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by McTaggart (1998). The present paper describes a methodology for evaluating the risk with respect
to cargo shifting. The risk is defined as the probability that at least one cargo unit will start to shift
during a given time period. This probability is called the risk of inirial cargo shiji, and can be seen as a
criterion for safe operation. This paper describes the methodology, which combines models for the
interaction between waves, ship and cargo with statistical methods. Some case studies are included in
order to evaluate the methodology and to show the influence of different parameters.

2 THE METHODOLOGY
Cargo shifting is a complex phenomenon, caused by the ship motions and largely influenced by the
properties of cargo and lashings as well as operational aspects. During its time at sea a ship will
encounter a large number of different conditions, defined by sea state, ship heading towards the waves,
ship speed and loading condition. In each such condition the ship motions will be different and thereby
also the forces acting on the cargo. Thus the probability of cargo shifting will differ in the various
conditions. In order to estimate the total risk of cargo shifting during a year, or the ship’s lifetime, the
probability of shifting must be calculated in all conditions the ship will encounter during that time. In
each condition the waves will have specific statistical properties and the ship will move in a certain
way in response to these waves. These motions will induce forces on the cargo, which will shift if
these forces are larger than what the cargo and its lashings can withstand. The total risk will depend on
the probability of shifting in each condition and the probability that the ship will encounter each
specific condition, as well as time. This section describes the cargo model used, and how the forces
acting on the cargo are calculated from the ship motion response to waves. Further, a description is
given of the statistical methods used for estimating the risk of shifting in a specific condition as well as
the total risk. A thorough description of the methodology has been given by Ericson et al. (1999).

2.1 Cargo Model
A purely twodimensional model of a cargo unit is used. This means that all forces act in the
transversal plane of the ship, and that the pre-tensions in the lashings on each side are equal (see
Figure 1). The cargo is assumed to be rigid, which means the lashing forces will be equal to the pre-
tension until the cargo shifts. Shifting is defined as an initial motion, either by sliding or tipping. Thus,
the risk presented is the risk of at least one initial motion of one cargo unit. For the case studies
presented in this paper a model of a container is used. This container model is shown in Figure 1. The
forces F and N are the forces corresponding to the combined effects of the ship motions, as described
in the section
2.2 Ship Motion Induced Forces. If these forces are large enough in comparison to the pre-tensions
and the friction, they will cause the cargo to shift. The tipping mode is neglected herein, since it can be
shown that sliding is the critical mode for the studied type of cargo, see Ericson (2000). Sliding will
occur if the total horizontal force is positive, that is if
F-F, -2.(F, -F,).sincp>O. (1)
The friction force (Ff) is found from vertical equilibrium, and the relation Ff = ~FN, where p is the
coefficient of friction. This means the friction force can be written as
F, =p(N+2*(F, +F,)*cosc~). (2)
Note that the friction force always acts in the opposite direction to the force F. Accounting for this and
inserting the relation for the friction force from Eqn. (2) into Eqn. (I), gives the expression:
Iq - p(N + 2. cos cp . (F, + F2)) - 2. sin cp (F, - F2) - sign(F) > 0. (3)
It should also be noted that in the methodology described herein, any cargo model can be used. For
each cargo type an appropriate model should be used, taking into account its specific characteristics.