Fatigue is a particularly complex topic, as there are several components to consider:

- The SN curve, which defines the number of cycles of a given maximum (hot spot) stress the material can withstand without breaking,
- The Stress Concentration Factors (SCF) which define maximum stresses in terms of the nominal ones, and
- The duration which defines lifetime history of the environment to which the structure has been exposed.

Normally the result of interest is a Cumulative Damage Ratio (CDR). This is simply a sum of ratio of the fraction of the life used for all stress ranges. Sometimes, however, one wishes to view the loading history independently of the SN curve. Thus, MOSES has the capability for counting either load cycles or stress cycles sorted into bins. One can compute fatigue (or cycles) for BEAMs, PLATES, tubular JOINTs and mooring lines and the details will vary with type. In general, one can compute fatigue in either the time or frequency domains.

One is really interested in fatigue at all points in an element, but in reality we only consider it at a set of "fatigue points": the ends, at points along a beam where the section changes, or at welds. Generalized plates are special in that fatigue is computed at the centroid of each subelement.. To really complicate these matters, some fatigue points have automatic methods to compute stress concentration factor and others do not. In particular, MOSES has automated methods for computing stress concentration factors for: tubular connections, tube/cone connections, and tubular joints. Stress concentration factors must be manually associated with all other fatigue points.

In MOSES there are two ways to compute fatigue damage, on an element by element basis, or on a tubular joint basis. The reason for the two methods is that for tubular joints, there is a body of knowledge for automatically computing the SCFs and the associated hot spot stresses. For non tubular joints, the information is much less extensive. Thus, for tubular members, one can do joint fatigue to capture the damage at the ends, but one must do element (beam or generalized plate) fatigue to get CDRs at intermediate locations. Also, element fatigue must be used to get the CDRs at the ends elements which are not part of tubular joints.

As with stress concentration factors, an SN curve must be associated with each fatigue point. Again, tubular joints are special in that one normally has only two choices for SN for a tubular joint and the association of SN is different for doing JOINT fatigue than it is for doing BEAM fatigue.

The definition of the environmental history depends on whether a time domain or a frequency domain simulation is being used. For frequency domain, a set of RAOs are computed and they are used along with a scatter diagram of environments which act for a specified time. In the time domain, one time domain simulation is performed per process. Load cases are defined at a reasonable number of times during this simulation and the system solved for the time traces of the stresses. A Rainflow Counting technique as outlined in ASTM E-1049, "Standard Practices for Cycle Counting in Fatigue Analysis" is then used to compute the stress cycles and perhaps the cumulative damage. These results are "scaled" by the ratio of duration time to simulation time. The results are summed over the selected durations, so one can compute fatigue in both domains and over all lifetime situations.

If a duration environment is defined with more than one spectrum then MOSES provides two ways to compute the "average period". The choice is governed with the **-T_AVERAGE** option of the **&PARAMETER** command.

In the following we specifically discuss the role of the **&REP_SELECT** command, but any of the options discussed for this command can be issued on the option which
requests fatigue or cycle information. In other words:

&REP_SELECT -SN X JOINT_POST FATIGUE

produces the same result as

JOINT_POST FATIGUE -SN X

The same can be said of the **BEAM_POST** or **PLATE_POST** commands.