This document has been consolidated into CSS
Code
ANNEX 13
Methods to assess the efficiency of securing arrangements For semi-standardized
and non-standardized cargo
The complete text of annex 13, together with its four appendices, is replaced by the
following:
"1 Scope of application
1.1 The methods described in this annex should be applied to semi-standardized and
non-standardized cargo including very heavy and/or very large cargo items.
Standardized stowage and securing systems, in particular containers on
containerships, are excluded.
1.2 Cargoes carried on towed barges should be secured according to the provisions of
this annex except that the assumed external forces may be determined using an
alternative method acceptable to the Administration instead of that described in
section 7.1 of this annex.
1.3 Very heavy and/or very large cargo items as addressed in chapter 1.8 of this Code
may require provisions and considerations beyond the general scope of this annex.
Examples of such provisions and considerations are given in appendix 3 of this
annex.
1.4 Semi-standardized cargoes, for which the securing arrangements are often designed
based on worst case assumptions on cargo properties, lashing angles and stowage
positions on board, may require provisions and considerations beyond the general
scope of this annex. Examples of such provisions and considerations are given in
appendix 4 of this annex.
1.5 Notwithstanding the general principles contained in this annex, the adequacy of
cargo securing may be demonstrated by means of detailed engineering calculations
based upon the general principles and encompassing the additional provisions and
considerations shown in appendix 3 of this annex. Computer programs used for that
purpose should be validated against a suitable range of model tests or full-scale
results in irregular seas. When using new software for new and unconventional
applications, the validation should be documented.
1.6 The application of the methods described in this annex is supplementary to the
principles of good seamanship and should not replace experience in stowage and
securing practice.
2 Purpose of the methods
The methods should:
-
.1 provide guidance for the preparation of Cargo Securing Manuals and the
examples therein;
-
.2 assist ship's staff in assessing the securing of cargo items not covered
by the Cargo Securing Manual;
-
.3 assist qualified shore personnel in assessing the securing of cargo items
not covered by the Cargo Securing Manual; and
-
.4 serve as a reference for maritime and port-related education and training.
3 Presentation of the methods
The methods are presented in a universally applicable and flexible way. It is
recommended that designers of Cargo Securing Manuals convert this presentation into
a format suiting the particular ship, its securing equipment and the cargo carried.
This format may include applicable diagrams, tables or calculated examples.
4 Strength of securing equipment
4.1 Manufacturers of securing equipment should at least supply information on the
nominal breaking strength of the equipment in kilonewtons (kN).footnote
4.2 "Maximum securing load" (MSL) is a term used to define the load capacity for a
device used to secure cargo to a ship. "Safe working load" (SWL) may be substituted
for MSL for securing purposes, provided this is equal to or exceeds the strength
defined by MSL.
Where practicable, the MSL should preferably be marked on the securing equipment.
The MSLs for different securing devices are given in table 1 if not given under 4.3.
The MSL of timber should be taken as 0.3 kN/cm2 normal to the grain.
Table 1 – Determination of MSL from breaking strength
Material
|
MSL
|
Shackles, rings, deckeyes, turnbuckles
of mild steel
|
50% of breaking
strength
|
Fibre rope
|
33% of breaking
strength
|
Web lashing
|
50% of breaking
strength
|
Wire rope (single use)
|
80% of breaking
strength
|
Wire rope (re-useable)
|
30% of breaking
strength
|
Steel band (single use)
|
70% of breaking
strength
|
Chains
|
50% of breaking
strength
|
4.3 Particular securing devices (e.g. fibre straps with tensioners or special
equipment for securing containers) may be marked with a permissible working load, as
prescribed by an appropriate authority. This may be taken as the MSL.
4.4 When the components of a lashing device are connected in series (e.g. a wire to a
shackle to a deckeye), the minimum MSL in the series should apply to that device.
4.5 Where temporary welded fittings are used, they should be designed to be adequate
for the expected loading, and installed by qualified welders in accordance with
established welding procedures. The design and placement of these fittings should be
such as to minimize bending.
4.6 Simple stoppers may be used to provide securing against sliding. These are
generally welded to a surface by fillet welds, characterized by thickness (a)
and length (l). A face plate should be provided against the cargo piece so
that welds are not loaded by a shear force at right angles to the weld direction or
by significant bending forces. As a simple rule of thumb for welded steel stoppers,
the MSL of single-lay weld leg can then be approximated as 4 kN/cm (l) normal
to the face plate, assuming 5 mm weld thickness (a). For a triple-lay weld
leg, MSL can be taken as 10 kN/cm normal to the face plate.
![](GUID-E1050ACA-ACD1-41FD-AC40-AB27FBB3F0FE-low.jpg)
Figure 16.1 – Welding of steel stoppers
4.7 All securing devices to be accounted for in the balance calculations described in
this annex should be capable of transferring forces directly from the vessel to the
cargo or vice versa, in order to reflect their MSLs. For that purpose, lashings
should be attached to fixed securing points or strong supporting structures marked
on the cargo item or advised as being suitable, or taken as a loop around the item
with both ends secured to the same side as shown in figure 7 in annex 5 of the Code.
Lashings going over the top of the cargo item, whose only function is to increase
friction by their pre-tension, cannot be credited in the evaluation of securing
arrangements under this annex.
5 Rule-of-thumb method
5.1 The total of the MSL values of the securing devices on each side of a cargo item
(port as well as starboard) should equal the weight of the item.footnote
5.2 This method, which implies a transverse acceleration of 1g (9.81
m/s2), applies to nearly any size of ship, regardless of the location of
stowage, stability and loading condition, season and area of operation. The method,
however, takes into account neither the adverse effects of lashing angles and
non-homogeneous distribution of forces among the securing devices nor the favourable
effect of friction.
5.3 Transverse lashing angles to the deck should not be greater than 60° and it is
important that adequate friction is provided by the use of suitable material.
Additional lashings at angles of greater than 60° may be desirable to prevent
tipping but are not to be counted in the number of lashings under the rule of thumb.
6 Safety factor
6.1 When using balance calculation methods for assessing the strength of the securing
devices, a safety factor is used to take account of the possibility of uneven
distribution of forces among the devices or reduced capability due to the improper
assembly of the devices or other reasons. This safety factor is used in the formula
to derive the calculated strength (CS) from the MSL and shown in the relevant
method used.
6.2 Notwithstanding the introduction of such a safety factor, care should be taken to
use securing elements of similar material and length in order to provide a uniform
elastic behaviour within the arrangement.
6.3 If securing devices of different elasticity are used in the same direction, e.g.
welded bottom stoppers and fibre belts or long wire lashings, the more flexible
securing devices in such an arrangement should be excluded if they, due to their
elongation, do not contribute to preventing initial movement of the cargo.
