194.NA August 2022 Q.8(b)

 The half breadths of the load waterplane of a ship 150 m long commencing from aft, are 0.3. 3.8. 6.0, 7.7, 8.3.9.0,8.4.7.8, 6.9.4.7 and 0 m respectively. Calculate: (a) area of waterplane (b) distance of centroid from amidships (c) second moment of area about a transverse axis through centroid.

Solution

common interval h = 15

a) Water plane area =  h / 3 x (∑A x 2)

                                 = 15/3 x (191.5 x 2)

                              A  = 1915 m2

b) dist of centroid from midship = h x [ (∑mf + ∑ma) / ∑A]

                                                  = 15 x [ (176.5 - 195.8) / 191.5]

                                              y  = 1.512 m fwd (- indicates fwd)

c) Second moment of area about midship = h3/ 3 x (∑i x 2)

                                                                   = 153/3 x (1065.1 x 2)

                                                                 I = 2396475 m4

Second moment of area about centroid = I - Ay2

                                                               = 2396475 - (1915 x 1.5122 )

                                                               = 2392097 m4