Dr. Hanson is literally such a supportive and helpful professor. Thank you for your videos! At my school, my engineering professors can be really intimidating and often advise students to change their majors after making even the smallest mistakes, which is really frustrating and not supportive. Thank you for making a positive difference!!
As an educator myself, I must compliment you on your videos. They are great! You break things down beautifully. Thank you for the videos and everything you do!
Really excellent presentation. I especially appreciate when you explained the significance of moment of inertia so we understand WHAT the number means (higher moment of inertia = higher resistance to bending = stronger shape). Thank you
It really has nothing to do with inertia. It is named "area moment of inertia" because the calculus that defines it is very similar to the calculus that defines moment of inertia in rotational dynamics. The essential difference is that the differential term is area, rather than mass. Second moment of area is a more accurate name. Moment in general means a quantity multiplied by a distance from an origin, added up with that value throughout a system. Second moment means that distance is squared as you calculate it. It comes about because fibers contribute to resistance to bending in two ways, that are both proportional to the distance from the neutral axis. The first way is that the fibers are stressed in proportion to how far they are from the neutral axis, and the second way is that the fibers contribute to resisting the applied bending moment with a "lever arm" that is the distance they are from the neutral axis. When you have a composite assembly of materials that form the beam, Young's modulus also plays a role in each term that gets added up. Beams of a uniform material put Young's modulus as a constant out in front when calculating deflection, because it is term that is the same for all fibers. Composite beams need to include the granularity of how Young's modulus applies to each portion of the beam specifically.
I've learned more from this youtube channel than the campus professor I'm paying thousands of dollars to teach me. Greatly appreciate the concise, well spoken lectures.
What amazes me is that I got the Hibbeler book and the Mechanics of Materials for Dummies and none of them actually helped me to work out the problem. And here you go, the parallel axis theorem that seemed like the most complicated thing, actually is simple after all. Actually, when I go back now and look at the for Dummies method, it makes sense now that I understand it, but at first appearance it just didn't make sense the way it was presented and they are meant to be books for people learning this stuff, not for people already knowing it.
Dr Hanson u reli help me get through this semester exam on this topic as I am not good at maths beforehand. Thank you so much!! u r funny and easy to understand even though I come from Hong Kong.
Claims 80's music is the best generation of music, immediately references a mediocre song from the 2000's lol. God bless you sir your videos have been awesome. (Do heat transfer next!)
The idea behind composite beams, is that you use E as a factor to make a weighted average when finding the neutral axis. And rather than only working with the 2nd moment of area as a purely geometric property, you are adding up E*I for every sub-material within the composite. So your centroid is more like a center of elasticity and area, than purely a center of area. And your 2nd moment of area, is more like a 2nd moment of elasticity and area.
The parallel axis theorem can be used for moving to and from the center of mass, or for this kind of "moment of inertia" rather, the centroid (center of area). For moving to the centroid, you subtract A*d^2, and for moving away from the centroid, you add A*d^2. You can use it to move between two axes that have nothing to do with the centroid, but you would deploy it twice, with the centroid as a waypoint in this calculation.
Dr. Hanson is literally such a supportive and helpful professor. Thank you for your videos! At my school, my engineering professors can be really intimidating and often advise students to change their majors after making even the smallest mistakes, which is really frustrating and not supportive. Thank you for making a positive difference!!
Whut! That is so mean of them
One of the best professors I have ever seen in my life keep it up sir love from India 🇮🇳
As an educator myself, I must compliment you on your videos. They are great! You break things down beautifully.
Thank you for the videos and everything you do!
Came here to say this!
Dr. Hanson has gotten me through my BSCE, FE Exam, and now my PE exam!! Keep studying, it gets better!
8:02 Only TH-cam math tutor I've ever seen to diss 90s and 2000s music and then lead that into a formula lmao.
then quote a song that came out in 1996 10:32
I swear you are one of the best doctors i have ever seen, your way it is so easy and also entertainment, i love you dr, your son from Saudi Arabia 🇸🇦
I'm reviewing subjects for PhD qualification and your teaching is really helpful, thank you.
