104
SINGLE DEGREE OF FREEDOM STRUCTURES
Realistic System parameters used to compute numerical values for monopod
platform rocking frequencies are listed in Table 5.1. The soil properties are those
suggested by Nataraja and Kirk (1977), measured properties that span a range
in the North Sea where gravity platforms hâve been placed. Computations
for the structural properties were based on the nominal dimensions given in
Figure 5.2, together with the following assumptions concerning the structure’s
five elementary structural components.
1. The deck and deck equipment are lumped as a thin dise 55 m in diameter.
2. The uniform section of the leg above the still water line is an empty,
thin-walled pipe.
3. The uniform submerged section of the leg is a thin-walled pipe filled
with water.
4. The tapered, submerged section of the leg is a thin-walled cône filled
with water.
5. The caisson is approximated as a cylinder consisting of two parts. Part
(a) is a cluster of vertical, cylindrical tanks 50 m high, together displacing 70
percent of the volume of seawater occupied by a cylinder of height z — 50 m
and radius ro — 45 m. These tanks are filled with oil, and the average density
of the tanks with their contents is 900 kg/m3. This tank cluster is assumed
to be a homogeneous solid of this density. Part (b), the base and ballast, is a
homogeneous cylindrical solid 10 m high with a density of 2000 kg/m3.
The following items were calculated for each of these five elementary structural components: the actual mass and the buoyant mass, with their respective
locations from the base point; and the virtual mass moment of inertia about 0,
the base centerline point. Also, for the submerged éléments, the added mass
coefficient was chosen as unity (Ca = 1). The properties of the solids in Appendix A, together with the parallel axis theorem, équation (2.5), were used to
compute Jo. In these calculations, the mass density of sea water and of concrète were chosen as 1025 kg/m3 and 2500 kg/m3, respectively. More detailed
calculations for this same problem were presented by Wilson and Orgill (1984).
The composite values of ttiq, nq
and ht for the whole structure, together
with the rocking frequencies calculated from équation (5.11), are listed in Table
5.1. The important results of these calculations are summarized. First, since
the total actual mass (3.56 x 108kg) is greater than the total buoyant mass
(2.59 x 108 kg), the structure will not float. Second, since the center hc of the
actuai mass is 1.0 m below the center of buoyancy /q. this structure is inherently
stable under small motion. Note that the moment due to the buoyant force
opposes that due to gravity, as shown in Figure 2.12b. Third, a lower bound on
the rocking frequency based on G„ = 10 MPa is w'O = 1.41 rad/s or f0 = 0.224
Hz. Fourth, the upper bound on the rocking frequency based on Gs = 50 MPa
is -7, - 3.17 rad/s or f0 = 0.505 Hz. Finally, since the period To is 1/fo, then
the bounds on the natural period of the platform are 4.46 s and 1.98 s, which
correspond to the reported lower and higher Ümits for the soil shear modulus in
the North Sea.
SINGLE DEGREE OF FREEDOM STRUCTURES
Realistic System parameters used to compute numerical values for monopod
platform rocking frequencies are listed in Table 5.1. The soil properties are those
suggested by Nataraja and Kirk (1977), measured properties that span a range
in the North Sea where gravity platforms hâve been placed. Computations
for the structural properties were based on the nominal dimensions given in
Figure 5.2, together with the following assumptions concerning the structure’s
five elementary structural components.
1. The deck and deck equipment are lumped as a thin dise 55 m in diameter.
2. The uniform section of the leg above the still water line is an empty,
thin-walled pipe.
3. The uniform submerged section of the leg is a thin-walled pipe filled
with water.
4. The tapered, submerged section of the leg is a thin-walled cône filled
with water.
5. The caisson is approximated as a cylinder consisting of two parts. Part
(a) is a cluster of vertical, cylindrical tanks 50 m high, together displacing 70
percent of the volume of seawater occupied by a cylinder of height z — 50 m
and radius ro — 45 m. These tanks are filled with oil, and the average density
of the tanks with their contents is 900 kg/m3. This tank cluster is assumed
to be a homogeneous solid of this density. Part (b), the base and ballast, is a
homogeneous cylindrical solid 10 m high with a density of 2000 kg/m3.
The following items were calculated for each of these five elementary structural components: the actual mass and the buoyant mass, with their respective
locations from the base point; and the virtual mass moment of inertia about 0,
the base centerline point. Also, for the submerged éléments, the added mass
coefficient was chosen as unity (Ca = 1). The properties of the solids in Appendix A, together with the parallel axis theorem, équation (2.5), were used to
compute Jo. In these calculations, the mass density of sea water and of concrète were chosen as 1025 kg/m3 and 2500 kg/m3, respectively. More detailed
calculations for this same problem were presented by Wilson and Orgill (1984).
The composite values of ttiq, nq
and ht for the whole structure, together
with the rocking frequencies calculated from équation (5.11), are listed in Table
5.1. The important results of these calculations are summarized. First, since
the total actual mass (3.56 x 108kg) is greater than the total buoyant mass
(2.59 x 108 kg), the structure will not float. Second, since the center hc of the
actuai mass is 1.0 m below the center of buoyancy /q. this structure is inherently
stable under small motion. Note that the moment due to the buoyant force
opposes that due to gravity, as shown in Figure 2.12b. Third, a lower bound on
the rocking frequency based on G„ = 10 MPa is w'O = 1.41 rad/s or f0 = 0.224
Hz. Fourth, the upper bound on the rocking frequency based on Gs = 50 MPa
is -7, - 3.17 rad/s or f0 = 0.505 Hz. Finally, since the period To is 1/fo, then
the bounds on the natural period of the platform are 4.46 s and 1.98 s, which
correspond to the reported lower and higher Ümits for the soil shear modulus in
the North Sea.