COMPUTERS AND STRUCTURES, INC., AUGUST 2010 AUTOMATIC WAVE LOADS TECHNICAL NOTE DEFINING WAVE LOADS This section describes how to define automatic wave loads. The automatic wave load is a special type of load pattern. It generates loads on the structure resulting from waves, current flow, buoyancy and wind. Wave Load Pattern Definition Define the automatic wave load as follows: 1. Click the Define menu > Load Patterns command in SAP2000 or the Loads > Load Patterns command in CSiBridge to open the Define Load Patterns form, as shown in Figure 1. 2. Type in the load name (e.g., W1), type (i.e., WAVE), and self-weight multiplier (e.g., 0) and select an Auto Lateral Load (i.e., API WSD2000). 3. Click the Add New Load Pattern button to add the W1 wave load pattern definition to the DEAD load pattern definition or click the Modify Load Pattern button to replace the DEAD load pattern definition with the W1 wave load pattern definition. Figure 1: Defining a Wave Load Pattern Wave Load Pattern Definition Page 1 of 21
Wave Load Parameters After the wave load pattern has been defined as described in the previous section, define the wave load parameters as follows. 1. Highlight the wave load in the Define Load Patterns form. 2. Click the Modify Lateral Load Pattern button, indicated in Figure 2. Figure 2: Defining a Wave Load Pattern The Wave Load Pattern form shown in Figure 3 appears. Use the Wave Load Pattern form and its associated sub-forms to define the various wave load parameters, including: Wave characteristics (wave height, period, wave theory, and so forth) Current profile information (velocity and direction versus depth) Marine growth definition (thickness versus depth) Drag and inertia coefficient definitions Wind load parameters (direction and coefficients) Buoyant load option Wave load direction Wave crest position information Wave load discretization length Various elevations related to the wave load Water properties Wave Load Parameters Page 2 of 21
Figure 3: Wave Load Pattern Form An explanation of how to define each of those parameters is provided in the sections that follow. Multiple parameters can be defined for wave characteristics, current profile, marine growth, drag and inertia coefficients, and wave wind loads. Only one of the defined parameters of each type can be assigned to a given wave load pattern. Note that any of the defined parameters is available for assignment to any of the wave load patterns. Wave Load Parameters Page 3 of 21
For example, while defining a wave load pattern named W1, you may define three Current Profiles named CUR1, CUR2 and CUR3. Only one of those Current Profiles can be assigned to wave load pattern W1. (A parameter is available for assignment when its name appears in one of the drop-down boxes in the Wave Load Parameters area of the Wave Load Pattern form.) Next suppose you define a second wave load pattern named W2. Any one of the three previously defined Current Profiles (CUR1, CUR2 and CUR3) is available for assignment to wave load pattern W2. The wave characteristics, marine growth, drag and inertia coefficient and wave wind load parameters behave similarly. Wave Characteristics Define a wave characteristic as follows: 1. With the Wave Load Pattern form displayed (see Figure 3), click the Add or Modify/Show button associated with the Wave Characteristics item to display the Wave Characteristics form shown in Figure 4. Figure 4: Wave Characteristics Form 2. Type a name into the Wave Characteristic Name edit box. Wave Characteristics Page 4 of 21
3. Enter the wave kinematics factor in the Wave Factors area of the Wave Characteristics form. The wave kinematics factor accounts for wave directional spreading and irregularity in the wave profile shape that is not typically accounted for in two-dimensional wave kinematics. Typical wave kinematics factors range from 0.85 to 1. 4. Enter the storm water depth. Storm depth is the depth measured from the storm water level to the mud line. The specified storm water depth is added to the specified mud line elevation to obtain the storm water level. 5. In the Wave Type area of the form, choose the method for determining the wave water particle velocities and accelerations: a. From Selected Wave Theory. Select the From Selected Wave Theory option. Then, i. Define the wave height and the wave period in the Wave Data area of the form. The wave height is distance from the wave trough to the top of the wave. The distance from the storm water level to the top of the wave is equal to half the wave height. The wave period is the period of the wave as viewed by a stationary observer. ii. Select the wave theory to be used to calculate the wave water particle velocities and accelerations in the Wave Theory area of the Wave Characteristics form. b. User-Defined. Select the User-Defined option. The Wave Characteristics form will change and the areas of the form will be as shown in Figure 5. The user-defined wave is specified by defining a rectangular grid of points in a horizontal cut through the wave and then inputting the water particle velocity, acceleration and pressure at each point in the grid. Thus, i. In the Use Wave Discretization area of the form, specify the number of horizontal and vertical points in the grid used to define the wave. Wave Characteristics Page 5 of 21
