![]() There is a quicker and more efficient method of obtaining the solution to the above problem. = 0.77 m aft of amidships IAB = 1 x (CI)3 x E3 x 2 i.e.Ġ, 1.2, 1.5, 1.8, 1.8, 1.5, 1.2 metres, respectively.įind the second moment of the waterplane area about a transverse axis through the centre of flotation.ĭistance of the Centre of = - X CI Flotation from forward The second moment about OZ can then be found by the theorem of parallel axes. Let OZ be a transverse axis through the centre of flotation. Once again the integral part of this expression can be evaluated by Simpson's Rules using the values of x2 y as ordinates and the second moment about AB is found by multiplying the result by two. To find the second moment of the waterplane area about a transverse axis through the centre of flotation. Find the second moment of the waterplane area about the centre line. The half-ordinates at equal distances from forward are as follows:Ġ, 1.2, 1.5, 1.8, 1.8, 1.5, and 1.2 metres, respectively. the half-breadths cubed), as ordinates, and Icl is found by multiplying the result by 3.Ī ship's waterplane is 18 metres long. The integral part of this expression can be evaluated by Simpson's Rules using the values of 圓 (i.e. Therefore, if Icl is the second moment of the whole waterplane area about the centre line, then: The second moment of a rectangle about one end is given by -, and therefore the second moment of the elementary strip about the centre line is given by y 3 X and the second moment of the half waterplane about the centre line is given by 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. To find the second moment of a ship's waterplane area about the centre line. Iqz - Iab _ Ay2 - parallel axis theorem equation Thus, in Figure 29.4, if G represents the centroid of the area (A) and the axis OZ is parallel to AB, then: 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 first reduced by the product of the area and the square of the perpendicular distance between the two axes.
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