An equivalent element representing local flexibility of tubular joints in structural analysis of offshore platforms

Compuwrs& SmrruresVol.47.No.6.pp.957-969. 1993

0045.7949193 $6.00 + 0.00 c’ 1993 Pergamon Press Ltd

Printed in Great Britain.

AN EQUIVALENT ELEMENT REPRESENTING LOCAL FLEXIBILITY OF TUBULAR JOINTS IN STRUCTURAL ANALYSIS OF OFFSHORE PLATFORMS YURENHu, BOZHEN CHEN and JIANPING MA Department of Naval Architecture and Ocean Engineering, Shanghai Jiao Tong University, Shanghai 200030, People’s Republic of China (Received 10 March 1992) Abstract-An equivalent element representing the local flexibility of tubular joints for structural analysis of offshore platforms is developed in this paper.

I. INTRODUCTION Conventionally, in the structural analysis of offshore platforms, the jacket structure is treated as a plane or space frame, with tubular members rigidly connected at joints. However, at tubular joints, where tubular members are connected, since the chord wall will deform locally after loading, the connection is not rigid.

There exists local flexibility at tubular joints. The conventional treatment would cause considerable error. It is more precise and closer to reality to take the local flexibility caused by local deformation of chord wall into account in the calculation. Research works reveal that the local flexibility of tubular joints has an important effect on the static and dynamic behaviour of the jacket structure. It will redistribute the nominal stresses, change the deformation patterns, decrease the buckling loads, as well as change the natural frequencies and mode shapes [l--3]. Offshore platform classification authorities, such as the American Petroleum Institute (API) and Det Norske Veritas (DNV), have required in their design codes that the designer should carry out a global analysis which incorporates the local flexibility of tubular joints (4,5]. Therefore, how to determine the local flexibility of tubular joints, how to take the local flexiblity of tubular joints into account in the structural analysis of offshore platforms, and how to evaluate the effect of the local flexibility of tubular joints on the static and dynamic behaviour of offshore platforms become important research subjects in the field of offshore engineering. Research on the local flexibility of tubular joints started at the beginning of 1980s. The local flexibility of tubular joints is defined as the local deformation caused by unit external load. For T-type and Y-type tubular joints, we have the following definitions

LJF,x = ip,

LJF,,, = $

and I

LJFope = $!-, 0

where LJF denotes the local flexibility of tubular joints (Local Joint Flexibility). Subscripts AX, IPB and OPB denote the cases in which axial force, in-plane bending moment and out-of-plane bending moment are applied respectively. 6 is the local translational displacement in the direction of brace axis at the intersection of chord wall and brace, which is caused by the axial force P. The deflection of the chord as a beam under bending is not included in 6. 4, and &, are the local rotations at the intersection of chord wall and brace, which is caused by the in-plane bending moment M, and the out-of-plane bending moment M,, respectively. The rotation or twisting of the chord as a beam under bending or torsion is not included in 4, or &. For K-type tubular joints, a local flexibility matrix is defined. Generally, the relation between local displacements (rotations) and external loads can be written as

.a, 41, 601

62 = [LJF]

e&! d 02

(2)

YUREN Hu

958

er a/.

where matrix [LJF] is the local joint flexibility matrix (LJF matrix). The leading diagonal elements of the LJF matrix represent the relation between external loads and corresponding local displacements (rotations). The elements off the leading diagonal represent the interaction between braces. If only axial force and in-plane bending moment are considered, i.e. for the plane frame case, the LJF matrix can be reduced to

a21

a2,

a2)

a24

a3l

a32

a33

ax

a41

a42

a43

a44

a21= ai2,

a31 =

013 9

a4l

=

aI4

a32 =

a42 =

a24 T

a4,

=

a34.

