Page 236 - Dynamic Loading and Design of Structures

Page 207

where N u and Mu are the ultimate strength under pure axial force and bending moment,
respectively. NE is the Euler buckling load.
The extreme values required for a design check can then most conveniently be based on the
short-term statistics of individual maxima of the process I(x , x ) obtained by simulation (see
1
2
Videiro and Moan, 1999).
Obviously, the long-term approach described by eqn (5.53) involves substantial effort when
significant non-linearities need to be considered and alternative probabilistic load models
therefore need to be used. Extreme load effects with, say, an annual exceedance probability of
2
10− may be estimated based on a limited set of sea states.
The overall aim of the design sea state concept is to estimate load (effects) corresponding to
4
2
a prescribed annual exceedance probability (e.g. 10− or 10−) without having to carry out a
full long-term response analysis.
An appropriate formulation of the design sea state concept is to use combination of
significant wave height and spectral peak period located along an iso-probability density
curve of fH m0Tp (h, t), denoted a contour line in the H m0 and T plane. Such contour lines can be
p
2
established in different ways. The simplest way to establish the 10−contour line, is first, to
2
estimate the 10− value of Hm0 together with the conditional mean of Tp. The contour line is
then estimated from the joint model of Hm0 and T p as the contour of constant probability
density going through the abovementioned parameter combination. Alternative approaches to
2
obtain the contour line are described by Haver et al. (1998). An estimate of the 10− action
effect is then obtained by determining a proper extreme value for all sea states along the
contour line and taking the maximum of these values.
If contour lines are used, the variability of the short-term extreme value needs to be
artificially accounted for to obtain a proper long-term extreme value. This may be achieved in
alternative ways, for example, by multiplying the expected maximum load effect calculated
for a given sea state with a predetermined factor, typically in the range of 1.1 to 1.3, or by
calculating the load effect as a predetermined, high fractile value, typically 90 per cent (see
NORSOK N-003, 1999). Contour line methods, therefore, would have to be calibrated.
Alternatively, linearized analyses may first be applied to identify the range of sea states that
contribute to the extreme value. Then, the complete non-linear short-term approach is used to
determine the expected maximum for relevant sea states to obtain the largest one, which is
taken to be the desired extreme value.
Instead of using a design sea state, a design wave specified by the wave height H, the wave
period T and direction may be used to determine the extreme load effect. Load effects with,
2
for example, annual exceedance probability of 10− can be determined in a simplified,
conservative manner by the design wave approach for preliminary design of fixed platforms
(NORSOK N-003, 1999). For fixed platforms with static behaviour, maximum action effects
occur for the highest waves. The relevant wave height H100 is then taken to be that with the
2
10− exceedance probability. H 100 may be taken to be 1.9 times the significant wave height
−2
H , corresponding to an annual exceedance probability of 10 , as obtained from long-term
m0
statistics, when the duration of the sea state is 3 hours.