Castigliano's Second Theorem - Deflection at a Point - Continuous Beam with Cantilever

[@AFMathandEngineering]

Click here for an additional practice problem for Castigliano's Second Theorem, a cantilevered beam with a distributed load! kzbin.info/www/bejne/inecnaGdoZlroaM Also, an intro into the method of least work which is related to this theorem: kzbin.info/www/bejne/rZm2g415mp2mr7s

[@AZ-pz2oq]

Didnt know you could still find good videos for 4th year engineering content, thx bro!

[@amiralihedayati3625]

You nailed it. Great job 👏🏼 100 percent better than other videos,which are really long and misunderstanding.

[@zjyub]

I have a final tomorrow, and I have not even looked at this method yet. Thank you for the vid. It's hopefully gonna help me tomorrow

[@FutballFocusTV]

woo it took me 11 minutes to understand the whole topic and solve my assignments as easy as i can . Thank you my engineering hero . You rock it sir

[@AFMathandEngineering]

Thanks for the kind words, glad we could help!

[@Corvanor]

Really do appreciate the content your channel provides. Very clear and concise.

[@AFMathandEngineering]

Thanks alot for the great compliment, very glad you found our content helpful!

[@alirezanejat]

Great video. Thank you. That table at the end is very useful. I was solving a problem that displacement at point (A) is given and Load (P) to be determined by Castigliano's theorem. The load was 1m away from point (A). I moved Load (P) to point (A) considered a bending moment at Point (A). It was an interesting problem. Your video was helpful.

[@carolinagarciaalonso2630]

We need more structural engineering videos!!! Please continue uploading

[@isabellagarcia3875]

Great video, amazing quality!

[@NdzaloBaloyi45]

Sensational!

[@yaraladilaramasarmadilar]

Thank you sooooooo much

[@justinsubs6477]

muchisimas gracias Fred

[@kroman4]

I'm confused as to why the distributed force would influence the deflection past the support at point B between B and C. In my head the deflection at point B would be zero and then you could just calculate from B to C- could you help explain that?

[@AFMathandEngineering]

Good question! Remember, we're dealing with one continuous member, not two discontinuous members. If support B was fully fixed, or ab and bc were completely separate members, your line of thinking woule be correct. But in the case of a monolithic concrete beam or a continuous steel member, they act as one and the elastic curve is continuous throughout the entire member. Try placing a ruler on two supports and hang one off the other end, and press down on the ruler between the supports. This will give you a good idea of how this behaves in real life. Thanks for the comment!

[@lucasmodena]

Hi! Thanks for sharing your knowledge. Why aren't you adding the shearing force when the beam is cut?

[@AFMathandEngineering]

Were taking the moment about where.we cut the beam, there is no moment created by the shear at that point as the distance to the shear force at the point we cut is 0.

[@lucasmodena]

@@AFMathandEngineering Got it! Thank you very much!

[@sadunperera8981]

Great video man it really helped heaps

[@AFMathandEngineering]

Great!

[@flameon8185]

what do u mean by the minus sign at the end?

[@dogansahutoglu2073]

thanks alot

[@Teekey90]

So if we want to find the slope at point C, but there's no moment, we have to derive those moment equations again as if there is a dummy moment at that point, correct?

[@AFMathandEngineering]

Correct! You have to apply the dummy moment regardless if theres a moment at that point. If theres a concentrated moment, then you substitute for your dummy moment later, as we did. If there isnt, substitute 0.

[@Teekey90]

@@AFMathandEngineering awesome. Thanks for the reply

[@oualidoualid1471]

Well done (y) thank you very much this was very helpful

[@AFMathandEngineering]

Excellent glad we could help!

[@momoha8504]

hi im interested in the castigliano derivation if u can post it plz

[@thisarupeiris6909]

good work

[@AFMathandEngineering]

+Thisaru Peiris thanks!

[@vanasumab3295]

I can't see the top of the page very well, so could you place the camera parallel to the sheet and move down as you proceed. Thank you.

[@AFMathandEngineering]

Puppy lala thanks for the feedback!

[@AFMathandEngineering]

To add to that, it's difficult as I film the videos myself to continuously go through the problem and move the camera, but I'm definitely thinking of a solution to this issue. Thanks again.

[@vanasumab3295]

AF Math & Engineering You could like larger at top. :D

[@vanasumab3295]

AF Math & Engineering You could like larger at top. :D

[@AFMathandEngineering]

Yea, good point! Thanks!

[@PoiiPP1]

You forgot writing " 4 " in the section AB which is. ( 30- 4P/3 )X-X^2 you wrote just (30 -P/3)X-X^2. ? But the answer in the end was absolutely right? ????

[@AFMathandEngineering]

butter fly occasionally well miss some small numbers, obviously we dont do calculations during the video we have them prepared beforehand. More importantly than missing a number is understanding the concept behind the problem and how its solved.

[@PoiiPP1]

oh no i misundderstood .. you were right! lol really sorry i thought it was By reaction.. sorryyyyy :D

[@PoiiPP1]

thank you very muchhhhhhhhhhhhhh

[@AFMathandEngineering]

butter fly no problem, glad we could help!

[@kanavgupta9136]

Derivation? ? ? without derivation its like cramping the science

[@AFMathandEngineering]

Kanav Gupta we did cover how these formulas were derived in another video on castiglianos theorem, however there are other youtube videos that focus on theory. Our channel focuses on problem solving and the tricks needed to get good grades.

[@kanavgupta9136]

Okay. . . Thank you. . . But i think there is no fun of getting good grades if you don't know where the formula came from. . . . Because we will get the degree but not knowledge

[@AFMathandEngineering]

We agree that just memorizing solutions isn't the point of school, and we try to provide basic theory in most of our videos..in a youtube format we don't want our videos to be 20+ minutes long with half theory. Your professor, textbook and other youtube channels focus on a ton of derivation and theory and it's our opinion that you need to combine them all to achieve a proper understanding. That being said, we do have quite a bit of video content that is theory, so by no means is our channel just problem solving. Thanks for the feedback though, we always welcome constructive criticism :D

[@AFan0fPS3]

Littt