7.1 Assumption of external forces
External forces to a cargo unit in longitudinal,
transverse and vertical direction should be obtained using the formula:
= m · a(x,y,z)
longitudinal, transverse and vertical forces
m = mass
of the unit
transverse and vertical acceleration (see table 2)
= longitudinal and transverse force by wind
= longitudinal and
transverse force by sea sloshing
acceleration data are presented in Table 2.
acceleration av in m/||Longitudinal acceleration ax in m/sec2|
|on deck high||7.1||6.9||6.8||6.7||6.7||6.8||6.9||7.1||7.4||3.8|
|on deck low||6.5||6.3||6.1||6.1||6.1||6.3||6.5||6.7||2.9||2.9|
|Vertical acceleration ax in m/sec2|
| ||7.6||6.2||5.0||4.3||4.3||5.0||6.2||7.6||9.2|| |
Table 2: Basic acceleration
The given transverse acceleration figures include
components of gravity, pitch and heave parallel to the deck. The given
vertical acceleration figures do not include the static weight
The basic acceleration data are to be
considered as valid under the following operational conditions:
1. Operation in unrestricted area.
2. Operation during the whole year.
3. Duration of
the voyage is 25 days.
4. Length of the ship is 100 m.
5. Service speed is 15 knots.
B/GM greater or equal to 13. (B: breadth of ship, GM: metacentric
For operation in a
restricted area reduction of these figures may be considered taking also
into account the season of the year and the duration of the voyage.
For ships of a length other than 100
m and a service speed other than 15 knots, the acceleration figures
should be corrected by a factor given in Table 3.
Table 3: Correction factors for
length and speed
In addition for
ships with B/GM less than 13, the transverse acceleration figures should
be corrected by a factor given in Table 4.
|B/GM|| 7 || 8 ||
9 || 10 || 11 || 12
| on deck high
|| 1.56|| 1.40||
1.27|| 1.19|| 1.11|| 1.05|| 1.00
| on deck low || 1.42|| 1.30||
1.21|| 1.14|| 1.09|| 1.04|| 1.00
| tween deck || 1.26|| 1.19||
1.14|| 1.09|| 1.06|| 1.03|| 1.00
| lower hold || 1.15|| 1.12||
1.09|| 1.06|| 1.04|| 1.02|| 1.00
Table 4: Correction factors for B/GM <
The following cautions should be
In the case of marked roll resonance with
amplitudes above +/- 30 degrees, the given figures of transverse
acceleration may be exceeded. Effective measures should be taken to
avoid this condition.
In case of heading the seas at
high speed with marked slamming shocks, the given figures of
longitudinal and vertical acceleration may be exceeded. An appropriate
reduction of speed should be considered.
In the case of running before large stern or aft
quartering seas with a stability, which does not amply exceed the
accepted minimum requirements, large roll amplitudes must be expected
with transverse accelerations greater than the figures given. An
appropriate change of heading should be considered.
Forces by wind and sea to cargo units above the
weather deck should be accounted for by a simple approach:
by wind pressure 1 kN per m2
- force be sea sloshing 1 kN per m2
Sloshing by sea can induce forces much greater than the figure given
above. This figure should be considered as remaining unavoidable after
adequate measures to prevent overcoming seas.
Sea sloshing forces need only be applied to a height
of deck cargo up to 2 metres above the weather deck or hatch top.
For voyages in restricted area sea
sloshing forces may be neglected.
7.2 Balance of forces and moments
balance calculation should preferably be carried out for
- transverse sliding in port and starboard direction
- transverse tipping in port and starboard
- longitudinal sliding under conditions of
reduced friction in forward and aft direction.
In case of symmetrical securing arrangements one
appropriate calculation is sufficient.
7.2.1 Transverse sliding
balance calculation should meet the following condition (see also Fig.
≤ μ · m · g + CS1
+ ··· + CSn
n is the number of lashings
Fy is transverse force from load
my is friction coefficient
(my = 0.3 for steel-timber or steel-rubber)
(my = 0.1 for steel-steel dry)
= 0.0 for steel-steel wet)
m is mass of cargo unit
g is gravity acceleration of earth = 9.81
CS is calculated strength of transverse
securing devices (kN)
f is function of my and
vertical securing angle alpha (see Table 5)
Figure 1: Balance of transverse forces
A vertical securing angle alpha
greater than 60 degrees will reduce the effectiveness of this particular
securing device in respect to sliding of the unit. Disregarding of such
devices from the balance of forces should be considered, unless the
necessary load is gained by the imminent tendency to tipping or by a
reliable pretensioning of the securing device which includes maintaining
the pretension throughout the voyage.
