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J. Construct. Steel Research 14 (1989) 167-180

Design and Analysis of Offshore Lifting Padeyes

Ai-Kah Soh a & Chee-Kiong Soh b

aSchool of Mechanical & Production Engineering, bSchool of Civil & Structural Engineering, Nanyang Technological Institute, Nanyang Avenue, Singapore 2263

(Received 16 March 1989; revised version received 21 June 1989; accepted 13 July 1989)

ABSTRACT

It has been a common industrial practice to design lifting padeyes for offshore structures based on some conservative assumptions and formulae in order to reduce design time and cost. Thus most of the padeyes are over-designed and therefore more costly to fabricate. The finite element technique has been employed to study some two-dimensional padeye models. The results obtained are compared with a three-dimensional finite element solution to enable the selection of a two-dimensional model which can best be used for practical designs.

NOTATION

A d E F Fx, G I Ip K P q,q '

qb, qt

Cross-sectional area Depth of a ring Young's modulus Shape factor for a cross-section Shear force in x' direction Shear modulus of elasticity Area moment of inertia of ring cross-section Area moment of inertia of the projected area of a padeye Spring stiffness Load component applied at a padeye Uniformly distributed loads Uniformly distributed loads due to bending and tension respectively

167 J. Construct. Steel Research 0143-974X/90/$03.50 ~ 1990 Elsevier Science Publishers Ltd, England. Printed in Great Britain

168 Ai-Kah Soh, Chee-Kiong Soh

a R t

tf tw

Point load applied at a padeye Nominal radius of a ring Thickness of a ring Thickness of a flange plate Thickness of a web plate

o/

A AH, A V

0

Inclination angle of the external load applied at a padeye Displacement of the centroid of a segment of ring Changes in the horizontal and vertical diameters, respectively, of a ring x and y nodal displacement components respectively Half of the angle subtended by flange plate

INTRODUCTION

A particular characteristic of offshore structures is that, unlike onshore structures, they cannot be constructed at their final locations. In fact, they must be built onshore, loaded out, transported to their actual sites, launched/lifted and installed. The dead loads of offshore structures are normally in the region of hundreds to thousands of tons. In most circumstances, these structures can be moved from one location to another only by cranes with the aid of slings and shackles which are attached to a number of padeyes built on the structure. Figure I shows a typical padeye employed for lifting of offshore structures.

The design of this type of padeye is normally based on some simplified two-dimensional models. Most designers have employed a ring subjected to a point load or a uniformly distributed load to simulate a padeye under

IHI ~~8-plate i

Fig. 1. A typical lifting padeye. Fig. 2. Two commonly used two-dimen-

sional models.

Design and analysis of offshore lifting padeyes 169

-t-- lliag Stiff mr

Fig. 3. A padeye with two ring stiffeners.

loading, as shown in Fig. 2. Note that this ring was assumed to be supported by tangential shear at the bottom. The idealised structure was then analysed using the formulae given by Roark & Young.1 It was found that the maximum stresses obtained by this design approach were always very high. As a result, two ring stiffeners were often required to strengthen the padeye instead of two flange plates, as shown in Fig. 3.

A multinational offshore company criticised this approach for being too conservative. They proposed a modified approach for padeye analysis in which the uniformly distributed load acting on the lower flange plate, i.e. qt + qb as shown in Fig. 4a, was imposed on the ring, which was used to simulate a section of pipe, as shown in Fig. 4b. This assumption was made because the connection between the padeye and pipe was subjected to both tension and bending with the maximum combined stress occurring at the lower flange. The uniformly distributed load (q') is given by 2

q' = qt + qb (1)

where

Qtf cos qt = (4Rtf sin 0 + htw) (2)

and

Qa(h + tf) tf sin a qb = 21p (3)

in which Ip = Area moment of inertia of the projected area of the padeye. However, this modified approach was not well received by most of the

certification companies because of the lack of technical literature for padeye designs to support it.


t + qb

Fig. 4a Stress distributions at padeye- pipe interface.

Fig. 4b. Two-dimensional model with uniformly distributed load calculated

from tension and bending.