(3)

According to the reciprocal theorem, we have

(4) a23 7

Therefore, the LJF matrix is a symmetric matrix. Theoretical and experimental works have been carried out to find the method for determining the local flexibility of tubular joints. A number of parametric formulas have been proposed, which include the formulas proposed by Fessler et al. based on the results from the acrylic model test [6-81, the formulas proposed by Ueda et al. based on the results from FEM calculation [9], and the formulas proposed by the authors of the present paper based on the results of the calculation by using the semi-analytical method [IO, 111. In respect of experimental work, apart from the above-mentioned acrylic model test by Fessler et al., some data from steel model test have been reported by Tebbett [12]. Tests on steel models of T-type tubular joints and on acrylic models of Y-type and TY-type tubular joints have been carried out by the authors of the present paper [13, 141. In order to take the local flexibility of tubular joints into account in the structural analysis of offshore platforms, it is necessary to establish a reasonable model in calculation, which can reflect the characteristic of the local flexibility. Generally, there are three basic methods. The first method is that an effective length is adopted to replace the real length of the brace, so that the leading diagonal elements of the stiffness matrix of the structure can be modified. This method is only an approximate one. It is difficult to choose an appropriate effective length to represent the exact value of the local flexibility of tubular joints. The second method is that a simple spring in the direction of the brace axis is used to represent the local joint flexibility. This is the easiest method, but for K-type tubular joints, the interaction of two braces cannot be reflected by this method. The third method is that the tubular joint is modelled as a three-dimensional finite element sub-structure. Obviously, this is the most accurate method, but a large computational effort and therefore cost penalty is involved in this method. In development of the finite element analysis package OFFPAF for offshore structures by Wimpey Laboratories Limited, five alternative models representing tubular joints were established [12]. Three of the five models include local joint flexibility. In addition, Ueda et al. developed a model in which a set of additional beam elements are used to represent the local flexibility of tubular joints [9]. In this paper, an equivalent element representing the local flexibility of tubular joints for structural analysis of offshore platforms is developed. At the tubular joint, brace and chord are considered to be connected through an equivalent element as shown in Figs I and 3. By considering the relation between external loads acting on the tubular joint and local deformations of the joint, stiffness matrix of the equivalent element is derived. After evaluating LJF or LJF matrix of the tubular joint from parametric formulas, the stiffness matrix can be calculated. The characteristic of local flexibility of tubular joints can well be modelled by the equivalent element. For K-type tubular joints, it can effectively reflect the interaction of two braces. The equivalent element can easily be used together with a general-purpose finite element analysis program, such as SAPS, for precise analysis of the jacket structure of offshore platforms. 2. EQUIVALENT ELEMENT REPRESENTING LOCAL FLEXIBILITY OF T-TYPE AND Y-TYPE TUBULAR JOINTS

First, we will develop the equivalent element representing the local flexibility of T-type and Y-type tubular joints in this section. Without loss of generality, consider a Y-type tubular joint as shown in Fig. 1. If the angle between brace and chord is 90 degrees, it becomes a T-type tubular joint. In Fig. 1, point i is the intersection of brace axis and chord wall, point k is the intersection of brace axis and chord axis. An equivalent element eLJFrepresenting the local flexibility of tubular joints is inserted between point i and point k. The

An equivalent element representing local flexibility of tubular joints

959

(a) Y-type tubular joint

\P

Beam element Rigidly coantcted

A Beam element (c) LJP is considered

(b) Conventional treatment

Fig. 1. Y-type tubular joint and its models in structural analysis.

following discussion will be limited to the case in which only axial force and in-plane bending moment are applied. The axial force applied to the tubufar joint, P, is resolved into two components Px and P,, which are in x and y directions respectively (see Fig. I). Forces acting on node i and node k of the equivalent element are denoted by X,, Yi, Z, and X,, Y,, Zk, respectively (see Fig. 2a). It is easy to find that Xi = Px, The equilibrium

Yi= -P,

and

&=M.

(5)

of the equivalent element yields Xk = -Xi,

Yk= - Yj and

Z, = Xi1 sin B + Yil cos 9 - Zi,

(6)

where t is the length of the equivalent element, which is

Id?.-

(7)

2sin9

where D is the diameter of the chord, 8 is the angle between brace and chord.

(b)

k

Fig. 2. Node forces and displacements of the equivalent element for Y-type tubular

YURENHu et al.

960

(a) K-type tubular joint

pr

h;\ Ml

/

Beam element

\

\

\

\

\

/

\

/

\

Be;m element

/

i-j

Ll

\I Rigidly connected

,/ i

LA

(c) LJP is considered

(b) Conventional treatment

Fig. 3. K-type tubular joint and its models in structural analysis.