Really excellent presentation. I especially appreciate when you explained the significance of moment of inertia so we understand WHAT the number means (higher moment of inertia = higher resistance to bending = stronger shape). Thank you
It really has nothing to do with inertia. It is named "area moment of inertia" because the calculus that defines it is very similar to the calculus that defines moment of inertia in rotational dynamics. The essential difference is that the differential term is area, rather than mass.
Second moment of area is a more accurate name. Moment in general means a quantity multiplied by a distance from an origin, added up with that value throughout a system. Second moment means that distance is squared as you calculate it. It comes about because fibers contribute to resistance to bending in two ways, that are both proportional to the distance from the neutral axis. The first way is that the fibers are stressed in proportion to how far they are from the neutral axis, and the second way is that the fibers contribute to resisting the applied bending moment with a "lever arm" that is the distance they are from the neutral axis.
When you have a composite assembly of materials that form the beam, Young's modulus also plays a role in each term that gets added up. Beams of a uniform material put Young's modulus as a constant out in front when calculating deflection, because it is term that is the same for all fibers. Composite beams need to include the granularity of how Young's modulus applies to each portion of the beam specifically.
Great addendum to my teacher's class. Thank you for your care for your students and your sense of humor, Professor Hansen.
*Hanson. Sorry.
He is a king among men, sharing this information with is in a way that can actually be understood. 👑
You’re helping me so much with my engineering degree, you’re an amazing teacher!! Much love from England !
We going for speed! Thanks for speeding things up, Dr. Hanson.
"You like to move it move it" made my day 😂😂
Lova ya Jeff Hanson! Been saving me for the past 3 years of engineering lol
This man is a gift from heaven.. Khan academy must work with you
Nahh he is much better then khan academy, dont need to compare him.
@@mirwaisliwal6530 i didn't compare them.. youre the one who's comparing them... Smh🤦
I've learned more from this youtube channel than the campus professor I'm paying thousands of dollars to teach me. Greatly appreciate the concise, well spoken lectures.
Prof. Hanson: "what's the greatest generation of music?"
Me: "The 60's!"
DR. Hanson, thank you for an excellent presentation of the Parallel Axis Theorem and the Area Moment of Inertia.
Great video; taking design courses rn, so this is vid is a terrific refresher!
I'm nearly at the end and actually really excited to see if you get the same answer twice.
You are the best teacher I have seen in my entire Life.😍👍🏻
You are awesome at explaining! You are easy to follow! Love it!
Thank you Dr. Hanson! Your videos are helping me prepare for the PE
You're the best! I owe you my grade - thank you!
What amazes me is that I got the Hibbeler book and the Mechanics of Materials for Dummies and none of them actually helped me to work out the problem. And here you go, the parallel axis theorem that seemed like the most complicated thing, actually is simple after all. Actually, when I go back now and look at the for Dummies method, it makes sense now that I understand it, but at first appearance it just didn't make sense the way it was presented and they are meant to be books for people learning this stuff, not for people already knowing it.
Dr Hanson u reli help me get through this semester exam on this topic as I am not good at maths beforehand. Thank you so much!! u r funny and easy to understand even though I come from Hong Kong.
The Ad's music is the best he said
I love the sense of humor😁
Love from Nigeria
You saved me all the way to my 3rd year in college :D , please consider doing theory of machines , i need u in my life xD.
You just solved my assignments for me. Everything is clear like the voices of 80's female singers 😅
Thank you 😊
I am from the India and i love the way you are teaching us ❤
how did you know we were going to answer 90s music
Thank you so much! That 80's music joke really helped me on my homework!
My lecturer has miss some important and key concept that have explained by you in this video! thanks to have your video !
