7.3 Balance of forces - alternative method
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Statutory Documents - IMO Publications and Documents - International Codes - CSS Code - Code of Safe Practice for Cargo Stowage and Securing1 – Resolution A.714(17) - Annex 13 - Methods to assess the efficiency of securing arrangements for non-standardized cargo - 7 Advanced calculation method - 7.3 Balance of forces - alternative method

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°.

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 =

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
Parent topic: 7 Advanced calculation method
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