From eqn (5) and eqn (6) we get the relation between external loads and node forces of the equivalent element, which can be expressed in matrix form as 1 0 0

'Xi yi

or

Z, = Xk Y!i G

0

0 0

0

1

0 1 -lcose

0 0

-1

-1 0 I sin e

P.T

PJ

-1

{XI = PXPIV where transformation

(8)

[ A4

(9)

matrix [T] is 0 0 0

-1 0

sine

01

0

-1 0

1

0

0

1 - -ic0se

0 -

-1

1 .

(10)

Then, displacements are considered. Let displacements at node i and node k be ui, vi, fIi and u,, vkr B,, respectively. The relative displacements between node i and node k are (see Fig. 2b) 6, = 4 - (Up- e,l sin e) 6,= -++(v,-eklCOSe)

(11)

An equivalent element representing local flexibility of tubular joints

961

where the positive directions of 6,, 6, and 4 are the same as those of Px, P, and h4, respectively. Equation (11) can be written in matrix form as r"i

1 0

0 -1

0 0

-1 0

01

0

0 1

(12)

00

-1

or (6) =

[r]r{u}.

(13)

Generally, the relation between relative displacements and external loads can be written in the following matrix form

(14)

or

(6) = Vl{PI.

(15)

From eqn (15) and eqn (13), we get {P} = [/I]-‘{is}

Substituting

= [A]-‘[T]T{ V}.

(16)

eqn (16) into eqn (9) yields Q-1 =

m[~l-‘[~lr~~~ = Kl{W,

(17)

where [K] is the stiffness matrix of the equivalent element eUF, which is kx

0

0

0

-kx

Lo

0

-

=

s2

-Cl1

Gil

[K] = [z-][A]-‘[T]T

s,

1

1

0

o-

k,

0

1 -

c22

c22

(18)

-s,

where s, = k,i sin 0,

icose

s2 = -

CII (19) 12cos* e s, = k,12 sin’ 8 + +‘. CII c22 Since the stiffness of the chord wall in axial direction is much greater than those in other directions, the tension and compression in x direction can be neglected in the calculation. Therefore, we can take kx+co in matrix [A]. In addition, according to the definition of the local flexibility of tubular joints, we have LJF, CII =2 sin 8 ’

~22 =

LJh,,

.

(20)

962

hIlEN

Hu

et ai.

After evaluating LJF,, and LJFira from parametric formulas, the stiffness matrix of the equivalent element eUF, [K], can be calculated from eqn (18). 3. EQUIVALENT ELEMENT REPRESENTING LOCAL FLEXIBILITY OF K-TYPE TUBULAR JOINTS

Now we derive the equivalent element representing the local flexibility of K-type tubular joints. A typical K-type tubular joint is shown in Fig. 3, in which point i is the intersection of the axis of brace I and chord wall, point j is the intersection of the axis of brace II and chord wall. Point k is located at the chord axis so that an isosceles triangle is formed by points i, j and k (see Fig. 3). The equal angle a can be calculated from geometry, which is

OL =arctan(g&+&+g)7 (21)

where d, and d2 are diameters of brace I and brace II respectively. 6, and 8, are the angles between brace I and brace II and the chord, respectively. g is the gap between two braces. The isosceles triangle is the equivalent element cur representing the local flexibility of K-type tubular joints. The stiffness matrix of the equivalent element will be derived as follows. Consider a K-type tubular joint as shown in Fig. 3. Axial forces, P, and P1, and in-plane bending moments, M, and M2, are applied. The axial forces are resolved into components in x and y directions, i.e. P,,, P,, and Pzx, Pzr as shown in the figure. Forces acting on the nodes i, j and k of the equivalent element are denoted by Xi, Y,, Zi; Xi, Y, Zj and X,, Yk, Z,, respectively (see Fig. 4a). Therefore Y,= -P,y,

Xi=PIX,

Zi= M,

(22) Xi= -Pzx,

From the equilibrium

q=

-Pzy,

Z,= M2.

of the equivalent element, we have (see Fig. 4a) X,= -(Xi+Xj),

Yk= -(Yi+

r,)

(23) Z, = (Xi + Xj)r sin a + (Y, - Y,)I cos a - (Z, + Z,), where 1 is the length of the two equal sides of the isosceles triangle, which is

I’&.

