ABSTRACT The Norwegian Petroleum Directorate recommend the structural damping ratio of welded individual members to be taken as 0.15% of critical damping when evaluating vortex induced vibrations. This paper descibres the background for the recommendation which mainly is based on the measurements of the vibrations on the Heimdal flareboom. Severe vortex induced vibrations in Norwegian flarebooms have occured twice. The first occurence was in 1978 on the flareboom at Statfjord A. The second incident was at the Heimdal flareboom in 1984/85. Both incidents gave valuable information about vortex shedding problems. STATFJORD-A VIBRATIONS At Statfjord A the vibration was an overall vibration of the tie, see figure 1. Calculations of the natural frequency of the individual panel sections of the main chord showed that it was close to the recorded frequency and to the vortex shedding frequency for the chord. The calculation of this natural frequency had not been included in the design. The problem was solved by spirally wrapping the main chords of the ties with 25mm diameter ropes. Three ropes was wrapped on each chord at a phase difference of 1200, each rope spiral had a pitch of one metre. The spirals on diagonally opposite chords of the tie had the same rotational direction (clockwise) and the other pair was wound in the opposite direction. Afterwards no more vibrations have been reported (Mobil, 1978). A large measurement program was planed, but was cancelled after the successful use of the ropes. Measurements were later performed to study the overall dynamic effects in the flare boom. It was concluded that the design gave a slight under estimation, but it was compensated for by conservative load calculations (AasJakobsen, 1979). No measurements were performed to actually obtain values for the damping in the vibrating parts of the structure.

ABSTRACT The paper describes a practical method of solving the beam-column problem of a conductor with casings and production tubing between the drill floor and the sea floor. With a recognized formula for the interaction between axial force and bending moment as the basis, it is explained how to determine the various quantities to be introduced in the formula, with emphasis on the axial force and the conductor systems resistance to same. Different from a method proposed earlier by other authors [1), no additional term is introduced in the interaction formula. Instead, a correction is made on the global resistance on the basis of the true local stresses. 1. INTRODUCTION The buckling calculation of a conductor involves certain problems which are not involved in the calculation of an ordinary beam-column. There are problems both with regard to the load and with regard to the resistance, even if all--relevant physical circumstances are known. In the case of an ordinary beam-column there is usually no doubt about what is the load and what is the resistance when the relevant physical circumstances are known. The conductor with casings and tubing consists of several tubes, one inside another. This fact in itself is hardly the reason for the trouble, because built-up structural elements are frequently used, and do not usually create any special problems. However, combined with the fact that internal and external pressures acting on the wall of a tube affect its stability, a problem occurs regarding the corresponding influence on the conductor system (the conductor with casings and tubing) when various pressures are acting inside and outside the various tubes. The problem is related not only to which load that produces the buckling tendency, but also to the buckling resistance of the conductor system.

1 Abstract This paper presents two simple and efficient frequency domain methods for the calculation of the dynamic tension of Single and multiple segment mooring lines The first method described (MODEL 1) IS an analytical approach based on the catenary equations and an estimate of the line drag resistance To Include inertia loads, drag loads and a dynamic description of the mooring line motion, a dynamic system based on a Single degree of freedom (SDOF) IS developed (MODEL 2) Both methods are extensively tested versus the non-linear finite element computer program RIFLEX, and the correspondance With respect to dynamic tension amplitudes IS very good for a wide range of line configurations, water depths and excitation levels MODEL 2 IS Implemented In the MARINTEK positioning computation program MIMOSA 2 4 Introduction Catenary mooring systems are extensively used for stationing of floating structures at sea Up to now, the basic design method IS still the quasi-static approach, I e the cable force IS determined by the terminal point position only High frequency forces and Imposed first order motions may, however, cause large dynamic tensions In the mooring lines, ref [2], [4] and [7] When moving Into deeper water, the relative Importance of the dynamic mooring line tension Increases The magnitude of the dynamic hne tension IS dependent upon several parameters Elastic, axial stiffness, line pretension and line weight are key parameters In assessing the dynamic load effect Advanced non-linear finite element computation programs are time consuming, which restricts the number of design cases to be considered One 15 an analytical method (MODEL 1) based on the catenary equations and an estimate of the drag resistance of the line The other describes a dynamic system based on a Single degree of freedom (MODEL 2).

ABSTRACT This paper presents a probability distribution of stress ranges and a spectral fatigue damage calculation of offshore structures subjected to non-narrow banded Gaussian stress processes. The stress range probability distribution is empirically formulated on the base of a number of stress range probability histograms obtained from the rainflow cycle counting algorithm using the Monte-Carlo procedure. Although the probability distribution introduced is general for both linear and nonlinear damage accumulations, in the paper the linear damage accumulation (Palmgren-Miner's rule) is used with a multi-linear SoN fatigue model. This model can also be used for a nonlinear fatigue model applying a piecewise linear approximation. Formulation of the mean damages in short-term and long-term sea states are presented in general. For a linear SoN model the customarily known damage correction factor is constructed. It is worked out that an empirical stress range probability distribution can be more generally used in the damage calculation than an empirical damage correction factor. INTRODUCTION In practical fatigue analysis of offshore structures it is often assumed that the stress process is narrow banded. Under further restriction of the process as to be Gaussian the mean fatigue damage can be calculated precisely from the stress range distribution which becomes Rayleigh. In this approach, the stress range is assumed reasonably to be double of the stress amplitude. This approach is appropriate if the stress spectrum has a single peak which may be observed under certain conditions e.g. a) when the wave frequency and the natural frequency of the structure lie within close proximity of each other or b) assumption of a quasi-static response of the structure neglecting the effect of the natural vibration which is applicable only in sever sea states and if the structure is not dynamically sensitive.

ABSTRACT Currently accepted codes advocate limits on allowable design stresses based on elastic stress analysis, together with strain limits which are not well defined This leads to inconsistencies with pipeline steel specifications which include plasticity effects A constitutive model for pipeline steels IS Introduced which allows the calculation of stresses and strains for significant design cases to be accomplished in a rational manner The procedures suggested should allow the question of the acceptability of current stress limits to be explored further INTRODUCTION The design of submarine pipelines is based on a variety of codes and regulations, which are, in many cases, open to conflicting interpretation This is particularly true in relation to the fundamental question of the choice of allowable hoop stress. Operating pressure and temperature, and also pipe diameter are effectively determined by product delivery considerations The outstanding question for the pipeline designer having chosen a material specification is the choice of wall thickness For a given diameter, steel grade and pressure, this effectively translates to the selection of hoop stress The combination of hoop stress with the axial stress arising from pressure, temperature, and bending requires the formulation of an appropriate theory of failure under multi-axial stresses and the definition of corresponding safety margins The choice of margin is complicated by the intervention of plasticity effects These are often ignored by design codes (1,2,3), which rely on elastic analysis to determine axial stress even when plasticity is known to be present The effect of plasticity is sometimes (2) allowed for by setting an arbitrary limit on strain without defining the means of calculation The purpose of this paper is to introduce a consistent procedure for the introduction of both elastic and plastic multi-axial stress-strain effects into the design process.

ABSTRACT A cooperative analytical and experimental technical program involving three organizations is described which is leading to the capability to predict the service life of dynamic flexible risers. The motions and loads on flexible risers require knowledge of static mechanical properties of the pipe Wellstream has developed a family of simple and accurate methods for calculating static failure and stiffness properties of flexible pipes. Degradation of risers may result from wear of the tensile armor wires as a result of slip during flexure. Wellstream has derived a formula for the magnitude of slip of the wires across each other during dynamic bending, and a criterion for a contact pressure that will prevent slip. These are being incorporated, with the help of personnel from the University College London, into a model of wire stress increases occurring over a bending cycle. This model considers non-slip as well as slip regimes during bending, and permits calculation of failure by metal fatigue due to stress increases with time as metal cross sectional area decreases due to abrasion. Zentech Consultants is encoding the degradation model as a module auxiliary to the riser analysis program Flexriser 4 so that a life prediction can be made as an output for a given user design study, for the expected lifetime current and wave excitation spectrum. Wear of the plastic barrier layer and of the other plastic layers as a result of flexure is also being addressed, and algorithms for predicting plastic degradation will be added to the model. In the interim, available public domain wear data is being used. INTRODUCTION The major limitation to flexible user life IS the degradation due to wear and fatigue that may occur in the two contrawound layers of tensile armor under the action of bending that results from wave and current action.

