C L DUBEY – EXERCISE – 02 : Simpson’s Rule

Total area = 616.4 m²

COG from aft = 41.33m
COG = (592.4 ⨯ 41.33) + (24 ⨯ 86.5)/616.4

         = 43.08m from aft

Q13. Three semi-ordinate spaced at equal distance of 20m are 7.5, 11.8 and 15.8m. Calculate

• Geometric centre of the area between first two and last two ordinates.

• Amount of cargo that can be loaded on the deck area between first two ordinates, if the load density of the deck is 10t/m² .

Solution –

Area between first two ordinate
= 2 ⨯ (20/12) ⨯ [5 ⨯ 7.5 + 8 ⨯ 11.8 – 15.8]
= 387m²

Area between last two ordinate
= 2 ⨯ (20/12) ⨯ [5 ⨯ 15.8 + 8 ⨯ 11.8 – 7.5]
= 553m²

Moment between first two ordinate
= 2 ⨯ (20 ⨯ 20/24) [3 ⨯ 7.5 + 10 ⨯ 11.8 – 15.8]
= 4156.67 tm

Moment between first last two ordinate from aft
= 2 ⨯ (20 ⨯ 20/24)  [3 ⨯ 15.8 + 10 ⨯ 11.8 – 7.5]
= 5263.335 tm