(24)

The relation between external loads and node forces of the equivalent element can be obtained from eqns (22) and (23), which is 0

0

0

0

0

0

0

0

1

0

0

0

0

0

xi

1

Yi

0

zi

0

0

0

0

0

0

0

0

0

0

0

0

0

0

I

0

0

1

0

0

1

0

0

1

0

-Isina

lcosa

X, I;

=

z, xk yk

Zk

-1 0 1 sin a

0 -1

-fcosa

-1

-1

0

-1

P IX P IY M, P 2x

(25)

P2Y M2

-1

or

w =mp~.

(26)

An equivalent element representing local flexibility of tubular joints

963

(b)

(a)

Fig. 4. Node forces and displacements of the equivalent element for K-type tubular joints where transformation

matrix [T] is 0

1 0

P-1=

0

0

0

0

0

0

0

0

0

0

1

0

0

0

0

0

0

0

0

-1

-1

0

0

0

0

0

0

0

0

0

1

-1 0 I sin u

-1

0

0

0

I

0

0

1

0

0

I

0

-Icosa

-1

-Isinx

Icoscc

(27)

-1

Let displacements at nodes i, j and k be u,, ui, Oi; uj, uj, 0, and uk, uk, On, respectively. The relative displacements are (see Fig. 4b) 6,,=ui-(u,--fI,1sincc) 6,, =

-7.++(vk-ekf

~0s~)

44= 4 - 0, 6,=

-u,+(u,-0,Isina)

6,=

-u,+(v,+e,lcosu)

(28)

where the positive directions of 6,, , 6,,, 4,, 6,, 6, and & are the same as those of P,,,P,,,M,, P2x,P,,, M2, respectively. Equation (28) can be written in matrix form as 4

-1

00 O-10

0

01

0

00-l

0 .o

0 00

0

0

/sine

0,

i

-Ic0se

4

0

0

00

0

0

00

00

00

1 0

0 0

-1

0

-1

0

0 01

0 00

-1

i

-Isine ~COS~

-I

9

vj 4

(29)

uk vk ek

or (30) CAS 47,6-F

YURENHu et al.

964

Generally,

the relation between relative displacements

and external loads can be expressed as follows:

~00000

P Ix

Xl

=

0

Cl1

Cl2

0

Cl3

Cl4

P IY

0

c21

c22

0

c23

c24

Ml

0

0

P2x

0

0

1

0

(31)

k, 0

C3l

c32

0

c33

c34

P2Y

0

Cdl

c42

0

c43

c44

M2

or

(6) = [Al{PJ.

(32)

From eqns (32) and (30) we have {P} = [A]-‘(S) Substituting

= [A]-‘[z-IT{ U}.

(33)

eqn (32) into eqn (26) yields (34)

where [K] is the stiffness matrix of the equivalent element eLIF, which is [K] = [T][,4-‘[TIT.

(35)

If axial tension and compression of the chord wall is neglected, we can take k,, -+ co and k, + co in matrix [A]. From the definition of the local flexibility of tubular joints, we have

C]I =7

aI2 c,2= c2,= 7 sm 0, ’

alI

sin 8, ’

aI3 Cl3

=

C3l

=

c22 =

a22

cjj =

-7---

1

aI4

c,4= Cd,= 7 sm 8, ’

sin (?Isin Q2’ $3

=

cj2

=

sm e2 ’

a33

sm2 e2 ’

c34

=

(36)

a23 7

c43

=

c24

=

a34 sin e2 ’

c42

=

a24,

c44 = aM.

7

Let matrix [C] be Cl1

[Cl = [

Cl2

Cl3

Cl4

c22

c23

c24

c33

c34

Sym

C44

I.

