SCF Equations for T/Y and K Square-to-Round Tubular Joint
Authors: Soh Al-Kah , Soh Chee-Kiong 
Published: December 2007

Summary
A parametric stress analysis of T/Y and K square-to-round tubular joints subjected to axial loads and in-plane and out-of-plane bending moments has been performed with the finite-element technique. Twenty-two and 26 sets of geometric parameters were used for the study of T/Y and K joints, respectively. This study was carried out to provide a sound basis for using square tubular sections in the design of offshore structures. The results of this analysis are presented as a set of 21 equations expressing the stress concentration factor (SCF) as a function of the relevant geometric parameters for various loading conditions. A comparison is made between the results obtained for square-to-round tubular joints and those obtained for round-to-round tubular joints and for square-to-square tubular joints. In general, the SCF's obtained from square-to-round tubular joints are closer to those of the corresponding round-to-round tubular joints than those of the corresponding square-to-square tubular joints.

Introduction
Conductor guides are important items on a drilling platform. The conventional conductor guides consist of a truncated cone attached to a section of pipe, and some gusset plates that serve as stiffeners, as shown in Fig. 1. These guides are expensive because their fabrication is not amenable to automation and is labor-intensive. These complicated guides could be simplified, however, if square hollow sections were used to fabricate the conductor framings (Fig. 2) instead of the pipes used in conventional designs. A preliminary study I shows that fabrication work-hours could be reduced by as much as 50 %, in addition to a 25 % saving in material cost, if square hollow sections were used to fabricate conductor framings. A feasibility study for the use of square hollow sections to fabricate conductor framings has to be carried out before an alternative conductor guide design can be proposed to the offshore industry as a standard design. One of the most important design factors to be considered for the use of square hollow sections is joint fatigue. This problem could be studied only if SCF's for various configurations of square-to-square and square-to-round tubular joints subjected to various loading conditions were available. Soh et al. obtained a set of empirical equations for estimating SCF's for various configurations of square-to-square tubular joints subjected to axial loads and in-plane bending moments. SCF's for square-to-round tubular joints, however, are still not widely available. Figs. 3 and 4 show the typical T/Y and K unreinforced square-to-round tubular joints, respectively. These two types of joints are commonly seen in framed structures and therefore were selected for this study. A tubular joint may be subjected to three basic types of loading conditions: axial loading, in-plane bending, and out-of-plane bending. It is important to note that only one-half of the joint needs to be considered for analyzing axial loads or in-plane bending moments, but not out-of-plane bending moments, because axial loads and in-plane bending moments are symmetrical about the plane of geometrical symmetry of the joint, whereas out-of-plane bending moments are not. Thus, out-of-plane bending moments can be analyzed only if the complete joint is considered. A parametric stress analysis of T[Y and K square-to-round tubular joints subjected to axial loads, in-plane bending moments, and out-of-plane bending moments was performed with a well-established finite-element software package, PAFEC, which operates on the VAX 8800. The SCF's of various T/Y and K square-to-round tubular joints can be estimated from this parametric study. A comparison is made between the results obtained for square-to-round tubular joints and those for round-to-round tubular joints by Kuang et al. and Wordsworth and Smedley and for square-to-square tubular joints by Soh er al.

Analysis
Finite-Element Models. Figs. 5 and 6 show the typical finite-element models devised for the investigation of T/Y and K square-to-round tubular joints, respectively. These half-joint models were used for analyzing axial loads and in-plane bending moments. Complete joints were modeled with mirror image for analyzing out-of- plane bending moments. These models used eight-noded, semilog, curved-shell elements, PAFEC element type 43210, which generally can be used for any curved and folded shell problems. This type of element can carry bending and membrane loads but 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 modeling of square hollow sections. The 43 degrees of freedom in this type of element are reduced to 32 (i.e., three translatory degrees of freedom at each of the eight nodes and one rotational degree of freedom at each of the eight points referred to as loof nodes) for merging by applying constraints on the motion. Too and Wong carried out a patch tests to ascertain the reliability and accuracy of this type of element for abrupt changes of geometry, such as 90deg. angles of a square tubular section. The results obtained were in good agreement with those obtained by the strain-gauging technique. This agreement is shown clearly in Fig. 7, where the direct stress distributions obtained by the finite-element and strain-gauging techniques, for a simply supported L-shaped aluminum beam subjected to point loads, are compared. It is important to note, however, that the welds of tubular joints could not be included in the finite-element models because of the use of semiloof curved-shell elements. This omission of welds should give rise to higher stresses at brace-to-chord intersections; therefore, the SCF's obtained should be conservative. A study was carried out to determine the convergence rate of the models devised, in terms of computation time and accuracy, by varying the number of elements used for the models. The purpose was to ascertain the number of elements required for the models to obtain reasonably good accuracy at stress-concentrated regions without excessive computation time. The optimum numbers of elements for the half-joint and complete-joint T/Y models were found to be 332 and 528, respectively. The corresponding numbers of elements for K joint models were 420 and 576, respectively. For the half-joint models, all the nodes lying on the cut surface of a joint were restrained in such a manner that consistency of deformation would not be violated if the joint were subjected to external loadings. Moreover, the two ends of the chord were simply supported. For the complete-joint models, only the two ends of the chord were simply supported. In the actual situation, the end condition of the chord was somewhere between simply supported and built in. Higher stresses would be expected at brace-to-chord intersections, however, if the chord ends were simply supported. Hence, this condition was adopted.

SCF.
Various loading conditions can be imposed on the models devised to determine the stress distributions in the joints. The SCF of a joint subjected to a particular loading condition can be obtained by taking the ratio of the absolute maximum principal stress (i.e., hot-spot stress), which occurs at the brace-to-chord intersection, to the nominal stress of the brace. Thus, it is obvious that if the SCF of a joint subjected to a particular type of loading is known, the hot-spot stress of the joint for this type of loading can be predicted. This hot-spot stress can then be used to predict the joint's fatigue life.
SPEDE