In this paper, various two-dimensional models are studied and the results obtained are compared with a three-dimensional finite element solution to determine whether a two-dimensional solution is adequate for padeye design, and if so which is the most acceptable two-dimensional approach. Note that all the two- and three-dimensional finite element analyses were performed using a well-established finite element software package called PAFEC 3 which runs on a VAX8800.

ANALYSIS

Simplification of padeye design

A simple two-dimensional model, which consisted of a ring supported by springs and subjected to a point load, was devised to simulate a padeye under loading, as shown in Fig. 5. Because of symmetry, only half of this structure needs to be modelled for finite element analysis, as shown in Fig. 6. A total of 18 curved beam elements, 4 PAFEC element type 34300 which consists of two end nodes with six degrees of freedom at each node, and 17 spring elements, PAFEC element type 30100, were employed in this model. The total number of nodal points used was 19. Note that the spring elements were used to simulate the interaction between a section of pipe and the neighbouring structure. This simulation method has to be proven reliable and accurate before it can be used in the analysis of complicated two-dimensional models.


P

Fig. 5. Two-dimensional model with springs used to create shear.

Consider a ring of nominal radius R and thickness t subjected to a point load P, as shown in Fig. 7. Let l be the length of segment abcd. Therefore, l = 2~'R/n, where n is the number of segments into which the ring is divided. The shear force acting on this segment is

P/ Fx, = ~ sin/3 (4)

A spring can be used to create this shear force. The stiffness of the spring is given by

K= P/sin____~fl (5) rRA

where A is the displacement of the centroid of segment abcd. It is obvious that the stiffness of all the springs used in the finite element

model cannot be determined because nodal displacements are unknown. However, these spring constants can be estimated as follows.

(a) Assume that nodal displacement is given by,

A = ~/(Ax) 2 + (Ay) 2 (6)


I l l -

0

Fig. 6. Two-dimensional finite element model with point ioad applied.

where Ax and Ay are the x and y nodal displacement components, and AH and Av are the changes in the horizontal and vertical diameters of the ring respectively. Note that An and Av are given by 1

PR 3 ~ k, AH = ~\~ - 1.) (7)

and

Av= E l \ 8 (8)


!1

Fig. 7. A ring subjected to a point load and supported by shear.

where

kl = 1 + I /AR 2 - FE I /GAR 2 (9)

and

kE = 1 + I /AR E + FE I /GAR E (10)

in which

E = Young's modulus; I = area moment of inertia of ring cross-section;

A = cross-sectional area; R = nominal radius of the ring; F = shape factor for the cross-section; G = shear modulus of elasticity.

Note that the depth of the cross-section is the thickness of the ring of 38.1 mm and the width is given by Roark & Young 1 as

d = 1.56M~-- (11)

(b) Assume that A is a constant and it is of the same order of magnitude as Av.

Figure 8 shows the moment distributions along the circumference of the ring obtained from Roark's formula and the finite element


I ~o

Z " 1o

-10-

-20

-30

1.o 2.0 I

/ I

!

3 . 0 ~ 0 14o I~o I~o 17o 1~o

I P = 200 1 R = 0.438 m

.v.G.

Fig. 8. Moment distributions along the circumference of the ring obtained from the Roark and finite element solutions. Roark's solution ( - - - ) . Solution obtained using the first proposed method to estimate spring constants ( ). Solutions obtained using the second proposed method to estimate spring constants (A, Q, ) where A is for A = 0.0015 m, O

is for A = 0.0025 m and is for A = 0.0075m.

model with different estimations of spring stiffnesses. It is obvious that all the finite element solutions are in good agreement with each other. All the maximum and minimum moments occur at/3 = 75 and /3 = 0 respectively. Moreover, the maximum discrepancy between the minimum bending moments occurred at/3 = 0 and is only 13.2%. The moment distribution obtained from Roark's formula agrees well with all the finite element results. The maximum and minimum moments of Roark's solution also occur at /3 = 75 and/3 = 0 respectively. It is worth noting that this solution is particularly close to the finite element solution obtained using the first method to estimate spring stiffnesses. The discrepancy between their minimum bending moments is only 7.8%. Thus, the first method was employed to estimate spring stiffnesses for two- dimensional finite element modellings.


