Stress analysis of extruded joints for use in offshore structures

Stress analysis of extruded joints for use in offshore structures X. N I U a n d W. D. D O V E R

London Centre for Marine Technology, Department of Mechanical Engineerhzg, University College London, Torrington Place, London, WCIE 7JE, UK Experimental and numerical stress analysis have been conducted on a proposed novel joint known as an extruded joint. It has been found that significant benefits could be obtained, in terms of fatigue strength; for extruded joints in comparison with conventional welded joints. The experimental results on acrylic models gave good agreement with f'mite element results and indicated that extruded joints could be accurately modelled with thin shell elements. The study included both T- and X-joints and examined optimisation of the joint geometry.

INTRODUCTION Offshore oil production platforms normally employ welded steel tubular joints, or nodes, to form the main frame. The strength of these joints has been extensively studied in various configurations. It has now been realised that one of the most influential factors affecting the strength of the joints is the peak stress which occurs in the vicinity of the weld toe. This peak stress can be considered as a combination of two stress concentration factors (SCF), a geometric SCF and a notch SCF. The former results from the difference in deformation between the brace and the chord; the latter arises because the intersection between the tube walls and the weld metal contains a small radius change in surface topography: The notch stress varies according to the geometry of the weld, and in consequence it is very difficult to provide a deterministic value of local stress. The geometric stress occurs in combination with the notch stress and is also difficult to determine. In order to avoid the difficulty, a fictitious stress known as the "hot-spot' stress was introduced into the analysis. This is defined as a stress which can be derived by linearly extrapolating the stresses in the vicinity of the intersection between the brace and chord, in a region where the decay of the stress is approximately linear, to the weld toe. This hot spot stress is considered to be suitable for characterising the intensity of the stress field around the intersection, and therefore can be used to estimate the strength of the joints. The underestimation of the local stress is not too important in strength calculations because failure is by fatigue crack growth and the hot spot stress does seem to be appropriate for this failure mechanism. The increasing demand for offshore-oil and gas means that future offshore structures are quite likely to be installed in deeper water and a more hostile environment than current platforms and, therefore, the structures will be subjected to greater loads caused by waves, storms etc. As a result, future structures will have to be designed to have a greater resistance to fatigue damage and this means it will be necessary to develop new types 0f joints. Accepted March 1986. Discussion closes December 1986.

0141-1187/86/030125-09 $2.00 9 1986 Computational Mechanics Publications

The first consideration for these novel joints is to reduce the stress concentration. Two ways of achieving this are: (1) changing the constructions of the joints to reduce the geometric stresses. (2) making improvement in the weld proFde to reduce the notch stresses. This study assesses the first of these possible approaches. A type of joint, named as an extruded-joint, has been under study at UCL. The joint is designed in such a way that the conjunction of the brace with the chord is a nozzle-like extrusion, as shown in Fig. 1. It was considered that due to the presence of the extrusion, the weld procedure would be simplified (a circumferential butt weld) and the peak stress and the weld toe would be separated. These two factors should lead to a considerable improvement in the fatigue strength. This possibility has been examined by conducting experimental and numerical stress analysis on typical geometries. This paper presents some of the results from this study.

DETAILS OF EXPERIMENTS The experiments were performed in order to measure local SCF's on two strain-gauged extruded-joint models o f T - and X-configurations. The models were made from commercially available acrylic tubes. As can be seen in Fig. 1, instead of directly attaching the brace to the chord, the so-called extruded-joint has a connection between the brace and chord formed by extruding part of the chord wall. Thus compared to conventional joints, the extruded-joints have a much smoother connection between the brace and chord. Acrylic material can be quite easily shaped into a required configuration at temperatures of about 150~ The extrusion of the type shown in Fig. 1 is formed as follows: (1) constructing a metal mould to suit the exterior contours required by the extruded-joint to be made, as shown in Fig. 2. (2) machining an appropriate elliptical hole in the tube to be used as a chord.

