Section 12.2 Longitudinal Strength (Bending Moments, Shearing Forces)

While transverse stability ensures a vessel’s ability to resist capsizing, longitudinal strength relates to its capacity to withstand forces that tend to bend or break its hull girder (the main body of the ship acting like a beam) along its length. For bulk carriers, which are often long vessels and can carry very dense cargoes distributed unevenly, managing longitudinal stresses – primarily bending moments (BM) and shearing forces (SF) – is of paramount importance. Exceeding permissible stress limits can lead to buckling, cracking, or even catastrophic structural failure, such as the vessel breaking in two. The Master and Chief Officer must ensure, through careful cargo and ballast distribution planned and monitored with the loading instrument, that these stresses remain within safe design limits at all times – in port, during cargo operations, and at sea.

1. Understanding Forces on the Hull Girder:

A ship floating in water is subjected to two primary sets of vertical forces:

Weight Forces: The downward forces due to the weight of the ship’s structure, machinery, cargo, fuel, water, and stores. These weights are distributed unevenly along the ship’s length.

Buoyancy Forces: The upward forces exerted by the water, distributed along the length of the underwater hull. The distribution of buoyancy depends on the shape of the underwater hull and, in a seaway, on the position of waves along the ship’s length.

When the distribution of total weight along the length of the ship does not exactly match the distribution of buoyancy, internal stresses – shearing forces and bending moments – are induced in the hull structure.

2. Shearing Forces (SF):

Definition: A shearing force at any transverse section of the hull is the net vertical force acting on one side of that section. It represents the tendency for one part of the ship to slide vertically relative to the adjacent part.

Cause: Occurs when there is an imbalance between the net weight and buoyancy forces over a particular segment of the ship. For example, if a hold is heavily loaded and the adjacent ballast tanks are empty, there will be a significant shearing force at the bulkheads bounding that hold.

Distribution: Shearing forces are typically highest near the ends of the cargo-carrying section of the vessel (e.g., near the forepeak bulkhead and the engine room forward bulkhead) and at transverse bulkheads between loaded and empty (or lightly loaded) compartments, especially in alternate loading conditions. They are generally lowest around midships if the load is somewhat evenly distributed.

Consequences of Excessive SF: Can lead to diagonal cracking or buckling of the side shell plating and internal web frames, particularly in areas of high shear.

Permissible Limits: The ship’s approved Loading Manual and loading instrument specify the maximum permissible shearing force at various stations (transverse sections) along the ship’s length for both still water (harbor) and sea-going (wave-inclusive) conditions.

3. Bending Moments (BM):

Definition: A bending moment at any transverse section of the hull is the net algebraic sum of the moments of all vertical forces (weights and buoyancy) acting on one side of that section, taken about that section. It represents the tendency of the hull girder to bend upwards (hogging) or downwards (sagging).

Types of Bending:

Hogging: Occurs when the ends of the vessel are more heavily loaded (or less supported by buoyancy) than the midship section, or when a wave crest is amidships and troughs are at the ends. The deck experiences tensile (stretching) stresses, and the bottom plating experiences compressive (squeezing) stresses. The vessel’s main deck arches upwards.

Sagging: Occurs when the midship section of the vessel is more heavily loaded (or less supported by buoyancy) than the ends, or when a wave trough is amidships and crests are at the ends. The deck experiences compressive stresses, and the bottom plating experiences tensile stresses. The vessel’s main deck sags downwards.

Still Water Bending Moment (SWBM): The bending moment experienced by the vessel in calm water due to the static distribution of all weights (ship, cargo, ballast, fuel, etc.) and the resulting buoyancy distribution. This is the component directly controlled by cargo and ballast stowage.

Wave Bending Moment (WBM): The additional, dynamic bending moment induced by waves passing along the hull. This is influenced by wave height, length, and direction relative to the ship. The design of the ship accounts for a maximum expected wave bending moment.

Total Bending Moment: The algebraic sum of SWBM and WBM.

Distribution: Bending moments are typically highest in the midship region of the vessel and reduce towards the ends.

Consequences of Excessive BM:

Excessive Hogging: Can lead to tensile fractures in the deck plating or compressive buckling of the bottom structure.

Excessive Sagging: Can lead to compressive buckling of the deck plating or tensile fractures in the bottom structure.

Catastrophic failure (breaking the ship’s back) is the ultimate consequence of exceeding bending moment limits.

Permissible Limits: The ship’s approved Loading Manual and loading instrument specify the maximum permissible hogging and sagging bending moments at various stations along the ship’s length for both still water and sea-going conditions.

4. Factors Influencing Longitudinal Stresses:

Distribution of Cargo: This is the most significant factor that the ship’s staff can control.

Concentrating heavy cargo in the midship holds tends to cause sagging.

Concentrating heavy cargo in the end holds (or leaving midship holds empty/light) tends to cause hogging.

Uneven loading between adjacent holds creates high shear forces.

Distribution of Ballast: Used to counteract cargo-induced stresses and to manage stresses in ballast condition. Improper ballasting can exacerbate stress problems.

Distribution of Fuel, Fresh Water, and Stores: While generally having a smaller impact than cargo or ballast on large bulk carriers, their distribution (especially large quantities of fuel in specific tanks) should still be considered.

Vessel Design:

Length of Vessel: Longer vessels are generally more susceptible to high bending moments.

Structural Arrangement: The design of the hull girder (scantlings of deck, bottom, side shell plating, longitudinal frames, girders) determines its strength.

