Moment-Area Method - Step by Step Explanation and Solved Example - Deflection and Slope

[@AFMathandEngineering]

Thanks for tuning in, let us know if you enjoyed the video in the comments below and what you'd like to see next! Example on how to solve for the max deflection using the moment-area method: kzbin.info/www/bejne/aIO0o4aQhq-HppY Difficult hinged practice problem for a continuous beam! kzbin.info/www/bejne/j5-6g6Fon7t6mZo

[@gordonloong1396]

how to get 800/EI and 600/EI ???

[@AFMathandEngineering]

@@gordonloong1396 Reaction at D (taken at A): (60(20)+40(30))/40 = Rd = 60 kip Moment at point B (cut at b, right side of beam) = -40(10)+60(20) = 800. Divide by EI. Will let you solve the rest.

[@muhammadmubbushirhussain4734]

You have no idea how this video helped me in my semester .THANK YOU

[@tornrobot3995]

Your exams must be easy bro

[@manpierre571]

Few hours to my final exam and studied this concept and it has helped me much.. 🔥 Thanks man

[@SurprisePickle]

Others have said it, but this was such a simple explanation with a relatively simple problem that was so easy to understand. I would not have gotten this concept without this video and your discussion. Thank you so much, I might pass my final now

[@chrisperez4533]

When we're finding delta DA at 7:07 does it matter if we calculate it from D or can we also start at the left from A?

[@jlnadua3625]

Good afternoon i love your explanation, but may i know if how you'd get the 0.015 rad? Thank you

[@cameronmays5422]

How do I find the rotation @ 'A' if EI are constant but not provided

[@maheshkumar559]

I am from India and I love this video because this help very well for preparing my semester exam

[@Abdul-c7o1o]

Thank you very much❤. Just have one question that how did youu get the valve of delta(B) i tried various ways but couldn't get the same answer. 11:40

[@swagner1112]

Multiply the numerator by (12^3) to go from ft^3 to in^3

[@prayingmantisas23]

Why is the centroid distance that you take for one triangle 1/3 and for the other one 2/3?

[@AFMathandEngineering]

We're taking it from a point, and the triangles are oriented in opposite directions, so one is going to be 2/3 away and 1 is going to be 1/3 away if we're taking moment about the same origin (A).

[@jamesvictorfabiodiez7608]

please help me with the units. i don't understand how the final answer become 2.43 inch while my calculator says different value.

[@johnanthony906]

At 9:10 min, where did you get the 12^2?

[@AFMathandEngineering]

Need to convert feet to inches or inches to feet, whichever you want. 12 inches in a foot.

[@johnanthony906]

@@AFMathandEngineering Thanks Sir!

[@freemankenyoane2883]

@@AFMathandEngineering Thanks. Was confused with that too because my country uses SI system. Thank you again

[@radhikabanerjea6601]

Why isn't it tan delta A = opposite over adjacent?

[@jonealmanuel6645]

This is a big help for me You can get 800/ei by RA which is 40× distance a to b which is 40×20=800/ei and for 600 RC which is also 60x distance d to c 60x10=600/ei

[@farahfarzanauzma2061]

THANK YOUUUUUUUU HEHE

[@ac_thebassist]

Arigathanks Huhu💖

[@gilbertcomora5766]

How did you get the delta B? How did you get 2.4 inches

[@kunnu6752]

How to find the location of max def with this example? can you help me

[@mwenge6355]

Doesnt using this method always give you the same slope at b?

[@kiran-jh7ze]

Hi, I enjoyed the video a lot, Thank you. Can the same method be used for cantilever beam as well? If so can you make a video on that? Thanks.

[@AndresGarcia-cl6td]

Hello in the delta DA in the big triangle for the centroid shouldn't it be [((800*20)/2)*(20+(40/3)) bc the formula 2/3*b in the other triangles our base was 10ft but in this big one is 20ft fast response from everyone please my exam is tomorrow

[@fitb_35_alvitofarandy68]

Can we use this method if there is a distributed load?

[@AFMathandEngineering]

Yup

[@derrickrono3075]

When you took moments of the M/EI diagram about D, was that mandatory? Would taking mmoments about A be wrong?

[@AFMathandEngineering]

Nope you'll get the same.answer.

[@derrickrono3075]

@@AFMathandEngineering OK. Thanks a lot.

[@herwin4946]

@@AFMathandEngineering I tried taking moments about A form M/EI diagram, i've got 513333/EI, which is a different asnwer. Did i calculated it wrong ?

