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.
Given
L = 12 m
To find
1. Second moment of area
Solution
Length is given as 12 m and there are 4 equidistant spaces.
So common interval h = 12/4 = 3
Area of surface a = h/3 x Σa
= 3/3 x 77
= 77 m2
Distance of centroid from bulkhead Ӯ = Σm / (2 x Σa)
= 587 / (2 x 77)
= 3.812 m
Second moment of area about bulkhead ib = h/9 x Σi
= 3/9 x 4859
= 1619.7 m4
Second moment of area about centroid ig = ib - aӮ2
= 1619.7 - (77 x 3.8122)
= 501.0 m4
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L = 12 m
To find
1. Second moment of area
Solution
Width
|
SM
|
Product for area
|
Width2
|
SM
|
Product 1st moment
|
Width3
|
SM
|
Product 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
|
Length is given as 12 m and there are 4 equidistant spaces.
So common interval h = 12/4 = 3
Area of surface a = h/3 x Σa
= 3/3 x 77
= 77 m2
Distance of centroid from bulkhead Ӯ = Σm / (2 x Σa)
= 587 / (2 x 77)
= 3.812 m
Second moment of area about bulkhead ib = h/9 x Σi
= 3/9 x 4859
= 1619.7 m4
Second moment of area about centroid ig = ib - aӮ2
= 1619.7 - (77 x 3.8122)
= 501.0 m4
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