Applied Ocean Research, 1986, Vol. 8, No. 3

125

Stress at~alysis o f extruded]obits for use in offshore structures: X. Niu and W. D.Dover (3) heating up the tube near the hole area to a temperature of about 150~ using a hot air fan. (4) forcing a cone shaped metal block from the inside of the chord until the walls of the extrusion are fully in contact with the mould. (5) cooling down the temperature of the model with the mould in air for half an hour. (6) removing the model from the mould and machining the end of the extrusion.

i

m

m

m

]

m

~

m

D

m

m

~

I

7or

m

~

For a conventional joint, such as a T.joint, the peak stress normally occurs at the saddle position. This is thought to be because the stiffness of this part of the intersection is greater than other areas and thus attracts additional load. In designing the extruded.joints, the fillet radius of the ex. trusion at the saddle was purposely designed to be larger than that at other locations on the extrusion. The objective of doing that was to reduce the stress concentration in this critical region. The dimensions of the acrylic models tested are shown in Fig. 1. These sizes were chosen to be identical to those of conventional joints which were the subject of an earlier study at UCL. The final dimensions of the models including values of the fillet radii at certain angles around the extrusion of the models were measured. The results of the measurements indicated that the f'dlet radii varied in

i

.1o

I

I I

i

5

Figure 1.

126

Dimension o f T-joint

Applied Ocean Research, 1986, Vol. 8, No. 3

J

Figure 2.

Mould to form extrusion

Stress analysis o f extruded ioints for use in offshore structures: X. Niu and W. D.Dover

t

i

I

Figure 3a.

t

U t

Figure 3b.

Loading cases for T-loint

++ Loading cases for X-ioint

a fairly linear manner from the saddle to the crown. The values of the ratios of the saddle radius, Rs, to the chord radius R, were 0.16 and 0.133 for the X- and T-joints respectively; the value of the ratio of crown radius, Re, to R was 0.067 for both X- and T-joints. These results were used for the finite element analysis on the joints described late. One quarter of an extrusion was intensively straingauged as the joint configurations and the loadings to be applied were symmetrical. At least five strain gauge rosettes were located at the deepest points of the fillet angles 0.0 ~ 22.5 ~ 45.0 ~ 67.5 ~ and 90.0 ~ respectively. This is because the largest local strains were expected to be obtained at these locations. A few more gauges were located along the cirumferencial line passing through the saddle in order to provide information on how the stresses decayed away from the highly stressed areas. Some rosettes were also located close to the intersection between the top of the extrusion and the brace as this region would contain the weld toe of a steel model and could be a potential failure site. Linear gauges were used on the braces remote from the joint to align the applied loading. The models were loaded at the free ends of the brace in axial, OPB and IPB modes, using a simple system of pulleys and weights. The ends of the chord were restrained by two brackets during the tests. The experiments were conducted following the procedure established in earlier w o r k ) It should be noted that for an X-joint there are two possible ways to load the joints in both IPB and OPB loading cases, as shown in Fig. 3. In this study, the models were tested under all these loading cases.

The strain gauges were monitored using a Solartron data-logger linked to a PDP-11 mini-computer. The strain readings were recorded on disc and subsequently used to calculate principal stresses. In these calculations two facts had to be considered: (1) The process of extrusion causes the local chord wall thickness to be reduced. However, the reduction of the wall thickness at the deepest points of the Fdlet around the extrusions, was found to be negligible, less than 5%. For this reason the influence of the reduction in wall thickness on the peak stress was not considered in this study. In the Fmite element analysis the thickness of the shell elements modelling the extrusion was also taken to be the same as the chord wall. (2) The Young's Modulus of the acrylic material in the extruded region was measured to assess the influence of the local heating and deformation on the material properties. Two pieces of material were cut from an extrusion made during early fabrication trials for this work. These were flattened using the hot air fan, and then machined into two rectangular strips of length 95 mm and width 50 mm. Some other specimens were also made but from a normal acrylic plate, bent and flattened several times at different temperatures ranging from 100~ to 150~ All these specimens were then strain gauged, and te:ted under uni.axial loading. The measured strains indicated that the Young's Modulus of all heat treated specimens decreased about 12%, regardless of the different ways in which the specimens were made. This reduction was taken into account in converting the measured strains into corresponding stresses.

z" z' Circle

0

I ~__~,_.~2~,_~b)~d 9

u

x

z

x

Figure 4.

