing ring are rigidly coupled together only along the contour of the ring, and a contact interaction may occur between

them under the internal pressure. In this study, the state of stress was determined in the shells by means of the most accurate

calculation model and an evaluation was performed on the applicability of an approximate calculation method.

The analysis employed FEM in three-dimensional and two-dimensional approaches. As there is symmetry in the

unit, the calculation models were constructed for 1/4 of the radial junction between cylindrical shells. The symmetry condi-tions were incorporated by means of appropriate boundary conditions.

Three-Dimensional Solution. We used a KAPRIS-DINAMIKA program [2] in the three-dimensional analysis of

the state of stress in a joint between intersecting shells.

The following cases were considered in simulating and calculating the shell joints:

case 1: shells joined without reinforcement;

case 1: shells joined and reinforced by a welded ring of thicknessHm =H+Hr (monolithic reinforcement);

case 3: shells reinforced by a ring without allowance for the contact interaction between the shell and the ring;

446

Fig. 1. Geometry of reinforcing shell joint with reinforcing ring:Hand h thicknesses

of main shell and pipe;Hr andLr thickness and width of ring; s meridional coordinate

of shell and ring; s1 meridional coordinate of pipe.


3/6

case 4: shells reinforced by a superimposed ring considered with allowance for the contact interaction between the

ring and the main shell.

The numerical simulation was performed by the FEM (displacement method) with the use of three-dimensional

eight-node isoparametric finite elements. At the preliminary stage, we examined the convergence of the numerical solution.

This gave a fairly detailed finite-element model for the joint: the elements arranged in the thickness of the main shell lay in

four layers, while those in the thickness of the ring lay in four layers, and those in the thickness of the pipe in six layers (cor-

respondingly, for connection with monolithic reinforcement, we used elements in eight layers in the reinforcement thickness).

The ring at the outside edge had a rim simulating the welded joint. In calculations on case 4, the contact region

between the outer surface of the main shell and the inner surface of the ring was determined automatically from the solution

for the contact problem. A finite-element model was derived from the model for case 3 by introducing the correspondingnumber of special contact elements joining the unit to the generators of the surfaces in the gap between the main shell and

the ring. The contact elements were oriented radially (normal to the interacting cylindrical surfaces). The characteristics of

the contact elements were variable. Their rigidity along the normal, which was initially low, was increased if the displace-

ment of nodes at their surfaces exceeded the established permissible gaps. The tangential components of the contact interac-

tion forces were not considered. The maximum permissible closeness of the parts connected by a contact element from the

initial state was established as 0.001 mm. The contact interaction was incorporated by a modification of the variable elastic-

ity parameter method, which was implemented in the computer program for handling tasks with nonlinear relations between

447

File Tools Help

SAISspecialized computing program for analysis of stresses in intersecting shell joints

Constructive jointJoining shell

CylinderCylinder

ConeCylinder

SphereCylinder

EllipsoidCylinder

Joint typeRadialNonradial

Tangential

Boundary conditions

Style

ReinforcementRing sleeve

Welded joint

Print

Geometrical parameters Load Material FEM parameters

Construct FEM Calculation Postprocessor Results Output

Sleeve

Main shell

D, d internal diameters of shells;L0, l lengths of shell parts;H, h thicknesses of shell walls

L0

H

h l

D

d

Fig. 2. Graphics interface for the SAIS program.


4/6

the stresses and strains. This method was supplemented with a scheme for recalculating the rigidities of the contact elements

in accordance with the actual distances between the nodes linked by those elements.At each iteration in the variable elasticity parameter method, the linear treatment was handled by interactive meth-

ods of solving systems of linear algebraic equations: the conjugate-gradient method and the Lanzos method, both supple-

mented with a procedure for cyclic acceleration of the convergence by the formation of a special structure for the rigidity

matrices by methods of enumerating the nodes in the finite-element model.

