Castigliano's Theorem - Cantilever Beam Distributed Load - Slope and Deflection - Choosing Origin

[@AFMathandEngineering]

Click here for our first video on this topic, a continuous beam with a cantilever, for an additional practice problem/explanation! kzbin.info/www/bejne/pnLLoWVmjNiBhMU Solving the deflection of a truss example using Castigliano's Theorem: kzbin.info/www/bejne/gHLUe62jbLl9j68 Also, an intro into the method of least work which is related to this theorem: kzbin.info/www/bejne/rZm2g415mp2mr7s

[@hikmetcelebi499]

Thank you SO MUCH. Ive been trying to solve my homework for like 2 hours and this helped me much.

[@amanuel3478]

Legend! So awesome dude, do some force method and slope deflection! Like FEM stuff.

[@isabellagarcia3875]

This video would have really helped me during my undergrad =)

[@NicholleWillisLoves]

If you could please do an example with simply-supported beam with a point load in the middle of the beam somewhere, that’d be awesome. 🙏🏻

[@arvindrodhiya2419]

Good explanation, you're doing great work, thank you

[@isaacclottey6196]

Can you please explain why the ficitious moment was placed in a clockwise direction and why not counterclockwise, and when do we use these two appropriately please?

[@oualidoualid1471]

it couldn't be any clear than that Thank you Sir

[@AFMathandEngineering]

Great, thanks for the feedback!

[@georgepreece1226]

Do P and m' always = 0? I am attmpting a question and as there is a point load at the point trying to find deflection, the moment equation therefore =. Not sure if this can be true?

[@Ahmed-cr9kv]

This was simple and great, any chance for more complicated examples?

[@AFMathandEngineering]

+Ahmed Faisal thanks a lot brother, much appreciated. I tried to include two rather simple examples that covered two different concepts that people usually have trouble with. I could do a more difficult example though for sure, stay subscribed and watch for a new video coming soon :D

[@AFMathandEngineering]

Also...if you didn't see it yet we have one more more difficult example here: kzbin.info/www/bejne/pnLLoWVmjNiBhMU

[@isaacclottey6196]

Thank you

[@miguelliszka6430]

thanks

[@bushraalsalay3719]

Thank you..😊

[@maramyaseen154]

Thank you so much 🙏🏼🙏🏼🙏🏼

[@AFMathandEngineering]

No problem! Thanks for the comment!

[@thomasgreen372]

hey great video, just wondering how would the moments equation change if you added a point load in with the distributed ? like as well with the distributed there was a point load 2/3 the way down the cantilever

[@AFMathandEngineering]

Thanks for the comment glad it helped! The only variable that is affected by change in external load in the equation for deflection and rotation is M. Thus your need to modify your M to include your point load. Hope that helps!

[@thomasgreen372]

Ok, sweet . would that just entail adding a -2/3(P)x to the moment equation .P being the added point load and 2/3x being the distance ? thanks for your help . i really do appreciate your time

[@AFMathandEngineering]

In cantilever problems we derive the M equation by cutting the beam before the support so we dont have to consider the reaction in our M equation . Thus our distance would be 1/3L for our term (assuming you meant 2/3 down the beam from the support).

[@thomasgreen372]

Awesome! you the man , yes since we moved the origin that makes sense . Do i just multiply the point to the 1/3L them add ....Well subtract ,due to rotation , in to the equation you wrote in the above example

[@AFMathandEngineering]

I'm going to have to check, I'm not home right now, but here adding a point load at some point not at the end will require you to take a second moment equation. So if you have ABC where A is the support, B is the pointload and C is the end, take CB and BA and sum the individual sections after applying the formula to both. Refer to our other video on this topic where we do this for a discontinuous loading.

[@jivandibiase3289]

hey,, just a question, if the pivot is at point B wouldn't the 2x mive the beam anticlockwise as 2 is pointing down? Making the moment positive

[@AFMathandEngineering]

Jivan Di Biase hey, good question. In my opinion it can get confusing to think of it this way, just cut the beam as we've done here, assign your positive sign convention and see how the moments act according to that convention. Our origin is B but were evaluating the moments from where we cut the beam, which is just before A. Hope that helps.

[@alexkrolicki8123]

M bar should be positive as its internal not negative.

[@AFMathandEngineering]

M bar being positive or negative depends entirely on our assigned sign convention, not whether or not it's internal or external.

[@thedude7671]

Speak slowly

[@AFMathandEngineering]

thanks for the feedback..do you find that we speak too fast in the videos? is english your first language? we like to hear feedback from those who english isnt their first languages. you can always enable the subtitles too if youre having trouble following.

[@AFMathandEngineering]

also, we try to keep the video moving quickly in order to keep the video time short. we apologize if you found it hard to follow.

[@Corvanor]

Consider using youtube's speed control feature, as for English native speakers he's speaking at a moderate pace.