Fatigue

Ashes provides a workflow for automatically gathering relevant stress series during simulation, applying stress concentration factors, then performing rainflow counting on the resulting stress series. Finally, lookup in S-N curves is performed to arrive at the total fatigue damage and lifetime of each construction detail. This section will describe the workflow for performing fatigue analysis in your simulations.

1 Joints

In order to peform fatigue analysis, the model must specify a set of Joint definitions. A joint specifies which members (elements) are to be designated as chord and brace members.
Selecting Support structure | Support structure type | Tubular tower on truss tower will produce a truss tower with all joints created. To follow this workflow yourself, you can use such a model. Exporting the truss tower to file will give a file that contains Joint definitions, to use as a working example.

1.1 Geometrical definition of tubular joint

Geometrical definition of a tubular K joint, showing directions of forces, saddle and crown points and various dimensions.

1.2 Joint definitions in support section text file

Joint definitions are placed in the section titled Joints.
Joints
# Joint name   Chord elements  Brace elements
4-A    3&4    36&39
4-B    3&4    188&191
7-A    6&7    44&47
Example of joint definitions in support section file
A joint should only have braces that lie in the same plane. If there are multiple brace planes, one joint must be specified for each plane.

1.3 Selecting a Joint and viewing information

Joints are visualized in a blueish color covering the chord and brace members. To view its properties, you can right-click the joint.
Joint information window (for tubular on truss tower), accessed by right-clicking a Joint.

2 Stress calculations

2.1 Stress concentration factors (SCFs)

For fatigue computations, the nominal stresses (as seen in  Beam element sensor) are multiplied by factors which depend on the geometry and loading of the joint. Ashes uses formulas from the  DNV-RP-C203 recommended practice.

The following sectional stresses are assumed to be known:
  • $$\sigma_x$$
    : axial stress
  • $$\sigma_{my}$$
    : bending stress from the moment about the y-axis. This stress arises from the in-plane bending moment, i.e. the bending moment that produces displacements of the braces within the joint plane.
  • $$\sigma_{mz}$$
    : bending stress from the moment about the z-axis. This stress arises from the out-of-plane bending moment, i.e. the bending moment that produces displacements of the braces perpendicular to the joint plane.

The following SCFs modify the stresses depending on the loading mode:
  • $$\text{SCF}_{\text{AC}}$$
    : axial stress concentration factor at crown
  • $$\text{SCF}_{\text{AS}}$$
    : axial stress concentration factor at saddle
  • $$\text{SCF}_{\text{MIP}}$$
    : in-plane bending stress concentration factor
  • $$\text{SCF}_{\text{MOP}}$$
    : out-of-plane bending stress concentration factor

2.2 Hot spot stresses

Stresses are computed at 8 hot spots at the intersection between the braces and the chord. A superposition of axial stress and bending stress (in-plane and out-of-plane), each multiplied by the corresponding SCF gives the effective stress used for fatigue.
Hot spot stress points and directions of forces.

The fatigue sensor names stress points according to their angle, as shown in the table below.
Hot spotField name in fatigue sensor
1Stress pt0
2Stress pt45
3Stress pt90
4Stress pt135
5Stress pt180
6Stress pt225
7Stress pt270
8Stress pt315
Fatigue sensor field names for hot spots

The normal stress at each of the 8 hot spots is calculated as a superposition of axial and bending stress contributions, each weighted by the appropriate stress concentration factor. The 8 equally-spaced points around the circular cross-section (at 0°, 45°, 90°, 135°, 180°, 225°, 270°, and 315°) account for combined axial and bending loads, where \(\sigma_x\) is the axial stress, \(\sigma_{\text{my}}\) is the in-plane bending stress, and \(\sigma_{\text{mz}}\) is the out-of-plane bending stress:

(pt0°) $$\sigma_1 = \text{SCF}_{\text{AC}}\, \sigma_x + \text{SCF}_{\text{MIP}}\, \sigma_{\text{my}}$$
(pt45°) $$\sigma_2 = \tfrac{1}{2}\!\left(\text{SCF}_{\text{AC}} + \text{SCF}_{\text{AS}}\right)\sigma_x + \tfrac{\sqrt{2}}{2}\,\text{SCF}_{\text{MIP}}\,\sigma_{\text{my}} - \tfrac{\sqrt{2}}{2}\,\text{SCF}_{\text{MOP}}\,\sigma_{\text{mz}}$$
(pt90°) $$\sigma_3 = \text{SCF}_{\text{AS}}\, \sigma_x - \text{SCF}_{\text{MOP}}\, \sigma_{\text{mz}}$$
(pt135°) $$\sigma_4 = \tfrac{1}{2}\!\left(\text{SCF}_{\text{AC}} + \text{SCF}_{\text{AS}}\right)\sigma_x - \tfrac{\sqrt{2}}{2}\,\text{SCF}_{\text{MIP}}\,\sigma_{\text{my}} - \tfrac{\sqrt{2}}{2}\,\text{SCF}_{\text{MOP}}\,\sigma_{\text{mz}}$$
(pt180°) $$\sigma_5 = \text{SCF}_{\text{AC}}\, \sigma_x - \text{SCF}_{\text{MIP}}\, \sigma_{\text{my}}$$
(pt225°) $$\sigma_6 = \tfrac{1}{2}\!\left(\text{SCF}_{\text{AC}} + \text{SCF}_{\text{AS}}\right)\sigma_x - \tfrac{\sqrt{2}}{2}\,\text{SCF}_{\text{MIP}}\,\sigma_{\text{my}} + \tfrac{\sqrt{2}}{2}\,\text{SCF}_{\text{MOP}}\,\sigma_{\text{mz}}$$
(pt270°) $$\sigma_7 = \text{SCF}_{\text{AS}}\, \sigma_x + \text{SCF}_{\text{MOP}}\, \sigma_{\text{mz}}$$
(pt315°) $$\sigma_8 = \tfrac{1}{2}\!\left(\text{SCF}_{\text{AC}} + \text{SCF}_{\text{AS}}\right)\sigma_x + \tfrac{\sqrt{2}}{2}\,\text{SCF}_{\text{MIP}}\,\sigma_{\text{my}} + \tfrac{\sqrt{2}}{2}\,\text{SCF}_{\text{MOP}}\,\sigma_{\text{mz}}$$

