Stress Concentration in Tubular Joints
Authors: Kuang J.G. , Potvin A.B. , Leick R.D. 
Published: October 2008

Abstract
Fatigue cracking caused by stress concentrations in tubular joints has been observed in some fixed platforms installed in hostile environments such as the North Sea. Consequently, the ability to assess the magnitude of the stress concentration is a prerequisite to dealing with the fatigue problem of tubular joints. This paper deals with the problem of computing the stress concentration in three types of simple, non-reinforced joints: T-Joints, K-Joints, and TK-Joints. Semi-empirical equations are presented for estimating the stress concentration due to axial loads and bending moments.

Introduction
In offshore structures such as fixed platforms and semisubmersible drilling vessels, stress concentrations usually occur at the intersections of tubular members (i.e. tubular joints). For some joints, the stress concentration can produce a maximum stress at the intersection as high as twenty times the nominal stress acting in the members. Stress concentrations have aggravated the fatigue of tubular joints in many existing offshore structures. Therefore, the accurate computation of stress concentrations is of utmost importance in a tubular joint design.
The first part of this paper presents a discussion of the finite element analysis method and the associated computer program developed exclusively for the analysis of tubular joints. The second part of this paper describes the parameter study carried out by means of the computer program. Formulas for estimating stress concentration factors for simple joints commonly used in offshore structures are derived from the results of the parameter study. The usage of the resulting formulas is illustrated by a numerical example.

The Analytical Technique
In offshore structures such as fixed platforms and semisubmersible drilling vessels, tubular members comprise the main load carrying components. Examples of cracking and even complete separation at the intersections of such members have been previously cited throughout the literature. A typical example of such an intersection is shown in Fig. 1. The member of greatest diameter will henceforth be referred to as the chord. The smaller diameter members framing into the chord will be called branches. The sections of the chord wall lying within the branch intersection line (if present) will be called plugs. Figure 2 shows the various simple joint types referred to in this paper.
Because of the relative complexity of the geometrical configuration of tubular intersections as well as the thin shell theory governing their behavior, reliable prediction of the stresses in such joints by analytical techniques has proven to be costly as well as most difficult. Early attempts at analysis ranged from elementary strength-of-materials approaches such as the "punching shear" method(l) to more complicated treatments which solve the governing equations by means of Fourier Series superposition. Such an attempt by Scordelis(2)'was limited to simpler geometries such as T-Joints and failed to properly account for the stiffening of the chord wall due to the presence of the branches. A more complete development by Dundrova(3) came close to giving correct results but did not completely model the connectivity of the branches to the chord.