Exersice 2008-1, TMR 4195 Design of offshore structures, Spring 2008
Problem 1: Show the activity chain of a field development and explain briefly what is done in the
various phases. In which phase is most of the money spent? Can you explain briefly what is meant by
CAPEX and OPEX?
Problem 2: Can you briefly explain the main differences between The Pierson-Moskowitz -, the
JONSWAP -, and the Torsethaugen-spectrum.
Problem 2: Regarding design against overload, where are typically the largest uncertainties occurring?
Load side or capacity side? Is the same picture valid for a fatigue consideration?
Problem 3: Select a Pierson-Moskowitz spectrum. The significant wave height is 10m and the spectral
peak period is 13s. Simulate a possible realization of duration 1000s from this spectrum. Select a
frequency solution that ensures that the signal does not repeat itself within the 1000s period.
Problem 4: Could you rank the following documents with respect to their level in the Norwegian HSE
regualation hierchy: Norsok N-001, The Framework Regulations, The Facility Regulations, Norsok N003 and The Management Regulations?
Problem 5: Sketch a sinusoidal wave profile and show on the figure where you have maximum
horizontal particle speed and maximum horizontal particle acceleration. If you are going to calculate
the maximum horizontal load on a slender vertical pile, show on a figure the position of the wave
when you expect to see the largest total load. Would you be concerned about using the Gaussian
assumption (or a sinusoidal design wave) for the surface process for such a problem? Why?
Problem 6: Can you in one figure show the following probability density functions: a) The probability
density for an arbitrary point in time, b) The probability density function for an arbitrary maximum
(global maximum) and c) The probability density function of the largest maximum out of n maxima.
Show the location of the characteristic largest out of n maxima. What is the probability of exceeding
this value by an arbitrary maximum?
Problem 7: At the Norwegian Continental Shelf, one may under certain conditions use maritime
legislations in the petroleum activities. In which regulation is this possibility referred to?
Problem 8: What is a typical range for largest natural period for a fixed platform? Will water depth
effect natural period assuming deck mass is the same?
Problem 9: Assume that two rather large piles at a distance 80m apart. The diameter of each pile is
10m. Let us assume that the load is given by the mass term of the Morrison equation. Calculate the
transfer function for the total base shear (i.e. sum of horizontal load on the two piles). As a minimum
one should at least determine the frequencies where the transfer function has its maxima and minima.
Problem 10: What is meant by ALARP? Illustrate the answer by an example showing the
consequence of ALARP.
Problem 11: Using the tool developed in Problem 3. Simulate 20 different realizations from the same
Pierson-Moskowitz spectrum. Identify the larges crest height for each of these data. Establish the
sample distribution of 20-min. crest height from these 20 observations. The distribution function for an
arbitrary maximum crest height (global maximum crest height) is the Rayleigh distribution. Calculate
the expected zero-up-crossing period and determine the theoretical distribution for the 20-minute
maximum crest height and compare it with the sample distribution.
Problem 12: Give some examples of a main safety function. What is the requirement regarding the
annual safety of the main safety functions?
Problem 13: You are working with a slender jacket structure in rather shallow water. Deck mass is
also rather moderate. The oil company you are working for have given you the following information
for determining the 10-2 – annual probability response:
10-2 – annual probability individual wave height, h0.01.
The wave period, t, associated with this wave height, and t is said to be between tl and tu.
10-2 – annual probability significant wave height, hs0.01.
The spectral peak period associated with the given significant wave height, tp.
The duration of the 10-2 annual probability storm is given by .
Problem 14: For an arbitrary 3-hour stationary sea state, the probability of exceeding the critical
response level by the largest response maximum in this event is found to be 107. What is the annual
exceedance probability? The response level referred to above is suggested as a proper level for the
accidental limit state. Do you agree in this suggestion? Explain your answer.
Problem 15: What do we mean by a linear mechanical system? What is the difference between a linear
mechanical system and a linear response system?
Problem 16: If the problem you are working with can be modelled as a linear response problem,
which method you select if you were going to describe how the system behaved in a given stationary
storm situation, i.e. the significant wave height, spectral peak period and duration are known.
Problem 17: What do we mean by super-harmonic loading on for example a jacket?
Problem 18: The dynamic amplification due to a impulse type of loading depends on the shape of the
loading and the duration of the impulse relative to the natural period. For a un-damped single degree
of freedom system, the dynamic amplification is given for some shapes of the impulse in Fig. 3.2
(page 36) in SH: Prediction of Characteristic Response.
Explain why an un-damped model can be useful for this sort of a problem. How could you prepare a
similar figure for a different form of the impulse function?
Problem 19: Can you briefly describe the steps involved when you are going to solve the equation of
motion in the time domain?
Problem 20: You are going to do a full long term analysis for the 3-hour maximum response denoted
X3h. The short term sea state is characterized by the significant wave height, Hs and the spectral peak
period, Tp. Thus the long term wave climate is described by the joint probability density function
f H sTp (h, t ) . Write the double integral giving the full long term distribution for X3h. Explain in your
own words what the long term distribution of X3h really represents.
In view of the problem you are looking at, you decide to merely account for sea states exceeding a
certain threshold of the significant wave height, h0. Show how you have to do in order to use the
information being available. The requirement is that annual probability of exceeding the target value is
10-2. Show how you can estimate this target value when just considering sea states above h0.