7 Advanced calculation method
7.1 Assumption of external forces
7.1.1 External forces to a cargo item in longitudinal, transverse and vertical
directions should be obtained using the formula:
- F(x,y,z) = m · a(x,y,z) +
Fw(x,y) + Fs(x,y)
where
-
F(x,y,z) = longitudinal, transverse and vertical
forces
m = mass of the item
a(x,y,z) = longitudinal, transverse and vertical
accelerations (see table 2 below)
Fw(x,y) = longitudinal and transverse forces by wind
pressure
Fs(x,y) = longitudinal and transverse forces by sea
sloshing.
The basic acceleration data are presented in table 2.
Table 2 – Basic acceleration data
![](GUID-74DA2F51-8C93-4B22-BB3C-EE5EF7B513D9-low.jpg)
Remarks:
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 component.
7.1.2 The basic acceleration data are to be considered as valid under the following
operational conditions:footnote
-
.1 operation in unrestricted area;
-
.2 operation during the whole year;
-
.3 length of ship is 100 m;
-
.4 service speed is 15 knots; and
-
.5 B/GM ≥ 13 (B = moulded breadth of ship, GM =
metacentric height).
7.1.3 For operation in a restricted area, reduction factors for accelerations may be
considered, taking into account the season of the year, the accuracy of the weather
forecast affecting the wave heights during the intended voyage and the duration of
the voyage. Restricted area means any sea area in which the weather can be forecast
for the entire sea voyage or shelter can be found during the voyage.
7.1.4 Reduction factors, fR, may be applied to significant
wave heightsfootnote, Hs, not exceeding 12 m for
the design of securing arrangements in any of the following cases:
-
.1 The required securing arrangement is calculated for the maximum expected
20-year significant wave height in a particular restricted area and the
cargo is always secured according to the designed arrangement when operating
in that area.
-
.2 The maximum significant wave height that a particular securing arrangement
can withstand is calculated and the vessel is limited to operating only in
significant wave heights up to the maximum calculated. Procedures for
ensuring that any operational limitation is not exceeded should be developed
and followed and documented in the ship's approved Cargo Securing Manual.
-
.3 Required securing arrangements are designed for different significant wave
heights and the securing arrangement is selected according to the maximum
expected wave height for each voyage for which an accurate weather forecast
is available. Thus, the duration of the voyage should not exceed 72 hours or
a duration as accepted by the Administration.
7.1.5 The basic acceleration data in table 2 may be multiplied by the following
reduction factor:
-
fR = 1 –
(Hs – 13)2 / 240, where
Hs
is:
-
.1 the maximum expected 20-year significant wave height in the
area according to ocean wave statistics; or
-
.2 the maximum predicted significant wave height on which the operational
limitations are based; or
-
.3 for voyages not exceeding 72 hours the maximum predicted significant wave
height according to weather forecasts.
7.1.6 When weather-dependent lashing is applied, operational procedures for the
following activities should be developed, followed and documented in the ship's
approved Cargo Securing Manual, or otherwise included in the ship's safety
management system:
-
.1 decision on the level of cargo securing based on the length of the voyage
and the weather forecast;
-
.2 communication to all concerned parties of the decided level of cargo
securing for the intended voyage;
-
.3 execution and supervision of appropriate cargo securing efforts in
accordance with the Cargo Securing Manual; and
-
.4 monitoring of environmental conditions and ship motions to ensure that the
applied level of cargo securing is not exceeded.
7.1.7 For ships of a length other than 100 m and a service speed other than 15 knots,
the acceleration figures should be multiplied by a correction factor given in table
3.
Table 3 – Correction factors for length and service speed
Length (m)
|
50
|
60
|
70
|
80
|
90
|
100
|
120
|
140
|
160
|
180
|
200
|
Speed (kn)
|
9
|
1.20
|
1.09
|
1.00
|
0.92
|
0.85
|
0.79
|
0.70
|
0.63
|
0.57
|
0.53
|
0.49
|
12
|
1.34
|
1.22
|
1.12
|
1.03
|
0.96
|
0.90
|
0.79
|
0.72
|
0.65
|
0.60
|
0.56
|
15
|
1.49
|
1.36
|
1.24
|
1.15
|
1.07
|
1.00
|
0.89
|
0.80
|
0.73
|
0.68
|
0.63
|
18
|
1.64
|
1.49
|
1.37
|
1.27
|
1.18
|
1.10
|
0.98
|
0.89
|
0.82
|
0.76
|
0.71
|
21
|
1.78
|
1.62
|
1.49
|
1.38
|
1.29
|
1.21
|
1.08
|
0.98
|
0.90
|
0.83
|
0.78
|
24
|
1.93
|
1.76
|
1.62
|
1.50
|
1.40
|
1.31
|
1.17
|
1.07
|
0.98
|
0.91
|
0.85
|
7.1.8 For length/speed combinations not directly tabulated, the following formula may
be used to obtain the correction factor with v = speed in knots and L
= length between perpendiculars in metres:
- correction factor = (0.345·v /
⁄)+(58.62·L-1034.5)L2⁄
This formula should not be used for ship lengths less than 50 m or more than 300 m.
In addition, for ships with B/GM less than 13, the transverse
acceleration figures should be multiplied by the correction factor given in table
4.
Table 4 – Correction factors for B/GM
B/GM
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
12
|
13 or above
|
on deck, high
|
2.64
|
2.28
|
1.98
|
1.74
|
1.56
|
1.40
|
1.27
|
1.19
|
1.11
|
1.05
|
1.00
|
on deck, low
|
2.18
|
1.93
|
1.72
|
1.55
|
1.42
|
1.30
|
1.21
|
1.14
|
1.09
|
1.04
|
1.00
|
'tween deck
|
1.62
|
1.51
|
1.41
|
1.33
|
1.26
|
1.19
|
1.14
|
1.09
|
1.06
|
1.03
|
1.00
|
lower hold
|
1.24
|
1.23
|
1.20
|
1.18
|
1.15
|
1.12
|
1.09
|
1.06
|
1.04
|
1.02
|
1.00
|
7.1.9 The following should be observed:
-
.1 In the case of marked roll resonance with amplitudes above ±30°, the given
figures of transverse acceleration may be exceeded. Effective measures
should be taken to avoid this condition.
-
.2 In the case of heading into the seas at high speed with marked slamming
impacts, the given figures of longitudinal and vertical acceleration may be
exceeded. An appropriate reduction of speed should be considered.
-
.3 In the case of running before large stern or 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.
-
.4 Forces by wind and sea to cargo items above the weather deck should be
accounted for by a simple approach:
-
.5 The wind force may be reduced by the same principles as the accelerations,
i.e. multiplying it with a reduction factor, fR,
based on the expected significant wave height.
-
.6 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.
-
.7 Sea sloshing forces need only be applied to a height of deck cargo up to 2
m above the weather deck or hatch top.
-
.8 For voyages in a restricted area and with forecast wave heights for which
no sea sloshing is expected, sea sloshing forces may be neglected.
7.2 Balance of forces and moments
7.2.1 The balance calculation should preferably be carried out for:
-
.1 transverse sliding in port and starboard directions;
-
.2 transverse tipping in port and starboard directions; and
-
.3 longitudinal sliding under conditions of reduced friction in forward and
aft directions.
