Relation between boom length & mast height on Hong KOng A frame derrick barge

• Relation btw boom & mast length on A frame barge

  
  To cope with the high free board of containers there is a trend of raising the boom pivot higher along the mast on A-frame barges
  in so doing the effective height of the mast is becoming shorter and shorter.
  The above diagram shows the relation of compression stress along the boom with different mast height/boom ratio
  of a 40 tonne cargo, 42m long 10 tonne boom with the boom making a 60 degree with horizon. (The dead man part of weight is left out.)
  At 75% the stress is 125% of the cargo weight whilst at 40% the stress is 242%.
  As can be seen the increase in stress along the boom of a 0.4 mast/boom ratio may be 100 percent more than that of a 0.75 mast/boom ratio.
  This may means that the design shear strength at the boom pivot pin and the buckle strength of the boom need to be increase accordingly.
  In the horizontal pivot pin for a .75 ratio mast the pin diameter is 84mm, while for a 0.4 ratio mast the pin diameter should be 117mm.
  One point of interest is that the incline angle of the boom makes not much different in the boom compression. It can be seen from the above graph that the 60 degree/ 40degree and 70 degree curves are almost coincide.
  The following is the actual figure
  where A is the mast height/boom length ratio         
             B is the compression stress acting along the boom in tonne
     A       B
  

  0.75	52.6576
  0.7	55.7768
  0.65	59.7859
  0.6	64.8515
  0.55	71.1923
  0.5	79.1151
  0.45	89.071
  0.40	101.7493

  
  
  
     The following graph is the tension of an individual wire in a 10 parts topping wire in the above setting
  
  From the graph it can be seen that  the tension is higher when the boom is making a 40 degree with horizontal
  than a 60 degree. Even with a 0.35 mast/boom ratio, the wire tension of 9 tonnes, although close, is still within the safe working load of a 28mm dia. steel wire.
  However when we look at the wire tension at 60 degree which is more less the most common working angle of the boom,
  the wire tension of a 0.40 set up is 100% higher than that of a 0.55 set up.
  Or we get 2 more container stacks of working height by increasing the stress of the topping assembly by 100%.
  
  The actual figure is as below: the incline angle of boom is at 60 degree with horizontal
  
  where A is the mast height/boom length ratio         
             B is the tensile stress of the wire in the topping assembly in tonne
  A       B
  0.75   1.117
  0.70   1.437
  0.65   1.838
  0.60   2.337
  0.55   2.955
  0.50   3.735
  0.45   4.694
  0.40   5.931
  0.35   7.549
  
  
  Righting moment
   
  The raising of boom pivot also affects the righting moment of the barge. For a listing angle of 5 degree, it may be proved that there is an increase of 50-60 tonne-m righting moment requirement (about 5% increase ) if the pivot is raised from deck surface to 14m above deck (0.33 of boom length). For a listing angle of 10 degree the right moment increased will be about 100 tonne-m.