Moment-Area Method - How to Solve for Maximum Deflection - Example Problem

Here's our introductory video on the topic: • Moment-Area Method - S...
Tricky hinged beam practice problem for the moment area method: • Moment-Area Method - T...
In this video, we show you how to solve for the maximum deflection of a simply supported beam using the moment area method. This involves finding the point at which the max deflection acts, then using the M/EI diagram to solve for the deflection.
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Пікірлер: 69

  • @AFMathandEngineering
    @AFMathandEngineering6 жыл бұрын

    Note: When calculating Xm at 7:25 by equating theta DA to theta A, we have to multiply 40Xm/EI * Xm * 0.5 for the area under the M/EI diagram, not just 40Xm /EI. Sorry about missing that, please make this correction. Check out our introductory video on the moment-area method before trying this one! kzread.info/dash/bejne/nJ-rstyvh9bXebw.html Difficult practice problem with a hinge here: kzread.info/dash/bejne/i6KLtNBrmrmtk5s.html

  • @manoranjanoinam9942

    @manoranjanoinam9942

    6 жыл бұрын

    That just got me cofused for almost 1 hour... anyway thanks...

  • @AsmiTAdhikari

    @AsmiTAdhikari

    6 жыл бұрын

    How theat DA is equal to area of m/EI diagram explain me please

  • @jamesclaridad4394

    @jamesclaridad4394

    5 жыл бұрын

    sir why should multiply 40Xm/Ei * 1/2 * Xm ? and how it is equal to area of moment diagram?

  • @omerozturk7424

    @omerozturk7424

    4 жыл бұрын

    we are calculating theta therfore we cant multiply with xm it should be like 40xm/EI*(1/2) BECAUSE of the integral we multiply xm when we are calculation tca in theta we dont need multiply xm again

  • @bakuaremiyaw

    @bakuaremiyaw

    4 жыл бұрын

    just notice that thank you

  • @mufaro.
    @mufaro.3 жыл бұрын

    You just saved this student. Lots of love from Zimbabwe

  • @AyushDevkota7
    @AyushDevkota73 жыл бұрын

    Thank you for this video! very helpful, keep it up

  • @hassanbabar830
    @hassanbabar8302 жыл бұрын

    Bro you are a life saver

  • @onlyone481
    @onlyone4816 жыл бұрын

    AF Math & Engineering thank's for this video

  • @AFMathandEngineering

    @AFMathandEngineering

    6 жыл бұрын

    mark ebrahim no problem!

  • @erzcav4793
    @erzcav479311 ай бұрын

    you just saved me. thank youuuu

  • @ebenezeryeboah6780
    @ebenezeryeboah67803 жыл бұрын

    Thank you very much sir But I have a question is it also right to take the centroid at point of zero slope from A to the point of zero slope. Thank you

  • @thebr0die985
    @thebr0die9853 жыл бұрын

    will I still get the same answer if I assumed that X distance if from the other end of support?

  • @arielluna3639
    @arielluna36394 жыл бұрын

    Why, didn't you use the triangle's area in finding theta(DA)?

  • @albensmaine3057
    @albensmaine30576 жыл бұрын

    hey AF MATH ! i really like your videos it really captivate me more than our basic "engineer" courses , that has no link with the real world :( now for this type of problem wouldn't be faster and easier to use a software that can evaluate forces applied on a surface such as "autodesk professional" or "solidworks"

  • @AFMathandEngineering

    @AFMathandEngineering

    6 жыл бұрын

    Hey buddy, thank you so much for this post. We're so glad we could reach you and help you enjoy your course material more. Let us know a bit more about yourself, what year are you in and in what country are you a student? As for your question, you're absolutely right. Very rarely in the field would we perform these types of calculations by hand. The programs you suggested though wouldn't be used by a structural engineer for analysis for this type of problem. Structural analysis software such as SAP2000, Staad Pro, Etabs, SAFE, and many more are used for the analysis of structures and typically they're much more difficult than just a simply supported beam with many variables. However, in an engineering education in University, you study how to perform these checks manually using different techniques. This is a large focus of our channel. Check out this video for how to solve a beam for deflection, shear and moment using an evaluation version of a structural analysis software that you can get as a student. This is how engineers evaluate structures in the industry, and you can use it for your assignments too! -> kzread.info/dash/bejne/dH5kw7GOd7HdZdo.html Thanks again for your post and question.

