Structural analysis in support of the waterborne transport of radioactive materials Page: 4 of 10
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in Figure 2, along with Minorsky's Equation 2 and the data that
Minorsky used to obtain Equation 2. Note that two sets of points are
enclosed within an ellipse. These points represent the same respective
collisions. The only difference being the calculation of RT by Gibbs and
Cox and Minorsky.
As shown, there is considerable variance between some of this
additional data and Minorsky's Equation for relatively low energy
collisions. The shaded area of Figure 2 represents additional low energy
ship collision data points available to Minorsky, but not used in
developing Equation 2. Minorsky stated that the considerable scatter in
the low energy range "undoubtedly stems from the fact that the masters
of the striking vessels tend to underestimate their speed at impact."
Better agreement with available ship collision data in Figure 2 can be
obtained by modifying Minorsky's equation in the low energy range, as
shown by the dashed lines. The proposed modified Minorsky equations
are shown below:
For 0 AEk 218 on-knots2:
AEk = 145RT (ton-knots2) (3a)
For 218 < AEk 7 ton-knots2.
RT = 00 (ft2-in) b)
For AEk > 44 ton-knots2:
Ek= 414.5RT+ 121,900 (ton-knots2) (original Minorsky Equation)(3c)
Equation (3a) is taken from (Jones 1983) in which he and his
colleagues developed a modified Minorsky Method for minor
collisions. As shown in Figure 2, Equations 3a and 3b better represent
450 - Gibbs & Cox
S33 0 Minorsky Data o
Minorsky Eq. (2)
--- Modified Minorsky Eq.
2 80 iI 10
Energy Absorbed in Collision, AE (1000 ton-knots2)
2. Comparison of Actual Ship Collision
Data to Predictions from Minorsky's
the collision data for the lower energy points. Equation 3a is attractive
because it begins at the origin (representing the obvious-that there is
no deformed material, RT, if no energy, AEk, is absorbed) and because
it traverses most of the low e1.ergy points. The physical meaning of
Equation 3b is less appealing, since it indicates a constant amount of
damage for increasing values of AEk. However, Equation 3b does
provide a more conservative estimate of damage, RT, than Minorsky's
original equation. Equation 3c is identical to Minorsky's original
equation, since there seems to be good agreement with the ship collision
data for these very high energy collisions. (RT values sor Equations 3a
and 3b should include the hull of the struck ship using the approach
described by Jones, whereas, the hull is not included in Minorsky's
Minorsky's original work was motivated by needs to design the
Savannah, the world's first nuclear-powered commercial ship.
Protection of the nuclear reactor from collision damage was the primary
concern and Minorsky's approach was employed to design the reactor
protection system. During this same time period (late 1950's and
1960's), ship collision research programs were also conducted in
Germany, Japan, and Italy in support of the design of nuclear powered
ships. In the 1970's there was some work devoted to liquefied natural
gas tanker safety in collisions; however, most of the recent and ongoing
ship collision research is devoted to the safety of oil tankers involved in
collisions and grounding. These programs are focused on the study of
improved tanker designs to minimize the probability of oil leakage in the
event of an accident.
The earlier work for nuclear-powered ships is more applicable to the
present study of RAM sea transport than the more recent studies. The
reason being that the nuclear-powered ship research was concerned
about extremely severe collisions, since protection of the reactor,
located near the middle of the ship's breadth, was its focus. Similar
damage would be required to threaten on-board RAM package integrity.
However, the tanker studies are primarily concerned with improving
designs to resist relatively minor collisions that could rupture the oil
tanks. Since it is not feasible to design tankers to resist all possible
collisions, there has been little attention to the extremely severe
Scale model ship collision experiments were conducted during the
nuclear ship design era as described by (Akita et al. 1972a,1972b). Akita
developed two sets of semi-empirical expressions for the load required
for a rigid bow to penetrate the breadth of a ship's structure. The first set
is for what was termed the "deformation type" of failure of the deck and
the second is for the "crack type" failure. He observed that the crack
type failure generally occurred when the strain underneath a bow was
greater than about 30%. The crack type failure mode, which is illustrated
in Figure 3, is more straightforward to use and seems to result in more
conservative estimates of penetration depth.
The load-deformation (P-S) relationship based on Figure 3 may be
derived from simple statics as (Akita et al. 1972a):
P = 2Nqgtan0 + 2Tcose
P= collision loading from striking ship,
S=penetration into the struck ship,
q = compressive reaction load per unit length on deck, = tdGo,
td = average deck thickness obtained by smearing deck stiffener areas
over deck width,
Go =effective crush stress, nay,
Gy =deck material yield strength,
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Ammerman, D.J. Structural analysis in support of the waterborne transport of radioactive materials, article, August 1, 1996; Albuquerque, New Mexico. (digital.library.unt.edu/ark:/67531/metadc673141/m1/4/: accessed December 13, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.