Page 463 - Marine Structural Design

Chapter 24 Random Variables and Uncertainty Analysis 439

In the case of ship structural design, these concepts were introduced by St. Denis and Pierson
when determining the ship motions, structural loads, etc. due to operating in a realistic random
seaway. At about the same time, other work was being carried out in the area of probabilistic
design of structures.
Freudenthal gave a basic application of the probabilistic approach to the safe design of
engineering structures, and later he dealt specifically with marine structures. Others have
considered the ship problem including Mansour (1972, 1997), Mansour and Fauikner (1973),
Stiansen et a1 (1980), where the theory of structural reliability was applied to ships. Nikolaidis
et a1 (1 991, 1993) evaluated uncertainties in stress analysis of marine structures and presented
a methodology for reliability assessment of ship structures.
Longitudinal strength analysis has been based mainly on elastic beam theory with emphasis on
the maximum expected load (bending moment) and the minimum strength that provides a
factor of safety against unspecified failure. It is possible to calculate the probability of failure
if we can clearly and completely define a probability distribution for loads (demand) and for
strength (capacity). The objective of this section is to discuss the uncertainties in loads
(demand) and strength (capacity).

24.5.2 Uncertainties in Loads Acting on Ships
The principal loads acting on a ship’s hull may be summarized as follows, with particular
reference to longitudinal hull bending:
Still-water bending moments resulting from uneven distribution of weights and buoyancy
in still water.
Quasi-static bending moments due to relatively long encountered waves.
Dynamic bending moments caused by wave impacts or high-frequency wave forces.
Thermal loads induced by uneven temperature gradients.
Other loads not mentioned in the above are internal loads caused by liquid cargoes, machinery
or propellers, collision grounding and docking loads, aerodynamic and ice loads.
Quasi-static Wave Bending Moment
Quasi-static wave bending moment has been dealt with using the probabilistic approach, since
the waves causing such bending moments could only be described statistically. A specific sea
condition can be fully described by its directional spectrum, defining the component wave
frequencies and directions present.
Uncertainties arise from:
Variability in the directional properties of wave spectra, with only limited data available.
0
Combined effects of two storms, or sea and swell.
Variability of spectral shapes for a given significant height.
Referring to Part I Chapter 3, short-term response, can be calculated statistically by linear
superposition of the calculated RAO (response amplitude operator) that is the amplitude of the
ship response to a unit sinusoidal wave at a frequency. Uncertainties involved in the
calculation of RAO’S are due to assumed linearity of response in relation to wave height,
inaccuracy of strip theory and effect of variation in weight distribution on motions. In addition,