Two-dimensional finite e lement mode l

Three two-dimensional models were devised, as shown in Fig. 9, for finite element analyses. The first model consisted of half a ring of curved beams supported by springs and subjected to a uniformly distributed load, which was calculated based on the assumption that the load component perpendicular to the longitudinal axis of the pipe was uniformly distributed over a sector of the ring of the same angle as that subtended by the flange plate. Note that the flange plates of the padeye were ignored in this model. A total of 36 curved beam elements and 35 spring elements were

(n) (B) (c)

Fig. 9. Two-dimensional finite element models.

employed in this model. The second model was exactly the same as the first, except that the uniformly distributed load was calculated using eqns (1)-(3). The third model consisted of half a flange plate and ring supported by springs. Sixteen eight-noded isoparametric curvilinear quadrilateral elements, 5 PAFEC element type 36210, were used to model the half flange plate. This type of element can only perform plane stress analysis. It consists of four corner and four mid-side nodes with two degrees of freedom at each node. The four sides of this element can be curved and isoparametric formulation is employed for the element. A point load was applied to the third model instead of a uniformly distributed load as for the first two models. Note that the angle subtended by the flange plate was set to 80 in these three models.


Fig. 10. The mesh of the three-dimensional finite element model of padeye.

Three-dimensional finite element model

Figure 10 shows the mesh generated for the three-dimensional finite element analysis. It consisted of 250 semi-loof curved shell elements, 6 PAFEC element type 43210, which can be used for any generally curved and folded shell problems. This type of element can carry bending and membrane loads but it does not account for shear deflection. Therefore, the shell should be thin. However, the element may be degenerated to a flat plate which is useful for the modelling of flange and web plates. This type of element has 43 degrees of freedom which are reduced to 32 (i.e. three translatory freedom at each of the eight nodes and one rotational freedom at each of the eight points referred to as Loof nodes) for merging by applying constraints on the motion.

Too & Wong 7 have carried out a patch test 8 to ascertain the reliability and accuracy of this type of element for an abrupt change of geometry, such as 90 angles at the flange plate and pipe intersection. The results obtained were in good agreement with those obtained by the strain gauging technique.

The three-dimensional model was clamped at z = 1369 mm to simulate

Design and analysis of offshore lifting pad.eyes 177

the constraints imposed on the pipe by the connecting members. Note that the plane z = 1369 mm was chosen in such a manner that further increase in pipe length would not change the hoop stress distribution around the padeye significantly. All the nodal points lying in the xz plane were constrained in such a manner that consistencyof deformation would not be violated if the structure were subjected to external loadings. The external load was applied as pressure loading at the circumference of the hole of the padeye.

DISCUSSION OF RESULTS

Figure 11 shows the moment distributions along the circumference of the ring obtained from the three two-dimensional finite element models described earlier. It is important to note that the moment distribution obtained from the second model varied with the inclination angle a of the external load applied at the padeye. However, the most critical moment distribution occurred at a = 50 . Therefore, this moment distribution is shown in Fig. 11 for comparison with the moment distributions obtained from the other two models. The moment distributions obtained from the first two models have the same shape and the moment ratio between the first and second models is always 1.47. These two moment distributions agree with that obtained from the third model in terms of shape except for the region between/3 = 0 and 60 which is due to the fact that the latter has a flange plate. The minimum moments are -15.2, -10.3 and

q'=qt + qb iP /2 b=017B m

i 20 q = 654.1 kN/m R=0.438 m 40" R 40" R 40

/ \ ( i ) -1C

2~0

Fig. 11. Comparison of the moment distributions obtained from the three two-dimensional finite element models.

178 Ai-Kah Soh, Chee-Kiong Sob

: 1.0,

~ 0.8-

= ~ 0.6- N

,4 0.4-

~ 0.2.

| 0

-0 .2 .

-0 .4 .

-0 .8 -

-0 .8 -

-1 ,0 -

%\%

o ~ [] ~ o Q

0.2 0.4 ~. OJ5 08 [~I0 "~2~ I I I I - J _ ~

A xi o

o

o o

Q = 8223 kN c~ = 501

1.4 I i

z (m)

Fig. 12. Hoop stress distributions in the vicinity of the padeye (outer surface)./3 = 0 ( - ) , 3 (O), 9 (O), 22.5 (A) , 36.5 (rq), 51.7 ( - - - ) .