[@SukhpreetSingh-fv9wt]

HI, HOW DID YOU GET 800 AND 600 DEVIDED BY EI THERE

[@AFMathandEngineering]

Sukhpreet Brar draw the bending moment diagram and divide by EI.

[@ralhpidocamos4100]

How do you get 0.015 rad

[@ralhpidocamos4100]

Can somebody help me to understand

[@ericliu5044]

life saver less than a week before my final

[@michaelkahsai8088]

Good Job! Can you a continuous Beam of solving the Reactions using Area Method? I would appreciate if you could that!

[@sarthakkumardas7287]

PRETTY GOOD EXPLANATION

[@itaizrihan5701]

can u help me with similar question?

[@kenjiloh7783]

at 11;04 min, while finding delta BA, why issit multiply (20/3) instead of multiplying (40/3) since u take x bar from left.

[@AFMathandEngineering]

KENJI LOH when finding delta ba we take the moment area about B between B and A, this x bar is 20 / 3.

[@Teckelly]

I love this.... Thanks. One more thing sire, taking moment about ∆BA, you only considered anti-clockwise, why's that? Cos I was thinking we'll consider both the CW and ACW moments

[@AFMathandEngineering]

We're taking the magnitude of the moment, the clockwise is just the direction we're assuming to be positive. It has nothing to do with not taking the moment in the other direction. We need to assign a sign convention to forces and moments and be consistent throughout the entire question we don't accidentally, for example, add a downwards and an upwards force.by accident.

[@Teckelly]

Understood 😁😁😁

[@kobe2266]

Thanks a lot man. You are a life saver.

[@AFMathandEngineering]

Thanks, glad you enjoyed!

[@matheusbayu6514]

why the area of ​​the moment diagram from B to A is not deltaBA + deltaB, while the area of ​​the moment diagram D to A is deltaDA

[@Dr.ArunKumarGS]

Very nice explanation

[@AFMathandEngineering]

Thanks!

[@ohenekwekukonaduoppong4752]

how did u get the maximum moment which is 800/EI and 600/EI

[@AFMathandEngineering]

Draw the bending moment diagram, divide by EI

[@theultimatepeace2322]

Love from Indian occupied Kashmir ❤️

[@n0rth_219]

What's the value of E and I??? I cannot read it.

[@muhammadfahad8627]

sir i am not able to understand why delta B is 2.41in and not 0.2 in

[@AFMathandEngineering]

What part specifically don't you understand? The entire video is finding delta B. Is there a step you got something different on?

[@sangbryan6028]

Can someone who understood where the (800/EI) and the (600/EI) came from explain it to me?

[@AFMathandEngineering]

Solve and draw the bending moment diagram and divide all of the terms by EI (doesn't change their values).

[@akebaharper5931]

we need more of the video

[@NiteshKumar-vr8hp]

I like your handwriting 😁

[@AFMathandEngineering]

First time I've ever heard that compliment lol!

[@NiteshKumar-vr8hp]

@@AFMathandEngineering but your explanation was great❤️

[@anoopgec4818]

Thankyou thankyou so much. I have to help a student to cheat to get 50$ and this video helped me alot

[@emmanuelbalino]

THANK YOU MASTER

[@aswan7714]

not all heroes wear capes Thanks boss!

[@roham1981]

Thanks a lot

[@mohammedalhajri1986]

you are the best

[@yukicchi9516]

Thank you for this!! Just, need some review of the topic and this sure helps a lot. 😭

[@onlyone481]

Engr. how to find the maximum deflection in area method? Thank you 😇

[@AFMathandEngineering]

Thanks for the comment, good question! You need to take advantage of the fact that at the point of the maximum deflection, the slope of the tangent is 0. I'll make my next video on this topic, stay tuned :D

[@onlyone481]

AF Math & Engineering thank you on this video is very usefull for student like me.

[@AFMathandEngineering]

Great man! We love to hear feedback from our viewers, and we're glad it helped. Are you a Civil Engineering student?

[@onlyone481]

AF Math & Engineering yes sir.. I am currently studying and Philippines.

[@AFMathandEngineering]

Great...are you enjoying your time so far? What year are you in? Please let us know if you hear of any particular problems you or your classmates have and we'd be happy to help :D

[@markjosephreyes9021]

Well said and explained sir. just a small comment please don't talk too fast cause I can't catch up what you are saying. Thanks, sir!