  • @albensmaine3057

    @albensmaine3057

    6 жыл бұрын

    AF Math & Engineering first thank you so much for taking time to answer my question and it's a pleasure for me to converse with a civil engineer ! i turned 18 a week ago , i live in france , i study at the esme sudria in paris (mechanical and robotics engineering), it's my first year out of the 5 years to get the degree, and it's pretty complicated for me to say the least , i took a classe for 2 years that is not really meant to give you the keys to succeed during these 5 years , still striving for my degree i will never let go ! if i get to my third year i'll have to choose a "path"?? renewable energy for me is the future ! that's my story , now you tell me mister Af Math did you have hard times when you were student too ?

  • @AFMathandEngineering

    @AFMathandEngineering

    6 жыл бұрын

    No worries man, we love chatting with young engineers. I'm Fred from the F in AF :D That's great, it must be an exciting time in your life to start your engineering journey. Learning how to succeed in engineering at University is half learning how to master fundamental mathematical and physics principles, the rest is just learning how to master school and studying! First year is always hard, it gets easier after that. As for your "path", you'll choose a specialization stream and thats when you really start learning about your career and profession! I had a very difficult time in my first semester as I returned to school at age 26 to start my engineering career after becoming a professional chef after high school. I hadn't seen any math, physics or chemistry in about seven years and jumped right into first year Civil engineering. It was so difficult, I had to study 6-8 hours a day in an attempt to catch up and almost dropped out. However, I stuck with it and managed to pass all of my first semester classes. After first semester I figured out how to study correctly and started achieving very good grades in all of my classes, and my grades just kept going up as I learned more about how to prepare for tests. That's the main reason why we stress tricks and tips in our videos: doing well in engineering in school is as much about knowledge as it is learning the tips and tricks you need to succeed. Don't give up, it only gets easier. Thanks again for sharing your experiences with us, please continue to comment on our videos if you have any questions and we'd be happy to help you out. Let us know how your progress is going too. Cheers!

  • @albensmaine3057

    @albensmaine3057

    6 жыл бұрын

    AF Math & Engineering thank you so much for you support ! and your story is very inspiring ! i'll take some of your videos as a secondary personal teaching for all the things we don't learn in school i always do that ! keep up you are doing a great job and i will recommend you to one of my great friends , god bless you !

  • @AFMathandEngineering

    @AFMathandEngineering

    6 жыл бұрын

    Thanks a lot man, great to get to know you better. Good luck!

  • @benedictackon4289
    @benedictackon42893 ай бұрын

    that's great, try getting us a video on the principle of virtual work 😎😎

  • @tomjason7327
    @tomjason73274 жыл бұрын

    thank you so much

  • @herwin4946
    @herwin49464 жыл бұрын

    Sir could u do one moment area method using superposition method ?

  • @mushficaislam
    @mushficaislam5 ай бұрын

    Can anyone explain- where is (1/EI) in the calculation of finding the value of (thetaDA)?

  • @nikhilaryanagarwal7477
    @nikhilaryanagarwal74772 жыл бұрын

    Good dude😎

  • @parkgimmy4225
    @parkgimmy42252 жыл бұрын

    Why didn't you multiply 2/3 to Xm for CG at the last equation?

  • @nishantamedhi4089
    @nishantamedhi40894 жыл бұрын

    Keep uploading videos

  • @MarkKevinCidro
    @MarkKevinCidro6 жыл бұрын

    @7:25 You said theta DA is simply the area of the 'moment over EI diagram' between A and D. Then it should be (1/2)(Xm)(40Xm/EI) ???? 😅😅😅

  • @AFMathandEngineering

    @AFMathandEngineering

    6 жыл бұрын

    Hey man, you're right, if you calculate 1/2 (xm)(40Xm/EI) you'll get the same value, 1333/EI. Not sure what time stamp you linked as that's the end of the video. As for delta DA, which is the moment area about D of the area between D and A of the moment area diagram? Theta is the area, delta is the moment area. So by taking the area of DA, which is 40xm/EI * xm * 1/2 , and multiplying by the distance to the centroid, which is xm/3, we get the moment area about D of section DA of the M/EI diagram. Hope that gave you a bit more info :D

  • @AFMathandEngineering

    @AFMathandEngineering

    6 жыл бұрын

    Also, theta DA and theta A are equal in this question.

