Trans RINA, Vol 161, Part A4, Intl J Maritime Eng, Oct-Dec 2019
Figure. 7 shows the distributions of equivalent stress of ship bow with impact velocity 4m/s. It can be seen that the contact areas include the upper deck and bulb bow. The maximum contact pressure is not always in the centre of bulb bow, since the upper deck also is involved during collision. This indicates that the impact forces are caused in the both parts, which should be included together in the development of theoretical formulae. The maximum equivalent stresses is 755 MPa in Figure. 7, which is larger than the tensile strength 370 MPa due to the hardening of material, since the failure strain is used to determine failure of structure instead of failure stress.
3.
COMPARISONS OF RESULTS BETWEEN DIFFERENT METHODS
After decades of study, several empirical formulae were developed for the assessment of ship impact force. At the present paper, five empirical formulae are investigated and compared with the FE analysis, which are the requirement of AASHTO (2007), IABSE (1983), TB (2005), JTG (2004) and Pedersen formula (1993).
The assessment formulae in requirement of AASHTO (2007) was revised from Woisin (1976) by including the velocity of striking ship, which is given by:
F max = DWT V 0.122 where max (MN) (3)
F is the maximum impact force and DWT is the deadweight tonnage of the striking ship. ( / ) impact speed of the vessel.
IABSE (1983) recommends the empirical formula as follows,
F max = DWT V Dact D )max 0.88
where max MN is the maximum impact force; V( / )m s is the impact speed; Dt and max
F () a ()ct Dt are the ship () displacement when impacting and fully loaded relatively.
Pedersen (1993) summarized the collision force of striking vessels with deadweight tonnage ranging from 500t to 300,000t according to the research on folding mechanisms of ship bow, which considered head-on collision accidents occurred. The assessment expression of impact force is given by.
F
max = 0 P L Eimp + − L L [
2.24 [0P E L] , imp
0.5
(5 ) ] , 1.6 0.5 imp for E L
for E L 2.6
imp 2.6 (MN) (5) ©2019: The Royal Institution of Naval Architects
where F veA (kN) is the average impact force; W (kN) is the weight of ship; V (m/s) is the ship impact speed; T (s) is
the duration time of collision, which is assumed as 1 second;
g (m/s ) is gravitational acceleration that equals 2 to 9.81.
The static impact force is often adopted in the anti- collision design of bridge. However, the history of impact force obtained from finite element method bases on the dynamic analysis, if the peak force is adopted during design that would be underestimate the capacity of bridge pier against vessel impact. Hence, the equivalent static impact force is generally adopted in the design of bridge against ship collision (Yuan & Harik,
( / 8) ( / 2/3 1/3 (MN) (4)
F WV = gT
Ave (kN) (7)
where =
imp imp
E E MNm 1
L L m =
pp / 275 E mxV= 2
imp /1425 2
0
and P0 is the impact load during crush of ship bow; max
F (MN) is the maximum load of ship bow; Lpp (m) is the ship length between perpendiculars; Eimp (MNm) is the energy absorbed due to plastic deformation; mx (10 t)
3
means the summary of the ship mass and added water mass that is considered as 5% of ship mass;
ship impact speed.
TB requirement (2005) provides an empirical formula on the basis of theorem of kinetic energy, which assume that the striking ship’s effective kinetic energy acting on the struck bridge equals to the work of the impact force. The formula is presented as.
FV W =CC
Ave sin where F veA (kN) 12 + is the average impact force; (s/m ) is 1/2
the reduction factor of kinetic energy, which is assumed as 0.2 when the ship obliquely collides the bridge and is 0.3 when head-on collision occurs;
V (m/s) is the ship impact
speed; is the impact angle of ship, which is assumed as 20 degrees;
W (kN) is the weight of ship; C1 and C2 in unit V m s is the
m/kN are the elastic deformation coefficients of the ship and bridge, respectively, which is defined as the ratio of deformation to impact load. The summary value of C1 and C2 is assumed as 0.0005 in requirement of TB (2005).
The formula in the requirement of JTG (2004) is proposed that bases on momentum theorem, which is given by
(kN) (6) V(m/s) is the
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