Page 136 - Marine Structural Design

112 Part I Siructural Design Principles

where [TI denotes the transformation matrix, which may be expressed in terms of sub-
matrices [L] and [0] as,

(6.18)

[i i n] (6.19)

where Ax denotes the cosine of the angle between the x and x axes, px denotes the cosine of
the angle between the y and x axes, V, denotes the cosine of the angle between the z and
axes, etc.
The stiffness matrix for the structural system may be established by assembling the stiffness
matrices for individual elements of the structural system. Once the system stifmess matrix for
the structure is established, boundary conditions can be applied to determine nodal
displacements/forces. The element nodal forces in local axes may then be determined and
nodal displacements and stresses in local axes estimated. For more information on the finite
element methods, reference is made to Zienkiewicz (1 977).

6.4 Design Loads and Load Application
Dead Loads
Structural weight can be calculated directly from the structural model based on the material
density and volume input. These loads are generated automatically by the FEM program as
nodal forces or uniform loads on members. Equipment and miscellaneous loads may be
applied by means of surface loads or concentrated nodal forces at their actual location.

Variable Loads
In design of structural members, the variable loads and weights must be analyzed for several
cargo distributions in order to capture the extreme values of loads. The variable loads are
usually included in the FEM model as surface pressure on relevant decks or tank boundaries.

Static Sea Pressure
Static sea pressure at each design draft is computed and applied in the FEM model as a surface
load, which acts like a constant surface pressure on the bottom and as a linearly varying
surface pressure on the side plates.
Wave Induced Loads
The wave-induced hydrodynamic loads and inertia loads due to vessel motion are considered
to be low-frequency dynamic loads and can be analyzed using a quasi-static approach. The
solutions for these ship motions and hydrodynamic loading are most frequently accomplished
through the use of strip theory.