You are like an angel sent by God,... helpful video.. Thank you
8:10 bro has never heard Graduation
You saved today, I will be forever grateful!
You are amazing dude, I am here doing Engineering at uni and honestly you explained it better than my tutor
What a great teacher, I thought the 80s joke was funny!
You are really a very good teacher Prof!!! Lord bless you!
I have a feeling I will be a regular viewer of your videos
You are my hero you save my exam 🥲❤️
Love your lecture... serious change the way I understood this topic ... Thanks 💯💯
Big help, thank you sir👊🏿
I need to submit an assignment by tomorrow and this video saved me
Prof Hanson is the best in the world
Ad'z squared 🤣🤣 Dr., you make learning FUN!!
I liked your 80s music :). Thank you about your helpful videos!
Now that's what i'm talking about! Was very helpful, Thankss
Claims 80's music is the best generation of music, immediately references a mediocre song from the 2000's lol.
God bless you sir your videos have been awesome. (Do heat transfer next!)
Thank you so much sir for sharing your precious knowledge.
Best teacher ever
Thank you so much this is really helpful 🙏🏽.
Thank you for this free content!
The 20s, 90s, 80s ---> area joke = peak comedy
8:10 "The 2000s...nothing good came out of 😂..."
Exactly what I needed. luv u sir. thanks
Thank you a lot for the video!
Love your lessons sir, keep it up :)
may i know why do we want to move the centroid from the smaller pieces to the center of the big pieces
, sir
The explanation is excellent
Best prof ever
you are such a king
Worth watching for the jokes alone.
Can you be my statics professor please? Mine sucks so bad and they have a Phd in Structural Engineering.
best explantion with perfect joke
80's is correct MR!
i could watch you just for entertainment!
Excellent teacher , thank you :)
Lovvvveeee uuuu soooo much u made my life much easier 😻
Keeping this guy to myself so i dont make the curve to high in my class
Hello fellow Hansen
@@carultch unite!
Thanks sensei
Is it the same process if cover plate was given?
Sir very great teacher
loved your 80s joke lmao, also really useful explanation thanks
static of inertia of composite beams pls? I can learn more if youre the one explaining it. thanks for all the vids
The idea behind composite beams, is that you use E as a factor to make a weighted average when finding the neutral axis. And rather than only working with the 2nd moment of area as a purely geometric property, you are adding up E*I for every sub-material within the composite.
So your centroid is more like a center of elasticity and area, than purely a center of area. And your 2nd moment of area, is more like a 2nd moment of elasticity and area.
ur the goat dr
Thank you my friend! Good luck on your finals!
Universities should pay you to train their professors on pedagogy.
it makes much more sense when you teach it. thank you!
thank you, you are the best!!
8:07 was so parasocial it made me wanna die
Does anyone know the name of the book he shows the formulas from
thanks, it explained well
Hi! How can i get your book ? is there any pdf ? because i live in a far country ... or what's your books name ?
Look up R.C. Hibbeler, "Mechanics of Materials"
Thank u sir😇
Thank you!
1990s is the greatest generation for music
Wow! So wrong!😘
Thanks 🌼
for some reason i am now using the Ad's joke to write the parallel axis formula😁😄👍
just thank you sir
7:52
You are a legend. 😂
Thank you for explaining (d)
thanks sir Jeff Hanson
80s = Ad^2 🎉😎 that's cool..
9:09 voice crack of the millennium
I love you man
Best Ever
veryyyyyyyyy helpful!
What if you want to find Ix and not Ix'
The parallel axis theorem can be used for moving to and from the center of mass, or for this kind of "moment of inertia" rather, the centroid (center of area). For moving to the centroid, you subtract A*d^2, and for moving away from the centroid, you add A*d^2.
You can use it to move between two axes that have nothing to do with the centroid, but you would deploy it twice, with the centroid as a waypoint in this calculation.
man has gotta hear more 2000s music fr
Thankyou