Q1. A ship's double bottom tank is divided by an oiltight centre girder to form equal port and starboard tanks. The tanks are 16 m long and have a constant plan area defined by equidistant ordinates from the centre girder to the sides of the ship of: 6.0, 5.5, 4.8, 4.0 and 3.0 metres At a displacement of 12000 tonne in sea water of density 1025 kg/m3, the centre of gravity is 5.8 m above the keel and both tanks are partially full of oil of density 900 kg/m3 to a depth of 0.8 m. Calculate the change in effective metacentric height when all of the oil in both tanks has been consumed, assuming the position of the transverse metacentre to remain constant. (16)
Q2. For a ship of 6000 tonne displacement floating in water of density 1025 kg/m3, the KG is 5.5 m. A centre double bottom tank 14 m in length, 6.4 m wide and 1.6 m deep is now half filled with oil of density 900 kg/m3. A mass of 120 tonne is lifted from a quayside by means of the ship's lifting gear. The top of the derrick is 18 m above the keel.
If the KM in the final condition is 7.8 m, calculate EACH of the following:
(a) the final effective metacentric height; (13)
(b) the maximum outreach of the derrick if the angle of heel is not to exceed 5o. (3)
Q4. A box shaped vessel 100 m long and 10 m wide floats at an even keel draught of 4 m in sea water of density 1025 kg/m3 with a KG of 5 m.
A full width, empty compartment has its after bulkhead 20 m forward of midships and its forward bulkhead 30 m forward of midships.
Calculate the end draughts of the vessel if this compartment is bilged. (16)
Q5. A box barge of length 50 m is of uniform construction and has a displacement of 600 tonne when empty.
The barge is divided by four transverse bulkheads to form five holds of equal length. Cargo is loaded as shown in Fig Q5, the cargo in each hold being uniformly distributed.
For this condition of loading:
(a) verify that the barge has an even keel draught; (2)
(b) draw to scale EACH Of the following:
(i) the load diagram; (6)
(ii) the shear force diagram; (5)
(c)using the diagrams drawn in Q5(b), determine the longitudinal position of the maximum bending moment. (3)
Q6) A ship of 10000 tonne displacement has a rudder area of 25 m2. The ship has a KM of 6.9 m, KG of 6.3 m and the centre of lateral resistance is 3.9 m above the keel.
The maximum rudder angle is 35 degrees, and the centroid of the rudder is 2.3 m above the keel. The force generated normal to the plane of the rudder is given by:
F = 590 A v2 sinα (N)
where, A = rudder area ( m2)
v = ship speed (m⁄s)
α - rudder helm angle ( degrees)
Calculate EACH of the following, when the vessel is travelling at 22 knots.
(a) the angle and direction of heel due to the rudder force only, if it is put hard over to port; (8)
(b) the angle and direction of heel due to the combination of centrifugal force and rudder force when the rudder is hard over to port and the vessel turns in a circle of 800 m diameter. (8)
Q5. A rectangular oil barge of light displacement 300 tonne is 60 m tong and 10 m wide. The barge is divided by four transverse bulkheads into five Compartments of equal length.
When compartments 2 and 4 contain equal quantities of oil and the other compartments are empty, the barge floats at a draught of 3 m in fresh water of density 1000 kg/m3.
(a) Plot EACH of the following curves on a base of barge length:
(i) curve of toads; (4)
(ii) curve of shearing forces; (4)
(iii) curve of bending moments. (5)
(b) State the magnitude and position of the maximum bending moment. (3)
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