Lifting Analysis for Heavy Ship Hull Blocks Using 4 Cranes
1
Lifting Analysis for Heavy Ship Hull Blocks using 4 Cranes Kyungsik Choi Korea Maritime University, Busan, Korea Dong Joon Kim Pukyong National University, Busan, Korea ABSTRACT Four-crane-lifting is a redundant problem. In addition to the force and moment equilibrium equations, a compatibility condition considering elongations of lifting slings is introduced to determine 4 unknown lifting forces. For lifting analysis of heavy ship hull blocks, the Euler angles are introduced to represent the rotation of a hull block. For verification of the method, a ship hull block with field measurements data is analyzed and the results show that the information obtained by the current method could be useful for engineers to conduct lifting work at shipyards. KEY WORDS: Four Cranes, Hull Block Lifting, Statically Indeterminate Problem, Inclination Angles INTRODUCTION During ship construction processes for the increase in productivity and reduction in construction time, it is the current trend to assemble larger hull blocks and to carry out as much outfitting work as possible on ground before erecting it on the dock. However, it is needed to lift and load the already assembled hull blocks all at the same time. Generally in small to medium size shipyards, where a large capacity crane is not available, smaller capacity cranes must be appropriately combined to lift the blocks. If the lifting force of each individual crane is insufficient or if the lifting task is difficult due to the arrangement of the cranes in the shipyard, 4 cranes are occasionally utilized in the case of heavy hull blocks. But the maximum block weight that can be lifted by combined cranes is based on a 3 crane utilization plan, however there are difficulties in that safety risks have to be accounted for as there are no design guidelines even though these cases are actually being practiced on site. The lifting forces of each crane in the case of a 3 crane arrangement can be determined by solving static equilibrium equations, but in the case where 4 cranes are used, if an additional compatibility condition between the block and the lifting slings is not used, this indeterminate problem cannot be solved and there is no unique solution for 4 crane lifting forces from 3 static equilibrium equations (Crandall et al., 1978). This study focuses on solving the block lifting problem using 4 cranes analytically (Choi and Kim, 2000). In addition to the 3 static equilibrium equations, an additional condition considering elongations of lifting slings has been proposed in this analysis. This method was applied to find the change in lifting force of the crane rope due to the rotation of the hull block occurring when it is being pulled up or moved. BLOCK LIFTING ANALYSIS USING FOUR CRANES Generally, the important point in the crane lifting work of hull blocks is the center of gravity of the block and the selection of the location where the lifting lugs are attached. In this study, it is assumed that the hull block itself is a rigid body without any deformation. Also dynamic effects are not considered in this study. Equilibrium Equations Because the location of the center of gravity changes according to the inclination and rotation of large hull block with substantial dimensions, the effects of the inclination and rotation are emphasized. Although the effects of the movements in the crane body and the boom caused by the wind are ignored, there will be an occurrence of disproportion in the lifting force due to the relative difference in control between each crane and the horizontal position cannot be maintained with the occurrence of an inclination. Generally, the rotation of the coordinates in 3 dimensional rectangular plane is expressed as follows. j ij i x x α = ' (1) where jk ik ij δ α α = and ij α in Eq.(1) is the nine directional cosines, jk δ the Kronecker delta. With the definition of Euler angles ψ , θ , φ , the final position after rotation of a block can be expressed as the multiplication of the rotation matrices in the x, y, z coordinates as in Eq.(2). ) ( ) ( ) ( φ θ ψ z y x R R R R = (2)
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Transcript of Lifting Analysis for Heavy Ship Hull Blocks Using 4 Cranes
Lifting Analysis for Heavy Ship Hull Blocks using 4 Cranes
Kyungsik Choi
Korea Maritime University, Busan, Korea
Dong Joon Kim
Pukyong National University, Busan, Korea
ABSTRACT Four-crane-lifting is a redundant problem. In addition to the force and moment equilibrium equations, a compatibility condition considering elongations of lifting slings is introduced to determine 4 unknown lifting forces. For lifting analysis of heavy ship hull blocks, the Euler angles are introduced to represent the rotation of a hull block. For verification of the method, a ship hull block with field measurements data is analyzed and the results show that the information obtained by the current method could be useful for engineers to conduct lifting work at shipyards. KEY WORDS: Four Cranes, Hull Block Lifting, Statically Indeterminate Problem, Inclination Angles
INTRODUCTION During ship construction processes for the increase in productivity and reduction in construction time, it is the current trend to assemble larger hull blocks and to carry out as much outfitting work as possible on ground before erecting it on the dock. However, it is needed to lift and load the already assembled hull blocks all at the same time. Generally in small to medium size shipyards, where a large capacity crane is not available, smaller capacity cranes must be appropriately combined to lift the blocks. If the lifting force of each individual crane is insufficient or if the lifting task is difficult due to the arrangement of the cranes in the shipyard, 4 cranes are occasionally utilized in the case of heavy hull blocks. But the maximum block weight that can be lifted by combined cranes is based on a 3 crane utilization plan, however there are difficulties in that safety risks have to be accounted for as there are no design guidelines even though these cases are actually being practiced on site. The lifting forces of each crane in the case of a 3 crane arrangement can be determined by solving static equilibrium equations, but in the case where 4 cranes are used, if an additional compatibility condition between the block and the lifting slings is not used, this indeterminate problem cannot be solved and there is no unique solution for 4 crane
lifting forces from 3 static equilibrium equations (Crandall et al., 1978). This study focuses on solving the block lifting problem using 4 cranes analytically (Choi and Kim, 2000). In addition to the 3 static equilibrium equations, an additional condition considering elongations of lifting slings has been proposed in this analysis. This method was applied to find the change in lifting force of the crane rope due to the rotation of the hull block occurring when it is being pulled up or moved. BLOCK LIFTING ANALYSIS USING FOUR CRANES Generally, the important point in the crane lifting work of hull blocks is the center of gravity of the block and the selection of the location where the lifting lugs are attached. In this study, it is assumed that the hull block itself is a rigid body without any deformation. Also dynamic effects are not considered in this study. Equilibrium Equations Because the location of the center of gravity changes according to the inclination and rotation of large hull block with substantial dimensions, the effects of the inclination and rotation are emphasized. Although the effects of the movements in the crane body and the boom caused by the wind are ignored, there will be an occurrence of disproportion in the lifting force due to the relative difference in control between each crane and the horizontal position cannot be maintained with the occurrence of an inclination. Generally, the rotation of the coordinates in 3 dimensional rectangular plane is expressed as follows.
jiji xx α=' (1)
where jkikij δαα = and ijα in Eq.(1) is the nine directional cosines,
jkδ the Kronecker delta. With the definition of Euler angles ψ , θ ,
φ , the final position after rotation of a block can be expressed as the multiplication of the rotation matrices in the x, y, z coordinates as in Eq.(2).
)()()( φθψ zyx RRRR = (2)