7.2.2 In the case of symmetrical securing arrangements, one appropriate calculation
for each case above is sufficient.
7.2.3 Friction contributes towards prevention of sliding. The following friction
coefficients (μ) should be applied.
Table 5 – Friction coefficients
Materials in
contact
|
Friction coefficient
(μ)
|
Timber–timber, wet or
dry
|
0.4
|
Steel–timber or
steel-rubber
|
0.3
|
Steel–steel, dry
|
0.1
|
Steel–steel, wet
|
0.0
|
A friction increasing material or deck coating with higher friction coefficients may
be used assuming a certified conservative friction coefficient and the endurable
shear stress of the material under repeated loads, as they occur in heavy weather at
sea. The applicability of these data should be reviewed with due consideration of
the prevailing conditions in terms of moisture, dust, greasy dirt, frost, ice or
snow as well as the local pressure applied (weight per area) to the material.
Specific advice on this matter as well as instructions for maintenance of coatings
should be included in the ship's Cargo Securing Manual, if appropriate.
7.2.4 Transverse sliding
7.2.4.1 The balance calculation should meet the following condition (see also figure
17):
-
Fy ≤ μ · m · g + CS1 · f1 +
CS2 · f2 + … + CSn · fn
Where:
n is the number of lashings being calculated
Fy is transverse force from load assumption
(kN)
μ is friction coefficient
m is mass of the cargo item (t)
g is gravity acceleration of earth = 9.81 m/s2
CS is calculated strength of transverse securing devices (kN)
CS = ![](svgobject/772B-435A-912F-90BC477705C6.xml_d5127161e2109.png)
f is a function of μ and the vertical securing angle α
(see table 6).
7.2.4.2 A vertical securing angle α greater than 60° will reduce the
effectiveness of this particular securing device in respect to sliding of the item.
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
pre-tensioning of the securing device and maintaining the pre-tension throughout the
voyage.
7.2.4.3 Any horizontal securing angle, i.e. deviation from the transverse direction,
should not exceed 30°, otherwise an exclusion of this securing device from the
transverse sliding balance should be considered.
![](GUID-3ADCFDE7-99BA-415A-9831-0A6AE272EB62-low.jpg)
Figure 17 – Balance of transverse forces
Table 6 – f values as a function of α and μ
ɑ
|
–30°
|
–20°
|
–10°
|
0°
|
10°
|
20°
|
30°
|
40°
|
50°
|
60°
|
70°
|
80°
|
90°
|
μ
|
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
|
Remark: f = μ · sin α + cos α
7.2.4.4 As an alternative to using table 6 to determine the forces in a securing
arrangement, the method outlined in paragraph 7.3 can be used to take account of
transverse and longitudinal components of lashing forces.
7.2.5 Transverse tipping
This balance calculation should meet the following condition (see also figure 18):
-
Fy · a ≤ b · m · g + CS1 · c1 +
CS2 · c2 + … + CSn · cn
where
Fy, m, g, CS, n are as explained under 7.2.1
a is lever-arm of tipping (m) (see figure 18)
b is lever-arm of stableness (m) (see figure 18)
c is lever-arm of securing force (m) (see figure 18)
![](GUID-4B846527-1124-4ED0-B663-97EFB2906914-low.jpg)
Figure 18 – Balance of transverse moments
7.2.6 Longitudinal sliding
7.2.6.1 Under normal conditions the transverse securing devices provide sufficient
longitudinal components to prevent longitudinal sliding. If in doubt, a balance
calculation should meet the following condition:
-
Fx ≤ μ · (m · g -
fz · Fz) +
CS1 · f1 + CS2 ·
f2 + … + CSn ·
fn
-
where
-
Fx is longitudinal force from load assumption
(kN)
-
μ, m, g, f, n are as explained under 7.2.1
-
Fz is vertical force from load assumption (kN)
-
fz is a correction factor for the vertical force,
depending on friction as indicated below:
μ
|
0.0
|
0.1
|
0.2
|
0.3
|
0.4
|
0.6
|
fz
|
0.20
|
0.50
|
0.70
|
0.80
|
0.85
|
0.90
|
7.2.6.2 CS is calculated strength of longitudinal securing devices (kN)
- CS =
![](svgobject/772B-435A-912F-90BC477705C6.xml_d5127161e2732.png)
Remark: Longitudinal components of transverse securing devices should not be assumed
greater than 0.5 · CS.
7.2.6.3 Instead of service speed, a reduced operational speed is allowed to be used
when the correction factor for length and speed is calculated according to table 3
for the correction of the longitudinal and vertical accelerations. The longitudinal
acceleration calculated using table 3 in this annex should be verified by monitoring
during the voyage. When necessary the speed should be further reduced in order to
ensure that the calculated acceleration is not exceeded. In the Cargo Securing
Manual, it should be noted that the speed has to be reduced in heavy head seas to
avoid longitudinal shifting of cargo. It should also be noted for which speed the
accelerations in longitudinal direction have been calculated.
Note: Correction factors for speeds less than the service speed are not allowed for
the correction of transverse accelerations.
7.2.7 Calculated example
A calculated example for this method is shown in appendix 1 of annex 13.
7.3 Balance of forces – alternative method
7.3.1 The balance of forces described in paragraph 7.2.4 and 7.2.6 will normally
furnish a sufficiently accurate determination of the adequacy of the securing
arrangement. However, this alternative method allows a more precise consideration of
horizontal securing angles.
7.3.2 Securing devices usually do not have a pure longitudinal or transverse
direction in practice but have an angle β in the horizontal plane. This
horizontal securing angle β is defined in this annex as the angle of
deviation from the transverse direction. The angle β is to be scaled in the
quadrantal mode, i.e. between 0° and 90°.
![](GUID-6DB436FE-7CE4-4AF1-83F4-692F37FB3528-low.jpg)
Figure 19 – Definition of the vertical and horizontal securing angles α and β
7.3.3 A securing device with an angle β develops securing effects both in
longitudinal and transverse direction, which can be expressed by multiplying the
calculated strength CS with the appropriate values of
fx or fy. The values of
fx and fy can be obtained from
table 7.
7.3.4 Table 7 consists of five sets of figures, one each for the friction
coefficients μ = 0.4, 0.3, 0.2, 0.1 and 0. Each set of figures is obtained by
using the vertical angle α and horizontal angle β. The value of
fx is obtained when entering the table with β
from the right while fy is obtained when entering with
β from the left, using the nearest tabular value for α and
β. Interpolation is not required but may be used.
The balance calculations are made in accordance with the following formulae:
- Transverse sliding: Fy ≤ μ · m · g +
fy1 · CS1 + … +
fyn · CSn
- Longitudinal sliding: Fx ≤ μ · (m · g –
fz · Fz) +
fx1 · CS1 + … +
fxn · CSn
- Transverse tipping: Fy · a ≤ b · m ·
g + 0.9 · (CS1 · c1 +
CS2 · c2 + … +
CSn · cn)
Caution:
Securing devices which have a vertical angle α of less than 45° in combination
with horizontal angle β greater than 45° should not be used in the balance of
transverse tipping in the above formula. All symbols used in these formulae have the
same meaning as defined in paragraph 7.2 except fy and
fx, obtained from table 7, and CS is as
follows:
- CS =
![](svgobject/772B-435A-912F-90BC477705C6.xml_d5127161e3060.png)
A calculated example for this method is shown in appendix 1 of annex 13.