Any horizontal securing angle, i. e. deviation from the transverse
direction, should not exceed 30 degrees, otherwise an exclusion of this
securing device from the transverse sliding balance should be
| alpha (degrees)|
-30|| -20|| -10|| 0 || 10 || 20 || 30 || 40 || 50 || 60 || 70 || 80 || 90 |
| 0.3 ||0.72||0.84||0.93||1.00||1.04||1.04||1.02||0.96||0.87||0.76||0.62||0.47||0.30|
| 0.1 ||0.82||0.91||0.97||1.00||1.00||0.97||0.92||0.83||0.72||0.59||0.44||0.27||0.10|
| 0.0 ||0.87||0.94||0.98||1.00||0.98||0.94||0.87||0.77||0.64||0.50||0.34||0.17||0.00|
f-values as function of alpha and μ / Remark: f = μ * sin(alpha) +
This balance calculation should meet the
following condition (see also Fig.2);
· a ≤ b · m ·
g + CS1
··· + CSn
, m, g, CS, n are
explained under 7.2.1
a is lever-arm of tipping (m)
b is lever-arm of stableness (m) (see
c is lever-arm of securing force (m) (see
Figure 2: Balance of transverse moments
7.2.3 Longitudinal sliding
Under normal conditions the transverse securing
devices provide sufficient longitudinal components to prevent
longitudinal sliding. If in doubt, a balance calculation should meet the
≤ μ · (m · g · Fz
··· + CSn
longitudinal force from load assumption (kN)
n, my m,
g are as explained under 7.2.1
Fz is vertical force
from load assumption (kN)
CS is calculated strength
of longitudinal securing devices (kN)
Remark: Longitudinal components of transverse securing devices should
not be assumed greater than 0.5 * CS.
Explanations and interpretation
to the "Methods to assess the efficiency of securing arrangements
for non-standardized cargo"
1. The exclusion from the
scope of application of the methods of very heavy units as carried under
the provisions of Chapter 1.8 of the Code should be understood to
accommodate the possibility of adapting the stowage and securing of such
units to specifically determined weather- and sea-conditions during
transport. The exclusion should not be understood as restriction of the
methods to units up to a certain mass or dimension.
2. The acceleration figures given in
Table 2 in combination with the correction factors represent peak values
on a 25-day voyage. This does not imply that peak values in x-, y- and
z-direction occur simultaneously with the same probability. It can be
generally assumed that peak values in the transverse direction will
appear in combination with less than 60% of the peak values in
longitudinal and vertical direction.
Peak values in longitudinal and vertical direction may join more
closely because they have common source of pitching and heaving
3. The advanced calculation
method uses the "worst case approach". That is expressed clearly by the
transverse components of simultaneous vertical accelerations.
Consequently there is no need to consider vertical accelerations
separately in the transverse balances of forces and moments. These
simultaneously acting vertical accelerations create an apparent increase
of weight of the unit and thus improve the friction in the balance of
forces, respectively the moment stableness in the balance of moments.
For this reason there is no reduction of the normal force m . g due to
the present angle of heel.
situation is different for the longitudinal sliding balance. The worst
case would be a peak value of the longitudinal force Fx accompanied by
an extreme reduction of weight through the vertical force Fz.
4. The friction coefficients
shown in the methods are somewhat reduced against appropriate figures in
other publications. The reason for this should be seen in various which
may appear in practical shipping as moisture, grease oil, dust and other
residues, vibration of the ship
There are certain stowage materials available which are said to
increase friction considerably. Extended experience with these materials
may bring additional coefficients into practical use.
5. The principal way of calculating
forces within the securing elements of a complex securing arrangement
should necessarily include the consideration of
Load-elongation behavior (elasticity)
arrangement (angles, length)
of each individual securing element
This approach would require a
large volume of information and a complex, iterative calculation. Still
the results would be doubtful due to uncertain parameters.
Therefore the simplified approach
was chosen with the assumption that the elements take an even load of CS
(calculation strength) which is reduced against the MSL (maximum
securing load) by the safety factor 1.5
6. When employing the advanced calculation
method the way of collecting data should be followed as shown in the
calculated example. It is acceptable to estimate securing angles, to
take average angles for a set of lashings and similarly arrive at
reasonable figures of the levers a, b and c for the balance of moments.
It should be born in mind that
meeting or missing the balance calculation just by a tiny change of one
or the other parameter indicates to be near the goal anyway. There is no
clear-but borderline between safety and non-safety. It in doubt, the
arrangement should be improved.