notes_11_balance - 13.122 Lecture 2 Shear force and bending...

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13.122 Lecture 2 Shear force and bending moment in floating platform Ship or freely floating offshore structure is a beam in equilibrium Overall summation and forces and moments = 0 But shear force and bending moments can and do exist Net force along length f(x) depends on buoyancy - weight at x Even though these are continuous (not in the mathematical sense) functions of location, typically they are represented by subtotals between regularly spaced locations or stations, normally 10 or 20 between perpendiculars, with segments forward and aft of FP and AP respectively Weight is dependent on conditions of loading as well as location of equipment (arrangement), structure etc. Buoyancy is dependent on the immersion of the platform along its length A typical weight and buoyancy distribution is shown below. Typical Weight and Buoyancy Distribution 0 5 10 15 20 25 30 35 40 45 50 20 18 16 14 12 10 8 6 4 2 0 Station wt buoy note that station 0 (FP) is to the right. 1
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To calculate local buoyancy, it is useful to have a set of curves at each station representing the section area. The local buoyancy per unit length is = area of the immersed section * density of sea water. Ref: Archimedes consider a section: 0 5 10 15 20 0 5 10 15 20 Body Plan at a Section offset waterline The section area is the area below each waterline. The curve of area below the respective waterline is the section area or Bonjean curve. 0 50 100 150 200 250 0 5 10 15 20 Bonjean Curve for this Section Section Area (both sides) waterline shown is the section area at the 10 waterline sa 10 ( ) 90.833 = note that the section area is typically a large number so it is typical to represent the area in "inches" on a plot or some scaled units. We'll see why for some plots below.
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