First and Second Moment of Area - Brain Waves

Here's a description of first and second moments of area along with some sample calculations. First moment of area is used to find centroid location and second moment of area is also called the area moment of inertia.

[@charlesrockson8095]

First moment of area is commonly used to determine the centroid of an area. The second moment of area is a measure of the 'efficiency' of a shape to resist bending caused by loading. A beam tends to change its shape when loaded. The second moment of area is a measure of a shape's resistance to change.

[@michaelacheampong2869]

Thanks you sir

[@LusidDreaming]

Great explanation. I would only add that the resistance mentioned can also be generalized to any sort of angular "movement" and is therefore also used when describing angular inertia (the resistance of a body to rotation about a particular axis).

[@smarakpradhan1304]

thanks bro

[@paulatreides4574]

Good explanation. To build off of your comment, the first moment of area (often denoted by Q) is the trait of area (not mass) rotating (moment) about a given axis - whether the x-axis, or y-axis - in which case fall into the centroidal x or y axes. This is reflected in the fact that there is a mathematical means to calculating Qx & Qy. If anyone is interested in knowing more about this, Dr. Mohammad Izadi's statics lecture(s) (CPPMechEngTutorials) is an excellent resource for actually gaining a deeper intuition of what Q is.

[@ningteris6018]

I like this lecture, you give a clear explanation about these concepts, thanks.

[@Virtualexist]

He is the kind of teacher, who takes care of anxious students of his class. So humble and equally knowledgeable.

[@jacobstokes8178]

you are single-handedly saving my gpa. Thank you so much. You're just so good at making something really abstract and complex make sense

[@BaconBandage]

Thats what separates someone who knows what they are talking about from those who really have no clue.

[@Freakybananayo]

10:42 "so even though that looks familiar, you don't need to freak out on me, ok? It's alright." absolute legend haha

[@9090Glenn]

finally - someone who knows wth they are talking about - the abuse of terminology on this topic is incredible - start here and you will not go wrong - avoid everything else being taught by "experts"

[@Structural_analysis]

Properties of Plane areas kzbin.info/www/bejne/fZuzoX-MebtpqsU

[@ryanpickart2111]

Thank you so much. My professor explained this so strangely, complexly, and ambiguously that I didn't get it at all, even though I've already done this in my mathematics classes but with much more complex problems. This really helped!

[@LifeofanElectronicEngineer]

If you're able to teach an electronic engineer a mech engineering concept, you must be a genius! Thank you!

[@Structural_analysis]

Properties of Plane areas kzbin.info/www/bejne/fZuzoX-MebtpqsU

[@LusidDreaming]

Great video! It's comforting to know I'm not alone in always having to squeeze in my constants after almost forgetting them.

[@rogersowden2369]

Really good delivery and explanation, its so good to see a teacher that can cut through stupid terms and explain things at the fundamental level. Keep up the good work!

[@sreeteja8728]

Thank you "SIR" you are so precise & understandable and understanding Professor ever !

[@BoZhaoengineering]

I like your way that uses the double integral to represent the area. This makes a lot of sense after learning the double integral. I wish my professor could have figured out this way of teaching the static moment of an area and the second order moment of an area.

[@guitarttimman]

Do you remember Professor Lordan? He was an awesome human being and an extraordinary mathematician. He is missed.

[@afsarabushra1769]

PurdueMET: "I've got a giant piece of wood here" Me, a 2nd year uni student: *cackles like a 6th grader*

[@purdueMET]

Heh. I would have, too.

[@afsarabushra1769]

@@purdueMET btw I love the way you explain things! Do you mind making videos solving some complex questions related to this topic and the theorems of pappus guldinus?

[@Farid_YGM]

3:14 but what about the 100? Couldnt we just use that as our upper limit?

[@kuienchou]

Hello I’m a student from Taiwan. The video teaches me a lot. Thank you professor.

[@d7ooom998]

Are you an engineer now? Or you still studying

[@TraceurArok]

Great video. I've been doing engineering two years and it's nice to know how this concept came about.

[@marceloalejandroroldancruz5821]

Hi I saw you are a new youtuber here..and you just got a subscriber.. i can see you will produce great material.. greetings from Guatemala and thanks!