Local and global coordinates

Applied Ocean Research, 1986, Vol. 8, No. 3

127

Stress analysis o f extntded ]oints for use hz offshore structures: X. Niu and W. D.Dover DETAILS OF THE FINITE ELEMENT ANALYSIS A finite element analysis has been conducted on the extruded-joints in order to calculate the stress distributions in the joints. The geometry of the joints was modelled using thin shell semi-loof elements. The calculations were conducted on a PRIME computer. It is apparent that the quality of the finite element analysis results depends to a large extent on how realistically an actual extrusion can be modelled in an analytical manner. In order to generate the finite element mesh for the extrusion region, a method for specifying the profile of t h e Fillet and its location in a global system was developed, as illustrated in Fig. 4. The approach used in this study was based on the theory of plane analytic geometry and will be briefly described as follows. As shown in Fig. 4 for the case of an extruded T-joint, cutting a simple T-joint model with a plane passing through the Z.axis at angle cz will give an ellipse with two lines parallel to the Z-axis. When r = 0 ~ the ellipse becomes a circle; when r = 90 ~ it degenerates to two lines parallel to the X-axis. The sharp discontinuity between the brace and the chord for a conventional joint is eliminated by the presence of the smooth profile of the fillet running gradually from the brace to the chord, as shown in Fig. 4. It is assumed that the fillet is a segment of a circle 0 of radius d, and that it has two tangential points C and B shared with one of the parallel lines and the ellipse respectively. The radius of the fillet d usually varies around the extrusion, and therefore, it can be regarded as a function of the angle iv. For simplicity in the following discussion, this function is referred to as the FILLET RADIUS FUNCTION. The position of the fillet in the local X'-Z' coordinate system can be determined quite easily provided that the coordinates of the circle centre 0 is known. It was found, however, that it would be easy to calculate the coordinate of the tangential point B, Xb, first, since the relationship between the coordinates of these two points would not be difficult to derive. The steps to solve the problem are stated as follows: (1) Establish an equation relating variables Xb and d with respect to angle a. (2) Solve the equation for the fillet at angle a and find the coordinates of the points on the fillet required by the finite element mesh in the local coordinate system X ' - Z ' . (3) Transfer the local coordinates into those of the global system. (4) Repeat (2) and (3) for the fillet at a different angle A theoretical equation was derived considering the fact that the derivatives of the first order for the circle 0 were identical to those of the ellipse and one of the parallel lines at point B and C respectively. The details of the derivation are given in ref. 2. Due to the complexity of the equation, it was only possible to solve it using a numerical approach. In this approach, an iteration method was adopted with respect to d as the known and Xb as the unknown. In order to supplement the information on the stress distributions, obtained experimentally using the acrylic models, the finite element study was used to estimate the effect resulting from the variation of the fillet profile on the stress distributions. This part of the study was aimed at answering two questions:

128

Applied Ocean Research, 1986, Vol. 8, No. 3

Figure 5.

A typical T-jofltt mesh

(1) How does the peak stress vary as the saddle Fillet radius changes? (2) How does the stress distribution vary as the fillet radius changes? The answers to these two questions may provide a guideline to the optimum design of extruded-joints. In answering the first question, one would face a relevant question con. cerning how far one can extrude the Fillet radius. This problem can be solved and is discussed in more detail in the next section. For the meshes used in this part of the study, the ratios between the saddle ffUet radius and the chord radius, d[R, were chosen as 1/7.5, 2/7.5, 3/7.5 and 4/7.5 respectively, and linear and parabolic functions were used as two fillet radius functions. The linear function was used for each mesh and the parabolic function was only used for the mesh of the d]R equal to 3]7.5. The study was restricted to T-joints. All the meshes required were produced using a mesh generation program which was specially developed for this study. A typical mesh of a T-joint is shown in Fig. 5. Both fine and coarse meshes were generated, but as there was little difference in the results the major part of the work was conducted with the coarse mesh. RESULTS AND DISCUSSION The fatigue strength of a welded tubular joint is dependent on the magnitude of the local stress, and this peak stress is usually found at the weld toe. For an acrylic extrudedjoint, the peak stress is found at a similar site, the fillet of the extrusion, and is in fact the maximum geometric stress in the joint. However, as the weld region is remote

Stress analysis of extruded ]oints for use in offshore structures: X. Niu and W. D.Dover 14

I

~2i

i

I

EL s GO v

from this s radius it is necessary to consider the fatigue strength at two sites; the fillet radius and the circumferential butt weld where the brace is joined to the chord. Figure 6 illustrates the stress distributions around the extrusions of the T-joint which were derived from both the experiment and the f'mite element analysis. It can be seen from this figure that the results from both methods are generally in very good agreement. In contrast, for conventional joints a satisfactory agreement is rarely achieved using these two techniques. This may result from two factors:

0 U

8

LL

\\

\

C 0

(1) The presence of the s extrusion excludes the uncertainties introduced by the irregularities in shape associated with weld metal deposits and the abrupt intersection of two cylinders. (2) The extrusions can be accurately modelled using thin.shell elements, but this is not possible for the intersection between the chord and brace of conven. tional joints. 3

u

s C OJ u

4

0

\

u'l t/3

2

0

. . . . .

