1.3. REFERENCES 7
Model #6: Multiple distributed stress amplitudes of cyclic loading levels with multiple given
cycle numbers.
Model #6 is also a common cyclic loading spectrum and can be used to describe many loading
conditions for the machines, the service of which are pre-scheduled. For example, the cyclic
loading spectrum of the component under design is:
Cyclic stress level 1 W n
L1
D 260;000 .cycles/I
a1
D N
.
20;000; 1890
/
Cyclic stress level 2 W n
L2
D 5000 .cycles/I ln
.
a2
/
D N.3:25; 0:108/:
Any cyclic loading for fatigue design can be described by one of the above six fatigue cyclic
loading spectrum models. us, they are a systematic description of cyclic loading spectrum.
1.3 REFERENCES
[1] Le, Xiaobin, Reliability-Based Mechanical Design, Volume 1: Component under Static Load,
Morgan & Claypool Publishers, San Rafael, CA, 2019. 1, 3
[2] Le, Xiaobin, e reliability calculation of components under any cyclic fatigue loading
spectrum, ASME International Mechanical Engineering Congress and Exposition, IMECE–
70084, Tampa, FL, November 3–9, 2017. DOI: 10.1115/imece2017-70084. 5
1.4 EXERCISES
1.1. Cyclic stress has a maximum stress
max
D 60:25 (ksi) and a minimum stress
min
D
9:32 (ksi). Calculate its mean stress, stress amplitude, and stress ratio.
1.2. Cyclic stress has a constant mean
m
D 15:72 (ksi) and a stress amplitude
a
D
25:39 (ksi). Calculate its maximum stress and the minimum stress of this cyclic stress.
1.3. What is cyclic loading spectrum? Describe one example.
1.4. What causes cyclic stress? Use two examples to explain the lists.
1.5. Describe an example in which model #1 cyclic loading spectrum can be used to describe
its cyclic stress.
1.6. Describe an example in which model #2 cyclic loading spectrum can be used to describe
its cyclic stress.
1.7. Describe an example in which model #3 cyclic loading spectrum can be used to describe
its cyclic stress.
1.8. Describe an example in which model #4 cyclic loading spectrum can be used to describe
its cyclic stress.
8 1. INTRODUCTION AND CYCLIC LOADING SPECTRUM
1.9. Describe an example in which model #5 cyclic loading spectrum can be used to describe
its cyclic stress.
1.10. Describe an example in which model #6 cyclic loading spectrum can be used to describe
its cyclic stress.
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