Offshore Structure Platform Design - Offshore Structures: Design, Construction and Maintenance - page 188

For dynamic analysis, the vessel mass and velocity were modeled; at first, the
results show a higher (20% to 30%) impact load in dynamic impact analysis than in
the static impact condition. Referring to the static impact results reveals that a
major portion of the impact energy is absorbed by the denting of the tubular mem-
ber and the software usually automatically models the denting progress of a pipe
during a static impact. The effect of denting is also very important in a dynamic
boat impact analysis: in impact between two bodies, the duration of the impact
directly affects the impact load. A softer surface in the impact increases the impact
time and reduces the impact force. Denting behavior is like a soft spring and makes
the impact condition a so it reduces the impact load.

We can use the API formula for modeling a denting spring. According to
API RP2A-WSD (21 st edition):

“ soft impact, ”

0 : 5

40F Y t 2 P d = ð X/D Þ (3.146)

where P d is the denting force and X is the denting depth. F Y , t and D are the
yield stress, wall thickness and diameter of the denting member, respectively.
This formula gives us the relation between denting depth and denting force,
and it can be modeled in the software as a nonlinear spring.
After modeling the denting springs, the impact load in the dynamic analysis
is reduced and is around 5% less than the static impact load. In some cases, the
impact analysis has been done for 12 m and 55 m water depth jackets, and after
modeling of the denting, the dynamic impact analysis gave an impact load simi-
lar to that in the static impact analysis.

3.9.5 Tubular Member Denting Analysis
Denting of a tubular member has a complicated behavior and there are few for-
mulas to describe the relation between denting force, denting depth and denting
energy, some of which are presented in the API RP2A standard. The important
point is that, in order to define how much a dent can progress in a tubular mem-
ber, we need to define the maximum allowable strain in a tubular member;
usually this value is 15% in an impact analysis. So the question becomes, how
much is the maximum denting depth that causes 15% strain in a tubular member?
The first solution is to model the tubular member in the finite element
method (FEM) and to check the strain in the dented tubular; this was done
for a 20 inch tubular member. The relation between denting load and denting
depth in the FEM analysis is very close to the API formula. This solution
requires extensive time for modeling the tube in FEM, so a simplified solution
is needed and one is described below.
Referring to FEM deformed shapes, we can conclude that denting deforms a
circular shape to approximately an oval shape, as shown in Figure 3.53 , and the
maximum stress and strain happen at the sides of the deformed tubular, as
shown in Figure 3.53 , where the radius is minimal.