Two-Dimensional Solution. We have developed an applied method of calculation for intersecting shells involving

the use of FEM and shell theory (in cases for thin shells and shells of medium thickness with allowance for the transverse

shear), which allows one to perform a systems analysis of this class of shell structures. The structural components of the

method are a unique classification of typical joints for intersecting shells of various shapes, the use of curvilinear coordinate

systems linked to the surfaces of the individual shells, and the use of FEM in a modified mixed variational formulation. This

method was employed in the specialized SAIS computational program, which employs a rational algorithm. Mixed shell

models and this algorithm provide reasonably accurate calculations with small resource demand. Also, the data preparation

and input for particular calculations are substantially simplified in this program.

The computerized generator for the finite-element model for a typical joint performs the rational splitting up of the

shells into elements with an irregular network and the determination of the nodal coordinates on the basis of geometrical rela-

tionships for the lines of intersection of the shell surfaces and with allowance for the geometry of the intersecting shell sec-

tions. The program is constantly being updated as it handles new tasks.

The processor module uses Fortran in the Compaq Visual Fortran 6.5 programming environment, which substan-

tially reduces the run times by comparison with previous versions. The graphics postprocessor working in interactive mode

provides for displaying the simulation and calculation results as a colored image for the finite-element model or parts of it,

and with the display of the initial and deformed states, color areas for lines for the stress level, and the construction of graphs

for the stress distributions in a given direction.

The program works interactively, and it employs an intuitive concept graphical user interface, which is used in for-

mulating the input data for transfer to the program model (Fig. 2).

Calculations with SAIS have employed not only shell elements but also rod ones, which approximate the

three-dimensional region of the shell intersection. Comparison of the calculations with experimental data [5] indicates that

the model enables one to revise the scheme for the interaction of the shells within the framework of the two-dimensional res-

olution. When one calculates for shells with a ring sleeve, the finite-element model includes elements from three individual

structures: the pipe line, the main shell, and the cylindrical shell representing the ring sleeve (allowance is made for the lack

448

Fig. 3. Variation in stress intensity si on the outside surface (a) and inner surface (b) of the reinforcing

ring in the meridional direction: 1) two-dimensional solution; 2) three-dimensional solution (neglecting

contact); 3) three-dimensional solution (contact case).


5/6

of coincidence between the median surfaces of the main shell and the ring sleeve). The outer edge of the ring joins on to the

main shell by the use of a special element of variable thickness, which simulates the welded joint.

Cases 13 are thus realized with the two-dimensional solution.

Results. Calculations were performed for radial joints of cylindrical shells with various basic geometrical parame-

ters [1]. We note some features of the states of stress of shells with and without reinforcement in the presence of an internal

pressure load.

The largest stresses in the shells occur in the principal plane of the joint, which passes through the axes of the two

shells. The meridional stresses in the shells are in the main bending ones, while the circumferential stresses are predominantly

membrane ones. At the hazard points on the outer surface, there is a state of strain of biaxial stretching type, while at the

points on the inner surface one has a biaxial mixed state of strain. One can use the stress distribution on the inner surfaces of

the shells [4] and compare the calculated results for the three-dimensional and two-dimensional solutions in terms of the

stress intensities, which represent a generalized characteristic of a stress state at a point in the body.

We compared the calculated results for the two-dimensional and three-dimensional solutions for a unreinforced (ini-tial) joint and a joint with monolithic reinforcement, which agreed quite well for the largest values of the stress components

(meridional and circumferential) and also for the stress distribution near the region of intersection. The main attention was

given to results from calculations for joints with sleeve rings.

Figures 35 compare the calculations for a reinforcing sleeve ring with d/D = 0.5; h/H= 2;D/H= 100;Hr/H= 1;

Lr/D = 0.125; they give the variation in the stress intensity i in the shells in the meridional direction in the principal plane

of the joint (Figure 1 shows the direction and origin for the meridional coordinates s for the shell and the ring and the same

s1 for the pipe, while Figs. 35 show the values of those coordinates in the dimensionless form s = 2s/D, s1 = 2s1/d).