Table 7 – fx values and fy values as a function of α,
β and μ
Table 7.1 for μ = 0.4
β
for fy
|
α
|
β
for fx
|
-30
|
-20
|
-10
|
0
|
10
|
20
|
30
|
40
|
45
|
50
|
60
|
70
|
80
|
90
|
0
|
0.67
|
0.80
|
0.92
|
1.00
|
1.05
|
1.08
|
1.07
|
1.02
|
0.99
|
0.95
|
0.85
|
0.72
|
0.57
|
0.40
|
90
|
10
|
0.65
|
0.79
|
0.90
|
0.98
|
1.04
|
1.06
|
1.05
|
1.01
|
0.98
|
0.94
|
0.84
|
0.71
|
0.56
|
0.40
|
80
|
20
|
0.61
|
0.75
|
0.86
|
0.94
|
0.99
|
1.02
|
1.01
|
0.98
|
0.95
|
0.91
|
0.82
|
0.70
|
0.56
|
0.40
|
70
|
30
|
0.55
|
0.68
|
0.78
|
0.87
|
0.92
|
0.95
|
0.95
|
0.92
|
0.90
|
0.86
|
0.78
|
0.67
|
0.54
|
0.40
|
60
|
40
|
0.46
|
0.58
|
0.68
|
0.77
|
0.82
|
0.86
|
0.86
|
0.84
|
0.82
|
0.80
|
0.73
|
0.64
|
0.53
|
0.40
|
50
|
50
|
0.36
|
0.47
|
0.56
|
0.64
|
0.70
|
0.74
|
0.76
|
0.75
|
0.74
|
0.72
|
0.67
|
0.60
|
0.51
|
0.40
|
40
|
60
|
0.23
|
0.33
|
0.42
|
0.50
|
0.56
|
0.61
|
0.63
|
0.64
|
0.64
|
0.63
|
0.60
|
0.55
|
0.48
|
0.40
|
30
|
70
|
0.10
|
0.18
|
0.27
|
0.34
|
0.41
|
0.46
|
0.50
|
0.52
|
0.52
|
0.53
|
0.52
|
0.49
|
0.45
|
0.40
|
20
|
80
|
–0.05
|
0.03
|
0.10
|
0.17
|
0.24
|
0.30
|
0.35
|
0.39
|
0.41
|
0.42
|
0.43
|
0.44
|
0.42
|
0.40
|
10
|
90
|
–0.20
|
–0.14
|
–0.07
|
0.00
|
0.07
|
0.14
|
0.20
|
0.26
|
0.28
|
0.31
|
0.35
|
0.38
|
0.39
|
0.40
|
0
|
Table 7.2 for μ = 0.3
β
for fy
|
α
|
β
for fx
|
-30
|
-20
|
-10
|
0
|
10
|
20
|
30
|
40
|
45
|
50
|
60
|
70
|
80
|
90
|
0
|
0.72
|
0.84
|
0.93
|
1.00
|
1.04
|
1.04
|
1.02
|
0.96
|
0.92
|
0.87
|
0.76
|
0.62
|
0.47
|
0.30
|
90
|
10
|
0.70
|
0.82
|
0.92
|
0.98
|
1.02
|
1.03
|
1.00
|
0.95
|
0.91
|
0.86
|
0.75
|
0.62
|
0.47
|
0.30
|
80
|
20
|
0.66
|
0.78
|
0.87
|
0.94
|
0.98
|
0.99
|
0.96
|
0.91
|
0.88
|
0.83
|
0.73
|
0.60
|
0.46
|
0.30
|
70
|
30
|
0.60
|
0.71
|
0.80
|
0.87
|
0.90
|
0.92
|
0.90
|
0.86
|
0.82
|
0.79
|
0.69
|
0.58
|
0.45
|
0.30
|
60
|
40
|
0.51
|
0.62
|
0.70
|
0.77
|
0.81
|
0.82
|
0.81
|
0.78
|
0.75
|
0.72
|
0.64
|
0.54
|
0.43
|
0.30
|
50
|
50
|
0.41
|
0.50
|
0.58
|
0.64
|
0.69
|
0.71
|
0.71
|
0.69
|
0.67
|
0.64
|
0.58
|
0.50
|
0.41
|
0.30
|
40
|
60
|
0.28
|
0.37
|
0.44
|
0.50
|
0.54
|
0.57
|
0.58
|
0.58
|
0.57
|
0.55
|
0.51
|
0.45
|
0.38
|
0.30
|
30
|
70
|
0.15
|
0.22
|
0.28
|
0.34
|
0.39
|
0.42
|
0.45
|
0.45
|
0.45
|
0.45
|
0.43
|
0.40
|
0.35
|
0.30
|
20
|
80
|
0.00
|
0.06
|
0.12
|
0.17
|
0.22
|
0.27
|
0.30
|
0.33
|
0.33
|
0.34
|
0.35
|
0.34
|
0.33
|
0.30
|
10
|
90
|
–0.15
|
–0.10
|
–0.05
|
0.00
|
0.05
|
0.10
|
0.15
|
0.19
|
0.21
|
0.23
|
0.26
|
0.28
|
0.30
|
0.30
|
0
|
Table 7.3 for μ = 0.2
β
for fy
|
α
|
β
for fx
|
-30
|
-20
|
-10
|
0
|
10
|
20
|
30
|
40
|
45
|
50
|
60
|
70
|
80
|
90
|
0
|
0.77
|
0.87
|
0.95
|
1.00
|
1.02
|
1.01
|
0.97
|
0.89
|
0.85
|
0.80
|
0.67
|
0.53
|
0.37
|
0.20
|
90
|
10
|
0.75
|
0.86
|
0.94
|
0.98
|
1.00
|
0.99
|
0.95
|
0.88
|
0.84
|
0.79
|
0.67
|
0.52
|
0.37
|
0.20
|
80
|
20
|
0.71
|
0.81
|
0.89
|
0.94
|
0.96
|
0.95
|
0.91
|
0.85
|
0.81
|
0.76
|
0.64
|
0.51
|
0.36
|
0.20
|
70
|
30
|
0.65
|
0.75
|
0.82
|
0.87
|
0.89
|
0.88
|
0.85
|
0.79
|
0.75
|
0.71
|
0.61
|
0.48
|
0.35
|
0.20
|
60
|
40
|
0.56
|
0.65
|
0.72
|
0.77
|
0.79
|
0.79
