Analysis of Stiffened Tubular Joints

INTRODUCTION The use of tubular joints has been spurned in recent years due largely to the availability of structural steel tubing and due to improved construction techniques. Examples of tubular joints are found in offshore drilling platforms, shipboard and dockside cranes, antenna towers, and highway sign supports. Interest in these joints began in 1930 with an investigation by Whitehorse and Brueggeman1 and has continued through to the present with a paper by Reimer and Liaw2 presented at the 1976 Offshore Technology Conference. In 1970, Mirza and Smith3 reported, in a state-of-the-art study, "There are very few recorded attempts at analytical solutions for the stress distribution at a tubular joint these published attempts have necessarily been of an approximate nature and the solutions obtained are somewhat lacking in precision " The available literature contains a single analytical solution for a stiffened tubular T-joint,4 and limited experimental data for stiffened tubular T-joints, including the thesis by Termechi.5 Tubular joints may be stiffened by various means including enlarging the cross-section of a chord member in the vicinity of a joint, and using gusset plates. Gusset plates may be utilized in various ways: inter welding the chord and web members and welding gusset plates between them, welding the gusset plate to the Chord member, and the web members to the gusset plate only, or slotting the chord member with the gusset plate extending through it and welding the web members to the gusset plate. This paper presents a method of analysis for a stiffened T-joint with a gusset plate welded to the chord member. The method utilizes a strain-energy solution for a cylindrical shell subjected to radial tractions to yield a displacement field compatible with that of the gusset plate. The distribution of radial tractions is obtained by constructing a Fourier series representation that will yield the desired displacement field. MATHEMATICAL MODEL An idealized planar T-joint with a gusset plate welded to the chord member and the web members welded only to the gusset plate is shown in Fig. 1. Since superposition is valid for this case, the effects of radial load and longitudinal moment are determined separately. The chord member is analyzed using cylindrical shell theory; the gusset plate is assumed to be rigid in the radial direction and the extensible in the longitudinal direction. The positive directions of the coordinate axes and dimensions are illustrated in Fig. 2. The strain energy stored in a deformed cylindrical shell may be written as (with ?y replaced by a??) (Mathematical equation available in full paper) where u, v, and w are the displacements in the x, y, and z directions, respectively, and a is the mean radius of the cylinder. The work done by the radial tractions during deformation may be expressed as (Mathematical equation available in full paper)