Page 315 - Marine Structural Design

Chapter 14 Offshore Structures Under Impact Loads 29 1

Table 14.1 Total Strain Energy Dissipation

* If the duration of the collision is significantly smaller than the hdamental period of
vibration.
where,
J = Mass moment of inertia of the column (including added mass) with respect to the
effective pivot point.
Z = Distance from the effective pivot point to the point of contact.

14.4 Examples

14.4.1 Mathematical Equations for Impact Forces and Energies in ShiplPlatform
Collisions
Problem:
Derive equations for calculating maximum impact force, impact energy during a collision
between ship and fixed platform (Soreide, 1985). The force-deformation relations for the ship
and platform may be modeled as linear springs of k, and k, respectively. The ship is assumed
to have weight of m (including added mass) and move at speed of v immediately prior to the
collision. In deriving the formulation, it is hrther assumed that the damping effect may be
ignored, and the impact mechanics may be expressed as free vibration a mass-spring system.

Solution:
The shiplplatform system may be considered as a mass-spring system. The deformations in the
ship and platform are denoted as x, and xp respectively. Denoting total deformation as
x = x, + x, , we may derive the following from the force equilibrium:
F = Irx = k,x, = k,x, ( 14.12)

where,