|
0.76
|
0.72
|
0.68
|
0.65
|
0.56
|
0.45
|
0.33
|
0.20
|
50
|
50
|
0.46
|
0.54
|
0.60
|
0.64
|
0.67
|
0.67
|
0.66
|
0.62
|
0.60
|
0.57
|
0.49
|
0.41
|
0.31
|
0.20
|
40
|
60
|
0.33
|
0.40
|
0.46
|
0.50
|
0.53
|
0.54
|
0.53
|
0.51
|
0.49
|
0.47
|
0.42
|
0.36
|
0.28
|
0.20
|
30
|
70
|
0.20
|
0.25
|
0.30
|
0.34
|
0.37
|
0.39
|
0.40
|
0.39
|
0.38
|
0.37
|
0.34
|
0.30
|
0.26
|
0.20
|
20
|
80
|
0.05
|
0.09
|
0.14
|
0.17
|
0.21
|
0.23
|
0.25
|
0.26
|
0.26
|
0.26
|
0.26
|
0.25
|
0.23
|
0.20
|
10
|
90
|
–
|
–
|
–
|
0.00
|
0.03
|
0.07
|
0.10
|
0.13
|
0.14
|
0.15
|
0.17
|
0.19
|
0.20
|
0.20
|
0
|
Table 7.4 for μ = 0.1
β
for fy
|
α
|
β
for fx
|
-30
|
-20
|
-10
|
0
|
10
|
20
|
30
|
40
|
45
|
50
|
60
|
70
|
80
|
90
|
0
|
0.82
|
0.91
|
0.97
|
1.00
|
1.00
|
0.97
|
0.92
|
0.83
|
0.78
|
0.72
|
0.59
|
0.44
|
0.27
|
0.10
|
90
|
10
|
0.80
|
0.89
|
0.95
|
0.98
|
0.99
|
0.96
|
0.90
|
0.82
|
0.77
|
0.71
|
0.58
|
0.43
|
0.27
|
0.10
|
80
|
20
|
0.76
|
0.85
|
0.91
|
0.94
|
0.94
|
0.92
|
0.86
|
0.78
|
0.74
|
0.68
|
0.56
|
0.42
|
0.26
|
0.10
|
70
|
30
|
0.70
|
0.78
|
0.84
|
0.87
|
0.87
|
0.85
|
0.80
|
0.73
|
0.68
|
0.63
|
0.52
|
0.39
|
0.25
|
0.10
|
60
|
40
|
0.61
|
0.69
|
0.74
|
0.77
|
0.77
|
0.75
|
0.71
|
0.65
|
0.61
|
0.57
|
0.47
|
0.36
|
0.23
|
0.10
|
50
|
50
|
0.51
|
0.57
|
0.62
|
0.64
|
0.65
|
0.64
|
0.61
|
0.56
|
0.53
|
0.49
|
0.41
|
0.31
|
0.21
|
0.10
|
40
|
60
|
0.38
|
0.44
|
0.48
|
0.50
|
0.51
|
0.50
|
0.48
|
0.45
|
0.42
|
0.40
|
0.34
|
0.26
|
0.19
|
0.10
|
30
|
70
|
0.25
|
0.29
|
0.32
|
0.34
|
0.35
|
0.36
|
0.35
|
0.33
|
0.31
|
0.30
|
0.26
|
0.21
|
0.16
|
0.10
|
20
|
80
|
0.10
|
0.13
|
0.15
|
0.17
|
0.19
|
0.20
|
0.20
|
0.20
|
0.19
|
0.19
|
0.17
|
0.15
|
0.13
|
0.10
|
10
|
90
|
–0.05
|
–0.03
|
–0.02
|
0.00
|
0.02
|
0.03
|
0.05
|
0.06
|
0.07
|
0.08
|
0.09
|
0.09
|
0.10
|
0.10
|
0
|
Table 7.5 for μ = 0.0
β
for fy
|
α
|
β
for fx
|
-30
|
-20
|
-10
|
0
|
10
|
20
|
30
|
40
|
45
|
50
|
60
|
70
|
80
|
90
|
0
|
0.87
|
0.94
|
0.98
|
1.00
|
0.98
|
0.94
|
0.87
|
0.77
|
0.71
|
0.64
|
0.50
|
0.34
|
0.17
|
0.00
|
90
|
10
|
0.85
|
0.93
|
0.97
|
0.98
|
0.97
|
0.93
|
0.85
|
0.75
|
0.70
|
0.63
|
0.49
|
0.34
|
0.17
|
0.00
|
80
|
20
|
0.81
|
0.88
|
0.93
|
0.94
|
0.93
|
0.88
|
0.81
|
0.72
|
0.66
|
0.60
|
0.47
|
0.32
|
0.16
|
0.00
|
70
|
30
|
0.75
|
0.81
|
0.85
|
0.87
|
0.85
|
0.81
|
0.75
|
0.66
|
0.61
|
0.56
|
0.43
|
0.30
|
0.15
|
0.00
|
60
|
40
|
0.66
|
0.72
|
0.75
|
0.77
|
0.75
|
0.72
|
0.66
|
0.59
|
0.54
|
0.49
|
0.38
|
0.26
|
0.13
|
0.00
|
50
|
50
|
0.56
|
0.60
|
0.63
|
0.64
|
0.63
|
0.60
|
0.56
|
0.49
|
0.45
|
0.41
|
0.32
|
0.22
|
0.11
|
0.00
|
40
|
60
|
0.43
|
0.47
|
0.49
|
0.50
|
0.49
|
0.47
|
0.43
|
0.38
|
0.35
|
0.32
|
0.25
|
0.17
|
0.09
|
0.00
|
30
|
70
|
0.30
|
0.32
|
0.34
|
0.34
|
0.34
|
0.32
|
0.30
|
0.26
|
0.24
|
0.22
|
0.17
|
0.12
|
0.06
|
0.00
|
20
|
80
|
0.15
|
0.16
|
0.17
|
0.17
|
0.17
|
0.16
|
0.15
|
0.13
|
0.12
|
0.11
|
0.09
|
0.06
|
0.03
|
0.00
|
10
|
90
|
0.00
|
0.00
|
0.00
|
0.00
|
0.00
|
0.00
|
0.00
|
0.00
|
0.00
|
0.00
|
0.00
|
0.00
|
0.00
|
0.00
|
0
|
Remark: fy = cos α · cos β + μ ·sin α fx =
cos α · sin β + μ · sin α.
