A structural mechanics analysis of this occurrence follows.
The forces that explain this effect are illustrated
in Figure 3.63. With the selected mean wave period Tz of
7.5 s and elevation Hs of 5.5 m, assume a wave length of
88 m and a boom that is positioned on top of the wave
crests. The top of the wave crests is shown as supports.
The boom should then be able to deflect at mid-section,
which is 5.5 m lower in order to be able to follow the
shape of the wave.
Due to the tension force Ft, the deflection is restricted to
a certain extent; this is reached when the moment around
the mid-point is zero due to combining Ft and qG only. It is
required that the possible deflection is greater than the
wave height.
Because the wave height (Hs = 5.5 m), wave length (l =
88 m), and the weight (qG= ~10 kN/m) of the boom are
known, the theoretical limit tension force in the boom at
which this deflection is still possible can be estimated
with the formula above.
Some assumptions that should be taken note of:
- Under the given length and forces, the moments are
large with respect to the bending stiffness of the boom
such that it behaves like a rope, having no bending
stiffness.
- The boom floats on top of the wave crests and
therefore the middle deflection needs to be equal to
the full wave height.
When the boom floats at wave trough level instead of
wave crest level, the boom section between the troughs
deflects upwards due to buoyancy force. This buoyancy
force is assumed similar to the gravitational force qG and
will thus come to the same result with the used formula.
When looking back at Figure 3.60 (3.5.4.2), this theoretical
limit tension force Ft of 1.8*103 kN can be linked to a
boom length with the formula given in this figure for the
Dyneema boom.
In which x is the boom length in m and Ft the limit tension
force in kN. Solving for x:
Before the modeled tension, the force in the boom becomes
so large that it is not able to follow these waves
anymore. For the steel boom this point is at:
It should be noted that the links between the steel sections
of this boom are as flexible as the neoprene boom,
and they are the main reason the steel boom has a relatively
low force in it.
The correlation of the three-hour return value of the sea
surface clearance and boom length for a Dyneema tensioned
boom is shown in Figure 3.64.