Inter-element forces can also be calculated at the nodes of a riser-type structure. As shown in Figure 13.2: Loads at Riser Nodes, Structure #2 is assumed to be a riser structure consisting only of a number of tube elements. The first node (with the user-defined node number k 0+1) of the first tube in this structure is located at the seabed; subsequently, the first node of the next element along the riser structure must be the second node of the previous element. A fixed point on the seabed constrains the riser via an articulation that links the point to the first node of the first tube element.
Denoting 
as the reaction force and moment matrix due to the
articulation at the seabed in the local structure axes (LSA), and 
as the coordinate of node (k
0+j) in the LSA, the nodal loads in the LSA
for a riser-type structure can be calculated from the total tube elemental
loads at each node, given by Equation 13–84,
as
 | (13–85) |
where the 3×3 sub-matrix 
is defined as
