Odd A. Oisen
The forces produced by wind, wave, and current are the primary design loads on mobile drilling units and other offshore structures. These forces are dynamic and ever-changing; rarely can they be expressed as a mathematical function of time. They are statistical in nature and should, if possible, be handled by means of statistical tools.
The most commonly used method so far for evaluating wave loads on an offshore structure has been to base the calculations on one or more design waves of specified height and period. This was also the practice in the shipbuilding industry some years ago. When ship sizes increased, however, it became obvious that the design wave method led to unreasonable results in many cases. It was realized that the random nature of the ocean waves and consequently the responses of a structure to these waves could only be described by statistical methods.
Research carried out several years ago revealed that the irregular wave pattern could be described linearly by superimposing regular waves of different frequencies, heights, and directions of travel. In this way, it was possible to take into account all the wave components present in a realistic sea. The development of methods for calculating the response of a floating structure to regular waves was also initiated in this period. Det norske Ver-
itas (DnV) was involved in this development and produced a number of computer programs related to ships' problems.1'2
Calculations based on the principles indicated proved successful for ships and these methods are now commonly used. It was a natural step to extend the same principles and methods to offshore structures, such as mobile drilling rigs.3
The wave loads on both floating and fixed offshore structures may in principle be handled by use of the methods described above. Considering fixed offshore structures, such as jacket type structures or gravitational structures of the caisson type, this method requires that the nonlinear loads (for instance, drag forces) be small in comparison to the linear loads (for instance, inertia forces). If not, nonlinear statistics have to be considered, making it more complicated to arrive at a useful solution.
Yet no such method for practical application exists that takes into account the nonlinearity of the loads. Consequently, when these nonlinearities are of significant influence to the overall loads, the old design wave method has to be applied in the
Thus, the structure is designed for a specified wind and current velocity as well as a wave of specified height and period. These criteria describe the "50 year storm" or the "100 year storm." This refers to the worst wind, wave, and current conditions expected in any arbitrarily chosen 50 or 100 year period. At DnV, the "100 year storm" has been chosen as the design criter-
Although the design wind and wave conditions are not uniform, they reflect the expected maximum values based on long term statistics. Typical design criteria (storm condition) for fixed offshore structures intended to operate in two different
Gulf of Mexico
North Sea
Water depth to L.A.T,
Wave height Wave period Wind velocity
Current velocity at surface
In summation, the two methods normally used in estimating the wave loads on fixed and floating offshore structures and some of their characteristic features are:
Applying the design wave method, the combined effects of wind, waves, and current on a fixed offshore structure are normally treated as quasistatic forces. This is valid in most cases, particularly if care is taken in determining the "worst case" loading. The environmental loads acting on different drilling units are simplified in Figure 1-37.
WIND
Wind velocity is an important parameter in wind forces. Normally, two different wind velocities are specified in the design criteria for offshore structures, the N year sustained and the N year gust wind velocity. These are defined as follows:
N Year Sustained Wind Velocity
This is the average wind velocity during a time interval (sampling time) of one (l) minute with a recurrence period of N years.
JACK-UP TYPE
MOBILE OR FIXED UNITS MOBILE UNITS
N Year Gust Wind Velocity
This is the average wind velocity during a time interval {sampling time) of three (3) seconds with a recurrence period of N years.
At DnV, the 100 year wind velocity is used as the design criterion. This velocity may be evaluated from wind statistics for the specified area. Which wind velocity, however, gust or sustained, is to be used in force calculations? DnV has adopted the following principle:
If gust wind alone is more unfavorable than sustained wind in conjunction with wave forces, the gust wind speed is to be used. If the sustained wind and wave forces are greater than gust wind alone, the sustained wind speed should be used.
It should be mentioned that recent research by the author has shown that the long term distribution of wind speed may be described by a Weibull distribution function (defined in the section on "Waves").4
Velocity Variation with Height above Sea Surface
The sustained wind velocity is often considered to vary with height above sea surface according to the following formula5:
Davenport5 has proposed a value ofr=7 for open country, flat coastal belts, and small islands situated in large areas of water. Davenport does, however, further state that if there are areas in which the highest probable velocities occur during severe local storms such as thunderstorms and frontal squalls, little or no increase in velocity with height would seem appropriate.
The 100 year storm in the North Sea must be considered to be a severe local storm, and, according to Davenport, little or no increase in wind velocity with height should be expected, especially when gust velocity is considered.
The following formula, adopted as basis for the DnV Rules6*7, is a compromise between the one-seventh power law (Equation 1) and Davenport's conclusion:
(It should be mentioned that other authorities use the one-seventh power law.)
According to the DnV Rules6'7, the gust velocity is not to be taken less than:
The gust wind velocity as determined by Equation (2) varies less with height than does the sustained wind velocity.
The three velocity profiles defined by Equations (1), (2), and (3) are shown in Figure 1-38,
Wind Forces of Individual Members
Wind forces have been found to increase with the square of the wind velocity and in direct proportion to the exposed area.
According to the DnV Rules6'7, the gust velocity is not to be taken less than:
Other factors which affect the wind forces are the shape of the exposed areas and their height above sea level.
Based on the one-seventh power law, the formula for calculating wind forces may be written as follows:
The height coefficient CH may be expressed as:
The shape coefficient C varies from 0.5 for cylindrical shapes to 1.5 for structural steel shapes.
The force acting on the area A in the direction of the wind then becomes i
The formula generally accepted at DnV for calculating wind forces is:
(The units are metric.)
The force acting on an area A in the direction of the wind then becomes:
As may be seen from Figure 1-39, these two formulae differ by sin at. The question of which formula gives the best estimate of reality has been long discussed. The disagreement between authorities is great. DnV has adopted the conservative estimate both because it is conservative and because they feel it is closer to reality.
Shape Coefficient
The shape coefficient for short individual members
(3-dimensional flow), according to the DnV "Rules," is to be taken as: / t \
This formula is to be applied for <5.0.
The shape coefficient Coo, according to the DnV "Rules," is shown in Figure 1-40.
A) DECOMPOSING VELOCITY FIRST
A) DECOMPOSING VELOCITY FIRST
wind
Fig. 1-39 Two different methods for decomposing wind or drag forces.
WIND
DIRECTION
Fig. 1-39 Two different methods for decomposing wind or drag forces.
The total wind force acting on a structure is determined by summing up the effects of wind forces acting on separate areas of the structure. The total wind force on a typical jack-up rig is shown in Figure 1-41. Note that the force due to a 56.3 m./sec, wind velocity is twice the force due to a 40 m./sec. wind velocity.
It should be emphasized that wind direction can be a factor in determining the "worst case" loading on a structure.
CURRENT
Current forces are often considered in connection with wave force by adding vectorially the water particle velocities due to
MEMBER |
RESTRICTION |
Cqo |
FLAT BARS, ROLLED SECTIONS, PLATE GIRDERS AND OTHER SHARP - EDGED SECTIONS |
SHARP- EDGED SECTIONS |
2.0 |
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