~,o ? o\ ~' / ' " . oX

V: . . !% o o

Fig. 13. Hoop stress distributions in the vicinity of the padeye (inner surface), p = 0 ( - ) , 3 (), 9 (O), 22.5 (A) , 36.5 (D), 51-7 ( - - - ) .


-10.2 kN m which occur at ~ = 0 , 0 and 40 for the first, second and third models respectively. It is obvious that these three models give much lower bending moments as compared with the case in which a point load is applied, as shown in Fig. 8.

Figures 12 and 13 show the hoop stress distributions in the vicinity of the padeye for the outer and inner surfaces respectively, obtained from the three-dimensional finite element analysis. The maximum hoop stress is 128.1 MN/m 2 which occurs at z = 0.4 m and fl = 0 on the inner surface, whereas the minimum stress is -82.8 MN/m 2 which occurs at z = 0.48 m and /3 = 0 on the outer surface. This shows that the first two two- dimensional models do give the same fl angle at which the maximum and minimum stresses occur, but the third model does not.

The maximum and minimum hoop stresses obtained from the two- and three-dimensional finite element models are shown in Table 1 for comparison. The stresses for two-dimensional models were calculated based on basic curved beam theory. Note that the stresses shown in Table 1 are the combined (axial and bending) stresses. The depth of the cross-section used for two-dimensional stress calculations was the thickness of the ring and the width was given by eqn (11). It is obvious that the designs based on two-dimensional models are very conservative. Howev- er, the third model can be improved to provide a better design by scaling down the point load to account for the effects of bending and tension. In other words, the ratio of q'/q (=0.68) should be multiplied to the point load of the third model. The moment distribution of this modified model can be obtained from that of the third model by multiplying it by a ratio of q'/q. Thus, the maximum and minimum hoop stresses of this modified model are 138.3 and - 146.5 MN/m 2 respectively, which are much closer to those of the three-dimensional solution. However, detailed studies are required before this modified model can be put into practical use.

TABLE 1 Comparison of Maximum and Minimum Stresses Between Two- and Three-Dimensional

Models

Two-dimensional solutions

First Second Third model model model

Three-dimensional solution

Maximum stress (MN/m 2) 303-0 205-3 203-3 128.1 Minimum stress (MN/m 2) -321.1 -217.6 -215.4 -82.8


CONCLUSION

The three two-dimensional models proposed can safely be used for design of lifting padeyes. The second model appears to be the best compared with the other two because it is easy to set up and analyse and it provides reasonably good results. However, this design is still too conservative. A promising solution to this problem is to modify the third model by scaling down the point load by a factor of q'/q. This possible solution should be studied in detail before it can be put into practical use.

REFERENCES

1. Roark, R. J. & Young, W. C., Curved beams. In Formulas for Stress and Strain, 5th edn. McGraw-Hill, Singapore, 1976, pp. 209-85.

2. Lo, M. H. & Kumar, S., SC1 Deck Lifting Analysis. MEPL Project No. 15531, McDermott Engineering Pte Ltd, Singapore.

3. PAFEC 75 Data Preparation, PAFEC Ltd, Strelley Hall, Nottingham, UK. 4. Tada, T. & Lee, G. A., Finite element solution to an elastica problem of

beams. Int. J. Num. Meth. Engng, 2 (1970) 229-41. 5. Cheung, Y. K. & Yeo, M. F., Quadratic isoparametric element for plane

elasticity. In A Practical Introduction to Finite Element Analysis, 1st edn. Pitman, London, 1979, pp. 80-116.

6. Ahmad, S., Irons, B. M. & Zienkiewicz, O. C., Analysis of thick and thin shell structures by curved finite elements. Int. J. Num. Meth. Engng, 2 (1970) 419-51.

7. Too, H. K. & Wong, C. F., Patch tests. In Stress Analysis of Square Tubular T and K Joints Using Finite Element Methods. B.Eng. Project Report, Nanyang Technological Institute, Singapore, 1986, pp. 18-25.

8. Macneal, R. H. & Harder, R. L., A proposed standard set of problems to test finite element accuracy. Finite Elements in Analysis and Design, 1 (1985) 3-20.

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