449

Fig. 4. Change in stress intensity si on the outer surface (a) and inner surface (b) of the shell in the

meridional direction (symbols as in Fig. 3).

Fig. 5. Changes in stress intensity si on the outer surface (a) and inner surface (b) of the pipe in the

meridional direction (symbols as in Fig. 3).


6/6

The stresses are represented in relative form:

si = i/0; 0 =pD/2H, (2)

where 0 is the nominal stress for the joint.

The two-dimensional solution for the joint with sleeve was obtained without allowance for the contact interaction

between the shells (main one and ring) although the calculations showed that there is contact between the corresponding sur-

faces: the radial displacements of the points on the surface of the main shell were more than the displacements of the corre-

sponding points on the ring.

The stresses were divided into certain categories in a check calculation [6]. For a PJ on the body of an apparatus,

the local membrane stresses and the reduced ones (stress intensities) fall in the second group, but the permissible stresses for

them are usually taken as different (for example, for the local membrane stresses []1 = 1.5[], for the local reduced stress-

es []2 = 2.5[], where [] is the nominal permissible stress). We therefore examined the effects of the parameters in the local

reinforcement on the maximum local membrane stresses and stress intensities.

Conclusions drawn from the analysis:

1. Monolithic reinforcement of a PJ provides somewhat greater reduction in the local maximal stresses in the shells

than does reinforcement with a ring, since more effective use is made of the material in the local reinforcement. However,

monolithic reinforcement is more desirable for reducing the maximal stress intensities than the maximal membrane ones.

2. The three-dimensional solutions for cases 3 and 4 show that allowance for the contact interaction between the

main shell and the supporting ring in the main reduces the stresses in the shells by comparison with the calculations without

allowance for that contact (mainly because this concerns the maximal stresses in the ring and main shell).

3. There is satisfactory agreement between the two-dimensional and three-dimensional solutions for a PJ with rein-

forcement with a ring. Calculations from the shell model give excessive stress intensities for a supporting ring (but these

stresses are the largest for the joint), and underestimates for the main shell (by comparison with the rigorous calculation:

three-dimensional solution including contact interaction). The maximum differences in the stress intensities in the ring were

about 17%, while for the membrane stresses they were about 10%.

On the whole, this analysis shows that one can use the approximate shell model (neglecting contact interaction) to

calculate PJ as intersecting shells with local reinforcement in the form of sleeve rings. Undoubtedly, further research is need-

ed on a wider parameter analysis of joints for various PJ: on cylindrical or conical shells, and on elliptical or spherical bases.

REFERENCES

1. A. M. Belostotskii, Numerical simulation of states of stress and strain and normative evaluation of strength in

pipeline systems: Achievements, problems, and prospects, in:Machine Design and Engineering Education, No. 2

[in Russian] (2006), pp. 2437.

2. S. S. Dmitrichenko and O. A. Rusanov, Experience with strength calculations, designing, and finishing welded

mobile machine metal structures, in: Tractors and Agricultural Machines, No. 1 [in Russian] (2006), pp. 813.

3. V. N. Skopinskii, Intersecting shells: Constructive objects for engineering, in:Machine Design and Engineering

Education, No. 2 [in Russian] (2005), pp. 3145.4. V. N. Skopinskii, Three-dimensional analysis of the state of stress in pipe joints for high-pressure apparatus, Khim.

Neftegaz. Mashinostr., No. 6, 911 (1998).

5. V. N. Skopinsky, Numerical stress analysis in intersecting cylindrical shells, Transactions of the ASME, Journal

of Pressure Vessel Technology, 115, No. 3, 275282 (1993).

6. Standards for Strength Calculation on Equipment and Pipelines for Nuclear Power Plant[in Russian], nergoat-

omizdat, Moscow (1989).

450

analyzing stresses in pipe joints

Documents