# Structural analysis in support of the waterborne transport of radioactive materials Page: 3 of 10

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behavior of a RAM package. The loading condition would be the bow

oC the striking ship on one side of the package backed by the internal

structure of the struck ship or cargo on the other. The potential for

damage to the package depends on the remaining velocity of the striking

ship upon reaching the required depth of penetration (i.e., the package

location) and the relative stiffness and strength of the striking ship bow,

the RAM package, and the supporting structures in the struck ship. The

wotk described in this paper only addresses the first of these two types

of analysis. The analysis of the "local" response of the package is a topic

for future research.

In the next section of this paper past research into the consequences

of ship collisions, and the implications of these consequences to

radioactive material package transportation will be discussed.

Following this a proposed simplified method for determining the

damage as a result of collision will be given. The final section will

discuss the results of detailed finite element calculations to determine

the response of a generic small freighter to impacts from vessels with

varying mass and velocity.

SUMMARY OF GLOBAL SHIP COLLISION MECHANICS AND

RELATED LITERATURE

Because of the complexity of the deformation processes during ship

collisions, most prediction methods have been based on simplified

methods for estimating the amount of damage to the respective ships.

The methods are normally composed of two main steps. First, the

amount of energy to be absorbed during impact must be computed. This

step is sometimes referred to as the "external mechanics" part of the

problem. The second step is to determine how the struck and striking

ships deform in order to absorb the kinetic energy.

To simplify the ship collision mechanics, only collisions at near right

angles are considered in this program. This seems to be a reasonable

assumption for assessing the safety of RAM transport by sea, since

transverse penetration into the RAM-carrying ship is the primary

concern in a collision and such penetration will be greatest in a right

angle collision.

External Mechanics

Calculation of energy to be absorbed is relatively straightforward,

based on conservation of momentum and energy principles for an

inelastic collision of two bodies (Minorsky 1959). First, assume that the

center of gravity of the striking ship passes through that of the struck

ship, such that there is no rotation of the ships during the collision. Also,

assume that the angle between the striking and struck ship, a, is near

90. The mass of the struck ship and striking ship is MA and MB,

respectively, with initial velocities of VA and VB before the collision, as

shown in Figure 1.

Based on conservation of momentum and kinetic energy

perpendicular to the struck ship before and after the collision, the

following expression can be derived for the amount of energy absorbed

by deformation of the ship structures, AEk:

A MB(M +AM) 2

AEk = 2M +M +AM (VBsin a) (1)

A B~A

As shown, AEk is a function of the masses of the respective ships, the

initial velocity of the striking ship, the angle between the ships just

before impact, and the effective mass of water surrounding the ships that

affects the collision mechanics, AM. The proper value of effective water'I

M

A A

B

B

Figure 1. Ship Collision Parameters

mass is somewhat uncertain. Based on experiments of a ship hull

vibrating in deep water, Minorsky estimated the effective mass to be

40% of the mass of the struck ship, MA.

Internal Mechanics

It is the second step of the solution process, solving the "internal

mechanics" problem, that is the most difficult. This step requires

estimation of how the two ships deform in order to absorb the required

amount of energy, AEk. One of the earliest methods is an empirical

approach developed by Minorsky in which a linear relationship was

established between the amount of energy to be absorbed and the

volume of material within the ships that is deformed during the

collision:AEk= (414.5RT + 121,900) ton-knots2

(2)

RT is known as a resistance factor, and is basically equal to the total

volume of damaged structural materials in the striking and struck ships,

except for the outer hull of the struck ship, which is accounted for in the

constant term. The units of RT are ft2-in. The method for computing RT

is given in Minorsky's original paper. Minorsky studied 26 actual ship

collisions, all of which involved nearly right-angle collisions. From

these collisions, nine were finally used to fit a straight line between the

points of AEk and RT. This line is represented by Equation 2 and is

shown in Figure 2. The remaining collisions were not used since they

involved relatively lower amounts of energy absorption and exhibited

considerable scatter. This so-called "Minorsky Method" has been

widely used and appreciated because of the simplicity that it brings to

this complex problem. However, it does not account for the detailed

mechanics of the collision process and, because of its empirical nature,

it may not be applicable for ship designs and impact velocities that are

outside the range of the parameters for which the method was

developed.

There have been some attempts to check the accuracy of the Minorsky

Method. These are documented in papers by (Akita et al.1972a) and

others. Computations of AEk and RT based on additional ship collisions

that, apparently, were not used by Minorsky have been performed

(Gibbs and Cox 1961). The data from the Gibbs and Cox report and for

the collision analyzed by MR&S (M. Rosenblatt & Son 1972) are shown

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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. (https://digital.library.unt.edu/ark:/67531/metadc673141/m1/3/: accessed March 24, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.