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

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  • @georgesadler7830
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    DR. Hanson, thank you for an excellent presentation of the Parallel Axis Theorem and the Area Moment of Inertia.

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  • @hmcsee
    @hmcsee3 жыл бұрын

    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

    @carultch

    3 жыл бұрын

    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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  • @cc-gg6cd
    @cc-gg6cd Жыл бұрын

    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!)

  • @ralfjoshua9203
    @ralfjoshua92033 күн бұрын

    80's is correct MR!

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    Can you be my statics professor please? Mine sucks so bad and they have a Phd in Structural Engineering.

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  • @angelineromanbautista6295
    @angelineromanbautista62952 жыл бұрын

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

  • @carultch

    @carultch

    Жыл бұрын

    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.

  • @nurrizzatimohammadzambree9553
    @nurrizzatimohammadzambree9553 Жыл бұрын

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

  • @emt4921
    @emt49213 жыл бұрын

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

  • @roso3141
    @roso314127 күн бұрын

    Is it the same process if cover plate was given?

  • @Binkertonbonkerton
    @Binkertonbonkerton10 ай бұрын

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

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    @chairlyai

    3 жыл бұрын

    @@muhammadfawad2725 Michigan Technological University. hby?

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    @isakhansen9572 Жыл бұрын

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  • @carultch

    @carultch

    Жыл бұрын

    Hello fellow Hansen

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    @isakhansen9572

    Жыл бұрын

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  • @son..2820
    @son..2820 Жыл бұрын

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

  • @joshuamorris7187
    @joshuamorris7187 Жыл бұрын

    1990s is the greatest generation for music

  • @1234jhanson

    @1234jhanson

    Жыл бұрын

    Wow! So wrong!😘

  • @aidenheffernan7556
    @aidenheffernan755611 ай бұрын

    man has gotta hear more 2000s music fr

  • @ShyShySchullie
    @ShyShySchullie Жыл бұрын

    Universities should pay you to train their professors on pedagogy.

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    @eryx90933 жыл бұрын

    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

    @carultch

    3 жыл бұрын

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

  • @Yo-pn9qp
    @Yo-pn9qp3 жыл бұрын

    and lol @ Ad^2!

  • @lcchong5822
    @lcchong58224 ай бұрын

    80s = Ad^2 🎉😎 that's cool..

  • @juanm_23
    @juanm_233 жыл бұрын

    What if you want to find Ix and not Ix'

  • @carultch

    @carultch

    Жыл бұрын

    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.

  • @alexfontaine6233
    @alexfontaine62338 ай бұрын

    @9:37 yes my wheels fell off finding d