2

. . . . .

i . . . . . .

G

8

!0

Xll~ | Angles oround the extrusion ( degrees ) Finite element Qnalgsis Experiments

Figure 6a. loading

Stress distribution of a T-joint under axial

The results of the stress distributions for the X-joint are not presented in this paper, however the agreement between the results of finite element analysis and the experiments is just as good as that in the T-joint. As expected, the peak stresses in the extruded-joints normally occur at the deepest point of the fillet regardless of the mode of loading. Like corresponding conventional joints, the extruded-joints have peak stresses at the saddle of the joints in axial and OPB loading cases, and at some distance away from the saddle in IPB loading cases. It has been observed however, from both experiment and finite

10

//

t...)

O t.a

A LL <--~ (.~

0 U

Ll_

\ 1\

]

O

4"

o l:J

s

\

C U C 0 C_)

0

2

2

i

k

L., r

Ln t,r, 0,,, s

/

LL

...) .,..) C

3.

v

\

I."

/

/

/

/

U'I

Of)

0 0

2

6

8

2

10

Angles orouno tDe extrusion ( degrees )

XlO I

Angles oround the extrusion ( degrees ) Finite element onoLgsls Experiments

F i n t l e element onolgsls Experiments

Figure 6b. loadfllg

Stress distribution of a T-joint under OPB

18

4

XI01

Figure 6c. loading

Stress distribution of a T-ioint under IPB

Applied Ocean Research, 1986, Vol. 8, No. 3

129

Stress attalysis o f extntded ]oints for use b~ offshore structures: X. Niu and W. D.Dover Table 1. Comparisonof peak stresses between extruded ]oints and conventiottal]oints Extruded joint

Conventional joint

Type of joint

Case of loading

EX

FE

EX

FE

Kuang

Wordsworth

Gibstein

T

Axial OPB IPB Axial OPB

11.6 8.45 2.66 15.5 8.24 10.0 3.33 2.65

10.7 8.47 2.90 14.8 8.07 10.47 3.09 2.96

8.57 5.88 2.30 18.56 8.91 9.54 2.68 2.87

11.50 10.14 3.94 16.6 8.90 10.4 3.92 3.99

15.77 9.89 2.99

12.30 11.58 3.61 20.20 10.94

11.50 10.14 3.50

X

IPB EX Experiments FE - Finite Element Method -

element analysis, that for the axial and OPB loading cases, the greatest stresses are not quite at the deepest point for the fillet at angles greater than 45 ~. The difference between these stresses and those at the deepest point are insignificant from the design point o f view and hence the stress distribution in the figures refer to those at the deepest o f the fdlet around the extrusions. The results for the extruded-joints have been compared in Table 1 with those o f corresponding conventional joints, part of an earlier study at UCL, and those calculated using empirical equations. 4-6 As can be seen from the table the peak stresses of the extruded-joints are comparable to those o f conventional joints. However, it is important to realise that the comparisons made here are between the actual peak stresses obtained from extruded-joints and the socalled 'hot spot' stresses for the conventional joints. They differ in that the former is obtained by directly converting the measured strains at most highly strained areas, whereas the latter is "derived by extrapolating the stresses in a linear manner to the intersection. It is known that the stress field is yery close to the intersection o f the conventional joints and decays away very rapidly in a nonlinear manner, so that the 'hot spot' stress is lower than the actual peak stress. Therefore, it would not be appropriate to directly compare the strength of these joints in terms o f the stresses which are defined in two different ways. The stress distributions along the circumferential line passing through the saddle, and towards the intersection between the brace and the extrusion are shown in Table 2. The inconsistency between the results o f experiments and finite element analysis is quite insignificant. This may be because the change of wall thickness o f the extrusions is negligible at the fillet, but this may not be the case for the areas approaching the intersection between brace

and chord. The finite element models currently being used do not take this into account, and therefore the results o f the finite element analysis may not be properly representative o f the stresses near the intersections. Despite this both results indicate that stresses decay away fairly rapidly from the deepest point o f the fillet and become considerably smaller near the chord brace intersection. In view of the fact that the finite element method produced good agreement with the acrylic models for the fillet stress distribution, it was decided to use this technique for a further study. As mentioned earlier, one of the aspects needing investigation was the effect o f the variation o f the fillet radius on the stress distribution around the extrusion. The results for the axial loading case from this study are presented in Fig. 7 and were obtained from the models which had identical r/R, Rc[R values and a fillet radius function o f the linear type, but a different ratio ofRs/R. As shown in these figures, the normalised peak stresses known as stress concentration factors (SCF) in the models decreased when Rs/R was increased. It has been noticed that in the case o f axial and OPB loading, the increment

of SCF, ASCF = (SCF) I -- (SCF)2 is approximately in direct proportion to the increment of

Re/R, ~ ( R J R ) = (g~/g )2 -- (RJR ), that is,

A(SCF) = k" A(Rs/g ) where k is a parameter depending on r]R, Rc[R and the loading cases.