Figure 5: Wave Characteristics Form for User-Defined Wave Type ii. After you have entered the number of horizontal points and pressed the Enter key on your keyboard, or clicked in another text box on the form, the number of rows in the grid in the Horizontal Coordinates and Surface Elevation area of the form changes to match the specified number of horizontal points. Similarly after you have entered the number of vertical points, the number of rows in the grid in the Vertical Coordinates area of the form changes to match the specified number of vertical points. This is illustrated in Figure 6. iii. Fill in the horizontal grid line locations and the wave surface elevation (measured from the vertical reference datum) at each horizontal grid line in the Horizontal Coordinates and Surface Wave Characteristics Page 6 of 21
Elevation area of the form. The horizontal grid locations should start at zero and proceed in ascending order to define a full wave length cycle. The horizontal grid lines are typically, but not necessarily, equally spaced. iv. Fill in the vertical grid line locations (relative to the vertical reference datum) in the Vertical Coordinates area of the Wave Characteristics form. The vertical grid locations should start at the top of the wave and proceed in descending order to the mud line elevation. The vertical grid lines are typically more closely spaced near the top of the wave. Figure 6: Wave Characteristics Form with User Grid Defined Wave Characteristics Page 7 of 21
v. Click the Modify/Show Wave button on the Wave Characteristics form to display the User Wave Data form shown in Figure 7. In the grid, the Horiz Loc (Horizontal Location) and Vert from Datum (Vertical from Datum) columns are automatically filled from the data that is specified on the Wave Characteristics form. vi. Fill in the Horiz Wave Vel (Horizontal Wave Velocity), Horiz Wave Acc (Horizontal Wave Acceleration), Vert Wave Vel (Vertical Wave Velocity), Vert Wave Acc (Vertical Wave Acceleration) and Pressure columns. Figure 7: User Wave Data Form The Display Options area of the User Wave Data form can be used to display subsets of the data at specified vertical or horizontal grid Wave Characteristics Page 8 of 21
locations. For example, Figure 8 shows data for the horizontal grid at 123.3543. Figure 8: User Wave Data Form Showing Data for Horizontal Grid at 123.3543 When entering data in the grid, enter zero if the considered point lies above the wave surface. The one exception to this rule is when the wave surface does not lie exactly at a specified grid vertical elevation. In that case, the velocities and accelerations at the wave surface are input at the point that lies immediately above the wave surface. It is understood by the program that these values apply at the wave surface, not at the grid location immediately above the wave surface. For example, for the data shown in Figures 6, 7 and 8, the surface elevation at the horizontal grid at 123.3543 is 11.4805. The data Wave Characteristics Page 9 of 21
specified in row 4 of the grid in Figure 8 applies at the surface elevation of 11.4805, not the grid line elevation of 15. When user waves are defined, it may be convenient to first define a wave from theory and then modify the resulting velocities and accelerations as desired. To do this, define the data for the wave from selected theory. Then, click the Show Wave Plot button or Show Wave Table button on the Wave Load Pattern form. This will cause the velocities and acceleration to be calculated based on the selected wave theory. Return to the Wave Load form and click the Modify button associated with the wave characteristics to display the Wave Characteristics form. Then change the wave type to user defined. Note that you cannot print or export the tabular data shown in the User Wave Data form. However, this same data is available in the Model Definition Tables and can be printed, exported or displayed from there. Delete a Wave Characteristic definition as follows: 1. With the Wave Load form displayed, display the definition to be deleted in the drop-down list. 2. Click the associated Delete button. Note that there must always be one wave characteristic parameter defined; thus, you cannot delete the last one. Current Profile A Current Profile defines the velocity and direction of the current as a function of depth (from storm water level to the mud line elevation). By default, a wave load is specified to have no current profile. Define a Current Profile as follows: 1. With the Wave Load Pattern form displayed (see Figure 3), click the Add or Modify/Show button associated with the Current Profile item to display the Current Profile Data form shown in Figure 9. Current Profile Page 10 of 21
Figure 9: Current Profile Data Form 2. Enter the current blockage factor in the Current Profile Factors area of the form. The current blockage factor accounts for the reduction in current speed at the offshore platform that occurs because the platform causes the current flow to diverge. Typical current blockage factors range from 0.7 to 1. Current Profile Page 11 of 21
3. Select the Current Profile Stretching Option. Two methods are provided to stretch (or compress) the current to the wave surface level at a given horizontal location. These methods are Linear and Nonlinear (see Current Profile in Calculation of Wave Load Values). 4. Input the number of vertical elevations at which the current profile data is specified in the Data Is Specified at This Number of Elevations area of the form. After you have entered the number of vertical elevations and pressed the Enter key on your keyboard, or clicked in another text box on the form, the number of rows in the grid in the Current Profile Data area of the form will change to match the specified number of vertical elevations. 