Solution Naval Numerical 15

Numerical 15:A forward deep tank 12 m long extends from a longitudinal bulkhead to the ship’s side. The widths of the tank surface measured from the longitudinal bulkhead at regular intervals are 10, 9, 7, 4 and 1 m. Calculate the second moment of area of the tank surface about a longitudinal axis passing through its centroid.

Solution: 

Width	SM	Product for area		SM	Product for 1st moment		SM	Product for 2nd moment
10	1	10	100	1	100	1000	1	1000
9	4	36	81	4	324	729	4	2916
7	2	14	49	2	98	343	2	686
4	4	16	16	4	64	64	4	256
1	1	1	1	1	1	1	1	1
		∑a=77			∑m=587			∑i=4859

Common interval (h)= =3m 

Area of surface a ==77  

Distance of centroid from Longitudinal Bulkhead

 y=

=3.812m 

Second moment of inertia about longitudinal bulkhead

=1619.7 

Second moment of area about centroid

501.0