96
WAVE FORCES ON STRUCTURES
Example Problem 4.5.
Calculate the transfer function for the total horizontal load on the box-type caisson shown in Figure 4.2 and described in Example Problem 4-3. Assume that the fluid-induced forces are diffraction-dominated.
It follows that the total horizontal load pix(t) is the product of Fkx given by
équation (4.19) and the diffraction coefficient Ch given by équation (4.11). Thus
the total load-wave height ratio is
1 = -2pgaCh ,
sin ka sin ut
(4.32)
H
k cosh kh
The required transfer function is this ratio expressed in complex notation, or
— ]2pgaCh-r———yy sin ka e3"'
(4.33)
k cosh kh
These examples illustrate that there is a different transfer function for each
flow régime and for each structural component of an offshore structure. In
practice, transfer functions for ail components are calculated and assembled
for the structure, ail based on linear wave theory and a single, simple wave.
Such results can then superimposed to account for the loading effects of many
simple waves selected to simulate the design sea State at the site of the offshore
structure. This simulation involving the sélection of simple waves over particular
ranges of H. u, and wave phase e is discussed in Chapter 6. The corresponding
structura] responses are then discussed in Chapter 7 for single degree of freedom
Systems and in Chapter 9 for multi-degree of freedom structures.
PROBLEMS
4.1
The total force pi(i) on a submerged, flexible pile in the inertia flow
régime is given by the right side of équation (4.3). For a single, simple wave
evaluate pi (t) by carrying out the necessary intégration.
4.2 The diameter of the submerged pile shown in Figure 4.1 is sufficiently
small so that the drag forces are comparable in magnitude to the inertia forces.
Evaluate pi(i) in this case by carrying out the intégrations of équation (4.8).
Figure 4.6 Monopod structure for Problems 4.3, 4.4, and 4.5.
WAVE FORCES ON STRUCTURES
Example Problem 4.5.
Calculate the transfer function for the total horizontal load on the box-type caisson shown in Figure 4.2 and described in Example Problem 4-3. Assume that the fluid-induced forces are diffraction-dominated.
It follows that the total horizontal load pix(t) is the product of Fkx given by
équation (4.19) and the diffraction coefficient Ch given by équation (4.11). Thus
the total load-wave height ratio is
1 = -2pgaCh ,
sin ka sin ut
(4.32)
H
k cosh kh
The required transfer function is this ratio expressed in complex notation, or
— ]2pgaCh-r———yy sin ka e3"'
(4.33)
k cosh kh
These examples illustrate that there is a different transfer function for each
flow régime and for each structural component of an offshore structure. In
practice, transfer functions for ail components are calculated and assembled
for the structure, ail based on linear wave theory and a single, simple wave.
Such results can then superimposed to account for the loading effects of many
simple waves selected to simulate the design sea State at the site of the offshore
structure. This simulation involving the sélection of simple waves over particular
ranges of H. u, and wave phase e is discussed in Chapter 6. The corresponding
structura] responses are then discussed in Chapter 7 for single degree of freedom
Systems and in Chapter 9 for multi-degree of freedom structures.
PROBLEMS
4.1
The total force pi(i) on a submerged, flexible pile in the inertia flow
régime is given by the right side of équation (4.3). For a single, simple wave
evaluate pi (t) by carrying out the necessary intégration.
4.2 The diameter of the submerged pile shown in Figure 4.1 is sufficiently
small so that the drag forces are comparable in magnitude to the inertia forces.
Evaluate pi(i) in this case by carrying out the intégrations of équation (4.8).
Figure 4.6 Monopod structure for Problems 4.3, 4.4, and 4.5.