5. Input the vertical elevation (measured from the datum), the current velocity and the current direction at each data point. The current direction is input as an angle in degrees measured counterclockwise from the positive global X axis. Enter the data in descending vertical elevation order. If necessary, click the Order Rows button to reorder the data in correct manner. Also note that the program will automatically order the data in descending vertical elevation order when you click the OK button to close the form. If the top specified elevation is below the storm water level, the program assumes that the current profile data at the storm water level is the same as the data specified at the top specified elevation. Similarly, if the bottom specified elevation is above the mud line, the program assumes that the current profile data at the mud line is the same as the data specified at the bottom specified elevation. Delete a Current Profile definition as follows: 1. With the Wave Load Pattern form displayed, display the definition to be deleted in the drop-down list. 2. Click the associated Delete button. Marine Growth The marine growth thickness on the structure is specified as a function of depth. By default a wave load is specified to have no marine growth. Marine Growth Page 12 of 21
1. With the Wave Load Pattern form displayed (see Figure 3), click the Add or Modify/Show button associated with the Marine Growth item to access the Marine Growth Data form shown in Figure 10. Figure 10: Marine Growth Data Form 2. Input the number of vertical elevations at which the marine growth data is specified in the Data Is Specified at This Number of Elevations area of the Marine Growth Data form. After you have entered the number of vertical Marine Growth Page 13 of 21
elevations and pressed the Enter key on your keyboard, or clicked in another text box on the form, the number of rows in the grid in the Marine Growth Data area of the form will change to match the specified number of vertical elevations. 3. Input the vertical elevation (measured from the datum) and marine growth thickness at each data point in descending vertical elevation order. If necessary, click the Order Rows button to reorder them in the correct manner. Note that the program will automatically reorder the data when you click the OK button to close the form. The marine growth value used at a particular vertical elevation is linearly interpolated from the specified data. For a typical pipe member, two times the marine growth thickness is added to the diameter of the pipe when calculating the force exerted on the pipe by the wave. Delete a Marine Growth definition as follows: 1. With the Wave Load Pattern form displayed, display the definition to be deleted in the drop-down list. 2. Click the associated Delete button. Drag and Inertia Coefficients The drag and inertia coefficients are used in Morison s equation when calculating the wave forces acting on the structure. By default a wave load is specified to have API Default drag and inertia coefficients. Define drag and inertia coefficients as follows. 1. With the Wave Load Pattern form displayed, click the Add or Modify/Show button associated with the Drag and Inertia Coefficients item (see Figure 3) to access the Drag and Inertia Coefficients form shown in Figure 11. Drag and Inertia Coefficients Page 14 of 21
Figure 11: Drag and Inertia Coefficients Form 2. Input the number of vertical elevations at which the drag and inertia coefficient data is specified in the Data Is Specified at This Number of Elevations area of the form. After the number of vertical elevations has been entered and the Enter key on the keyboard has been pressed, or clicked in another text box on the form, the number of rows in the grid in the Drag and Inertia Coefficient Data area of the form will change to match the specified number of vertical elevations. Drag and Inertia Coefficients Page 15 of 21
3. Input the vertical elevation (measured from the datum) and drag and inertia coefficients at each data point in descending vertical elevation order. If necessary click the Order Rows button to reorder the data in this manner. Note that the program will automatically reorder the data in descending vertical elevation order when you click the OK button to close the form. The drag and inertia coefficient values used at a particular vertical elevation are linearly interpolated from the specified data. Delete a Drag and Inertia Coefficients definition as follows: 1. With the Wave Load Pattern form displayed, display the definition to be deleted in the drop-down list. 2. Click the associated Delete button. The values for the API Default drag and inertia coefficients depend on whether the location considered is above or below the specified high tide elevation as shown in the following table. API Default Drag and Inertia Coefficients Location Drag Coefficient Inertia Coefficient Above High Tide Elevation (Smooth) Below or At High Tide Elevation (Smooth) 0.65 1.6 1.05 1.2 Wave Wind Load Parameters Wave wind loads act on the portion of the structure that is not submerged. By default a wave load is specified to have no wind load. Define wind load parameters as follows. 1. With the Wave Load Pattern form displayed, click the Add or Modify/Show button associated with the Wind item (see Figure 3) to access the Wave Wind Load form shown in Figure 12. Wave Wind Load Parameters Page 16 of 21
Figure 12: Wave Wind Load Form In the Wind Load Parameters area of the Wave Wind Load form, 2. Specify the wind direction angle. The wind direction angle is input as an angle in degrees measured counterclockwise from the positive global X axis. 3. Specify the one-hour mean wind speed at 32.8 feet (10 meters). 4. Specify the averaging time period. The averaging time period, t, is in the range 0 < t 3600 seconds. In the Other Data area of the Wave Wind Load form, 5. Specify the mass density of air and the typical shape coefficient. The typical shape coefficient applies to all objects in the model unless the wind load shape coefficient for that object has been overwritten in the wave overwrites. Wave Wind Load Parameters Page 17 of 21
