FLUID-INDUCED STRUCTURAL FORCES
31
Figure 2.12 A gravity platform partially submerged in a mud layer or in liquefied
soil.
The three buoyant forces on this platform are: (1) a buoyant force due to
the mud of 'YmVm., which is located at a distance of hm from the base and acts
upward at the centroid of the displaced mud volume Vm; (2) a buoyant force
for the portion of the caisson in water of 7WVC , which is located at hc from the
base and acts upward at the centroid of its displaced water volume Vc\ and (3)
a buoyant force on the submerged portion of each leg of 7WV/, which is located
at h.g from the base and acts at the centroid of its displaced water volume of
Vg. If the structure has N identical legs, the total buoyant force m^g and its
statically équivalent location hb on the structure are, respectively
mb9 = 7nX + 7™ K + ^7w^
(2.25)
hb = —— (/im7mVm + /ic7wK + N heywVe)
m^g
(2.26)
Here, hb is located on the vertical centerline of the upright structure, where
the identical legs are symmetrically placed with respect to this axis. However,
that if the structure is tipped at angle 0. the résultant buoyant force retains
its same magnitude for ail practical purposes, but its location shifts to an offcenter position, from B to B’. The location of B’ relative to the mass center G
détermines the static stability of the whole structure, as the following example
problem demonstrates.
31
Figure 2.12 A gravity platform partially submerged in a mud layer or in liquefied
soil.
The three buoyant forces on this platform are: (1) a buoyant force due to
the mud of 'YmVm., which is located at a distance of hm from the base and acts
upward at the centroid of the displaced mud volume Vm; (2) a buoyant force
for the portion of the caisson in water of 7WVC , which is located at hc from the
base and acts upward at the centroid of its displaced water volume Vc\ and (3)
a buoyant force on the submerged portion of each leg of 7WV/, which is located
at h.g from the base and acts at the centroid of its displaced water volume of
Vg. If the structure has N identical legs, the total buoyant force m^g and its
statically équivalent location hb on the structure are, respectively
mb9 = 7nX + 7™ K + ^7w^
(2.25)
hb = —— (/im7mVm + /ic7wK + N heywVe)
m^g
(2.26)
Here, hb is located on the vertical centerline of the upright structure, where
the identical legs are symmetrically placed with respect to this axis. However,
that if the structure is tipped at angle 0. the résultant buoyant force retains
its same magnitude for ail practical purposes, but its location shifts to an offcenter position, from B to B’. The location of B’ relative to the mass center G
détermines the static stability of the whole structure, as the following example
problem demonstrates.