Trans RINA, Vol 161, Part A4, Intl J Maritime Eng, Oct-Dec 2019
2009). It was found that the maximum force appear around between 0.1 and 0.2 seconds at the beginning, which is twice of the mean impact force (Woisin, 1976). The peak forces occur between 0.2 second and 0.4 second for impact speed with 4, 6 and 8 m/s, however is around 1 second for 2m/s, see Figure. 5. The time of maximum collision load depend significantly on the impact velocity, but slightly on ship mass for the same type vessel.
Figure. 8 compares the impact forces for different methods, in which the results is presented in bars with different colors for empirical formulae and in line for average and maximum values assessed from numerical simulations. The impact forces in various methods have the same tendency as expected: the larger initial kinetic energy of the ship is, the bigger the forces are. The maximum impact forces calculated by AASHTO, IABSE and Pedersen formulae are close to that assessed in the FE analysis, which increase with the increase of the impact velocity. Because of the formulae in the requirements of AASHTO and IABSE were regressed by experimental data and information from impact accident, which give the maximum impact force. The ship type with bulb bow used in the experiment is similar with that used in the present simulation.
15 30 45 60 75 90
0 (a) Full load
15 30 45 60 75 90
0
AASHTO IABSE Pedersen TB JTG
Average force FA Maximum force FM
AASHTO IABSE Pedersen TB JTG
Average force FA Maximum force FM
The static impact forces in TB and JTG requirements are significantly smaller than that the average and maximum impact forces in FE analysis, and the other requirements of AASHTO, IABSE and Pedersen formula. TB formulae were developed from kinetic energy theorem and momentum theorem relatively. However, the kinetic energy reduction factor (γ) and elastic deformation coefficients (C1) in TB formula (Eq. (6)) are assumed as constant. Chen et al. (2013) conducted some experiments research on elastic deformation coefficient. It was found that the recommended values in TB might not appropriate. Du (2015) investigated the dynamic response during ship-bridge impact by means of numerical simulations, reaching a conclusion in which the larger initial kinetic energy of the striking ship is, the lower the transformation ratio of it to deformation energy will be. This means that the bigger initial kinetic energy of the ship is, the lower elastic deformation coefficient will be. The stiffness of ship bow should be different for various ship types and impact velocities.
Hence, the kinetic energy reduction factor (γ) and elastic deformation coefficient (C1) in TB formula (Eq. (6)) should be different for various kinetic energies to improve the accuracy of assessment. If the results calculated in TB is adopted in the design of bridge against ship collision, which could cause danger situation in the anti-collision design of bridge. It is necessary to revise the formula in TB requirement by considering different elastic deformation coefficient (C1). According to Eq. (6), the kinetic energy reduction factor γ, is revised as
FV W CC
Ave FEM / sin 12 + F − is obtained from 2 4 6 Velocity (m/s) 8 10
where the average impact force Ave FEM FE analysis.
For elastic deformation coefficients, since the stiffness of the bridge pier is significantly larger than that of impact vessel,
C is significantly smaller than 1 2 1 thus C is generally assume as zero. Chen (2006)
conducted many calculations on the elastic deformation coefficients for several ship bows, which are presented in Table 1. When a ship crashes against a bridge with an initial velocity, the kinetic energy reduction factor means that initial kinetic energy
2 (b) Ballast load
Figure. 8 Comparison of the impact forces assessed in different methods.
4 6 Velocity (m/s) 8 10
are not totally transformed into the energy due to the deformation and failure of ship and bridge. It can be seen that the elastic deformation coefficients of striking ship decrease as the increase of the deadweight tonnage and displacement of ship. A bulk carrier with 5,000t DWT and 6,500t displacement is considered herein. According to the three 1
A-432 ©2019: The Royal Institution of Naval Architects
= −
(8)
C , and
C values of
Impact force (MN)
Impact force (MN)
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