4  Practical examples
[German version]

4.2  Direct securing with chains at unfavorable angles

This example is intended to demonstrate that a tolerable cargo movement may improve an unfavorable geometry of the securing arrangement in such manner that securing becomes possible without exceeding admissible forces, while the conventional calculation yielded a negative result.

A heavy cargo unit is secured at the front and back with diagonal chains against sliding in the longitudinal and transverse directions. Unfavorably, the chains have very small longitudinal components. The cargo unit itself stands on flat wooden boards. This example solely investigates securing against rearward sliding.

Cargo mass m = 12 t, dimensions l x b x h = 4,0 x 2,3 x 2,2 m, m = 0,3

2 chains at the front: X = 0,5 m, Y = 2,4 m, Z = 2,2 m; L = 3,294 m
  LC = 30 kN, elongation at LC = 1,5%, pretension F0 = 1,0 kN

Figure 18: Securing a heavy item against rearward sliding

The external force is determined as conventionally agreed.

Conventional assessment of the securing against rearward sliding:


According to the conventional assessment, securing is not adequate, with a shortfall of a good 4%.

Taking account of cargo sliding:

If the cargo is permitted to slide longitudinally, the X component of the two chains grows and thus so too does their securing effect. The exact sliding distance to reach static equilibrium may only be calculated by elaborate adaptation of the balance formula to include the spring constant of the chains. The relationship becomes clearer if the sliding distance until the LC of the chains is reached is calculated and it is then checked whether the balance is fulfilled.

The spring constant of the chains amounts to DCh = DF / DL = 30 / (3.294 × 0.015) = 607 kN/m. On increasing the force from a pretension of 1.0 kN to LC = 30 kN, the chains lengthen by 29 / 607 = 0.04778 m to 3.342 m. As a result, the X component of the chains increases to

The cargo unit has shifted rearward by approx. 25 cm. The adapted balance now reads:

The balance is achieved with a surplus of a good 3%. While the improvement is indeed not enormous, the positive trend is indicative for such securing situations. Static equilibrium is reached with a smaller shift of the cargo unit. However, when force equilibrium is reached, the unit has reached a distinguished speed relative to the loading area which must be absorbed by an excess of securing force. This observation leads to a dynamic analysis which is not to be carried out here.

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