Stability, Strength & Loading

Every loading condition that goes in front of the master for approval is being checked against several completely independent standards at the same time, and it only takes one of them to fail for the whole condition to be refused. The intact stability criteria from the IS Code have to be met. Any damage case the ship is required to survive has to be met. The hull girder's still-water bending moment and shear force have to sit inside the approved limit curves. The tank tops and decks have to carry what is stowed on them without local overload. And the trim and draught have to fit whatever the port, canal or berth allows. None of these substitutes for another — a condition can clear every intact stability check and still be refused because the tank top under one hold is carrying more than it is rated for.

The loading computer does the arithmetic, and on a modern ship it will flag a failure clearly enough. What it will not do is decide which of several possible stowage plans is sensible, or notice that a condition which passes on paper depends on a ballast tank that nobody has actually sounded being exactly where the plan assumes it is. The master's signature is the point at which someone takes responsibility for having read the output, not merely for having run it — worth keeping in mind before treating a green light on a screen as the end of the exercise.

The IS Code's intact criteria look like an arbitrary list of numbers until you separate what each one is actually protecting against. GM₀ has to be at least 0.15 m — that is the floor on initial stiffness, the tendency to come back upright from a small angle before anything about the ship's shape further out matters. The righting lever at 30° of heel, GZ₃₀, has to reach at least 0.20 m, and the angle at which GZ is greatest, θmax, has to be at least 25°. Those two together are less about the first few degrees and more about how much righting force is still being generated well into a roll, which is exactly where a beam sea or a gust puts a ship under way.

The area criteria go further still: the area under the GZ curve from 0° to 30° must reach 0.055 m·rad, from 0° to 40° (or the angle of downflooding, if that comes sooner) must reach 0.090 m·rad, and from 30° to 40° must reach 0.030 m·rad. Area under a curve of righting lever against angle is energy — the work the ship can absorb from wind and sea before she is pushed past the point of no return. A ship can satisfy GM₀ comfortably and still fail an area criterion if her GZ curve falls away quickly past 20° or so, which is exactly the shape a high, slab-sided deck cargo or a full grain hold tends to produce.

The damage case a ship has to survive depends on her type and her damage stability notation, and it is worked from an assumed extent of flooding rather than from any single accident the ship happens to be expected to have. What the calculation gives back is a residual condition — GM, range of stability and freeboard with one or more compartments open to the sea — that still has to clear its own, generally lower, minima. A condition that comfortably clears the intact criteria can still fail the damage case if too much of the ship's reserve buoyancy and stability margin has already been spent getting her down to a deep, upright, intact trim in the first place.

The point examiners keep coming back to is the arrival condition. Consumables — fuel, fresh water, stores — are drawn from tanks that sit low and are burned off progressively over a voyage, so KG on arrival is not the same as KG on departure; it is very often higher, because the weight lost has come off the bottom of the ship. A stowage plan approved against a comfortable departure GM can arrive with a GM that is thin, or with a damage case that no longer clears its minima, purely because of how the consumables were drawn down. Approving a condition on the departure figures alone, without running the arrival case, is treating half the voyage as though it did not exist.

The hull girder is a beam, and the still-water bending moment and shear force it carries at any point along its length depend on how weight is distributed against the buoyancy supporting it. Concentrate cargo over one part of the ship and leave another part light, and the beam bends more than the same total tonnage spread evenly would produce. The ship's approved loading manual gives permissible SWBM and shear force curves along the length, separately for hogging and sagging, and every condition — harbour or at sea — has to sit inside them. Because the curves are tightest at particular stations, usually somewhere near amidships, two stowage plans with the same total deadweight can produce very different bending moments.

Local loading is a separate question from the overall bending moment. A tank top or deck is rated in tonnes per square metre, not tonnes — the total weight in a hold says nothing about whether the steel underneath one stack of cargo or one pile of bulk can take it. And because a ship is loaded and ballasted in a sequence, not delivered fully stowed in one moment, the bending moment and shear force have to be checked at each intermediate stage of that sequence as well as on completion. It is common, not exceptional, for the tightest moment of the whole operation to occur partway through loading, before the ballast intended to counteract it has actually been discharged.

• Total deadweight — tells you almost nothing about bending moment on its own.
• Distribution along the length — what actually drives SWBM and shear force.
• Tonnes per square metre — the separate check on the tank top or deck itself.

A weight resting on deck acts at its own height above the keel, wherever that happens to be. The moment a crane or derrick takes the strain and lifts it clear, that stops being true — the load is now being carried into the ship's structure through the point of suspension, so for the purposes of GG and GM it behaves as though it had been moved bodily up to the derrick head, however high above the deck that happens to sit. The shift in G this produces, w·d/Δ, where d is the vertical distance from the weight's original position to the derrick head, can be a large fraction of the GM the ship had to begin with, particularly on a ship carrying a light GM to start with or lifting a genuinely heavy piece of plant.

The examinable point is timing. The rise in G happens at the instant the load comes off the deck, not gradually as the boom slews it outboard and not only once it is set down somewhere else — the ship has to be stable enough to take the lift the moment the wire takes the strain, wherever the derrick subsequently swings it. If the derrick head also stands off the centreline once the load is plumbed outboard — over the quay, over a barge alongside — the same logic applies transversely, and the ship takes up a list from the shift in G across the beam as well as up it. Both effects have to be worked before the lift is taken, not discovered afterwards from how the ship is actually sitting.

Grain is a granular cargo with no fixed surface of its own — trimmed as full as practicable, it still settles and can shift its own free surface at an angle of repose when the ship rolls, and any void left above a trimmed surface, however small, gives it room to do so. The Grain Code's answer is to require a heeling moment to be calculated for every compartment that is not completely full and trimmed, tabulated against the compartment's shape and fill, and to check the resulting condition against its own criteria: an initial GM of at least 0.30 m, an angle of heel that does not exceed 12° or the angle of deck-edge immersion, whichever comes first, and a residual area between the heel angle and 40° (or the downflooding angle) of at least 0.075 m·rad.

None of those three checks stands in for another. The GM requirement sits above the general intact minimum precisely because a grain ship carries a standing risk of a shifting cargo that an ordinary dry cargo does not present. The heel-angle limit caps how far she is allowed to go over if the worst tabulated shift actually happens. The residual area is the reserve of righting energy left over after that heel has already been taken up — the margin still available to survive weather on top of the shift itself. A partly filled compartment is not a minor exception to work around; it is the specific condition the whole of this calculation exists to control, and every one of the three checks has to be run against it.

The three conditions below are worked the way a loading computer's audit trail, or an oral exam, expects to see them — a given block, each reasoning step shown before its arithmetic, and a decision stated in plain terms at the end.