Understanding the Area Moment of Inertia
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- เผยแพร่เมื่อ 13 เม.ย. 2020
- The area moment of inertia (also called the second moment of area) defines the resistance of a cross-section to bending, due to the shape of the cross-section. It is a key parameter for the analysis of beams and columns.
In this video I take a detailed look at the area moment of inertia, how's it calculated, and how it's used. I also cover key related topics, including the polar moment of inertia, the parallel axis theorem and Mohr's circle for moments of inertia.
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The Efficient Engineer is a channel aimed at mechanical and civil engineers. The mission is to simplify engineering concepts, one video at a time!
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Why square of distance?
Why we multiply dA with sqaure of distance?
What is the physical meaning of square of distance here ?
If we do not take squared distance, some integrals give out zero. This is practically not possible ie it cannot have zero resistance to bending.
@@shashankmohan8422 Hmm that makes sense. But then, can we say that any even power of the distance will be ok 2, 4 or 6?
dA's contribution to the bending moment about the neutral axis is the tensile stress on dA times the distance between dA and the neutral axis. The tensile stress equals Young's modulus times the tensile strain. For limited curvature, so when no plastic deformation takes place, the strain at dA is linearly proportional to the distance to the neutral axis. So in the contribution to the bending moment the distance has a squared influence, one time as the "length of the lever" and one time because the local strain in bending is linearly dependent on it.
Excellent explanation, thank you Jaap. I should have mentioned this in the video. I will pin this comment to the top.
@@jamjamme nice sir.
Anybody can understand engineering, all it takes is a good teacher!
@allen thompson Honesty you spoke my mind
@allen thompson similar feeling mate
@allen Thompson honestly I feel so grateful for having a good engineering professor. He always focused on making sure you understood the subject intuitively and the effects it would have in the real physical world, then he would introduce the math. Even then he would still say this " remember these math equations are simply an attempt to model the real world, remember to do external testing to make sure everything goes a planned".
@@ipodtouch470 I did have a lecturer like that too in my final year, but he was only one lecturer(may be another one too) out of all the lecturers I came across- the odds suck.
@allen Thompson That's because most professors never worked in the "real world" they most probably spent all their life in school deriving equations to earn their PhD's and therefore can never trace any engineering concept to real world application and tend to focus on the derivation and math. It's so frustrating and honestly they make a lot of students lose interest in the first year itself.
Even though I graduated with a bachelor's in MechE I felt like we were always rushing to cover material that I never developed the intuition on this topic. Thank you for filling in that I-beam hole!
yes. most professors worry more about rushing through to finish talking about all required subject in the big book instead of actually making sure students are getting it or not.
Yeah. University has in my opinion too high a pace.
If we had a few less useless filler courses we'd have time to actually focus on stuff important to an engineer like this.
In most cases in uni, you see an equation once and are expected to understand it completely and be able to adapt it to any situation. Without anyone ever explaining why the equation is what it is. Heck, half the time they don't even tell you what the variables are.
You could say, you're being told what you need to go learn for yourself. Instead of being directly taught the subject.
the fact that i spent four hours pulling my hair out over this at uni and gave up for the day, and in 11 minutes i now feel like i understand. all i can say is thank you!
This man is the 3Blue1Brown of engineering concepts. The clear and concise explanations, coupled with excellent animations makes me remember why engineering is so great!
Oh yes!!
What is 3 blue 1 brown mate
he's a mathematics youtuber@@Raju-jb3sk
I feel so bad for giving so much money to college and none for you :(
Haha, well if you want a clear conscience you can always support the channel on Patreon! www.patreon.com/efficientengineer. Glad you like the videos in any case!
@@TheEfficientEngineer you should prolly start an intitute or smthin!!
Or maybe you can advertise your content nd editing skills to colleges.
Both the world and you can greatly benifit from your works!
Same thoughts on myside too!!
the colleges really be scamming us at this point
Only someone who truly understands a subject can explain it in simple terms, and I believe you are one of those people. Thank you.