Note that at the crown points (0° and 180°), only \(\text{SCF}_{\text{AC}}\) and \(\text{SCF}_{\text{MIP}}\) contribute, while at the saddle points (90° and 270°), only \(\text{SCF}_{\text{AS}}\) and \(\text{SCF}_{\text{MOP}}\) apply. At the intermediate 45°-increment points, both axial SCFs contribute with equal weight and the bending terms are scaled by \(\tfrac{\sqrt{2}}{2} \approx 0.707\).


Location of pt0: crown heel or crown toe

The location of pt0 in Ashes is always at either the crown heel or the crown toe, depending on the order of the nodes in which the brace element was defined in the text file:
  • If node 1 in the element definition is the joint node (i.e. the node at the intersection with the chord) and node 2 is the outer node, then pt0 will be at the crown heel and pt180 will be at the crown toe, as defined in DNV-RP-C203.
  • If node 1 is the outer node and node 2 is the joint node, the assignment is reversed: pt0 will be at the crown toe and pt180 will be at the crown heel.

As defined in DNV-RP-C203, compression produces a negative stress. In the figure below, the applied load produces a compressive in-plane bending moment at the crown heel (resulting in a negative stress at the corresponding stress point) and a tensile in-plane bending moment at the crown toe. This sign convention can be used to verify that the stress points are correctly defined in the model.



K joint with a force that produces compression at the crown heel


2.3 Classification of joints

Different SCF equations are used, depending on the classification of the joint. The classification of a joint (Y, K, X) depends on its geometry, but also on the actual loading of each brace. Ashes will automatically determine the classification of each brace every time step during simulation and apply the corresponding SCFs. For example, if a brace is determined to be 50 % Y and 50 % K, the effective SCF used will be 50 % * SCFY + 50 % * SCFK.
Example of a joint where one brace is classified as a mix of K and Y due to the actual loading.

3 S-N curves

Ashes comes with a set of S-N curves. This window is found by going to Preferences | Fatigue | S-N curves...

3.1 Assigning S-N curves to joints and sensors

Default S-N collection and category are set in Preferences | Fatigue. All joints and fatigue sensors will be set to use these defaults when they are added.

The S-N collection and category to be used for fatigue computations can be assigned individually to each joint or sensor. To assign a sensor, right-click the sensor, select Options and change the settings in the opened dialog.
Dialog for assigning S-N curve collection and category to a fatigue sensor

S-N curve and category can also be specified per joint when importing from file (not implemented yet)..

4 Workflow

A more detailed explanation of the workflow is given in the Theory Manual, in the  Fatigure analysis procedure document

4.1 Relevant settings and parameters

Analysis parameters | Analysis | Misc. | Fatigue calculations start time specifies at which simulation time fatigue calculations should start. Usually, initial transients should be excluded. To achieve this, set this parameter to e.g 30 seconds.

4.2 Workflow summary

  1. Define Joints. Specify each joint to be included in fatigue computations in the Joints section of the support section file, then import it (this is only required if you perform a fatigue analysis on a truss tower).
  2. Add sensors. Right-click each joint and click the Add sensor button. For joints, this will produce two sensors for each brace, one for stresses chordside and one for braceside. If you want to add a sensor for every joint, click  in the Sensors window and choose Add fatigue sensors to all Joints.
  3. Assign S-N curve and category. Each sensor will be assigned default S-N settings when they are added. To change these settings, right-click the sensor and choose Options. Default S-N settings can also be assigned per joint in the Joints section of the support section file.
  4. Run simulation(s). Run your simulations, either in Time simulation or in Batch. The fatigue sensors will collect stress ranges for each hot spot during simulation.
  5. View report. If you run in Time simulation, you can generate the fatigue report by clicking  in the Sensors window and checking the Generate fatigue report...option. If you run in batch, there will be report PDF file called Jointssummary.pdf placed in the results folder.