(37)

Assume that the inverse matrix of [C] has the following form

(38)

An equivalent element representing local flexibility of tubular joints

965

Therefore, we have

[A]-’

Substituting element

=

(39)

[A]-’ into eqn (35) and after manipulating,

k XI

we get the following stiffness matrix of the equivalent

0

0

0

0

0

-kx,

b,,

-b,,

0

b,,

-b,4

0

0

-62,

b,,

0

km

0

0

-k,

b33

-b,

b 22

WI =

0

-b,,

SI

-b,,

s2

b,2 - b,,

s3

0

34

-b,J - b3,

S5

0

b,4 + b,

kx, + km

0

-s,

-s4

b,, + 2bu + b,,

-s2

-

bu

Sym

0

sb

s5

Sl

where s, = kx, 1 sin a s2 =

(b,, - b,$

cos a + (b,, + b,,O

x3 =

-(b,, - b&l cos a - (bz2+ bN)

s5 =

(b,, - bJ3)l cos a + (b23+ b,)

sb =

-

(41) (b14 - b,)l cos a - (b24+ b4)

s, = (k,, + km)12 sin2 a + (b,, - 2b,, + b13)12COS’ a + 2(b,, + b,4 - b,, - bM)l cos a +

(b2,+ 2b,,+ bd.

After evaluating a,, , a,,, q3, a,*, u22,Use,a,,, a,,, au, and a, from parametric formulas, matrix [C] can be formed from eqn (37). Then by inversing matrix [Cl, the stiffness matrix [K] can be obtained from eqn (40). 4. APPLICATION OF EQUIVALENT ELEMENT TO FINITE ELEMENT ANALYSIS OF JACKET STRUCTURES

With the stiffness matrix of the equivalent element derived in previous sections, we can take the local flexiblity of tubular joints into account in finite element analysis of the jacket structure of offshore platforms. For example, if the general-purpose finite element analysis program SAPS is used, the read-in stiffness matrix element in SAPS element library can easily be used as the equivalent element. The stiffness matrix to be read in is the stiffness matrix of the equivalent element derived in previous sections. Take the Y-type tubular structure shown in Fig. 1 as an example. Conventionally, brace and chord are treated as two beam elements rigidly connected at point k (see Fig. 1b) . For inclusion of the local joint flexibility, an equivalent element, eUF, is inserted between point i and k (see Fig. lc). Similarly, for the K-type tubular structure shown in Fig. 3, an equivalent element of isosceles triangle, eUF, is inserted between point i, j and k to represent the local flexibility of tubular joints.

966

YUREN

y(Iocal)

Hu

et al.

y&global) ,

Fig. 5. Local a global coordinate systems.

Fig. 6. Example: K-type tubular structure.

In program SAPS, the read-in stiffness matrix element is with respect to the global coordinate system of the structure, while the stiffness matrix of the equivalent element derived in previous sections is with respect to the local coordinate system of the tubular joint. Generally, if the angle between the local coordinte system of the tubular joint and the global coordinate system of the jacket structure is (b (see Fig. 5) then the following coordinate transformation should be carried out for the stiffness matrix,

where [K,] is the stiffness matrix of the equivalent element with respect to the global coordinate system, i.e. the stiffness matrix which can be read in directly in SAPS. [T,] is the coordinate transformation matrix. For T-type and Y-type tubular joints

ITsI= :, ; [

1

t1

and for K-type tubular joints Kl=

0

0

i 0

t

0 ,

0

0

t

(43)

where cos f#l

[t] =

-sin4

sin C#J

[

0

0

COSC) 0

0

(45)

1

A preprocessing program for automatically generating data of the read-in stiffness matrix, which coincide with the input format of SAPS, has been developed by the authors, which can easily be used together with SAPS. As an numerical example, the K-type tubular structure shown in Fig. 6 is calculated. The sizes of the structure are listed as follows: diameter of chord: thickness of chord: length of chord: diameter of brace: thickness of brace: length of brace: angle between brace and chord: gap between braces:

D = 100.0 cm T=2.50cm L = 500.0 cm d, = d2= 60.0 cm t, = t, = 1.25cm I, = 1, = 250.0 cm 8, = f$ = 45 degrees g= 15.147cm.

Braces and chord are clamped at both ends. A forced translational displacement of A., = 0.1 cm, which is in the direction parallel to the chord axis, i.e. in the x direction of the local coordinate system of the tubular joint, is applied to the upper end of brace I.

