Page 270 - statbility for masters and mates
P. 270
258 Ship Stability for Masters and Mates
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Fig. 29.3
IAB lb3 3
The Theorem of Parallel Axes
The second moment of an area about an axis through the centroid is equal to the second moment about any other axis parallel to the ®rst reduced by the product of the area and the square of the perpendicular distance between the two axes. Thus, in Figure 29.4, if G represents the centroid of the area (A) and the axis OZ is parallel to AB, then:
IOZ IAB Ay2 parallel axis theorem equation
To ®nd the second moment of a ship's waterplane area about the centre line.
In Figure 29.5:
Area of elementary strip yEdx L
Area of waterplane
yEdx
It has been shown in chapter 10 that the area under the curve can be found by Simpson's Rules, using the values of y, the half-breadths, as ordinates.
O
