## SHIPBUILDING

 There are two basic parts to a ship- the hollow HULL, and the SUPERSTRUCTURE. The hull is subjected to two forces: 1) gravity due to the mass of the ship and the cargo, and 2) buoyancy of the hull. While these forces balance, they are not always uniformly distributed, and can be strongly affected by cargo loading. For shorter cargo ships, "HOGGING" is common, as the buoyancy in the center is larger per unit length than it is at the ends. Longer ships tend to "SAG", even in still water, but the worst case comes from riding the waves. The hull is subjected to a large bending moment, and so tends to fail in panel buckling. The superstructure is used as a panel stiffener to prevent hull buckling. We can analyze this using simple beam bending:

The first performance measure will be to minimize the mass of the ship:

subject to the constraint of no failure:

The second performance measure is to minimize the deflection subject to the failure constraint:

Since these are two DIFFERENT MOP's, we can't generate a coupling equation. Look at potential materials using a multi-stage selection.

SELECTION STAGE 1) SIGMA versus RHO = CHART 2, slope = 1, upper left

CANDIDATE MATERIALS:

• CFRP
• GFRP
• Steels
• Ti alloys
• Al alloys
• Wood

SELECTION STAGE 2) MODULUS versus SIGMA = CHART 4, slope = 1, upper left

CANDIDATE MATERIALS:

• Al alloys
• Steels
• Ti alloys
• CFRP, GFRP, Wood

PERFORMANCE:

 CANDIDATE MATL SIGMA [MPa] RHO [Mg/m^3] E [GPa] M1 M2 CFRP 700 1.6 30 440 0.043 GFRP 400 1.6 20 250 0.050 Steels 1800 7.8 220 230 0.122 Ti Alloys 1000 4.2 100 240 0.100 Al Alloys 430 2.6 60 165 0.140 Woods 110 0.6 1 185 0.009
For M1 the best performers are polymer composites, but they lose out to steel in M2 for which they show deflections three times larger than the steels. Ti and Al look pretty good, but they lose out when we throw cost into the equation. HIGH TENSILE STRENGTH STEEL is the commonly used material, except in high performance weight-driven designs.

STEEL SHIP PLATES AND FRACTURE

In the early 1900's, ship plates were completely riveted together. At the end of WWI a push for faster construction times drove shipbuilders toward using substantially welded ship plates, but as the war stopped, the money for development dried up. In 1921 a small merchant ship (the FULLAGAR, 150 ft. long) was the first fully welded ship to hit the water, and worked in England for many years.

At the start of WWII, the push came on to rapidly produce ships for the merchant marine fleet to supply the war effort, and welding technology was again pushed. The rapid and massive scale-up required by the war meant that unskilled laborers and inadequate welding practice were used. The approach was a "cookie cutter" one, with a small number of ship plans, and many shipyards producing the same design. The construction was begun in 1941, and in total,

2500 Liberty Ships
500 T-2 tankers
400 Victory ships

were constructed. Shortly after these ships entered service, they began breaking apart, sometimes spectacularly!

Two major causes of the failures were found:

1) STRESS RAISERS: access holes through the decking plates and structural plates were cut for ladderways and cargo loading. These were initially cut as rectangular holes. Many cracks initiated at the corners of these holes. By changing the design to rounded holes, many fewer failures were reported.

2) UNKNOWN EFFECTS: (at the time)

No correlation was found between failure and the tensile strength of the steel samples taken from various parts of the failed ship plates. Loading at failure was typically around 700 MPa, well within the design load.

Extensive study of the brittle fracture energy (toughness) using the Charpy impact test found the following:

Ductile to Brittle Transition Temperature (DBTT) is arbitrarily set as about 15 ft-lbs of fracture energy. ANSWER: the DBTT was too high.

REFERENCE: "Brittle Behavior of Engineering Structures", E. R. Parker, John Wiley and Sons, NY, 1957.

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