Page 37 - Introduction to Naval Architecture
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SHIP FORM CALCULATIONS 25
Table 3.1
X y SM F(A) xy f(My ) x*y Fry f f(M x) / F(4)
0 1.0 1 1.0 0 0 0 0 1.0 1.0 1.0 1.0
1 1.2 4 4.8 1.2 4.8 1.2 4.8 1.44 5.76 1.728 6.912
2 1.5 2 3.0 3.0 6.0 6.0 12.0 2.25 4.50 3.375 6.750
3 1.6 4 6.4 4.8 19.2 14.4 57.6 2.56 10.24 4.096 16.384
4 1.5 2 3.0 6.0 12.0 24.0 48.0 2.25 4.50 3.375 6.750
5 1.3 4 5.2 6.5 26.0 32.5 130.0 1.69 6.76 2.197 8.788
6 1.1 2 2.2 6.6 13.2 39.6 79.2 1.21 2.42 1.331 2.662
7 0.9 4 3.6 6.3 25.2 44.1 176.4 0.81 3.24 0.729 2.916
8 0.6 ] 0.6 4.8 4.8 38.4 38.4 0.36 0.36 0.216 0.216
Totals 29.8 111.2 546.4 38.78 52.378
First moment about ^axis
Centroid from y-axis
First moment about x-axis
Centroid from x-axis
Second moment about y-axis
Second moment about as-axis
The second moment of an area is always least about an axis
through its centroid. If the second moment of an area, A, about
an axis x from its centroid is 7 X and / xx is that about a parallel axis
through the centroid:
In the above example the second moments about axes through the
centroid and parallel to the ^-axis and y-axis, are respectively:
