Statics: Lesson 68 - Parallel Axis Theorem, Area Moment of Inertia

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8:02 Only KZbin math tutor I've ever seen to diss 90s and 2000s music and then lead that into a formula lmao.

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then quote a song that came out in 1996 10:32

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*Hanson. Sorry.

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Prof. Hanson: "what's the greatest generation of music?" Me: "The 60's!"

[@hmcsee]

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

[@carultch]

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.

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how did you know we were going to answer 90s music

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@@mirwaisliwal6530 i didn't compare them.. youre the one who's comparing them... Smh🤦

[@georgesadler7830]

DR. Hanson, thank you for an excellent presentation of the Parallel Axis Theorem and the Area Moment of Inertia.

[@minhashamayim4824]

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.

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I'm nearly at the end and actually really excited to see if you get the same answer twice.

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You are awesome at explaining! You are easy to follow! Love it!

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8:10 bro has never heard Graduation

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Thank you so much! That 80's music joke really helped me on my homework!

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Thank you Dr. Hanson! Your videos are helping me prepare for the PE

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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.

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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.

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You just solved my assignments for me. Everything is clear like the voices of 80's female singers 😅 Thank you 😊

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What a great teacher, I thought the 80s joke was funny!

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Ad'z squared 🤣🤣 Dr., you make learning FUN!!

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Worth watching for the jokes alone.

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My lecturer has miss some important and key concept that have explained by you in this video! thanks to have your video !

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The 20s, 90s, 80s ---> area joke = peak comedy

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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!)

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8:10 "The 2000s...nothing good came out of 😂..."

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7:52

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I liked your 80s music :). Thank you about your helpful videos!

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Is it the same process if cover plate was given?

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[@nurrizzatimohammadzambree9553]

may i know why do we want to move the centroid from the smaller pieces to the center of the big pieces , sir

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[@Ahmed-Afkir]

The explanation is excellent

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Thanks sensei

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Does anyone know the name of the book he shows the formulas from

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Love your lessons sir, keep it up :)

[@eryx9093]

Hi! How can i get your book ? is there any pdf ? because i live in a far country ... or what's your books name ?

[@carultch]

Look up R.C. Hibbeler, "Mechanics of Materials"

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Keeping this guy to myself so i dont make the curve to high in my class

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Hello fellow Hansen

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thanks, it explained well

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loved your 80s joke lmao, also really useful explanation thanks

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80's is correct MR!

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[@angelineromanbautista6295]

static of inertia of composite beams pls? I can learn more if youre the one explaining it. thanks for all the vids

[@carultch]

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.

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best explantion with perfect joke

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[@juanm_23]

What if you want to find Ix and not Ix'

[@carultch]

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.

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8:07 was so parasocial it made me wanna die

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I agree 80s music ❤️

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Best Ever

[@son..2820]

for some reason i am now using the Ad's joke to write the parallel axis formula😁😄👍

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1990s is the greatest generation for music

[@1234jhanson]

Wow! So wrong!😘