Gerber & ASME Elliptic Fatigue Failure Criteria | Torsional Fatigue | First Cycle Yielding

LECTURE 24:
Here the Gerber and ASME Elliptic fatigue failure criteria are presented and discussed in light of experimental data. A problem is completed in which a torsion rod is used to provide spring force to a roller, which induces a fluctuating torque in the rod as the roller goes over bumps. This fluctuating torque is examined to determine midrange and alternating torsional stress components, including a torsional fatigue stress concentration factor. A fully corrected endurance limit is found by evaluating surface, size, loading, and reliability Marin factors. The factor of safety formulations given in Shigley for the Gerber and ASME Elliptic criteria are transformed to make them appropriate for shearing stresses and strengths, and these factors of safety are then computed. The factor of safety against first-cycle yielding is also computed. The load line and fatigue and yielding failure lines for this example problem are plotted on midrange-alternating stress axes and discussed with respect to potential for fatigue and yielding failure.
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This lecture was presented on February 7, 2018. All retainable rights are claimed by Michael Swanbom.
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I am a professor of ME and have recommended my students to watch your videos and given them this weblink. Great job. You are an excellent and dedicated professor. Thank you.

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Thank you so much for putting up these lecture you don't know the difference you are making....

[@TheBomPE]

It feels good to feel like I'm helping! All the best to you!

[@outrigr]

As a consulting engineer for many years and an adjunct professor in the ME department int the CSU system, I like the way you present your lectures. Everything is shown and the students are given example problems where they can see all the arithmetic.

[@TheBomPE]

Thanks for the positive feedback! Yes, I believe it helps the students to see all of the problem solving processes down to the nitty- gritty. Which CSU campus do you teach at? I grew up in Fresno (well, Clovis really) so I'm familiar with Fresno State. Also, what kind of consulting do you do typically?

[@outrigr]

My company is Applied Analysis & Technology, HB CA and for 15 years I also taught undergraduate & graduate classes as a part-time adjunct professor at CSULB. The consulting work is mostly aerospace, however recently we have been on a concrete cracking kick. The last project was degradation of concrete runways at LAX. For a long time I was a Beta tester for MSC Nastran, Marc and Femap/NX. I've written over 50 articles for the technical and trade magazines... mostly Machine Design & Desktop Engineering... I you Google my name "David R. Dearth MSC Concrete Cracking" or "David R. Dearth Machine Deign" or "MSC Applied Analysis and Technology " topics like FEA & concrete cracking might show up.. you might find some good material for your lectures.

[@oscarrincon7366]

Thanks for all your videos, profesor. They have been useful for me, I learned more about fatigue and my knowledge about this topic has increased thanks to you. My best wishes for people like you. Believe me when I say that they help too much.

[@TheBomPE]

Your gratitude sounds heartfelt, and that is moving. I'm very glad I could be a part of your learning journey. All the best to you in your life and career endeavors!

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Hello professor, Your video lectures are really helpful for me . Indeed, I have gained much more insight into machine elements design! Neat explanations! Thanks,

[@nave2n]

Great explanation :)

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Well Done TheBom_PE

[@TheBomPE]

Thank you! Thanks for watching!

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thank you!

[@TheBomPE]

you're welcome!

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Best in the game.

[@TheBomPE]

You are very kind! Thanks for spreading the word; I'm excited that my subscriber base continues to grow! All the best to you!

[@xgamer2011]

Thank you for helpimg me in my machine design class

[@xgamer2011]

helping

[@estoylopez]

Hi, thanks for your videos, they are helping me a lot in my project. Following this video, we have an example of stress concentrator in torsion with a shaft with difrent radios link each other with another radio. What would happen if we have a shaft with different radios tappered. So, with no radio tu use in the Kt table. In my case, my shaft has max radio of 100 mm and min of 80mm but they are link thogether in a link or tappered not by radios between them. How can I use the table with that radious values? Thanks

[@wangqiaozhang4827]

ohhh boi all the those knowledge

[@TheBomPE]

Haha, I hope it is helpful!

[@oneofyk]

Hello, thank you for this lecture. Helped a lot. Little unsure still though how you would calculate the slope of the load line. It is r= Sm/Sa, but unsure how to find those values.

[@gabewebb8936]

It’s your actual load that you’re applying

[@amirmohammadn.k5596]

Hello sir, thank you for your really great videos, they are very helpful and its so nice to see that you cover some real and interesting engineering cases with the examples you solve. There is something in this problem that I think maybe is not right, everything is okay until the moment that you are going to calculate factor of safety. As we see in this problem due to pre displacement we are going to have some constant pre static torsion stress in the torsion bar, so by this it means that our load line should not start from Taum=0,Taua=0 instead it should start from Taum=pre stress , Taua=0.(there is some same scenario used for bolts in page 438, figure8-20 of Shigley tenth edition) And if we use this new load line that I described above I guess the value of factor of safety is going to change. I will be so happy to know your idea about this case🙏🏻🙏🏻. Thank you very much

[@TheBomPE]

I will respond more fully soon, but let me say for now that whether or not you decide to move the origin of the load line is a matter of how you want to interpret the load line...which loading factors you assume are fixed versus variable. (This concept is probably worthy of its own video, actually.) Thanks for your patience, I'll respond more fully in some form or fashion soon.