ABSTRACT This paper presents an outline of a comprehensive program system developed by the authors, which includes many functions for response analysis of a wide variety of offshore structures. Typical calculated results by this system are also presented being compared with field measurements and model test data as well as calculations by the other analysis programs. Through the comparative calculations the validity and flexible applicability of the system have been confirmed and the results presented here may be valuable and useful for the designers and researchers of offshore structures. 1 INTRODUCTION Various analysis program packages for offshore structures have been developed by many companies and organizations in the world so far. Most of the existing program packages for floating offshore structures are composed of motion and structural analysis programs based on Hooft's method [Hooft, 1971]. In these conventIOnal program packages hydrodynamic analysis is based on the Morison equation and/or two-dimensional potential flow theory, and global structural analysis IS executed by using spatial framework model, e.g., see [Akita et al, 1978). Recent remarkable progress of electronic computers, however, has enabled three-dimensional diffraction/radiation analysis to be in practical use and to be incorporated into a conventional analysis program package. This extends the applicability of analysis program and it may become possible to take into account three-dimensional effect of hydrodynamic loading, e.g., on massive structures such as floating artificial islands and floating crane semisubmersibles, on jackups under floating conditions, and on huge-scale barges with large breadth and shallow draft or m shallow waters. We recently completed a comprehensive computer program system in order to respond to diverse analytical problems of a wide variety of offshore structures. This new system, the integrated program system for offshore structures, is abbreviated to IPOS in this paper.

ABSTRACT Two main varieties of ice strength change are considered: the first one - variation at purposeful strengthening methods affecting ice by using certain cooling facilities and the second one - strength variation under natural conditions at the ice contact with engineering structures and soil. In the first case only manufactured ice obtained by a spray cone method is studied; such ice is considered as structural material for different engineering structures. The second case concerns interaction of natural ice cover with structures and of manufactured ice with the soil foundation; here we have the less scope of investigations. GENERAL PROBLEMS Structure building using manufactured ice requires solutions of specific structural and engineering problems many of which are now in engineering practice. Regardless of the location and purpose of ice structures there are problems and contradictions common for all ca-, ses. The larger the ice structure is the higher the intensity 9_f its building must. b~. BU, t at a high intensity of ice mass formation it is difficult to cool it, and due to low ice strength it is impossible to build up large ice structures. The review of the completed works and examples of the problem are given at the end of this paper. The stressed state of ice structures is connected with the seasonal fluctuation of natural processes. In the case when dikes, wharves and other hydraulic structures are considered, particularly its building in the mouth of the northern rivers and on the shelf of arctic seas, it becomes obvious that these areas are very cold and have little water available in winter, and due to this fact the ice mass strength is maximal whereas loads on it are minimal. In summer the conditions change: loads increase and ice strength characteristics decrease.

