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Q5. A box barge of 64 m length, 8 m breadth and 4.5 m depth has a hull mass of 322 tonne evenly distributed throughout its length. Bulkheads located 2 m from the barge ends, form peak tanks which may be used for ballast. The remainder of the barge length is divided by 4 transverse bulkheads into 5 holds of equal length. The holds are full of bulk cargo having a specific volume of 1.543 m³/ t. The peak tanks are empty.

(a) Calculate the midship bending moment during discharge when both end holds are half empty.  (8)

(b) Calculate the minimum depth Of sea water ballast which must be added to the peak tanks to allow complete discharge of the end holds if the midship sagging bending moment is to be restricted to a maximum of 19.8 MNm. (8)