## Superstructures

Superstructures and deckhouses are major discontinuities in the ship girder. They contribute to the longitudinal strength but will not be fully efficient in so doing. They should not be ignored as, although this would 'play safe' in calculating the main hull strength, it would run the risk that the superstructure itself would not be strong enough to take the loads imposed on it at sea. Also they are potential sources of stress concentrations, particularly at their ends. For this reason they should not be ended close to highly stressed areas such as amidships.

A superstructure is joined to the main hull at its lower boundary. As the ship sags or hogs this boundary becomes compressed and extended respectively. Thus the superstructure tends to be arched in the opposite sense to the main hull. If the two structures are not to separate, there will be shear forces due to the stretch or compression and normal forces trying to keep the two in contact.

The ability of the superstructure to accept these forces, and contribute to the section modulus for longitudinal bending, is regarded as an efficiency. It is expressed as:

o0-o where a0; a, and fl are the upper deck stresses if no superstructure were present, the stress calculated and that for a fully effective superstructure.

The efficiency of superstructures can be increased by making them long, extending them the full width of the hull, keeping their section reasonably constant and paying careful attention to the securings to the main hull. Using a low modulus material for the superstructure, for instance GRP!5, can ease the interaction problems. With a Young's modulus of the order of rs of that of steel, the superstructure makes little contribution to the longitudinal strength. In the past some z z

designers have used expansion joints at points along the length of the superstructure. The idea was to stop the superstructure taking load. Unfortunately they also introduce a source of potential stress concentration and are now avoided.

Nowadays a finite element analysis would be carried out to ensure the stresses were acceptable where the ends joined the main hull. A typical mesh is shown in Figure 7.11.

Example 7.2

The midship section of a steel ship has the following particulars:

Cross-sectional area of longitudinal material = 2.3 m2 Distance from neutral axis to upper deck = 7.6 m

Second moment of area about the neutral axis = 58 m4

A superstructure deck is to be added 2.6 m above the upper deck. This deck is 13 m wide, 12 mm thick and is constructed of aluminium alloy. If the ship must withstand a sagging bending moment of 450 MNm. Calculate the superstructure efficiency if, with the superstructure deck fitted, the stress in the upper deck is measured as 55MN/m2.

### Solution

Since this is a composite structure, the second moment of an equivalent steel section must be found first. The stress in the steel sections can then be found and, after the use of the modular ratio, the stress in the aluminium.

Taking the Young's modulus of aluminium as 0.322 that of steel, the effective steel area of the new section is:

The movement upwards of the neutral axis due to adding the deck:

0.322

2.35

The second moment of the new section about the old NA is:

The second moment about the new NA is: 63.23 - 2.35(0.218)2 = 63.12m4 The distance to the new deck from the new NA = 7.6 + 2.6 - 0.218 = 9.98 m

Stress in new deck 450 x 9.98

63.12

Stress in deck as aluminium = 0.322 X 71.15 = 22.91 MN/m2

The superstructure efficiency relates to the effect of the superstructure on the stress in the upper deck of the main hull. The new stress in that deck, with the superstructure in place, is given as 55 MN/m2. If the superstructure had been fully effective it would have been:

63.12

With no superstructure 450 x 7.6

Hence the superstructure 58.97 - 55

Stresses associated with the standard calculation

The arbitrary nature of the standard strength calculation has already been discussed. Any stresses derived from it can have no meaning in absolute terms. That is they are not the stresses one would expect to measure on a ship at sea. Over the years, by comparison with previously successful designs, certain values of the derived stresses have been established as acceptable. Because the comparison is made with other ships, the stress levels are often expressed in terms of the ship's principal dimensions.Two formulae which although superficially quite different yield similar stresses are:

Acceptable stress = 77.2\—— + 1 j MN/m2 with L in metres.

\1000

Until 1960 the classification societies used tables of dimensions to define the structure of merchant ships, so controlling indirecdy their longitudinal strength. Vessels falling outside the rules could use formulae such as the above in conjunction with the standard calculation but would need approval for this. The societies then changed to defining the applied load and structural resistance by formulae. Although stress levels as such are not defined they are implied. In the 1990s the major societies agreed, under the International Association of Classification Societies (IACS), a common standard for longitudinal strength. This is based on the principle that there is a very remote probability that the load will exceed the strength over the ship's lifetime.

The still water loading, shear force and bending moment are calculated by the simple methods already described. To these are added the wave induced shear force and bending moments represented by the formulae:

Hogging BM = 0.19MCL^BCb kN m

Sagging BM =-0.11 MCL2B(Q, + 0.7) kNm where dimensions are in metres and:

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