Table 2. Stresses at intersection and circumferential line passing through saddlefor T-joint

Type of loading Axial OPB IPB

EX FE EX FE EX FE

1.75 1.81 1.07 1.18 0.33 0.314

Intersection

Circumferential line through saddle

Saddle ~ Crown

Chord ~ Brace

1.I 1.52 0.76 0.917 0.54 0.56

EX - Experiments FE - Finite Element Method

130

Applied Ocean Research, 1986, Vol. 8, No. 3

1.0 0.90 0.50 0.34 0.68 0.66

0.95 0.52 0.19 0.0 0.72 0.67

0.90 0.42 0.20 0.0 0.67 0.852

5.31 4.28 4.38 4.30

11.6 10.7 8.45 8.47

2.10 3.50 1.20 2.52

1.75 1.81 1.07 1.18

Stress analysis of extruded /ohzts for use in offshore structures: X. Niu and I4I.D.Dover 12

4

\

"

LL

(--) r v

o

L

03 v

8

.-

o .+

~ LJ

/

"

/

U ~

U.. ~

C

o

6

~~

u

4

t.J

c" ~

y

2

0

m

t~

tn

2

1

~

0

0 0

2

4

6

8

10

0

2

4

6

8

XIB 1

Angtes around the e x t r u s i o n ( degrees

AngLes around the e x t r u s i o n ( degrees

)

Rs/R Rs/R Rs/R Rs/R

= : = =

v

1.0/7.5 2.0/7.5 3.8/7.5 4.0/7.5

)

Rc/R = 1 . 0 z 7 . 5 , Rs/R = 3 . 0 / 7 . 5 Rc/R = 1 . 5 / 7 . 5 , Rs/R = 3.g/7.5

A z v ---a-o

10 XIO1

Figure 8a. Effect of ratio Rc/R on stress distribution of a T-/oint under 1PB loading

Figure 7a. Effect of Ratio Rs/R on stress distribution of T-joint under axial loading <10-

I

~2

1

I1

%, 10

3

\ \

C, ""0

'=% b'

2~

9

~D

\

7

2

4

6

8

10

X101 6: I

AngLes around the e x t r u s i o n ( degrees 4

2

5

6 X1(3-1

Ratio

Figure 7b.

Rs /

A

R(a) = 3.0-2.0a/90.0 R(a) = 3 . 0 - 1 . 5 a / S 0 . 0 R ( a ) = 2 . 0 - 2 . 0 c a/SO.O) 2

R

Variation of peak stresses versus ratio Rs/R

)

Figure 8b.

Fillet radius functions

Applied Ocean Research, 1986, Vol. 8, No. 3

131

Stress analysis o f extruded johzts for use h2 offshore structures: X. Niu and IV. D.Dover For the models under consideration, which have: r

-- = 0.667 R

Rc

.,_ f...)

- - = 0.067 R

co v t

k has the following values:

-o o

7.2 axial loading

LL

U

k=

5.75 OPB loading

In the case o f IPB, the location of the maximum SCF varies according to the Rs/R. When Rs/R is less than 1/7.5, the maximum SCF is at a position between the saddle and crown; when larger than 2/7.5, it shifts to the crown. Moreover, the maximum SCF at the crown increases proportionally to the increase of Rs/R. This is thought to be because the Fillet radius function used was a linear function so that Rc/R was kept as a constant. Increasing the ratio Rs/R, therefore, will result in an increase of the fillet radius around the whole extrusion except at the crown. The proportion of the load attracted by the crown will increase, thus causing the maximum SCF to take place at the crown. Clearly; this should not be allowed t o happen from optimum design point of view, and in fact can be avoided by simply increasing Re[R, as shown in Fig. 8. As shown in Fig. 9, when Rs/Ris increased, the stresses decay more rapidly along the circumferential line passing

Rs,~l

=

1:7.$

Rs.R

=

47..5

SCF

I

10.7/~ 7,4

os

-~ 0~ t.J c o U1

m (D ~-

oh

,/ 0 0

2

2/'8

Figure 9. Stress distribution along circumferential line passing through saddle.