ABSTRACT This paper presents the description of a higherorder boundary element method (HOBEM) for calculating linear hydrodynamic loadings on large floating bodies and comparison with constant panel methods and HOB EMs that are employed in conjunction with the hybrid boundary integral equation procedure, for a variety of structural configurations. It was concluded from the study that HOB EM has several important features: it uses many fewer boundary elements and much less computer time, with higher accuracy than conventional methods. In addition to these, the computer code for hydrodynamic loadings can easily be used for finite element structural analysis. INTRODUCTION Reliable estimates of the hydrodynamic loadings on large offshore structures are critical in the assessment of structural response, stability and fatigue life. The constant panel method (CPM) introduced by Hess-Smith (1964) has been widely used for calculating hydrodynamic loadings, for example by Faltinsen-Michel sen (1974); Garrison (1979); InglisPrice (1980); Ostergaard-Schell in (1987); and Korsmeyer et al. (1988). In the constant panel approach, the surface of a three-dimensional body is replaced by quadrilateral or triangular facets. Each facet (or panel) represents a source distribution of constant strength with satisfaction of a Newmann boundary condition required at the center (control point) of each panel. Consequently, the constant panel approach has several limitations: the source distribution is discontinuous, i.e., the source strength is constant over each panel and jumps stepwise at the boundary of neighboring panels; for curved body surfaces, the quadrilaterally faceted surface becomes discontinuous as all the four corner points generally do not coincide with those of the neighboring panels. Thus, the faceted surface introduces so-called "leaks". To overcome the foregoing limitations, Webster (1975) proposed the use of triangular panels with linear source distributions located just beneath the actual body surface.

ABSTRACT A common model for short crested seas is considered in view of wave measurements from the Norwegian continental Shelf. The directional spectrum is given as a product of a frequency spectrum and a frequency dependent spreading function. The spreading function is assumed to attain a cosine law and emphasis is herein given to the choice of the corresponding exponent. The sensitivity of the predicted response to uncertainties in the modeling of short crested sea is indicated for two different structural systems. Both extremes and fatigue life are considered. Based on these structural calculations a simplified spreading function being convenient for structural response calculation is recommended. INTRODUCTION To the first order the wavy sea surface is conveniently modeled as a Gaussian stochastic process. For short time periods and limited spatial areas, the process can furthermore be assumed to be stationary and homogeneous. The adequacy of the assumption of a cosine-law will not be explicitly considered herein. The difference is not expected to be crucial regarding structural response and we will adopt a cosine model for the spreading function. In order to easily compare the previous results with the available measurements, Eq. (3) will be adopted for the intermediate part of this work. However, in the structural response calculations, an equivalent spreading function in the form of Eq. (2) will be determined. This can be done by simply setting n = 0.46 s, Mitsuyasu et ale (1975). STOCHASTIC LONG TERM RESPONSE ANALYSIS The consideration is herein restricted to linear structural systems or systems which can be linearized with a reasonable degree of accuracy. By now introducing parameterized models for the frequency spectrum and the spreading function, long term response extremes and fatigue life can be estimated along the lines reviewed into some detail in Haver and Natvig (1990).

ABSTRACTS The most exposed area for fatigue loading in an offshore platform is the area where the deck connects with the shafts of the base structure. The fatigue loading of the deck is becoming more and more often the governing factor of the design. A feasability design study has been carried out to determine if concrete is a material for use in offshore deck structures. The conclusion is clear: Concrete trusses are a good alternative to steel for deck structures, especially when fatigue loading is the governing factor. INTRODUCTION The design of platforms for the North Sea has been moving steadily towards use in larger depths. At the same time, the decline of oil prices since 1986 has caused a demand for less expensive structures. This has lead to platforms which are more slender and less stiff than were the first Condeep structures, and therefore more sensitive to cyclic loading. For a number of years, steel has been the obvious material for use in the deck structures, primarily because of its relatively low weight. A secondary reason is because truss structures in steel give high flexibility with respect to the placement of equipment between the trusses. The fatigue loading of the deck is becoming more and more often the governing factor of the design. This, in turn, has lead to the search for new solutions, for example, methods to uncouple the fixed connection between the deck and the shaft without sacrificing safety or increasing maintenance costs. The company Dr.techn. Olav Olsen a.s has been largely involved in the design and development of concrete offshore structures in Norway, and the experience so far is that concrete has high resistance against fatigue loading response, for instance at shaft top where the concrete meets the steel in deck structure.