An equivalent element representing local flexibility of tubular joints

961

In [lo], the following parametric formulas were proposed by the authors of the present paper for evaluating elements of LJF matrix of symmetric K-type tubular joints 4.71y2.17e -3W(sin

a,, =

@)2.‘32

a33 =

(46)

ED 169.0~ ‘.68e-4.58/J(sin

a22=a44=

=

u3,

(47)

ED’ 1.79y2.39e

a,,

(9)1.25

-2.498(sin

e)3.‘37

=

(48)

ED 19.1y 1.43e-3.W(sin a24= a42= -

e)“.86

(49)

ED3

6.691,1-68e-2-62B(sin e)1.20 a,4=a4, = -a23 = -a32 =

(50)

ED2

Equation (46) can also be used to evaluate LJF,, of T-type and Y-type tubular joints, and eqn (47) to evaluate LJF,,, of T-type and Y-type tubular joints. From these formulas, elements of LJF matrix in above examples can be obtained, which are a,, = uJ3 = 1.107 x 10e7 cm/N, x 10-l’ l/Ncm,

a,,=u,=5.383

aI3 = u3, = 8.920 x lo-‘cm/N,

u24= a,, = -8.498 x lo-l2 l/N cm, aI4 = a41= -a23 = -ax2 = 7.027 x lo-”

l/N.

From eqn (36), we get matrix [Cl, which is 2.215 x 10-r

0.0

1.784 x 1O-7

5.383 x lo-”

-9.938

x lo-”

9.938 x lo-” -8.498

2.215 x 10-r gym

[Cl =

x lo-l2 0.0

5.383 x lo-”

1.

The inverse matrix of [C] is 2.478 x IO7 -4.941

x 108

3.067 x 10” [Cl-’ = :

-2.218 x IO7 -5.356 x IO8 5.356 x IO8

1.396 x IO”

2.478 x IO7

4.941 x 108 3.067 x IO”

Sym

1 .

The stiffness matrix of the equivalent element in the local coordinate system can be obtained from eqn (40), which is the first equation overleaf. Here we take kX, = k, = 1.0 x lO”cm/N. From Fig. 6 we can see that the angle between the local coordinate system of the tubular joint and the global coordinate system is 30 degrees. Therefore

K]=[;

;

81,

]I]=[::~:’

-:i:

81.

After coordinate transformation, the stiffness matrix of the equivalent element in the global coordinate system is obtained, which is the second equation overleaf.

V&l=

WI =

Sym

Sym

2.519 x IO9

7.506 x lo9

2.678 x lo*

x 106

9.604 x 10”

-5.545

3.067 x 10”

x lo*

4.279 x 10’

-2.470

0.0 1.000 x 10’0

3.067 x 10”

0.0 0.0

0.0

4.941 x 10’

0.0

2.478 x 10’

7.506 x IO9 4.319 x IO9

- 1.000 x 10’0 0.0

x 10’

x lo7

x 10’

x 10’

2.519 x lo9

4.319 x 109

-4.638

-1.664

9.604 x IO6

2.478 x 10’

0.0

-5.356

-2.218

0.0

x 108

x 10’

x 10’ 3.067 x 10”

-4.279

2.470 x lo*

1.396 x 10”

4.638 x 10’

-2.678

3.067 x 10”

-4.941

0.0

1.396 x 10”

5.356 x lo8

x lo9

x 109

x 10’

x lo9

x 109

1.500 x 10’0

2.076 x 10’

-4.329

-7.501

-2.076

-4.329

-7.501

2.000 x 10’0

0.0

0.0

- 1.000 x 10’0

0.0

0.0

- 1.000 x 10’0 0.0 x lo6

x IO6 x 10’

x lo9

x lo9

x 10”

x 10”

5.012 x lOI

-5.000

5.004 x 109

6.848 x lo9

2.489 x 10”

4.337 x 10”

-8.660

x 10’

x lo9

x lo9

6.848 x IO9

2.511 x 10”

4.324 x 10”

5.012 x 10”

0.0

1.000 x 10’2

6.848 x lo9

- 1.319 x 109

5.000 x 10”

6.848 x lo9

1.319 x 109

5.000 x 10”