Delete a Wind load definition as follows: 1. With the Wave Load Pattern form displayed, display the definition to be deleted in the drop-down list. 2. Click the associated Delete button. Other Parameters on the Wave Load Pattern Form Buoyant Load Option a. Check the Buoyant Loads check box in the Wave Load Parameters area of the Wave Load Pattern form (see Figure 3) to include buoyant loads as part of the wave load pattern. b. Uncheck the checkbox if you do not want to include buoyant loads in the wave load pattern. Wave Load Discretization 1. Specify the wave load discretization length in the Wave Load Discretization area of the Wave Load Pattern form (see Figure 3). The wave load discretization is the maximum discretization length for distributed wave loads that are applied to objects in the model. For example, consider a distributed wave load acting along a frame element. A value is calculated for the wave load at points along the frame element that are no further apart than the specified wave load discretization length. The magnitude of the distributed wave load is assumed to vary linearly between these calculated locations. Wave Crest Position In the Wave Crest Position area of the Wave Load Pattern form (see Figure 3), 1. Specify global X and Y coordinates of a point on the initial wave crest position. 2. Specify the number of wave crest positions to be considered. Other Parameters on the Wave Load Pattern Form Page 18 of 21
Specified initial wave crest position WL = Wave length (Distance between wave crests) Position of next wave crest when previous wave crest is at the specified initial wave crest position Structure a) Initial Wave Crest Position (Plan View) First considered position of wave crest Second considered position of wave crest Third considered position of wave crest 4 @ WL / 4 = WL Fourth considered position of wave crest b) Considered Positions of Wave When a Total of Four Wave Crest Positions are Considered First considered wave crest position shown solid Second considered wave crest position shown dashed Structure Mud line c) Horizontal Section Cut Through Wave Figure 13: Example for Number of Wave Crest Positions To Be Considered The meaning of the number of wave crest positions to be considered is explained by the example shown in Figure 13, which shows a case of four wave crest positions. The location of the initial wave crest position is uniquely identified by the specified global X and Y coordinates on the initial wave crest and the specified wave approach angle (wave direction). Other Parameters on the Wave Load Pattern Form Page 19 of 21
The distance from one wave crest to the next wave crest is equal to the wave length, identified as WL in Figure 13. When four wave crest positions are considered, the wave length is broken into quarters and the four positions considered are as shown in Figure 13b. The first position considered is at the specified initial wave crest position. The second position considered is one quarter the wave length away from the initial position measured in the direction of the wave. The third position considered is one half the wave length away from the initial position, and the fourth position is three quarters the wave length away from the initial position. More generally, when n wave length positions are considered, the distance from the specified initial wave crest position to the n th wave crest position is given by: d ( n 1) WL = n In the previous equation, d is the distance from the specified initial wave crest position to the n th wave crest position and WL is the wave length. Wave Direction 1. Specify the wave approach angle in degrees in the Wave Direction area of the Wave Load Pattern form (see Figure 3). The wave direction angle is input as an angle in degrees measured counterclockwise from the positive global X axis. Elevations Related to the Wave Load Various elevations are specified in the Vertical Reference Elevation for Wave area and the Other Vertical Elevations Relative to Datum area of the Wave Load Pattern form (see Figure 3). The specified elevations consist of a vertical reference datum, a mud line elevation referenced to the datum and a high tide elevation referenced to the datum. 1. Specify the Global Z Coordinate of Vertical Datum to locate the vertical reference datum. All other vertical elevations in the wave load definition, including those used in defining currents, marine growth and drag and inertia coefficients, are specified with reference to this datum. The location of the vertical reference datum is arbitrary. Any convenient Other Parameters on the Wave Load Pattern Form Page 20 of 21
location can be selected. One convenient location for the datum is at the storm water level. 2. Specify the Mudline from Datum to locate the mud line with respect to the vertical reference datum. No wave loads are applied below the mud line. 3. Specify the High Tide from Datum to locate the high tide with respect to the vertical reference datum. The high tide elevation is used when determining the default drag and inertia coefficients. See the previous subsection entitled Drag and Inertia Coefficients for more information. Water Properties 1. Specify the water properties in the Sea Water Properties area of the Wave Load form (see Figure 3). The water properties consist of the water weight density. This is the unit weight of the water in Force/Length 3 units. Other Parameters on the Wave Load Pattern Form Page 21 of 21