34
STRUCTURE-ENVIRONMENTAL FORCE INTERACTIONS
(2.28a)
(2.28b)
(2.29)
solidification, modifies the drag coefficient as follows:
Cd =
for 0 < < 0.6
Cd = 2, for > 0.6
where the solidity ratio is given by
projected area of truss members only
projected area of the enclosed solid
Here the projected area is in a plane normal to the prevailing direction of the
wind.
For members of the superstructure closer than nine diameters, shielding effects (sometimes referred to as sheltering) are apparent. For instance, a cylinder
just behind a lead cylinder facing the wind expériences a considérable drop in
drag force, and sometimes a négative drag force at close spacings. Wind tunnel
data for the shielding of cylinders are reported by Pagon (1934) and Wilson and
Caldwell (1971). Numerous references to calculated results based on classical
hydrodynamics are discussed by Muga and Wilson (1970). Values of shielding
factors varying from 0 to 1.0 and useful for design purposes are recommended by
Graff (1981). To obtain the drag force for a shielded component, the shielding
factor is multiplied by the static drag force of its unshielded counterpart.
In addition to these static loads, the dynamic effects of wind on offshore
structures should be considered also. For instance, for a moored structure whose
fondamental period in free oscillation is close to the period of wind gusts, the
dynamic deflection of the structure could become significant. However, for a
truss structure with fixed legs, the overall dynamic response due to gusts alone
are generally insignificant. This is because the time lag between gust arrivai
at the leading edges and its arrivai on the downstream portions of the open
structure tends to minimize the overall loading. Static loading of individual
members to gusts could be significant since wind gust speeds may be quite
high. For instance, a value of 120 knots is often used for the design of structures
in the North Sea, a value about 1.4 times the steady or sustained wind speed
“(*) at a height of 30 m (Graff, 1981).
On the other hand, adverse vibrations of a structural component may arise in
stead\ w inds due to vortex shedding, if these vortex frequencies are in tune or in
résonance with a free vibration frequency of a structural member. This may lead
to arge displacements or flutter of platelike members and to galloping beam and
ca e components. As discussed earlier in this chapter, helical strakes or other
pot ers can be used to eliminate periodic vortices on tubular members. Vortex"iumu re“"ance 1S further discussed by Blevins (1977), Gould and Abu-Sitta
’ a*1
*m*u ^d Scanlan (1978). Extended discussions concerning the
p }sica asis or both wind and océan currents are given in the classical treatise
of Aeumann and Pierson (1966).
In his summary of océan currents, Gaythwaite (1981) indicates that tidil cur•«. uni .,tn currents are the two most relevant ones in the structural
STRUCTURE-ENVIRONMENTAL FORCE INTERACTIONS
(2.28a)
(2.28b)
(2.29)
solidification, modifies the drag coefficient as follows:
Cd =
for 0 <
Cd = 2, for > 0.6
where the solidity ratio is given by
projected area of truss members only
projected area of the enclosed solid
Here the projected area is in a plane normal to the prevailing direction of the
wind.
For members of the superstructure closer than nine diameters, shielding effects (sometimes referred to as sheltering) are apparent. For instance, a cylinder
just behind a lead cylinder facing the wind expériences a considérable drop in
drag force, and sometimes a négative drag force at close spacings. Wind tunnel
data for the shielding of cylinders are reported by Pagon (1934) and Wilson and
Caldwell (1971). Numerous references to calculated results based on classical
hydrodynamics are discussed by Muga and Wilson (1970). Values of shielding
factors varying from 0 to 1.0 and useful for design purposes are recommended by
Graff (1981). To obtain the drag force for a shielded component, the shielding
factor is multiplied by the static drag force of its unshielded counterpart.
In addition to these static loads, the dynamic effects of wind on offshore
structures should be considered also. For instance, for a moored structure whose
fondamental period in free oscillation is close to the period of wind gusts, the
dynamic deflection of the structure could become significant. However, for a
truss structure with fixed legs, the overall dynamic response due to gusts alone
are generally insignificant. This is because the time lag between gust arrivai
at the leading edges and its arrivai on the downstream portions of the open
structure tends to minimize the overall loading. Static loading of individual
members to gusts could be significant since wind gust speeds may be quite
high. For instance, a value of 120 knots is often used for the design of structures
in the North Sea, a value about 1.4 times the steady or sustained wind speed
“(*) at a height of 30 m (Graff, 1981).
On the other hand, adverse vibrations of a structural component may arise in
stead\ w inds due to vortex shedding, if these vortex frequencies are in tune or in
résonance with a free vibration frequency of a structural member. This may lead
to arge displacements or flutter of platelike members and to galloping beam and
ca e components. As discussed earlier in this chapter, helical strakes or other
pot ers can be used to eliminate periodic vortices on tubular members. Vortex"iumu re“"ance 1S further discussed by Blevins (1977), Gould and Abu-Sitta
’ a*1
*m*u ^d Scanlan (1978). Extended discussions concerning the
p }sica asis or both wind and océan currents are given in the classical treatise
of Aeumann and Pierson (1966).
In his summary of océan currents, Gaythwaite (1981) indicates that tidil cur•«. uni .,tn currents are the two most relevant ones in the structural