APPENDIX 1
CALCULATED EXAMPLE 1
(refer to paragraph 7.2, Balance of forces and moments)
Ship:
|
L = 120 m; B = 20 m; GM = 1.4 m; speed = 15
knots
|
Cargo:
|
m = 62 t; dimensions = 6 × 4 × 4 m;
|
|
stowage at 0.7L on deck,
low
|
![](GUID-1D9A3DF9-AC79-43AA-8757-36C948B67F8F-low.jpg)
Securing material:
- wire rope (single use): breaking strength = 125 kN; MSL = 100 kN
- shackles, turnbuckles, deck rings: breaking strength = 180 kN; MSL = 90
kN
- stowage on dunnage boards: μ = 0.3; CS = 90/1.5 = 60
kN
Securing arrangement:
-
side
|
n
|
CS
|
α
|
f
|
c
|
STBD
|
4
|
60 kN
|
40°
|
0.96
|
–
|
PORT
|
2
|
60 kN
|
40°
|
0.96
|
–
|
PORT
|
2
|
60 kN
|
10°
|
1.04
|
–
|
External forces:
- Fx = 2.9 × 0.89 × 62 + 16 + 8 = 184 kN
- Fy = 6.3 × 0.89 × 62 + 24 + 12 = 384 kN
- Fz = 6.2 × 0.89 × 62 = 342 kN
Balance of forces (STBD arrangement):
- 384 < 0.3 × 62 × 9.81 + 4 × 60 × 0.96
- 384 < 412 this is OK!
Balance of forces (PORT arrangement):
- 384 < 0.3 × 62 × 9.81 + 2 × 60 × 0.96 + 2 × 60 × 1.04
- 384 < 422 this is OK!
Balance of moments:
- 384 × 1.8 < 2 × 62 × 9.81
- 691 < 1216 no tipping, even without lashings!
Calculated example 2
(refer to section 7.3, Balance of forces – alternative method)
A cargo item of 68 t mass is stowed on timber (μ = 0.3) in the
'tween deck at 0.7L of a vessel.
L = 160 m, B = 24 m, v = 18 knots and GM = 1.5 m.
Dimensions of the cargo item are height = 2.4 m and width = 1.8 m.
The external forces are: Fx = 112 kN,
Fy = 312 kN, Fz = 346 kN,
fz= 0.8 and fz·
Fz = 276.8 kN
The top view shows the overall securing arrangement with eight lashings.
![](GUID-90392620-7331-4E44-A46F-9E8B7E462E9A-low.jpg)
Calculation of balance of forces:
No.
|
MSL (kN)
|
CS (kN)
|
α
|
β
|
fy
|
CS ×
fy
|
fx
|
CS ×
fx
|
1
|
108
|
80
|
40° stbd
|
30° fwd
|
0.86
|
68.8 stbd
|
0.58
|
46.4 fwd
|
2
|
90
|
67
|
50° stbd
|
20° aft
|
0.83
|
55.6 stbd
|
0.45
|
30.2 aft
|
3
|
90
|
67
|
50° stbd
|
20° fwd
|
0.83
|
55.6 stbd
|
0.45
|
30.2 fwd
|
4
|
108
|
80
|
40° stbd
|
40° aft
|
0.78
|
62.4 stbd
|
0.69
|
55.2 aft
|
5
|
108
|
80
|
40° port
|
30° aft
|
0.86
|
68.8 port
|
0.58
|
46.4 aft
|
6
|
90
|
67
|
20° port
|
30° aft
|
0.92
|
61.6 port
|
0.57
|
38.2 aft
|
7
|
90
|
67
|
20° port
|
10° fwd
|
1.03
|
69.0 port
|
0.27
|
18.1 fwd
|
8
|
108
|
80
|
40° port
|
30° fwd
|
0.86
|
68.8 port
|
0.58
|
46.4 fwd
|
Transverse balance of forces (STBD arrangement) Nos. 1, 2, 3 and 4:
- 312 < 0.3 × 68 × 9.81 + 68.8 + 55.6 + 55.6 + 62.4
- 312 < 443 this is OK!
Transverse balance of forces (PORT arrangement) Nos. 5, 6, 7 and 8:
- 312 < 0.3 × 68 × 9.81 + 68.8 + 61.6 + 69.0 + 68.8
- 312 < 468 this is OK!
Longitudinal balance of forces (FWD arrangement) Nos. 1, 3, 7 and 8:
- 112 < 0.3 (68 × 9.81 – 276.8) + 46.4 + 30.2 + 18.1 + 46.4
- 112 < 258 this is OK!
Longitudinal balance of forces (AFT arrangement) Nos. 2, 4, 5 and 6:
- 112 < 0.3 (68 × 9.81 – 276.8) + 30.2 + 55.2 + 46.4 + 38.2
- 112 < 287 this is OK!
Transverse tipping
Unless specific information is provided, the vertical centre of gravity of the cargo
item can be assumed to be at one half the height and the transverse centre of
gravity at one half the width. Also, if the lashing is connected as shown in the
sketch, instead of measuring c, the length of the lever from the tipping axis
to the lashing CS, it is conservative to assume that it is equal to the width
of the cargo item.
![](GUID-A96D1433-8CF8-44A9-BBAB-EEC89DE8B390-low.jpg)
- Fy · a ≤ b · m · g + 0.9 · (CS1 ·
c1 + CS2 · c2 +
CS3 · c3 + CS4 ·
c4)
- 312 × 2.4/2 < 1.8/2 × 68 × 9.81 + 0.9 × 1.8 × (80 + 67 + 67 + 80)
- 374 < 600 + 476
- 374 < 1076 this is OK!
APPENDIX 2
EXPLANATIONS AND INTERPRETATION OF METHODS TO ASSESS THE EFFICIENCY OF SECURING
ARRANGEMENTS
1 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 directions 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 directions.
2 Peak values in longitudinal and vertical directions may be associated more closely
because they have the common source of pitching and heaving.
3 The advanced calculation method uses the "worst case approach". That is expressed
clearly by the transverse acceleration figures, which increase to forward and aft in
the ship and thereby show the influence of transverse components of simultaneous
vertical accelerations. Consequently, there is no need to consider vertical
accelerations separately in the balances of transverse forces and moments. These
simultaneously acting vertical accelerations create an apparent increase of weight
of the item and thus increase the effect of the friction in the balance of forces
and the moment of stableness in the balance of moments. For this reason there is no
reduction of the force m · g normal to the deck due to the presence of an
angle of heel.
4 The 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.
5 The friction coefficients shown in the tables of this annex are generally lower
than the ones given in other publications, such as the CTU Code. The reason for this can be seen in various influences which
may appear in practical shipping, such as: vibration of the ship, moisture, grease,
oil, dust and other residues.
6 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.
7 The principal way of calculating forces within the securing elements of a complex
securing arrangement should necessarily include the consideration of:
-
.1 load-elongation behaviour (elasticity);
-
.2 geometrical arrangement (angles, length); and
-
.3 pre-tension, of each individual securing element.
8 This approach would require a large volume of information and a complex, iterative
calculation. The results would still be doubtful due to uncertain parameters.
9 Therefore, the simplified approach was chosen with the assumption that the elements
take an even load of CS (calculated strength) which is reduced against the
MSL (maximum securing load) by the safety factor.
10 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 to
arrive at reasonable figures of the levers a, b and c for the
balance of moments.
11 It should be borne in mind that this annex contains a number of assumptions based
on approximations. Even though safety factors are also incorporated, there is no
clear-cut borderline between safety and non-safety. If in doubt, the arrangement
should be improved.
