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 = 
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.
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)
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 =
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.