“Stress-Monitoring Holds”: Some bulk carriers, particularly larger ones or those designed for specific trades (e.g., alternate hold loading), may have certain holds or ballast tanks designated as critical for stress monitoring.

Cargo Density: Very dense cargoes (e.g., iron ore, concentrates) occupy less volume for a given weight. If a full deadweight of dense cargo is loaded, large portions of the ship’s length (e.g., some holds) may be empty, leading to significant stress concentrations. This is why alternate hold loading is common for such cargoes.

Wave Conditions at Sea: The height, length, and period of waves, and their direction relative to the ship’s heading, significantly influence the wave bending moment. Head seas or stern seas generally produce the largest bending moments. Quartering seas can induce torsional (twisting) stresses in addition to bending.

Vessel Speed in Waves: Reducing speed in heavy weather can significantly reduce wave-induced stresses and slamming.

5. Managing Longitudinal Stresses – The Role of the Loading Manual and Loading Instrument:

A. Approved Loading Manual:

This Class-approved document is specific to the vessel and contains:

Permissible still water and sea-going shear force and bending moment limits for various stations along the ship’s length (often presented as envelope diagrams).

Guidance on approved loading conditions, including any specific restrictions for alternate hold loading, block loading, or carrying high-density cargoes.

Information on tank top strength limits.

Procedures for calculating stresses (though this is now primarily done by the loading instrument).

The Master and Chief Officer must be thoroughly familiar with the contents of the Loading Manual.

B. Loading Instrument (Loading Computer / Loadicator):

This mandatory electronic tool (for most bulk carriers) is used to calculate and display the vessel’s stability, drafts, trim, and, crucially, the shearing forces and bending moments at multiple stations along the hull for any given loading condition (cargo, ballast, consumables).

Input: Requires accurate input of all weights (cargo per hold, liquid levels in all tanks, etc.) and their centers of gravity.

Output: Displays calculated SF and BM values, often graphically as curves superimposed on the permissible limit envelopes. It will typically provide alarms or warnings if any calculated value exceeds or approaches (e.g., >95-98%) the permissible limits.

Simulation: Allows for the simulation of loading/discharging sequences and ballast operations to check stresses at intermediate stages.

Verification: The accuracy of the loading instrument must be regularly verified against approved test conditions, and records kept.

6. Practical Stress Management During Cargo and Ballast Operations:

Stowage Planning: The initial stowage plan must be designed to ensure that the final loaded condition, as well as anticipated arrival condition (after consuming fuel/water), will have SF and BM values well within permissible sea-going limits.

Loading/Discharging Sequence: This is where stresses are most actively managed.

The sequence of loading or discharging cargo from holds, and the concurrent ballasting or de-ballasting operations, must be carefully planned and executed to keep SF and BM within permissible still water limits at all intermediate stages.

Avoid creating large disparities in loading between adjacent holds without appropriate ballast compensation.

For alternate hold loading of dense cargoes, follow the approved sequences in the Loading Manual meticulously. Deviations can be extremely dangerous.

Continuous Monitoring:

During cargo and ballast operations, the officer on watch must regularly update the loading instrument with actual quantities loaded/discharged and tank levels.

After each significant step, re-calculate and check SF and BM values.

If calculated stresses approach permissible limits, operations must be slowed down or stopped, and the sequence adjusted.

Communication: Maintain clear communication with the terminal/stevedores regarding the required loading/discharging sequence. The ship must control this sequence if safety is at stake.

Ballast as a Tool: Use ballast strategically to counteract undesirable stresses induced by cargo distribution. For example, if loading end holds causes hogging, ballasting midship tanks can help reduce it.

7. Considerations for Sea Passage:

Departure Condition: Ensure the vessel sails with SF and BM values comfortably within the sea-going permissible limits, providing a margin for the additional stresses imposed by waves.

Heavy Weather:

Reducing speed and altering course in heavy weather are the primary means of reducing wave-induced bending moments and slamming forces.

Be aware that severe pitching can significantly increase dynamic stresses.

Consumption of Consumables: The consumption of fuel and water during the voyage changes the weight distribution and thus the SWBM. The loading instrument should be used to check the stress condition for the anticipated arrival condition and any critical intermediate points of the voyage. Large shifts in consumables (e.g., transferring large quantities of fuel between tanks) should also be checked for their stress implications.

8. Master’s Responsibilities:

The Master has the ultimate responsibility for ensuring the vessel is not overstressed at any time.

Approval of Plans: Review and approve all stowage plans and loading/discharging sequences, paying particular attention to calculated stress levels.

Ensuring Competence: Confirm that the Chief Officer and other relevant officers are proficient in using the loading instrument and understand the principles of longitudinal strength and the ship’s specific limitations.

Setting Operational Limits: May decide to operate with a larger safety margin below permissible stress limits, especially on older vessels or if severe weather is anticipated.

Stopping Unsafe Operations: Must not hesitate to stop cargo or ballast operations if calculated or suspected stresses are approaching or exceeding limits.

Reporting Structural Concerns: If any signs of structural distress are observed (e.g., new cracks, buckling, unusual hull vibrations), these must be reported immediately to the company and Class society, and appropriate action taken (e.g., reduce stress, seek shelter, arrange for inspection).

Proper management of longitudinal strength is essential to prevent catastrophic failure of the hull girder. It requires a diligent, analytical approach to cargo and ballast distribution, effective use of the approved loading instrument, and an unwavering commitment from the Master and officers to operate the vessel within its designed structural limits at all times.