APPENDIX 3
ADVANCED PROVISIONS AND CONSIDERATIONS APPLICABLE TO VERY HEAVY AND/OR VERY LARGE
CARGO ITEMS
This appendix contains additional advice that may be considered for the stowage and
securing of cargo with unusual characteristics, as referenced in chapter 1.8 of this
Code and may include items of exceptional mass and/or dimension. However, the listed
considerations do not claim to be complete.
1 Longitudinal tipping
For the securing of large and tall cargo items in longitudinal direction, the balance
calculation should also consider longitudinal tipping and meet the following
condition:
-
Fx⋅ a ≤ b⋅ (m ⋅ g -
fz ⋅ Fz) +
CS1 ⋅ c1 +
CS2 ⋅ c2 +...+
CSn ⋅ cn [kNm]
-
Where:
-
Fx, m, g, Fz, CS, n
are as explained under 7.2.1 of this annex.
- a is lever-arm of tipping (m) (see figure 18)
- b is lever-arm of stableness (m) (see figure 18)
- c is lever-arm of securing force (m) (see figure 18)
The factor fZ is obtained by the applicable relation of b/a as shown
below:
b/a
|
0.1
|
0.2
|
0.3
|
0.4
|
0.6
|
1.0
|
2.0
|
3.0
|
fZ
|
0.50
|
0.70
|
0.80
|
0.85
|
0.90
|
0.94
|
0.98
|
1.00
|
2 Rotational inertia of large cargo items
2.1 The algorithm used in 7.2.2 of this annex and section 1 above for defining the
tipping moment acting on a distinct cargo item replaces the physical extent of the
item by its centre of gravity. The tipping moment is then declared as the determined
horizontal force Fx or Fy,
multiplied by the vertical distance "a" of this centre of gravity to the edge
of the footprint, i.e. the tipping axis of the item. This is sufficiently accurate,
as long as the spatial dimensions of the item remain below about 6 metres.
2.2 Larger items, however, will develop a substantial additional tipping moment by
their rotational inertia against the rotational acceleration of the ship in rolling
or pitching motions. The additional tipping moment is independent from the stowage
position of the item in the ship and always positive, i.e. intensifying the tipping
impulse. This phenomenon requires additional securing measures and, therefore,
should be included in tipping balances for large cargo items by the use of a simple
algorithm.
2.3 Transverse tipping balance
2.3.1 For cargo items of width w (measured athwartships) and height h,
where (w2 + h2) > 50 m2, the additional
tipping moment k ⋅ J due to rotational inertia of the cargo item
should be added to the ordinary tipping moment Fy ⋅ a in
the transverse tipping balance.
2.3.2 The appropriate figure of the moment of rotational inertia J should be supplied
by the shipper related to the centre of gravity of the item for the plane of
transverse tipping. If such information is not available, an estimated figure may be
used by:
The reverse angular acceleration k may be taken as
[s-2].
2.4 Longitudinal tipping balance
2.4.1 For cargo items of length l (measured fore and aft) and height h, where
(l2
+ h2) > 50 m2, the additional
tipping moment k ⋅ J due to rotational inertia of the cargo item
should be added to the ordinary tipping moment Fx ⋅ a
in the longitudinal tipping balance.
2.4.2 The appropriate figure of the moment of rotational inertia J should be supplied
by the shipper related to the centre of gravity of the item for the plane of
longitudinal tipping. If such information is not available, an estimated figure may
be used by:
The reverse angular acceleration k may be taken as
[s-2].
3 Separate consideration of wind and sea sloshing
3.1 The algorithm used in this annex for defining the horizontal force
Fx or Fy, acting on a
cargo item stowed on deck, combines horizontal weight components, inertia forces and
wind/sloshing forces for reasons of simplification. This is correct for the balance
of sliding; however, it is an approximation only for the balance of tipping.
Particularly, high deck cargo items with their major wind exposed area well above
the centre of gravity should be given a separate compilation of moments from wind
forces, sea sloshing forces and gravity/inertia forces in order to get a more
realistic tipping moment. The inertia forces strike on the centre of gravity of the
cargo item, the sea sloshing strikes on the cargo area not more than 2 m above the
weather deck and the wind forces strike on the lateral area of the cargo item
exposed to wind.
Example: The figures of the tipping lever "a" relate to a large portal
harbour crane shipped on deck of a heavy lift ship. The centres of attack by wind
and spray deviate considerably from the centre of gravity. A separate compilation of
the longitudinal tipping moment reads:
|
Fx
|
a
|
Fx ⋅
a
|
Gravity/inertia
|
1373 kN
|
13.0 m
|
17849 kNm
|
Wind
|
170 kN
|
20.0 m
|
3400 kNm
|
Spray
|
4 kN
|
1.0 m
|
4 kNm
|
Total
|
1547 kN
|
|
21253 kNm
|
3.2 The conventionally computed tipping moment would be only:
Total
|
1547 kN
|
13.0 m
|
20111 kNm
|
3.3 The surplus over the conventional tipping moment here is about 6%. The potential
additional tipping moment by rotational inertia has not been reflected in this
example.
4 Interpretation of "on deck high"
4.1 The stowage level "on deck high" in table 2 of annex 13 has been positioned at a
distance above the water line of about two thirds of the ship's breadth. With
extremely large cargo items this level can easily be exceeded. In order to avoid
uncertainties in the determination of transverse and longitudinal accelerations in
such cases, it is recommended to use the original mathematical model, which has been
the basis for acceleration tables in annex 13. This model may easily be programmed,
e.g. in a suitable spreadsheet.
4.2 The shown mathematical model is identical to that used in the
International Code for the Construction and Equipment of Ships Carrying
Liquefied Gases in Bulk (IGC
Code) (resolution MSC. 5(48)). However, while in the IGC Code the probability
level of accelerations refers to the lifetime of a ship of 104 days,
annex 13, in order to remain within the scope of practical cargo securing
experience, applies a reduction factor of 0.74, corresponding to the 25-day
significant wave height in the North Atlantic. Furthermore, the model has been
expanded to supply reasonable K-parameters for B/GM-relations less
than 7, applicable to ships with exceptional large GM-values.
