Introduction

In an earlier article, we saw how to design stoppers for seafastening. Stoppers are items that are used to contain the translation movements (longitudinal and transverse directions) of a cargo on the deck/hold of a vessel.

That brings us to the question – what about tipping of the cargo? If the cargo is subjected to external forces that cause it to tip, how do we protect the cargo against tipping?

Thinking in basic terms, to prevent cargo from tipping/overturning, we will need something that pins or clips it to the deck. Such a seafastening item is called a ‘Clip’ or a ‘Dog Plate’. Imagining such an item, it can be an ‘L-shaped’ structure that clings on to the base of the cargo. If we see the figure below, the dog plate is like a jaw that clamps down on the base frame of the cargo. We can also see that this kind of structure will help prevent the overturning of the cargo, as compared to stoppers which can prevent only translation. At times, both dog plates and stoppers may be used together on the same cargo with dog plates resisting overturning and stoppers resisting translation.

Designing a Dog Plate:

In this section, we’ll see how do we go about designing a dog plate for a particular operation.

Any design takes up the following flow:

1. Evaluate the forces acting on the structure
2. Check the stresses on the structure due to the forces
3. Iterate the design until the stresses are within the acceptable levels

Forces on the structure:

The cargo on the vessel will experience forces in the three directions – longitudinal, transverse, and vertical (uplift), besides the self-weight of the cargo. The first three forces depend on the environment in which the vessel is operating, and one simple but conservative way of calculating these forces is to follow DNVGL guidelines (See DNVGL-ST-N001, also see our product on Cargo Forces and Accelerations)

Longitudinal or Transverse Forces

In the figure below that shows the plan of a vessel’s deck carrying cargo, we can see that there are multiple dog plates in each direction to resist the respective force (transverse or longitudinal).

If the number of dog plates in the transverse direction is n_T and the total transverse force on the cargo is F_T, then the transverse force on a single dog plate in the transverse direction is

F_T1 = F_T/n_T

Similarly, in the longitudinal direction, the total longitudinal force divided by the total number of dog plates in that direction gives the force on one dog plate.

Uplift Force

The uplift force is a vertically upward force due to the cargo motion. It is calculated from a motion analysis or from empirical relations (See our product for Cargo Forces and Accelerations).

Self-Weight of Cargo

The cargo also experiences its own self-weight that acts vertically downwards.

The force diagram of the Cargo can be drawn as below:

We can see that given the location of the dog plate, the following forces and moments will be experienced by it:

1. The transverse force F_T will be borne by all the dog plates.
2. An overturning moment on the whole cargo, M_T, due to F_T, Uplift Force, and Self-Weight will also be borne by all dog plates. We can see that while F_T and F_V will cause the cargo to tip, the restoring moment due to self-weight protects it from tipping.

M_T = F_T x H/2 – W x B/2 + F_V x B/2

The above force and moment can be divided by the number of dog plates (n_T in the transverse direction) to give the force and moment per dog plate.

F_T1 = F_T/n_T

M_T1 = M_T/n_T

Translation of forces to the Dog Plate

The net overturning moment MT1 on a single dog plate translates effectively to an uplift force on the dog plate due to the moment. Considering the uplift force to be acting at the dog plates on either side, the effective uplift force on each dog plate is

F_V1 = M_T1/B

where B is the width of the cargo.

Next, we see the force diagram of the Dog Plate itself:

We can see that the following forces are acting on the dog plate:

• The translation force F_T1, which gets directly translated from the cargo
• The uplift force F_V1, which occurs due to the overturning moment

Stresses on the dog plate

The above two forces lead to various stresses for which the dog plate needs to be analyzed:

1. Shear Stress: The force F_T1 leads to shear stress on the dog plate
2. Tensile stress: The effective tensile force is calculated from the moment of the two forces F_T1 and F_V1 about the base, divided by the length of the base, L2.
3. Bending Stress: bending moment at the base is calculated by adding the bending moments due to F_T1 and F_V1 at the base.
4. Weld Check: The weld of the dog plate to the deck also needs to be checked similarly for shear, tensile and bending stresses

By calculating the forces and moments applicable, the stresses can be calculated, and the suitability of the dog plate evaluated. Some sample calculations are shown below:

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