In my lifetime I have never seen such a good illustration for teaching engineering subjects. Amazing job. Please keep posting more videos. I personally love it so much. Many thanks! 👍✨
Properties of Plane areas
th-cam.com/video/GjPpLVDV6tc/w-d-xo.html
The result of combining engineering, arts, esthetics, didactics, 3D modeling, rendering, virtual animation and video editing... Something this good engineer understood and took the time to develop it...
This is how Engg should be taught
so true
You are right
Yeah. In 10 minutes this guy explained better than a lot of people fails trying to explain in hours. I get everything, and I dont even speak english
Yaa that is how Engineering because they don't care about the question""WHY?""
Just wow!!!
Thank you for providing such clear explanations of engineering topics. The comments are right: THIS IS HOW ENGINEERING SHOULD BE TAUGHT! I've had 3 hours of lectures and read 2 textbooks on this topic and I didn't really understand it until I watched your 11-minute video. The same is true for your videos on Shear Force & Bending Moments and Understanding & Analyzing Trusses. These are clear, concise, and understandable. Just in time for summer finals, too! Honestly, thank you!
Glad you enjoyed the videos Ryan! Good luck with the finals!
there is a saying of Albert Einstein that says ''if you cant explain it simply u dont understand it well enough'' I hope u can understand why Teachers get hard time to explain sth very simple like these. Thanks for this video, I now understand things that I learnt 2 years ago just within some minutes with simply explanations.
Yup. Too true. Either that or they're extremely smart -- since people like those never struggle, and never had a need to break down things any further. But still, anyone should be able to give a direct, concise explanation. They're the best! because there's no room to hide in just the details you're most familiar with.
4 years of structural analysis for a Civil Engineering degree, and this is the first time I actually understand area moment of inertia. :)
I don't think I could've found a better online teacher for Mechanical subjects than you! The material you have provided is simply amazing, thank you very much! :)
ENG + Graphic Design = OutOfThisWorldLearning
11 min video > 2 hour lecture.
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Being a student of IIT G and going through a rigorous ME course ,your videos helped me develop a practical sense to these things
Back in the day while taking my electrical engineering core courses we were required to take things like statics and dynamics. It's really too bad that my professors didn't provide such basic instructions and insight. I may not have taken so long to figure out what on earth they were talking about! Keep up the good work.
Love these concept. Even after engineering don't know exactly the real story and logic behind these concept. Thank you so much ❤️💖
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I've been wanting to understand this topic for quite some time now but no video came close to the visuals and explanations such as this one! At first, I was confused about the importance of the area moment of inertia and the meaning of the the radius of gyration (since no videos had great explanations about the topic) but after watching your video, it makes it easy to understand! Thank you! I highly recommend this to anyone wanting to understand the topic!
I am truly deeply greatly thankful to you for making these videos & channel. All of my concepts, understandings & most importantly my reasons of studies & using formulae have been getting cleared. Really A true teacher is what we needs.
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The result of combining engineering, mathematics, arts, esthetics, composition, color theory, didactics, 3D modeling, rendering, virtual animation and video editing... Something this good engineer understood and took the time to develop it... Cheers from an architecture student!!
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Like I said before this channel is the GOAT (greatest of all time) when it comes to engineering tutorials, and gives me inspiration everyday. The graphics really help in getting the concept. Maybe you can do a video concerning steps for designing a beam using ACI code
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You are the engineering equivalent to 3blue1brown. These videos are phenomenal and definitely saved me (as well as many other viewers) many hours of trying to understand this material.
Formulas:
2:46 Area Moment of inertia
5:00 Parallel axis theorem
7:20 Area MOI vs Mass MOI
9:34 Perpendicular Axis Theorem
10:13 Rotation of Reference Axis
This guy is the 3blue1brown of mechanical engineering. Words can't express how much appreciation I have for these videos.
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dear sir , your presentation and explanation were really awesome, this is what exactly students are expecting from you
i request you to please make a video on thick cylinders by showing the variation of pressure, hoop stresses . from inside to outside as well as from of side to inside.
take cases of both external pressure and internal pressure
i hope you will be making video on thick cylinder also..
