A tapered stress joint or TSJ is assumed to be conical in shape. The specification of geometric properties for a set of elements which together comprise a TSJ is reasonably similar to that of a set of standard beam elements when the Rigid Riser format is used. Specifically, you input Young’s modulus, shear modulus, mass density etc. However, instead of specifying single (constant) values for the various diameters (drag, buoyancy etc.), you actually enter two values for each diameter, one for the start of the tapered stress joint and one for the end. The diameters vary linearly from the start to the end of the TSJ.
It is important to note that all of the properties of the elements of the tapered stress joint set are specified using tapered stress joint data - no properties are assigned to these elements using the normal facilities for beam-column elements. This reflects the reality that a tapered stress joint is normally an integral part of a riser system (as opposed to a bend stiffener, which provides additional stiffness to a section of riser). The calculation of the standard beam-column properties from the tapered stress joint data is straight-forward. Note that as all beam elements in Flexcom have uniform diameter along their length, tapered stress joints are in fact represented using a series of beam elements of varying diameter. External diameters at the start and end of an element of the set are found by linear interpolation, and these are averaged to give an equivalent external diameter for the element. The process is repeated to find equivalent internal diameter, drag diameter and buoyancy diameter values if necessary. The average external and internal diameter values for an element are used to calculate A, I and J, and these are combined with the user-specified values for Young’s modulus and shear modulus to get bending, axial and torsional stiffnesses for the element. Multiplying the material mass density by A and J in turn gives respectively the mass per unit length and the polar inertia per unit length. From this point on the tapered stress joint element is treated exactly like any other beam-column element.
•*TAPER is used to assign properties to a set of elements that collectively comprises a tapered stress joint, typically in a model of a rigid riser.
If you would like to see an example of how this keyword is used in practice, refer to A02 - Spar Production Riser.