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Hull Girder Shear Forces and Bending Moments - Bulk Carrier Limitations

As with any cargo ship it is important to load the cargo so that stresses in the ship remain at a minimum or at least evenly distributed. This is especially so with large bulk carriers. All ships are designed with limitations imposed upon their operability to ensure that the structural integrity is maintained. Therefore, exceeding these limitations may result in over-stressing of the ship's structure which may lead to catastrophic failure.

The ship's approved loading manual provides a description of the operational loading conditions upon which the design of the hull structure has been based. The loading instrument provides a means to readily calculate the still water shear forces and bending moments , in any load or ballast condition, and assess these values against the design limits.

A ship's structure is designed to withstand the static and dynamic loads likely to be experienced by the ship throughout its service life. The loads acting on the hull structure when a ship is floating in still (calm) water are static loads, one of the major ones being created by the cargo.

The main hull stresses set up by the cargo are hogging , sagging and shearing . These can be minimised by evenly distributing the cargo - homogenous loading.

Dynamic loads are those additional loads exerted on the ship's hull structure through the action of the waves and the effects of the resultant ship motions (i.e. acceleration forces, slamming and sloshing loads). Hogging and sagging forces are at a maximum when the wave length is equal to the length of the ship.

Sloshing loads may be induced on the ship's internal structure through the movement of the fluids in tanks/holds whilst slamming of the bottom shell structure forward may occur due to emergence of the fore end of the ship from the sea in heavy weather.

Cargo over-loading in individual hold spaces will increase the static stress levels in the ship's structure and reduce the strength capability of the structure to sustain the dynamic loads exerted in adverse sea conditions.

In harbour, where the ship is in sheltered water and is subjected to reduced dynamic loads, the hull is permitted to carry a higher level of stress imposed by the static loads, so a certain amount of difference in the loading of each hold is allowable.

bulk carrier strain monitoring sensor
Fig: bulk carrier strain monitoring sensor

Most modern bulkers have strain monitoring equipment so that hull stresses that cause hull fractures as above are minimised.

Bending Moment

The bending moment is the amount of bending caused to the ship's hull by external forces. For example, the bending moment is the highest in the midship section when the ship's ends are supported by crests of a wave known as `sagging' or `positive bending'. When the ship is riding the crest of a wave at its midships, the bending moment is known as `hogging' or `negative bending'. Bending moments are measured in tonne- metres.

Shearing Force

When two external parallel forces act in opposite directions on any part of a structure to break it apar or shear it, the forces are known as shearing forces and are measured in tonnes. Shearing stress is, therefore, the stress that may break or shear the structure apart.

 Bulk carrier at rough sea conditions

All classification society member bulk carriers are assigned with permissible still water shear forces (SWSF) and still water bending moment (SWBM) limits. There are normally two sets of permissible SWSF and SWBM limits assigned to each ship, namely:

i) Seagoing (at sea) SWSF and SWBM limits.

ii) Harbour (in port) SWSF and SWBM limits.

The seagoing SWSF and SWBM limits are not to be exceeded when the ship puts to sea or during any part of a seagoing voyage. In harbour, where the ship is in sheltered water and is subjected to reduced dynamic loads, the hull girder is permitted to carry a higher level of stress imposed by the static loads. The harbour SWSF and SWBM limits are not to be exceeded during any stage of harbour cargo operations.

When a ship is floating in still water, the ship's lightweight (the weight of the ship's structure and its machinery) and deadweight (all other weights, such as the weight of the bunkers, ballast, provisions and cargo) are supported by the global buoyancy upthrust acting on the exterior of the hull. Along the ship's length there will be local differences in the vertical forces of buoyancy and the ship's weight. These unbalanced net vertical forces acting along the length of the ship will cause the hull girder to shear and to bend ,inducing a vertical still water shear force (SWSF) and still water bending moment (SWBM) at each section of the hull.

At sea, the ship is subjected to cyclical shearing and bending actions induced by continuously changing wave pressures acting on the hull. These cyclical shearing and bending actions give rise to an additional component of dynamic, wave induced, shear force and bending moment in the hull girder. At any one time, the hull girder is subjected to a combination of still water and wave induced shear forces and bending moments.

The stresses in the hull section caused by these shearing forces and bending moments are carried by continuous longitudinal structural members. These structural members are the strength deck, side shell and bottom shell plating and longitudinals, inner bottom plating and longitudinals, double bottom girders and topside and hopper tank sloping plating and longitudinals, which are generally defined as the hull girder.

Related guideline

Risk of Heavy cargoes & Monitoring the Ship's Loading limits

How to avoid risk of vessel being overloaded

Local loading criteria defining maximum allowable cargo weight in each cargo hold

Structural standards & strengthening of bulk carriers

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Operation of sea going bulk carriers involved numerous hazards . Careful planning and exercising due caution for all critical shipboard matters are important . This site is a quick reference to international shipping community with guidance and information on the loading and discharging of modern bulk carriers so as to remain within the limitations as specified by the classification society.
It is vital to reduce the likelihood of over-stressing the ship's structure and also complying with all essential safety measures for a safe passage at sea. Our detail pages contain various bulk carrier related topics that might be useful for people working on board and those who working ashore in the terminal. For any remarks please Contact us

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