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A systematic study of stresses in tubular Y and T-joints(Figure 5.1) have been conducted using the general-purpose finite element analysis package, ABAQUS/Standard(HKS 1992 a). Two types of generally curved thin shell elements, namely quadrilateral eight-noded elements denoted 'S8R5' and triangular six-noded elements designated as 'STRI65', have been chosen to model tubular joint. They are fully compatible and allow displacements normal to their surfaces and rotations about their edges. These displacements and rotations give rise to a stress distribution which varies linearly across the element. Stresses are initially calculated at the Gauss integration points and then extrapolated to obtain values at the nodal positions.

It should be noted that the tubular joints are modelled as intersecting cylindrical tubes at the mid-surfaces of the walls. Thus the weld is not modelled and some detail of the stresses are lost. This leads to hot spot stress locations which are different to steel models especially for the brace. This is the reason why there are some discrepancies between the finite element results and those obtained from steel model test, especially on the brace side. However, the difference is generally quite small when comparing with results from strain-gauged acrylic models in which the weld is also omitted. The thin shell elements do provide, in many cases, an acceptable compromise between accuracy and computational cost except for situations where the chord and brace are of similar dimensions. For this reason the present study does not include SCFs in tubular joints for which P exceeds 0.8.

In order to conduct a parametric study, 330 different tubular Y and T-joints have been chosen for finite element analyses under axial, IPB and OPB loading respectively. Covering the majority of tubular joints used in offshore structures, they spanned the following ranges of the geometric parameters: 6.0 < a < 4 0 .0 ( 5 - 1 ) 0.2< P <0.S ( 5 - 2 ) 7 . 6 < y < 3 2 . 0 ( 5 - 3 ) 0.2< t < 1.0 ( 5 - 4 ) 0.19447: < 0 < - 2 ( 5 - 5 )

In the present study, the for all joints was assigned to the realistic value of 8 in order to avoid the effect of short brace length.

Based on the mesh generation program for tubular X and DT-joints(Chang and Dover, 1996), a pre-processing program was developed to automatically produce the input files for finite analysis of tubular Y and T-joints in A B A Q U S fo rm a t. This program is capable of producing relatively fine elements in the vicinity of the brace/chord intersection, and coarse elements near the ends of the chord and brace, in order to obtain accurate results whilst avoiding unnecessary computational effect. It can reliably generate meshes for joints having widely differing geometric parameters a , (3, y, t and 0. As the hot-spot stress is defined by Departm ent of Energy(DEn) as the linear extrapolation to the maximum principal stresses, from outside the region of weld geometrical influence to the weld toe. So the size of the element in the immediate vicinity of the intersection was carefully chosen in order to make the linear stress distribution region similar to that as DEn recommended. The program requires only a small am ount o f user input, usually only either absolute dimensions or non-dimensional geom etric ratios.

Figure 5.1 illustrates three modes of loading, i.e. axial, in-plane bending(IPB) and out-plane bending(OPB) loading. Only one half of each joint geometry needs to be modelled, owing to symmetry under axial and IPB loading. Although for out-plane bending the situation is no longer symmetric, it was found(Connolly et al 1990) that satisfactory results could be obtained with the same meshes used for the other load cases by applying appropriate restraints on the bisecting plane. A typical Y-joint mesh, shown in Figure 5.2, comprises 2178 nodes and 705 elements. It ju st to o k few seco n d s o f CPU time to generate mesh on a DEC Alpha open VMS workstation.

In the case of axial loading, the nominal stress was defined as the total applied load divided by the sectional area of the brace. Nominal stresses for moment loading were calculated from simple beam bending theory, using a moment arm measured from the brace end along its outer surface to the crown position for IPB, and to the saddle position for OPB. In order to make post processing easy, loads applied to the brace end were always set to give a unit nominal stress.

It is im portant to use the correct boundary conditions to obtain a realistic solution of stress distribution in tubular joints. Both chord ends were rigidly fixed for all loading cases. Under axial and IPB, no out-of-plane displacements and rotations are permitted at nodes on the symmetry plane. For OPB the situations are no longer symmetrical, the in-plane displacements are restrained over the bisecting plane.

The finite element analyses were mn on a DEC A lpha workstation with open VMS operating system. The Young's modulus and Poisson's ratio were taken to be 207 G pa and 0.3 respectively. In order to save CPU time, each joint was analysed consecutively for three modes of loading cases, without the need for recomputing the element stiffness matrices.

A convergence test was performed firstly in order to check that the meshes used for this study were sufficiently fine to predict the stresses at the brace/chord intersection with reasonable accuracy. Three meshes with 16, 20 and 24 elements respectively around the half intersection were analysed and the SCF results from these meshes are compared in Table 5.1. Comparison of SCF values obtained from these meshes generally has shown a good convergence. The coarsest mesh, having 16 elements around one half of the intersection, was chosen for this study as an acceptable compromise between accuracy and the computational costs.

Systematic finite element analyses were carried out for 330 different tubular Y and T-joints under axial, IPB and OPB loading. With the powerful DEC Alpha workstation, it just took about 4 minutes of CPU time to analyse a typical joint. ABAQUS/Post(HKS 1992 b) was used to post process the results from ABAQUS/Standard analyses. Figures 5.3-5.5 show typical examples of the external stress distribution of a tubular Y-joint under three modes of loading respectively.

The numerically greatest principal stress on the outer surface of the tube, at each node around the intersection, was used to calculate the SCF. Stresses at nodes shared by adjacent elements were averaged around, but not across the intersection. The SCF distributions along the intersection have been extracted from the 330 ABAQUS output files for curve-fitting by using some batch files in open VMS operating system.