[@amirmohammadn.k5596]

TheBom_PE Thank you 🙏🏻 I will be so happy to see your ideas about load lines in different cases, cause sometimes they get a little tricky, another case which had deferent load line was Example 6-11 on page 319 Shigley tenth edition. Which in that case the designer draw load line by changing the value of pre deflection. And it ends to have a horizontal load line. I’ll be so happy to watch your video about the main concept of load lines an how to draw them properly for deferent cases. Thank you very much🙏🏻🙏🏻

[@amirmohammadn.k5596]

TheBom_PE Hello sir, I was wondering if it’s possible for you open the concept of load lines, in such problems that the load line is drawn from a point that is no origin of our coordinate system. Such as in bolts fatigue procedure and also Example 6-11 on page 319 of the reference book. Actually its a bit mind bugling(specially Example 6-11) Thank you very much🙏🏻🙏🏻🙏🏻

[@dogansahutoglu2073]

Sir, in minute 12.32, does the question states that there is a displacement of 12 deg. when there is no conveyor in contact or we assume that so for solving the problem?

[@dominickdacosta8368]

So we can now substitute substrate foe a stronger material that Sut = 180 Kai and we would be good to go!

[@michaelswanbom6023]

If you found this video useful, consider helping me upgrade the old tablet PC I use to create these videos! Thanks! www.gofundme.com/help-replace-my-2011-tablet-pc

[@cyrusIIIII]

I still don't get the last part of the solution. If the component going to yield on first cycle, why do we even bother going to calculate all the fatigue stuff? Isn't yielding failure? Shouldn't it to be avoided?

[@TheBomPE]

Teaching is different than solving problems in practice. You are quite right that in practice I would likely check for yielding first and only after that looked ok would I check for infinite life. But since fatigue is the new thing being introduced to learners watching these videos, it is helpful to get right into the new topics, then to remind them at the end that first-cycle yielding (which is basically like a static failure they have previously dealt with) is still important too.

[@cyrusIIIII]

if the shaft is pre loaded 12 degrees, and then later it goes over one of those boxes, the direction of the twist will change. Shouldn't we consider minimum shear to be a negative stress?

[@TheBomPE]

The boxes cause even more twist the same direction as the preload twist, so it does not cause a direction change. All torsional stresses are in the same direction for this problem, they just go from one positive value to another positive value and back again.

[@MuhammadAhmad-yu9kv]

Sir this is my favourite subject and your lectures help a lot. I have a question i was solving a problem and by using elliptic approach i got diameter 2.77 and by using gerber i got 2.85 by using the same data for both but shouldn't it be like greater dia for asme elliptic than gerber for same loading and FOS condition.

[@TheBomPE]

Yes, ASME elliptic is more conservative than Gerber, so you'd expect that it would call for bigger dimensions on parts to achieve a similar FOS. You are certain you didn't make any errors in your solution process? Thanks for watching!

[@MuhammadAhmad-yu9kv]

@@TheBomPE yes actually i even checked the answers i am using the machine design book by norton and the answers were right but didn't make any sense Sir i asked my university teacher he said that it depends on midrange and alternating stresses that which theory from the above two will give more diameter but i am still confused

[@andrieslouw6588]

What about the region between Langer and Gerber where midrange stress is low. i.e. a load with high cyclic nature and low midrange stress. Would Langer still be accurate for those situations ? Because all criterions would give a factor of safety

[@TheBomPE]

In those situations it just means that there will be a non- infinite number of stress cycles before failure, even though the material never yielded macroscopically. Sorry it took me a while to get back to you!

[@andrieslouw6588]

@@TheBomPE Thank you, no problem.

[@ainguyen7350]

A rotating shaft is loaded with a bending moment of M=420N·m. The shaft transmits a steady torque of T=275N·m. Assume the shaft is machine from a material with Sut=510 MPa and Sy=390 MPa, and a fully corrected endurance limit of Se=191 MPa. Let Kf=2.0 and Kfs=1.8. With a design factor of 2.5 determine the minimum acceptable diameter of the shaft using the MSS-Gerber criterion. can you help me to solve this problem or at least give me a fomular

[@bishaldas4370]

why you are not modifying the Sut for a temperature other than room temperature ....in case of Se it get adjusted but using Sut in other places of equation is not adjusted whee we have to use it directly?

[@wangqiaozhang4827]

Question: what is the advantage of using Gerber, ASME fatigue failure criteria comparing to s-N curve, feel like S-N curve is a lot easier, if i know the stress I can get the life circle immediately

[@wangqiaozhang4827]

soo S-N curve is only for fully reversed stress situation right?

[@TheBomPE]

@@wangqiaozhang4827 correct. It looks like you answered your own question :)