8.658 x lo9

-3.596

-2.502

-4.329

3.596 x 10’

-2.502

-4.329

5.208 x lo6

0.0

-4.152

-2.604

0.0

4.152 x IO7

-2.604

An equivalent element representing local flexibility of tubular joints

969

Table 1 LJF considered LJF not considered

LJF considered

LJF not considered

Upper end of brace I

axial force (kN) shear force (kN) bending moment (kN m)

868.5 89.21 113.2

772.9 156.6 175.0

0.890 1.755 1.546

Upper end of brace II

axial force (kN) shear force (kN) bending moment (kN m)

256.4 28.44 33.91

420.7 9.273 43. I1

1.641 0.326 1.271

Left end of chord

axial force (kN) shear force (kN) bending moment (kN m)

419.2 157.8 212.3

474.1 10.43 61.96

I.131 0.066 0.292

Right end of brace II

axial force (kN) shear force (kN) bending moment (kN m)

419.2 191.9 224.8

474. I 121.3 102.7

1.131 0.632 0.457

Results of calculation by using SAP5 are listed in Table 1. Although we are not going to discuss the effect of the local flexibility of tubular joints on the static and dynamic hchaviour of the structure in this paper, we can see obviously from Table 1 that, when LJF is considered, forces and bending moments at chord ends

and brace ends will change, in other words, redistribution of the norminal stress in tubular members will occur. Therefore, we can conclude that it is necessary to take the local flexibility of tubular joints into account in the structural analysis of offshore platforms. REFERENCES

1. E. C. Rodabaugh, (1980).

Review of data relevant to the design of tubular joints for use in fixed offshore platforms. WRC

2. J. G. Bouwkamp, J. P. Hollings, B. F. Malson and D. G. Row, Effect of joint flexibility on the response of offshore structures. In Proc. Offshore Technol. Conf, Houston, TX, Paper OTC 3901 (1980). 3. Atkins Research and Development, Node flexibility and its effect on jacket structures-a pilot study on two-dimensional frames. Underwater Engineering Group, London, UEG Publ. UR22 (1984). 4. Recommended practice for planning, designing and constructing fixed offshore platforms. American Petroleum Institute, RPZA 17th Edn (1987). 5. Rules for the design, construction and inspection of fixed offshore structures. Det Norske Veritas, reprinted with corrections (1982). 6. Underwater Engineering Group, Design of tubular joints for offshore structures. Underwater Engineering Group, London, UEG Pub]. UR33 (1985). 7. H. Fessler, P. B. Mockford and J. J. Webster, Parametric equations for the flexibility matrices of single brace tubular joint in offshore structures. In Proc. Insfn. Civ. Engrs., Part 2 (1986). 8. H. Fessler, P. B. Mockford and J. J. Webster, Parametric equations for the flexiblity matrices of multi-brace tubular joint in offshore structures. In Proc. Instn. Civ. Engrs., Part 2 (1986). 9. Y. Ueda, S. M. H. Rashed and K. Nakacho, An improved joint model and equations for flexibility of tubular joints. In Proc. 6th Int. Symp. Offshore Mechanics and Arctic Engineering, Houston, TX (1987). 10. B. Z. Chen, Y. R. Hu and M. J. Tan, Local joint flexibility of tubular joints of offshore structures. Marine Sfructures No. 3 (1990).

11. J. P. Ma, Local flexibility of tubular joints of offshore platforms and its effect on structural analysis. Master’s thesis, Department of Naval Architecture and Ocean Engineering, Shanghai Jiao Tong University, China (1990). 12. I. E. Tebbett, The reappraisal of steel jacket structures allowing for the composite action of grouted piles, In Proc. Offshore Technol. Con& Houston, TX, Paper OTC 4194 (1982). 13. B. Z. Chen, H. T. Xu, Y. R. Hu and H. Pan, Steel model test on local flexibility of tubular joints of offshore platforms. Inr. Symp. Marine Structures, Shanghai, China (1991). 14. H. Pan, Model test and parametric analysis on local flexiblity of tubular joints of offshore platforms. Master’s thesis, Department of Naval Architecture and Ocean Engineering, Shanghai Jiao Tong University, China (1990).