My confusion with different MOI's is now settled, never cracked this in my undergraduate days. I wish I can support you more. Thank you very much!
इस वीडियो लेक्चर को जो भी बना रहा है, वो बहुत ही बढ़िया तरीके से समझा रहा है, इन लोगों से हमारी सरकारों को सीखना चाहिए कि कैसे पढ़ाना चाहिए। दिल से शुक्रिया आपका सर जी।
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Keep doing what you do !
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Preparing for an exam and you just summarized a whole topic in 11mins ...Thank you ❤
Great animation. Before, I did not really understand about its real concept, and just memorized the formula. It really helps me to understand about moment of inertial visually. Thanks from Korea.
Legit this should be shown to everybody that tackles the centroid and moment of inertia lessons of the statics course! I just now learned that seeing an animation or understanding conceptually and intuitively is important before you even try to use the formulas in the text books. Or maybe im just not able to visualize how tf will there be a moment in a cross section. But this video taught me that, i cant thank u enought
Moment of Inertia has always been my loophole in Mechanical Engineering. Thanks a lot.
Properties of Plane areas
th-cam.com/video/GjPpLVDV6tc/w-d-xo.html
Which kind of moment of inertia? The kind with units of meters^4 that has nothing to do with inertia, or the kind with units of kg-meters^2, whose name actually makes sense for what it means?
@@carultch inertia means resistance to change, in this case bending. we also have thermal inertia
My respect for this channel increasing exponentially for every video...thanks for the beautiful explanation and animation...pls do more videos
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This explains an hour-long lecture in 11 minutes, and clearly. Thank you!
Properties of Plane areas
th-cam.com/video/GjPpLVDV6tc/w-d-xo.html
Literally covered all the portion of this concept....😇really love ur videos....keep going....
Man, thanks for making this kind of videos, it helps a lot. This year in my college the Static and Material´s Resistance´s teacher say he can't go to classes cause of covid and the only work he does is to send a mail telling us what to study from a book whose author is he. He doesn't explain anything and his book is terrible. Thank you man because you are saving a lot of students who make their best effort but some teachers seem to hate teaching.
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Finally, I have understood intuitively the meaning of radius of gyration. Thank you for the great video.
the best explanation have ever seen yet for moment of inertia
Never understood this in college so just memorized the formulas but this video helped me understand it very well. Makes a lot of sense! Thank you!
Thank you for uploading in these hard times
It's like you took everything out of Chapter 10 of Russell C. Hibbeler's textbook and actually explained what the hell it meant 😂 Thank you so much for this!
Russell is real engineer
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This video makes it very easy to understand the principles of inertia. Especially with the diagrams that show how bend ability goes into the moment area of inertia.
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I've learned these contents and I'm learning again.
I am glad that it will be of great help in learning in the future.
Super helpful!!! Also, love the background music. The beat drops as my mind is getting blown
Another great video. THANK YOU. I am sharing these with my students. I look forward to your video on bending.
With everything done with computers for thirty years, or more. It’s nice to have your lectures for a refresher!
Properties of Plane areas
th-cam.com/video/GjPpLVDV6tc/w-d-xo.html
Your videos are amazing and essential for engineering education. Please don't stop making more.
Smooth and flawless explanation.
Awesome explanation of moment of inertia using mohr circle
This is the Best Video I've ever seen about Area Moment of Inertia. This is the Best explanation ever!! Congratulations, greetings from Perú 😎
Why cant we have a teacher like you! Incredibile work
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Properties of Plane areas
th-cam.com/video/GjPpLVDV6tc/w-d-xo.html
Amazing! I've been struggling with the basics. Thank you.
the blessing to mankind (Civil and Mechanical Engineers)..God bless you man
This video is amazing and very clear! Thanks for your labor.
Wow best illuustration of Moment of Inertia. Mechanics should be taught this way right for every beginners.! Thanks
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This the best lecture on MOI on you tube. Thankyou sir
Amazing explanation
Couldn't have understood it properly without you
Thanks a lot