A ship 160 m long has 1/2 ordinates of waterplane of 1.6,5.7, 8.8, 10.2, 10.5, 10.5, 10.5, 10.0, 8.0, 5.0 and 0 m respectively. Calculate the second moment of area of the waterplane about the centreline.

 A ship 160 m long has 1/2 ordinates of waterplane of 1.6,5.7, 8.8, 10.2, 10.5, 10.5, 10.5, 10.0, 8.0, 5.0 and 0 m respectively. Calculate the second moment of area of the waterplane about the centreline.

Reference: REED'S NAVAL ARCHITECTURE FOR MARINE ENGINEERS (4^th edition), Exercise – 3.10

 

Solution:

½ ord	SM	(1/2 ord)2	SM
1.6	1	4.096	4.096
5.7	4	185.193	740.772
8.8	2	681.472	1362.944
10.2	4	1061.208	4244.832
10.5	2	1157.625	2315.25
10.5	4	1157.625	4630.5
10.5	2	1157.625	2315.25
10.0	4	1000	4000
8.0	2	512	1024
5.0	4	125	500
0	1	0	0
			∑f(SM) = 21137.64

 

Common interval, h = 160/10 = 16

SM about centerline = 2 * h/3 * 1/3 * ∑f(SM)

                                  = 2 * 16/3 * 1/3 * 21137.64

                                  = 75156.05 m⁴