Mathematical model of the acceleration tables 2 to 4
4.3 The longitudinal, transverse and vertical accelerations acting on a cargo item
may be obtained alternatively by the set of formulas as follows:
- ax = c1 ⋅ c2
⋅ c3 ⋅ ax0 ⋅
g [m/s2]
- ay = c1 ⋅ c2
⋅ c3 ⋅ ay0 ⋅
g [m/s2]
- az = c1 ⋅ c2
⋅ c3 ⋅ az0 ⋅
g [m/s2]
ax: longitudinal acceleration (gravity component of pitch included)
ay: transverse acceleration (gravity component of roll included)
az: vertical acceleration (component due to static weight not
included)
c1: correction factor for navigation area, taken as 1.0
worldwide in annex 13
c2: correction factor for season, taken as 1.0 for whole year in
the annex 13
c3: correction factor for 25 navigation days,
taken as 0.6 + 0.1⋅ log1025 = 0.74 in annex 13
-
ax0 = ± a0 ⋅ ![](svgobject/772B-435A-912F-90BC477705C6.xml_d5127161e8666.png)
-
ay0 = ± a0 ⋅ ![](svgobject/772B-435A-912F-90BC477705C6.xml_d5127161e8730.png)
-
az0 = ± a0 ⋅ ![](svgobject/772B-435A-912F-90BC477705C6.xml_d5127161e8879.png)
therein:
-
a0 = 0.2 ⋅ ![](svgobject/772B-435A-912F-90BC477705C6.xml_d5127161e9061.png)
-
A = ![](svgobject/772B-435A-912F-90BC477705C6.xml_d5127161e9127.png)
-
K = R ⋅
, but never less than 1.0
-
R=
, but never greater than 1.0
L = length between perpendiculars [m]
B = moulded breadth of ship [m]
GM = metacentric height of ship [m]
Cb = block coefficient of ship
x = longitudinal distance from amidships to calculating point, positive
forward [m]
z = vertical distance from actual waterline to calculating point, positive
upward [m]
v = service speed [knots]
g = gravity acceleration = 9.81 [m/s2]
5 Structural strength assessment
5.1 Dry cargo ships are typically designed on the assumption that cargo is
homogeneously distributed. The maximum permissible surface load is usually specified
in the ship's documentation and given in t/m2 for all relevant stowage
areas, i.e. double bottom (tank top), top of stepped side tanks, 'tween deck
pontoons, weather deck and weather deck hatch covers.
5.2 Heavy cargo items tend to produce concentrated strip or point loads rather than
homogeneous loads. Then care should be taken that the stress parameters,
corresponding to the maximum permissible homogeneous load, are not exceeded by the
load induced by the heavy item. The essential parameters for stresses in deck
sections, hatch covers and 'tween deck pontoons or panels are shear forces and
bending moments. Suitable steel or timber beams or equivalent panel structures
should be used to transfer the strip or point load to the primary members of the
load-bearing structure.
5.3 Where a loading situation appears to be too complex to be safely examined by
manual calculation or where stress parameters obtained by a manual calculation
method come close to the applicable limit of the supporting structure, utilization
of finite element analysis should be considered.
6 Weather routeing
6.1 Utilizing weather routeing services may significantly contribute to performing a
safe passage. Care should be taken that the engaged service complies with the
recommendations laid down in MSC/Circ.1063 on Participation of ships in weather
routeing services.
6.2 In case of transporting heavy and/or large cargo items, where safe securing is an
essential requirement, the routeing decisions should be oriented to the avoidance of
severe ship motions rather than to other criteria, such as swift passage or fuel
economy. However, the engagement of a weather routeing service does not eliminate
the need for the application of securing measures as required in this annex.
7 Other considerations
When planning the transport of very heavy and/or very large cargo items on deck of a
vessel, particular consideration should be given to:
-
.1 the observation of sight line requirements as stipulated in SOLAS regulation
V/22, and, in case of non-compliance, the conditions for a
temporary exemption by the Flag State Administration;
-
.2 the provision of unimpeded radar transmission with due observation of
resolution MSC.192(79) on Revised performance
standards for radar equipment and SN.1/Circ.271 on Guidelines for
the installation of shipborne radar equipment; and
-
.3 the provision of visibility of navigations light as required by annex I of
International Regulations for Preventing Collisions at Sea and specified in
resolution MSC.253(83)
on Performance standards for navigation lights, navigation light
controllers and associated equipment.
APPENDIX 4
ADVANCED PROVISIONS AND CONSIDERATIONS APPLICABLE TO
SEMI-STANDARDIZED CARGOES
This appendix contains advice that may be considered for the stowage and securing of
semi-standardized cargoes in addition to the other provisions of chapter 4, annex 4
and annex 13 of this Code.
The provisions in section 1 below may be used for the following conditions:
-
.1 worst case accelerations are used for the design of securing arrangements
of semi-standardized cargoes, i.e. the most severe external forces within
the particular deck or otherwise defined region of the vessel are applied;
-
.2 uniform securing arrangements are used for types of cargo items
considering stepped weight classes, whereby arrangements always cover the
highest weight within a class and the most unfavourable position of the
centre of gravity;
-
.3 the range of lashing angles is well defined by the pattern of securing
points in the vessel, as well as on vehicles. The assessment uses worst case
angles, i.e. the worst combination of vertical and horizontal angles within
the given ranges; and
-
.4 securing equipment is regularly inspected when used for recurrent
application.
1 Performance factor for short voyages
For cargo securing arrangements considered in section 7.1 case .3 (short duration
voyages up to 72 hours), the forces and moments on the right side of the balance
equations in section 7.3 may be multiplied by the FP
performance factor of 1.15, as illustrated below:
Transverse sliding: Fy ≤ (μ · m · g +
fy1 · CS1 + … + fyn
· CSn)· FP
Longitudinal sliding: Fx ≤ (μ · (m · g –
fz · Fz) +
fx1 · CS1 + … +
fxn · CSn )·
FP
Transverse tipping: Fy · a ≤ (b · m · g
+ 0.9 · (CS1 · c1 + CS2 ·
c2 + … + CSn ·
cn)) · FP
2 Asymmetrical securing arrangements
For asymmetrical lashing arrangements and for cargoes resting on supports with
different coefficients of friction, separate sliding of the item's fore and aft ends
should be considered in the transverse direction. The calculations for each end
should be based on the part of the item's weight resting on each support and the
characteristics of the cargo securing devices attached to each end.
3 Safety factor
In the case of elementary securing arrangements, where no more than two devices per
impact direction are used and loads are evenly distributed by proper orientation to
the centre of gravity of the cargo item, the calculated CS of securing
devices may be obtained by:
![](svgobject/772B-435A-912F-90BC477705C6.xml_d5127161e9721.png)
The specific conditions for the use of the reduced safety factor should be outlined
in the ship's Cargo Securing Manual.
4 Friction coefficients
In addition to the friction coefficients in table 5 in section 7.2, the following
friction coefficients (μ) may be applied.
Table 8 – Additional friction coefficients
Materials in
contact
|
Friction coefficient
(μ)
|
Steel–rubber tyre, dirty, wet or
dry
|
0.3
|
Steel–solid rubber tyre, dry and
cleanfootnote
|
0.3
|
Steel–air rubber tyre, wet and
cleanfootnote
|
0.4
|
Steel–air rubber tyre, wet and
cleanfootnote
|
0.45
|
5 Effect of parking brake and wheel chocks
For wheel-based cargoes, the effect of parking brakes as well as the effect of wheel
chocks may be taken into account when dimensioning securing arrangements against
movement in the rolling direction. Usually parking brakes have a braking capacity
corresponding to a force equal to 0.2 · g · GVM (kN), where GVM
is the gross vehicle mass of the item in tonnes and in most cases the parking brake
is applied on one axle only. If a wheel is chocked it can be considered not to roll
and the friction in the rolling direction should be taken as the lesser of the
friction between the tyre and the ship's deck, and the chock and the ship's
deck."