3  Extended approaches

3.4  Semi-dynamic approach to calculation

Taking account of cargo movement and elastic deformation of the securing devices makes approaches to calculation other than those conventionally used necessary, since the input variables for simple equilibrium methods are initially unknown. They are only obtained in the course of a relatively long calculation process. A distinction may be drawn between a semi-dynamic and a fully dynamic approach.

The term "semi-dynamic" is here intended to indicate that while cargo movements are indeed taken into consideration, they are only used to determine the different loads assumed by the securing devices up until equilibrium with the external force. Further dynamic effects arising from the cargo having started to move are ignored and are still to be covered by the safety margin between LC and breaking load.

3.4.1  Iterative method

In an iterative calculation method, the cargo is moved stepwise under the action of an external force in a predetermined manner (sliding, tipping, racking). For each step, on the basis of this movement, the deformation of the securing devices involved and the force it has developed is determined. The developed force is added to the initial pretension and is broken down as a securing force into Cartesian components.

These components are included in the securing balances against horizontal sliding/racking and against tipping. Horizontal components act directly against sliding/racking and vertical components act via the coefficient of friction, while against tipping the horizontal and the vertical components are introduced into the calculation with the associated levers to the applicable tipping axis. If the securing arrangement consists of tie-down lashings, a similar procedure must be applied which also takes account of Euler’s friction at the edges of the cargo unit.

The calculation is terminated once equilibrium with the external force or with the external moment is reached. It may then be established which loads have been assumed by the individual securing devices and how large the cargo movement or deformation has become. The suitability or admissibility of the securing arrangement in question may be assessed on the basis of these two items of information. In addition, the results may point to possible improvements and increases in efficiency for a securing arrangement.

If reliable experience relating to additional dynamic loads is available, the iterative calculation procedure may also be terminated a little later than when static equilibrium is reached. The amount of this allowance could be selected to be approximately proportional to the cargo movement which has occurred up to equilibrium. This would enable a pragmatic step to be taken towards a dynamic approach to calculation.

Obviously, this calculation process can only be carried out with a programmed computer and thus cannot be considered for on the spot dimensioning or verification of a securing arrangement, but it may be considered for individual planning of critical transport operations or for designing standard securing arrangements for long-term use.

3.4.2  Selective methods

A selective approach to direct securing starts from the securing device in the arrangement in question which is definitely the first to reach its admissible load (LC). On the basis of the deformation of the selected securing device, this loading is converted into a cargo movement/deformation. The latter is used to determine the deformations and loads developed by all further securing devices and these values are input into a balance.

The balance indicates whether the securing arrangement is adequate or requires further improvement. It also makes it possible to identify which securing means may possibly be only inadequately contributing to securing.

For frictional securing, i.e. tie-down lashing, the selective approach should be modified such that the calculation starts from the maximum tolerable cargo movement and uses this as a basis for determining the changes in length, forces and geometric components of the lashings and inputs these values into the sliding and tipping balances.

These selective methods involve less complex calculation and may in most cases also be calculated manually. They are thus also suitable for staff training. A result, one has oneself calculated, carries more weight than a result passively accepted from a computer.