# Allowable Stress

Hi,

There are tons of equations out there to determine the stresses in a material due to forces/torques etc. My problem is, I never know how much stress is allowed! I understand that different applications require different factors of safety, but I never really know what factor to use.

Maybe an example will illustrate my point:
I need to design a shaft to transmit torque. Lets say I want to use steel (Yield 220MPa, UTS 341MPa). I can vary the diameter to set the amount of stress the component will see. If I want the shaft to last 20 years, and it isn't a safety critical component, what nominal stress should I design it for? 50Mpa, 100MPa...?

Cheers!

## Answers and Replies

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Mech_Engineer
Gold Member
Hi,

There are tons of equations out there to determine the stresses in a material due to forces/torques etc. My problem is, I never know how much stress is allowed! I understand that different applications require different factors of safety, but I never really know what factor to use.

Maybe an example will illustrate my point:
I need to design a shaft to transmit torque. Lets say I want to use steel (Yield 220MPa, UTS 341MPa). I can vary the diameter to set the amount of stress the component will see. If I want the shaft to last 20 years, and it isn't a safety critical component, what nominal stress should I design it for? 50Mpa, 100MPa...?

Cheers!

This would be a fatigue problem, and as such you should study an S-N graph for the particular steel you are interested in. Based on the number of cycles you expect the shaft to see, you can decide exactly how much stress the material can take. The graph will basically have a logarithmically increasing number of cycles on the x-axis, and stress on the y-axis.

Additionally, the material's "fatigue strength" is defined as the amount of stress a material can take for an infinite number of cycles. Most steels have a defined fatigue strength, but many materials do not. You should also add in a safety factor to help account for surface defects and material inconsistencies. Perhaps 80-90% of the material's fatigue strength would be a good place to start for a non-safety related item as long as you know exactly what the material you're dealing with is.

Mech_Engineer
Gold Member
Some links for you:

http://en.wikipedia.org/wiki/Fatigue_%28material%29" [Broken]

http://en.wikipedia.org/wiki/Fatigue_strength" [Broken]

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That's a superb answer thanks!

Okay, so continuing my shaft example:

So I assume 1 cycle = shaft is stopped, shaft rotates, continues at x rpm for x amount of time then stops again.

So, my Steel (Yield 220MPa, UTS 341MPa) which has a Fatigue Strength of about 125MPa can safely run 10^5 cycles with a peak stress of 100MPa (80% of 125) each cycle?

Mech_Engineer
Gold Member
That's a superb answer thanks!

Okay, so continuing my shaft example:

So I assume 1 cycle = shaft is stopped, shaft rotates, continues at x rpm for x amount of time then stops again.

So, my Steel (Yield 220MPa, UTS 341MPa) which has a Fatigue Strength of about 125MPa can safely run 10^5 cycles with a peak stress of 100MPa (80% of 125) each cycle?
If your material has a fatigue strength of 125MPa, and you will be seeing about 80% of that, your shaft can tolerate that stress indefinitely (e.g. a very long time).

Great stuff, I feel we're on a bit of a roll here...

I understand it's pretty rare to get an instance when fatigue doesn't come into play, because most things go through some sort of stress cycle but what if cycles were expected to be <10,000, and rarely at high stresses? I was reading on the wiki link that typical values for fatigue strength in steels are 0.5 UTS, so could I use that as a general rule of thumb for bog-standard designs that aren't safety critical?

More importantly, there must be a thought process/procedure engineers go through to determine what level of stress they will design something to operate in nominal conditions, OR a reference on factors of safety?

I'd be very interested to find out more about this, because often, you know the material you want to use, because of the wear properties, chemical stability, heat properties or how pretty the colours are etc. but not how to size it! Materials are getting more expensive and if there are ways I can reduce that cost and still be safe, by going down to the next diameter steel or something, then I'd really like to know how.
Cheers!

Mech_Engineer
Gold Member
I understand it's pretty rare to get an instance when fatigue doesn't come into play because most things go through some sort of stress cycle...
Not at all, it all depends on the application. In my line of work, I very rarely have a design that requires fatigue anlysis. For "static" applications, I usually try keep things at about 50-75% of the material's yield strength (if not far less) just to be safe. For designs where every gram counts, I might go right up to the yield strength of the material; but this depends heavily on application and intended use, plus consequences if it fails... and of course deflection comes into play also. It could be you are not in a stress-limited application but rather a deflection limited application, where limiting deflection means stresses are negligeble.

Of course there are also applications where trying to minimize material is cost-prohibitive, as in it's easier to do two machining operations and call it good since you don't really care about weight much. It is VERY common for us to make our products out of Aluminum 6061 however. It's cheap, easy to machine, strong for its weight, and lots of suppliers have it readily available. "Default" designs for me will default on Al 6061, and when I need more strength, hardness, or other properties, then I may consider a stainless steel or perhaps brasses or ceramics.

...but what if cycles were expected to be <10,000, and rarely at high stresses? I was reading on the wiki link that typical values for fatigue strength in steels are 0.5 UTS, so could I use that as a general rule of thumb for bog-standard designs that aren't safety critical?
It's better to design based on the material's yield strength, so that if it does deflect, it will at least return to its previous shape. Ultimate strength should only be used for predicting failure modes (e.g. it will probably break here first), rather than a design parameter for stress analysis IMO.

More importantly, there must be a thought process/procedure engineers go through to determine what level of stress they will design something to operate in nominal conditions, OR a reference on factors of safety?
Depending on application of course, I would say that Yield Strength and Fatigue Strength are the two most commonly used material stress properties used in my line of work. Safety factors are largely a personal preference for my field, but safety-related applications like in Aerospace or Automotive will even have minimum safety factors called out I think.

I'd be very interested to find out more about this, because often, you know the material you want to use, because of the wear properties, chemical stability, heat properties or how pretty the colours are etc. but not how to size it! Materials are getting more expensive and if there are ways I can reduce that cost and still be safe, by going down to the next diameter steel or something, then I'd really like to know how.
Cheers!
This is a mechanical engineer's bread and butter- designing parts and sizing components based on expected loads and cycles. Bolts, shafts, beams, etc. are all sized using basic stress analysis and deciding how big is "big enough."

If you're interested in learning more, you could buy a few textbooks on the topics of https://www.amazon.com/dp/0534553974/?tag=pfamazon01-20&tag=pfamazon01-20 is a staple book for any mechanical engineer looking for quick answers to stresses in simple (or not-so-simple) geometries.

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Hey thats great cheers!

Was hoping this thread would get you up to 500 posts, but im outta questions, you keep smackin' them out the park!