ABSTRACT Results are presented from two different case studies related to extreme response estimation of tension leg platform (TLP) tendons in stochastic waves. The first investigation is devoted to the influence from non-linearities when analysing stresses m large-diameter tendons. For this case both axial and bending stresses are important, and a non-linear coupling between the two components exists. The results indicate, however, that this nonlinearity can be neglected even under extreme environmental conditions. The second pan of the paper deals with correlation between first and second order surge motions and how extreme' tendon response is influenced by this correlation. Time domain simulations indicate that the two response types are correlated. It is also concluded that by taking correlation into account, the predicted extreme response will be reduced compared to results based on uncorrelated motion components. INTRODUCTION When dealing with TLP tendon design one has to estimate lifetime extreme stresses as a pan of a conventional Ultimate Limit State check. Excluding operational aspects that certainly are important, the problem is still quite complex involving environmental statistics and response calculation. In principle, lifetime extreme response must be found from long-term statistics of the response parameter of concern. It is, however, quite laborious to establish this kind of probability distributions, which means that rational short-cuts need to be taken. The long-term statistical problem is hence apparently reduced to the far less complicated short-term problem. The present paper is not a complete discussion on TLP tendon extreme response estimation, but reports results from limited studies of two aspects of this task. For both cases it is assumed that a "design storm approach" can be used. What then is needed is to perform an adequate load effect analysis for the actual seastate and to estimate extreme values from these results.

ABSTRACT It is demonstrated how information about the undisturbed wave at all frequencies of interest can be retrieved by constrained deconvolution of the outputs of several sensors with different known linear response characteristics, placed on or around a floating structure. A model of the sea state which retains information about the amplitude, phase and direction can then be used to calculate the resulting non-'linear drift forces by means of known quadratic transfer functions. It is shown how, with certain limitations, the wave and drift force calculation can be implemented in real time using frequency domain techniques. The resulting force time history could be used as feed forward information by the controller of a dynamic positioning system, to improve performance and efficiency. This could be further enhanced by applying linear prediction techniques (eg an auto-regressive model) to the force time history. 1 INTRODUCTION The dynamic position control problem arises because wave frequency forces are too large to be counteracted, and varying the demanded thrust at these frequencies would cause needless wear and tear on the thrusters. Simple low pass filtering would introduce a lag that would tend to degrade the performance of the system. The most widely used technique to overcome this is Kalman filtering, which was presented in the context of dynamic positioning by Balchen, Jensen and Saelid (1976). The method uses a state space model of the first order dynamics of the vessel to separate out the second order responses and predict" them for one or more steps ahead. What is more desirable however is to estimate the instantaneous forcing so that the appropriate preventative action can be taken before the vessel starts moving off station. He showed that this related to one component of the mean drift force and it was used successfully to improve position keeping.

ABSTRACT Sample calculations illustrate uncertainties in predicting second-order wave forces and low-frequency motions of a large moored structure. The results, for a "deep-draught floater" in regular and irregular waves, demonstrate sensitivity to numerical modelling procedures and to assumptions made about the damping. When there was no current, the damping was affected by first-order velocities, and the damping coefficient by boundary layer forces and by the partial development of flow separation and vortex shedding at low Keulegan-Carpenter numbers. The introduction of a current substantially increased the damping, but had generally a simplifying influence. The calculations also illustrate different ways of estimating the extreme second-order response, and combining this with the first-order response. 1. INTRODUCTION In 1989 BMT took part in a comparative evaluation of computer programs, organised by the Royal Norwegian Council for Scientific and Industrial Research (NTNF). The results of this investigation were discussed at a Workshop in Bergen, and will no doubt be published in due course. The project highlighted several sources of uncertainty in predicting low-frequency responses of floating and moored structures in waves, in particular those of estimating the damping and extreme responses. The present paper describes results from a follow-up study at BMT, which demonstrated how recent research data may be used in calculations of this type, and how changes in the assumptions and procedures affect the results. The problem posed by NTNF was to calculate wave forces on, and motions of, two vessels in regular and irregular waves; to estimate maximum responses in a storm of six hours duration for first and second-order motions separately, and then for the combined process. The two vessels were a turret-moored production ship of 230m length, and a four-column deep-draught floater (DDF), the latter being a very large semi-submersible type structure.