[@raghwendrapratap6050]

Great thanku.. i like your attitude and way of teaching and delivering concepts.. why' I ' don't know there are 26 letters just pick one.. lol

[@purdueMET]

Thank you :-)

[@jeffbeltramo9836]

Hi Mark, fellow Engineering Technology professor here. I love your videos and definitely try to channel some of your vibe when explaining things. When it comes to 2nd moment of area, in addition to stiffness, I tell my students it describes how the area is distributed around the centroid...large I, lots of material away from the centroid. First moment of area (aka statical moment) is used in calculating vertical shear in a beam. What I have always struggled is providing a physical feel for first moments, similar to what I can do with 2nd moments. As engineering technology students, I try to avoid getting into the weeds of deriving vertical shear stress and show them where the first moment shows up. Do you have a good physical explanation of what the first moment represents? I love to hear it if you do.

[@makaylalawrence9085]

This video was super clear and very useful! Thank you so much.

[@ravipratap5811]

Best teacher in world

[@neilpetroff6758]

Hi Mark, greetings from Texas! Thanks again for all the great videos. I tell all my students about them. The history is so fascinating - how did someone figure out the second moment of area had a practical application? Regarding the use of the letter 'I' for (area) moment of interia, James Boyd's "Strength of Materials" book, published in 1911, uses I for the moment of inertia. So, it goes back at least that far!

[@purdueMET]

Just getting back to some older comments. Thanks very much for the kind words and for the info on the 1911 reference.

[@Jam555s]

Thanks again Mark, keep em coming

[@rinzler5703]

i have an exam tomorrow, ur a life saver

[@michaelbuchan203]

Can you please explain why the double integral of dxdy equals the area? I don't see it and curious as to why.

[@anniewesolek2893]

Thank you so much!! this helped to explain a lot of the simplified formulas we've been using in machine design.

[@aniketsaw6049]

Hey mam can you please suggest me the standard book for machine design ?

[@Structural_analysis]

Properties of Plane areas kzbin.info/www/bejne/fZuzoX-MebtpqsU

[@YouGotTheCob]

u r literally a god

[@purdueMET]

Dang, busted...

[@sumrz2655]

very nice video, .. with all the details i was looking for :). Thanks a lot. and Please kindly continue what you are doing

[@vikasbarhela3593]

cleared my doubt .you are straight forward. i like it. thank you

[@abdulahadkhattak7121]

Wonderful explanation Sir, but Sir the unit of Area is cubic square. While you have used cubic meter

[@ytlad5879]

At 3:31 could we just put the outer limit from 0 to 50 in place of 2*( 0 to 25)?

[@shubhangbhargava682]

No, that would be wrong.

[@sunnykumarsharma3619]

Loved it. Just loved it.

[@CAGE-CODE_30LU7]

Excellent Explanation. Thank you! CT

[@someone2879]

Well Explained! many thanks.

[@pinesyeet]

Fantastic! Thank you!

[@PurwokoHaryadiSantoso]

thank you, sir. I've understood after watching your description

[@eoincoleman4537]

But why does raising it to the second power make it work? No one seems to be explaining this, it's just stated.

[@ahmedkamla2109]

Thank you for the great explanation!

[@Structural_analysis]

Properties of Plane areas kzbin.info/www/bejne/fZuzoX-MebtpqsU

[@ΗλίαςΦασουλάς-π8γ]

like the best explanation, from a junior in mechanical engineer

[@wolverine119]

Sir what about the first moment of mass

[@rajkumarhazra7441]

I like your style !

[@eduardocarazas8570]

Excellent, I learned a lot.

[@purdueMET]

You're most welcome :-)

[@pinghsiuhsieh]

This is a great explanation of what mathematicians mean by the kth moment. Could you make a video on "product moment" (e.g., I_xy) if possible? Thanks!

[@pankajkompella]

oh my .... god what a wonderful video!!!

