# Fatigue Life Equation



## loudog (Aug 26, 2015)

I'm working through the 2001 NCEES sample test right now, and question 503 for the Machine Design afternoon section says something like:

A specimen experiences a completely reversing bending stress of 15,000 psi and has an ultimate strength of 45,000 psi and endurance limit of 10,000 psi. How many cycles could it likely experience before failure?

The solution is attached. Does any one have a reference for where they got this equation? I would like to look into the theory behind the equation some more and fully understand what each parameter is, especially Sf.

I found a similar, but way more complicated, approach to the problem on page 170 of Ugural's _Advanced Strength and Applied Elasticity _but that's all I could find. Nothing in the MERM or Mark's, or Shigley (unless I'm missing something, which is surely possible).

Thanks for any help.

LP


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## denver1000 PE (Aug 26, 2015)

Hello. You must follow the logic used in example # 6-15 in shigley's instead of the ncees answer... the answer given assumes you've already simplified the equation to the form shown in there... the expanded form is on page 293 (10th version) of shigley and it will be around the same place in older editions as well.


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## loudog (Aug 26, 2015)

Thanks! With that help, and digging around some in my Shigley 6th edition, I found what I'm after, and what you're talking about, on page 372-373.

Finally good to go.

Thanks for the help.

LP


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## denver1000 PE (Aug 26, 2015)

No problem


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