Applied Ocean Research, 1986, Vol. 8,No. 3

4

6

10

8 XlO1

AngLes a r o u n d t h e e x t r u s i o n

( degrees

)

R(~) = 3.0-2.0~/90

v

R(~) = 3,0-2.g( o/9@):

Figure 10. Effect o f JTllet radius function on stress distribution era T-joint under IPB loading through the saddle, and stresses around the intersection decrease to an even lower level. Although the results shown in Fig. 9 are only representative of the stress distributions in the axial loading case, it has been found from this study that in the IPB a n d OPB loading eases the stress distributions were also affected by the variation of the ratio Rs[R in a rather similar way. Briefly, by increasing Rs[R, the peack stress at the fillet can be reduced to a lower level in comparison with that in a conventional joint, and the stress at the weld toe of a steel extruded joint can be considerably reduced as a result of the decrease in the local geometric stress. In order to ensure that the structure of the extrudedjoints will not be too distorted due to the extrusion of large Rs/R ratios, it is necessary to determine the maximum d]R which can be achieved in practice. The maximum d[R can be readily worked out according to the criterion that the material needed to form the extrusions should not be in excess of that the chord can provide. This consideration only needs to be applied to the saddle section of the extrusion, because this is the region where the largest deformation of the extrusion takes place. The problem can be solved from theory and an equation was derived as follows:

r/R + d/R l + d[R

132

f

c O .4.)

[ sin ~

~

zr d/R \ +-I 0 l + d[R 2 l + d/R)=

The details are given in ref. 2. For the joints currently being studied, the ratio r]R is equal to 0.667 and ~ is equal to 30 ~ so that the maximum d[R, according to the calculation by above equation, is 0.586. This indicates that the peak stress of the joints can be further reduced by increasing Rs up to 0.586R.

Stress analysis o f extruded ]oints for use in offshore structures: X. Niu and W. D.Dover In investigating the effect of the fillet radius function on the stress distribution, the two functions chosen were linear and parabolic, as shown in Fig. 8. The radii at the saddle and crown were kept as constants, while the radius between these two positions varied according to the radius function. As observed in Fig. 10, when the joints are subjected to IBP loading, the joint having a parabolic t'diet radius function has a lower stress distribution than the joint having a linear •let radius function. However, the difference produced by these functions is not significant. In the axial and OPB loading cases the effect of the fillet radius function is even less significant than that in the IPB loading case. The implication is that the value of the peak stress and the manner of the stress distribution around the extrusion are dominated by the radii of the saddle and crown.

CONCLUSIONS Some conclusions drawn from this study are stated as follows: (1) By using strain-gauged acrylic models or finite element method, the actual peak stress in extruded joints of T- or X-configurations can be determined more accurately than those in conventional welded joints. (2) An extruded-joint can be made to have a smaller stress concentration factor at both f'diet and weld

(3)

(4)

toe than that in conventional welded joint providing the ratio between the saddle fillet radius and chord radius, Rs[R , are adequately large. The increment of stress concentration factor at the saddle site is in a direct proportion to the increment of ratio Rs/R, for the joints of T-type subjected to axial or OPB loading. The stress distribution around the extrusion is dominated by R s and Re, and is fairly insensitive to the way the/'diet radius varies between the saddle and crown sites.

REFERENCES 1 Dharmavasan, S. and Dover, W. D. Stress clis~/ibution formulae and comparison of three stress analysis techniques for offshore structures, Proc. 3rd h2t. Syrup. on Offshore Mechanics and Arctic Engineeri~zg,ASME 1984, New Orleans, USA 2 Niu, X. Effect of local stresses on fatigue strength of welded tubular joints, PhD thesis to be submitted to University of London 3 Dover, W. D. and Holbrook, S. J. Fatigue crack growth in tubular welded connections,lnt. 3".Fatigue January 1980 4 Kuang, J.G. etal.,OTCPaperNo. 2205, 1975 5 Wordsworth, A. C. and Smedley, G. P. European Offshore Steel Research Seminar, Cambridge, Paper 31, November 1978, European Offshore Steels Research Seminar, Cambridge, Paper 26, November 1978 6 Cribstein, M. B. Parametric stress analysis of T joints, European Offshore Steels Research Seminar, Cambridge, Nov. 1978, Paper 26.

Applied Ocean Research, 1986, Vol. 8, No. 3

133