[@ajgarcia3786]

you can change the playback speed to 0.75x

[@dogansahutoglu2073]

thanks alot, it is very clear and helpful

[@simonfryer6075]

It was helpful

[@TeamMananap]

sir pls answer me. how did you get the 800 and 600 . thank you

[@AFMathandEngineering]

It's mentioned in the video, also read some of the previous comments some people asked the same thing

[@Gagandeepsingh-qs8wq]

wish my nincompoop teacher at university explained like this.

[@AFMathandEngineering]

Gagandeep singh haha, thanks glad you enjoyed!

[@mohmera]

thank You

[@samanthadelpilar7876]

How did (8500/EI)x20-(53333/EI) become 2.43in???

[@AFMathandEngineering]

Did you try converting the units and calculating it?

[@AFMathandEngineering]

I answered the same question for another person, here's the response below. The units of the original equation are kip-ft^3, so you should have 116,667 kp-ft^3 * (12)^3 / 1800 * 46000 depending on the units you want to use.

[@tajudeenolusegun2304]

Thanks

[@yoonabii2007]

Is it 600/EI ? I got 400/EI.

[@AFMathandEngineering]

600

[@yoonabii2007]

Thank you very much sir😇

[@lealy5695]

thank youuuu~

[@kane7283]

CAN SOMEBODY PLEASE EXPLAIN TO ME WHY 40FT IS THE ADJACENT AND WHY ISN'T IT NOT DELTA DA? 40 FT IS CLEARLY OPPOSITE OF THE LONGER SIDE!!!

[@hhcdghjjgsdrt235]

thank u sir

[@lesiaamavere6587]

800EI and 600EI ????????

[@AFMathandEngineering]

As mentioned in the video, calculate the bending moment diagram, divide by EI

[@soniamatteazzi1561]

Did you find out how he got those numbers?????

[@AFMathandEngineering]

It's mentioned multiple times in the comments and the video, just calculate the bending moment diagram and divide by ei

[@niketanchettri5650]

Amazing

[@AFMathandEngineering]

Thanks alot!

[@pratikpatil9806]

Are you sure you're not MKBHD?

[@Spongesauce90]

How did I get here? I barely know how to do fractions 😂

[@jervinnabo940]

Nice video!

[@AFMathandEngineering]

Thanks!

[@WFAP23]

not seeing how you got 800 and 600 im getting 600 and 200

[@AFMathandEngineering]

Not trying to be mean by saying this but if you can't solve the 800 600 here you really need to go back and review how to solve your bending moment diagrams, if you're at this point and can't solve them you'll be in trouble on your exam, this one is extremely straight forward. Reaction at D (taken at A): (60(20)+40(30))/40 = Rd = 60 kip Moment at point B (cut at b, right side of beam) = -40(10)+60(20) = 800. Divide by EI. Will let you solve the rest.

[@nishanifernando1047]

Thanx...

[@mAymanov]

so what about over hanged cantilever beam with uniform load allover the beam?? how can i calculate the angle of the support beside the cantilever?? thank you 😇

[@AFMathandEngineering]

good question! so because the load condition changes, the M/EI diagram will change. Then, you need to sketch the elastic curve, use the relationships we showed in this and the other two videos and you're good. You'll take the reference tangent as the one beside the cantilever, you know the deflection at the far support is 0, so that would be delta BA, assuming your supports are labelled AB from left to right. Then use the techniques we showed in these videos to solve directly for the rotation. Hope that helps :D

[@mAymanov]

ok good but if it was a double overhanging cantilevers, how will i deal with that??

[@AFMathandEngineering]

In this method, you always just start by drawing the shear and bending moment diagrams. Once you have these, you can sketch the elastic curve and just continue with the same methods for any question. If you understand that you can always find the distance between the tangent and the support, you can use the methods outlined in these videos to solve it. The techniques for solving different methods though you'll have to practice problems in your book after gaining the understanding from either your professor or videos like ours. Good luck!

[@mAymanov]

got it thanks a lot 😍

[@AFMathandEngineering]

no problem man, welcome to the channel :)

[@fiaksenyo9649]

You dey rush

[@productsnextdoor]

😂😂

[@muhammadmusa5009]

I have no learning in this video

[@diegolopezpereyra9721]

te amo

[@bharathnalla8665]

sexy

[@CLICKS14]

sir how at last deflecion will be calculated plz describe also with coversion

[@venkykrishnan]

Ni yabba ardam ayinattu slow cheppu bey

[@frankmahumuza8425]

thank you sir

[@sosoalsabahi3784]

Awesome you are my hero

[@AFMathandEngineering]

You're too kind! Thanks for the great compliment!