Background to New Formulas for the Ultimate Limit State of Tubular Joints
Authors: Billington Colin J. , Lalani Minaz , Tebbett Ian E. 
Published: December 2007

Summary
Tubular joints constitute one of the main high-cost and problem areas in design, construction, and maintenance of steel offshore structures and have been the subject of considerable research. Recently a study of various design documents was funded by the U.K. Dept. of Energy, with particular emphasis on the static strength of tubular joints. This study concluded that no two published design documents made identical recommendations and that major inconsistencies exist. Therefore, a complete review of available static strength test data was undertaken. This paper presents the derivation of new formulas describing the ultimate limit state of tubular joints. The ranges of application of the formulas are discussed in relation to typical joint configurations and loading, and areas for future research are identified.

Introduction
Most steel offshore structures consist of three-dimensional (3D) frames composed of cylindrical steel members with hollow sections, which provide the best compromise to the requirements of low drag coefficient, buoyancy, and high strength-to-weight ratio. The hollow sections also allow use of the inner space for transportation, fire protection, or additional strength. The principal design and fabrication problem for this form of structure principal design and fabrication problem for this form of structure is the welded joints between members. Typical simple tubular-joints and the notation system used in this paper are shown in Fig. 1. The word "simple" refers to joints without overlap of brace members and without the use of gussets, diaphragms, stiffeners, or grout. Design certification of such offshore structures has led to many codes of practice, rules, regulations, guidance notes, and published research data concerning tubular joints. Recently, a published research data concerning tubular joints. Recently, a study of the various design documents was carried out for the Underwater Engineering Group and funded by the U.K. Dept. of Energy. The study includes an exhaustive review of available static strength test data, since major inconsistencies exist in current design documents for the calculation of static strength, particularly in inherent levels of safety. particularly in inherent levels of safety. Database
Careful study of all available test data revealed inconsistencies, particularly in documentation of material properties. In many particularly in documentation of material properties. In many cases, only the minimum specified material yield stresses are quoted, rather than actual values. The use of such values can lead to unconservative recommendations. Therefore, all such reported results were omitted from the data base. A number of test results were discounted where insufficient information was available or where inadequate testing procedures were adopted. The modes of failure for tubular joints are procedures were adopted. The modes of failure for tubular joints are discussed in Ref. 2. Test results where failure of the specimen was caused by a problem other than joint failure, such as brace yielding, were eliminated from the data base. The limit state design approach adopted in this paper differentiates between the two limit states of strength and serviceability. The former is taken as the maximum load achieved during the test and the second as a deflection or some other local damage criterion. Thus for the tension tests the maximum load achieved during the test has been used. The "first-crack" load is related to a serviceability limit state. The ultimate moment is taken as that value of moment at the intersection of the brace and chord rather than that at the centerline of the chord. The available test data for K-joints all relate to the case in which the net force perpendicular to the chord is zero, as is generally required by the design codes for the joint to be designed as a K-joint. Under such conditions, failure is always associated with the compression-loaded brace, and therefore the ultimate load values used for K-joints are those associated with this brace. After these criteria were applied, the data base presented in Ref. 1 was developed, giving the results for 207 tests (Table 1).

General Form of Strength Equations
In line with current trends, the format of the equations developed is based on brace member loads. This approach (1) avoids the need to introduce the concept of "punching shear," (2) is directly compatible with computer-based analysis methods that provide member loads, and (3) is also amenable to hand calculation. provide member loads, and (3) is also amenable to hand calculation. JPT
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