4.28.1
Guidance to detailed calculation
of internal pressure for static design purpose
4.28.1.1 This section provides guidance for the
calculation of the associated dynamic liquid pressure for the purpose
of static design calculations. This pressure may be used for determining
the internal pressure referred to in 4.13.2.4, where:
-
.1 (Pgd
)max is the associated
liquid pressure determined using the maximum design accelerations.
-
.2 (Pgd
site)max is the
associated liquid pressure determined using site specific accelerations.
-
.3
Peq
should be the greater
of Peq1
and Peq2
calculated
as follows:
-
Peq1
|
= |
Po
+ (Pgd
)max
(MPa),
|
-
Peq2
|
= |
Ph
+ (Pgd
)site
(MPa),
|
4.28.1.2 The internal liquid pressures are those
created by the resulting acceleration of the centre of gravity of
the cargo due to the motions of the ship referred to in 4.14.1. The
value of internal liquid pressure Pgd
resulting
from combined effects of gravity and dynamic accelerations should
be calculated as follows:
where:
αβ
|
= |
dimensionless acceleration (i.e. relative to the acceleration
of gravity), resulting from gravitational and dynamic loads, in an
arbitrary direction β (see figure 4.1).
For large tanks, an acceleration ellipsoid taking account
of transverse vertical and longitudinal accelerations, should be used.
|
Zβ
|
= |
largest liquid height (m) above the point where the pressure
is to be determined measured from the tank shell in the β direction
(see figure 4.2).
Tank domes considered
to be part of the accepted total tank volume shall be taken into account
when determining Zβ
, unless the total
volume of tank domes Vd
does not exceed the
following value:
|
-
-
with:
-
Vt
|
= |
tank volume without any domes; and |
-
FL
|
= |
filling
limit according to chapter 15. |
ρ
|
= |
maximum
cargo density (kg/m3) at the design temperature.
|
The direction that gives the maximum value (Pgd
)max
or (Pgd
site)max should be considered. The
above formula applies only to full tanks.
4.28.1.3 Equivalent calculation procedures may
be applied.
4.28.2
Guidance formulae for acceleration
components
4.28.2.1 The following formulae are given as guidance
for the components of acceleration due to ship's motions corresponding
to a probability level of 10-8 in the North Atlantic and
apply to ships with a length exceeding 50 m and at or near their service
speed:
-
- vertical acceleration, as defined in 4.14.1:
-
- transverse acceleration, as defined in 4.14.1:
-
- longitudinal acceleration, as defined in 4.14.1:
where:
a0
|
= |
|
L0
|
= |
length of the ship for determination of scantlings as defined
in recognized standards (m); |
B
|
= |
greatest
moulded breadth of the ship (m); |
x
|
= |
longitudinal
distance (m) from amidships to the centre of gravity of the tank with
contents; x is positive forward of amidships, negative aft of amidships; |
y
|
= |
transverse
distance (m) from centreline to the centre of gravity of the tank
with contents; |
z
|
= |
vertical
distance (m) from the ship's actual waterline to the centre of gravity
of tank with contents; z is positive above and negative below the
waterline; |
K
|
= |
1
in general. For particular loading conditions and hull forms, determination
of K according to the following formula may be necessary: |
-
K
|
= |
13GM/B, where K ≥ 1 and GM = metacentric
height (m);
|
A
|
= |
: and
|
V
|
= |
service
speed (knots); |
ax, ay, az
|
= |
maximum dimensionless accelerations (i.e.
relative to the acceleration of gravity) in the respective directions.
They are considered as acting separately for calculation purposes,
and az
does not include the component due
to the static weight, ay
includes the component
due to the static weight in the transverse direction due to rolling
and ax
includes the component due to the static
weight in the longitudinal direction due to pitching. The accelerations
derived from the above formulae are applicable only to ships at or
near their service speed, not while at anchor or otherwise near stationary
in exposed locations.
|
4.28.3.1 For the purpose of stress evaluation,
stress categories are defined in this section as follows.
4.28.3.2
Normal stress is the component
of stress normal to the plane of reference.
4.28.3.3
Membrane stress is the component
of normal stress that is uniformly distributed and equal to the average
value of the stress across the thickness of the section under consideration.
4.28.3.4
Bending stress is the variable
stress across the thickness of the section under consideration, after
the subtraction of the membrane stress.
4.28.3.5
Shear stress is the component
of the stress acting in the plane of reference.
4.28.3.6
Primary stress is a stress
produced by the imposed loading, which is necessary to balance the
external forces and moments. The basic characteristic of a primary
stress is that it is not self-limiting. Primary stresses that considerably
exceed the yield strength will result in failure or at least in gross
deformations.
4.28.3.7
Primary general membrane stress is
a primary membrane stress that is so distributed in the structure
that no redistribution of load occurs as a result of yielding.
4.28.3.8
Primary local membrane stress arises
where a membrane stress produced by pressure or other mechanical loading
and associated with a primary or a discontinuity effect produces excessive
distortion in the transfer of loads for other portions of the structure.
Such a stress is classified as a primary local membrane stress, although
it has some characteristics of a secondary stress. A stress region
may be considered as local, if:
and
,
where:
S1
|
= |
distance in the meridional direction over which the equivalent
stress exceeds 1.1f;
|
S2
|
= |
distance in the meridional direction to another region where
the limits for primary general membrane stress are exceeded; |
R
|
= |
mean
radius of the vessel; |
t
|
= |
wall
thickness of the vessel at the location where the primary general
membrane stress limit is exceeded; and |
f
|
= |
allowable
primary general membrane stress. |
4.28.3.9
Secondary stress is a normal
stress or shear stress developed by constraints of adjacent parts
or by self-constraint of a structure. The basic characteristic of
a secondary stress is that it is self-limiting. Local yielding and
minor distortions can satisfy the conditions that cause the stress
to occur.