  • @MarkKevinCidro

    @MarkKevinCidro

    6 жыл бұрын

    @7:25 LOL. Hahah.

  • @AFMathandEngineering

    @AFMathandEngineering

    6 жыл бұрын

    :D

  • @AFMathandEngineering

    @AFMathandEngineering

    6 жыл бұрын

    Are you currently a Civil Engineering student?

  • @hexdzn7704
    @hexdzn77043 жыл бұрын

    How do you get 8.16m? Even after the 0.5 correction in the pinned comment, I get Xm as 66.65m not anywhere near the length of the beam.

  • @AFMathandEngineering

    @AFMathandEngineering

    3 жыл бұрын

    Check your units...you shouldn't be that far off..

  • @tutstorial8474
    @tutstorial84743 жыл бұрын

    why isn't it sin of thetaA ?

  • @cyruzvanenoviso5082
    @cyruzvanenoviso50823 жыл бұрын

    How did you comeup with xn =8.16

  • @AFMathandEngineering

    @AFMathandEngineering

    3 жыл бұрын

    See the pinned comment

  • @devkar9765
    @devkar97655 жыл бұрын

    is the moment area method and macauly's method the sam thing?

  • @AFMathandEngineering

    @AFMathandEngineering

    5 жыл бұрын

    I dont believe so no, macaulays method is a double integration concept.

  • @devkar9765

    @devkar9765

    5 жыл бұрын

    Thanks, from my understanding they both share similar roots, where the integral of moment is slope and the integral of slope is deflection. Right?

  • @AFMathandEngineering

    @AFMathandEngineering

    5 жыл бұрын

    In the moment area, integration of the M/EI diagram is equal to the change in slope or deflection between two points, not the value itself. Then we need to do some additional operations to get the actual values. Macaulay method is similar to deflection by integration, where you derive moment expressions for each section of the beam then solve accordingly. We have a video on deflection by integration which is very similar to this.

  • @devkar9765

    @devkar9765

    5 жыл бұрын

    Thanks a lot. :)

  • @AFMathandEngineering

    @AFMathandEngineering

    5 жыл бұрын

    @@Phoenix67614 Thanks man! Glad you're enjoying them!

  • @carloss.6250
    @carloss.62503 жыл бұрын

    how did you get 400/ei in the beginning

  • @AFMathandEngineering

    @AFMathandEngineering

    3 жыл бұрын

    It is mentioned in the video, BMD, divide by EI

  • @bsce5378
    @bsce53785 жыл бұрын

    Good day! Thank you! This video is very helpful! Can you upload a tutorial for Influence Line using the Muller Breslau? Thankss !! :)

  • @AFMathandEngineering

    @AFMathandEngineering

    5 жыл бұрын

    Thanks alot, we definitely considered it but it does seem like a difficult topic to explain over video. We'll add it to the list though! Thanks!

  • @cetinaydn2478
    @cetinaydn24785 жыл бұрын

    ı dont find xm=8,16 please help me :(

  • @AFMathandEngineering

    @AFMathandEngineering

    5 жыл бұрын

    There's a mistake in the xm part of this video, refer to the comments below for clarification

  • @ayra_gr

    @ayra_gr

    5 жыл бұрын

    can you solve it? coz im trying to solve the said correction but it gives me zero answer : (

  • @muhammadfahad8627
    @muhammadfahad86275 жыл бұрын

    i watched the video more than 7 times but still not got it how did you find out the theta DA by BMD. :(

  • @AFMathandEngineering

    @AFMathandEngineering

    5 жыл бұрын

    Did you read the pinned comment? There's a correction regarding Theta da

  • @brunofernandes4298
    @brunofernandes42982 жыл бұрын

    I'm taking a structural analysis exam tomorrow. Wish me luck guys :)

  • @brunofernandes4298

    @brunofernandes4298

    2 жыл бұрын

    Thanks for the video btw, so helpful :)

  • @Madnesstein
    @Madnesstein2 жыл бұрын

    I LEARNT SO MUCH WITH YOU, BUT YOU ARE SO MESSY BRO XD

  • @leonelreybon1652
    @leonelreybon1652 Жыл бұрын

    this is misleading

  • @user-xm4rr9ic4h

    @user-xm4rr9ic4h

    5 ай бұрын

    What is misleading here?

  • @lebeymijares7606

    @lebeymijares7606

    5 ай бұрын

    Yes