I have taken up this topic to explain the fatigue analysis (

**Click here to read the basic article on Fatigue Analysis**) methodology using caesar II with an example problem of a typical piping system. To perform fatigue analysis we need to calculate the thermal and pressure fluctuations the piping system will undergo in its design life. We have to calculate the worst possible cycles from preliminary data provided by process/operation department. Lets assume we received the following data from process for a typical piping system.- Operating cycle from ambient (40°C) to 425°C (400,000 cycles anticipated)
- Shutdown external temperature variation from ambient (40°C) to -20°C (300,000 cycles anticipated)
- Pressurization to 5.5 Bars (400,000 cycles anticipated)
- Pressure fluctuations of plus/minus 1.5 Bars from the 5.5 Bars (1,000,000 cycles anticipated)

Now, in order to do a proper fatigue analysis, these should be grouped in sets of load pairs which represent the worst-case combination of stress ranges between extreme states which we can do in the following way (Refer Attached Figure, Fig.1 for proper understanding):

**Fig. 1: Explanation of worst case cycle combination for fatigue analysis**

- From -20°C, 0 Bars to 425°C, 7 Bars. 300,000 Cycles
- From 40°C, 0 Bars to 425°C, 7 Bars.: 100,000 Cycles
- From 425°C, 4 Bars to 425°C, 7 Bars: 600,000 Cycles
- From 425°C, 4 Bars to 425°C, 5.5 Bars: 400,000 Cycles

So in Caesar II we can define the above data as follows (Refer Fig. 2):

**T1= 425°C;**

**T2= -20°C**

**P1= 5.5 Bar;**

**P2= 4 Bar and**

**P3= 7 Bar**

**Fig.2: Caesar II spreadsheet explaining the input requirement**

Now go to the load case editor and define load cases as shown in Fig.3 for fatigue analysis.

Click on load cycles button to input the number of cycles calculated above.

**Fig.3: Load cases for Fatigue Analysis**

Don’t forget that all load cases with stress type FAT (for fatigue) must have their expected number of Load Cycles specified.

After load cases are prepared run the analysis and find out the results from output processor. Part of the output results are provided in the below attached figures for your reference (Fig. 4 and Fig. 5)

The fatigue stress range (Maximum Stress Intensity as calculated in Expansion stress case) may be checked against the fatigue curve allowable for each fatigue load case as shown in Fig 4.

**Fig 4: Output Screen showing stress range**

However, this is not a true evaluation of the situation, because it is not a case of “either-or.” The piping system is subjected to all of these load cases throughout its expected design life, not just one of them. Therefore, we must review the Cumulative Usage report, which shows the total effect of all fatigue load cases (or any combination selected by the user) on the design life of the system. Refer Fig 5 for example.

**Fig. 5: Output Screen showing Cumulative usage factor**

This report lists for each load case the expected number of cycles, the allowable number of cycles (based upon the calculated stress), and the Usage Ratio (actual cycles divided by allowable cycles). The Usage Ratios are then summed for all selected load cases; if this sum exceeds 1.0, the system has exceeded its fatigue capabilities.

**Please provide your inputs in comments section.**

Terrific article! That is the typpe of information that are meant to

be shared across the internet.

Dear sir

as per your example pressure variation you have taken From 425°C, 4 Bars to 425°C, 7 Bars: 600,000 Cycles

i think you it should be 1000,000 and other pressure case need not to be take care.

Dear PANKAJ. 6000 cycles that is correct

Your Figure 5 is not a Cumulative Usage Report.

Could anyone please explain the following conditions. I am confused with cycles for each condition.

From -20°C, 0 Bars to 425°C, 7 Bars. 300,000 Cycles

From 40°C, 0 Bars to 425°C, 7 Bars.: 100,000 Cycles

From 425°C, 4 Bars to 425°C, 7 Bars: 600,000 Cycles

From 425°C, 4 Bars to 425°C, 5.5 Bars: 400,000 Cycles