[@aboudgh5909]

I hope I can distinguish between playing the wicks and the bending moment

[@cartercohen7312]

Really dope video

[@byaringan13]

Hello Professor. Firstly, thank you for your videos which I love. I had a question. As a structural engineer I've been designing floors slabs using only the loading they experience, span ratios and support conditions (BS8110) is it safe to assume this is using statics and why when I design with an FEA software like Robot I get much smaller moments and therefore require less reinforcement? Thanks

[@purdueMET]

It's dangerous to generalize too much when designing structures. Here's the big idea - statics assumes that the stiffness is infinite because that makes the analysis much simpler. Finite element analysis is at the other end of the spectrum of sophistication and estimates stiffness and displacement all across the structure. By using a more accurate mathematical description of the structure, FEA will often give you slightly (we hope) different answers than will statics. Whether there are any general trends in the differences between the two depends on a lot of things, including the geometry. I wouldn't recommend trying to make any general observations before comparing a large number of results, including test data.

[@byaringan13]

ok. thank you for your reply

[@MoHonda90]

FEM results are more accurate for sure, but there should not be that kind of big difference between FEM and simplified method (Code method). Even when using the software, it doesn't mean perfectness, if you tried the same model with the same input data but with another software probably you'll some differences.

[@majermike]

Byaringan "much smaller moments" is a red flag. Verify your software.

[@ZZJ1995]

I still understand why Y (the distance between centroidal axis of the triangle and X-axis) is second power... What does it mean exactly in the real world ? What does it mean if it's third power ?

[@brianambelis5869]

fantastic! thank you for the clarification!!

[@ritickghimire9948]

May I know why is the upper limit under definite integral taken 25 & 4x ?

[@Structural_analysis]

Properties of Plane areas kzbin.info/www/bejne/fZuzoX-MebtpqsU

[@majermike]

Thanks Mark that was great

[@researchsounds5106]

Amazing explanation!

[@purdueMET]

Thanks :-)

[@DieselVids]

I had a question I was hoping you could answer: For the rectangle you take y to be the distance from the centroid to the outer surface, but for the traingle you take y to be the distance from the bottom of the triangle. You mentioned that the bending axis for a rectangle would be through its centroid, is this not also the case for a triangle? Very informative video thanks for sharing.

[@majermike]

If your beam is a triangle, the bending axis is through the centroid. However, more complex problems may require an off-center axis.

[@MrVenki787]

why is the equation of the line considered as y=4x? Can somebody please explain.

[@mechgate]

hello sir, Thank you for such great video. I have one question that how rapid change in cross section affect the second moment of area. is there any book or reference for suggestion. Hoping for your positive reply. Thanks in advanced.

[@purdueMET]

Sorry for the delay in replying. Just about any good book on Strength of Materials will have an explanation of Second Moment of Area. One popular text is by Beer and Johnson. Another is by Mott.

[@Tushar_roy_11]

I like your sarcasm on mathamatitian 😂

[@rajkumarhazra7441]

I finding you sir ! I just can't understand ittt. Now it is useful to me . You are good teacher👍! Thank you

[@AdityaKumar-tu7he]

THANKS A LOT FOR THIS CONCEPT CLEARING VIDEO BUT I HAVE A QUESTION. why s and I are chosen out of 26 alphabets.

[@purdueMET]

There are 26 letter in the Latin alphabet that is used to write in English :-)

[@sayna3]

Thank you

[@SaadKidwai]

Thank you!

[@alechill3286]

Really helpful sir. Thanks!

[@vfgrfbgrb]

Why 4x

[@zmcup3958]

Me like Thor: "I like this one"

[@dhanikotiphanikumar6968]

Sir please explain influence line diagram problemd

[@MortazaHussein]

Very usefull, and actually brilliant, ;any thanks

[@purdueMET]

You're most welcome :-)

[@kk978608]

nice video Keep on!

[@AhmedKhan-tq8ru]

i love the video ,thnks

[@anant_goyal]

really helpful, thankyou

[@muhammadzaidhasan1426]

Thanks a lot SIR. ...

[@NaV_Tiger]

Thanks

[@jkk87]

Thanks professor, you saved my day

[@aman2426]

Brain waves?

[@herbertattema9890]

It has 26 letter, pick one XD. Thanks for the video

[@ayushchoubey635]

😊

[@DAMN__________]

9:55 😂

[@stinkyoldmonk8982]

Professor, you look a lot like Mark Knopfler...

[@tachikomah4203]

Average y of das

[@Browniesisi]

i like this man... lol

[@rexyadav5180]

Maths doesn't care about you !! totally agree

[@markbisa7654]

needing to do this is why I dont want to live in this world anymore

[@JUJUTHEDJ]

You're so handsome ☺️