Example of Double Integration Method for Beam Deflections - Mechanics of Materials

A simple example problem showing how to apply the double integration method to calculate the displacement function (or equation of the elastic curve) for a cantilever beam

[@kuhl374]

Thank you so much my professor is terrible. I skip class and watch you lectures instead and am doing better then just about everyone else in my class. You explain things so well and have some better methods of solving problems than my textbook or professor does. I wish I could watch your full lectures.

[@ahefner]

Would have failed my test without these videos. Thanks!!

[@xDaBears55x]

Thanks so much! My professor explained this concept very poorly in class and this helped a lot!

[@fasihurrehman3839]

God bless you man.....Your are really great,Thanks for videos.
I have got no words to express how comfortable i feel after watching these videos.You have structure analysis much easier.Thanks once again

[@JoKeRAzzam]

THANKS A LOT MAN, AWESOME CHANNEL, HELPED ME FOR MY FINALS, DESERVE A BIG THUMP UP

[@dezkelz]

Hey, thank you for these videos, they are an awesome supplement to course lectures.
I also noticed that the bending arm for the moment equation should have been 2/3x. Other than that it's top stuff.
Thanks again!

[@mrzeppelin4life]

+Dez Kelz It's moment about the cut, not the support, so it IS x/3

[@structurefree]

Thank you for your support. I hope your semester went well!

[@DonnieLev]

wow it took me 2 years of watching you videos to realize your teaching in a class room and writing on a smart board lmao

[@structurefree]

At least that is how it was in my first year of making videos...since then I learned how to edit. :) Wow 2 years!! You have been with me since the beginning...thank you!! O.G. baby.

[@shinedulpurevdorj2220]

Doesnt the sign convention for moment affect the moment equation? Basically, isnt the 81 supposed to be -81?

[@rubenonline1001]

Excellent, excellent explanation. Thanks

[@cholosabban]

these videos are timeless

[@structurefree]

cholosabban "if you're lost, you can look, and you will find me..." - C. Lauper

[@cholosabban]

@@structurefree time after time ♩

[@Johndavid1451]

So we would use the first equation to find our theta max and the second equation to find our V max (in addition to plugging in x=9')?

[@Million1110]

Hi, the centre of the triangle shld it b 2/3 x instead of 1/3 seeing as you are measuring from the top of the triangle goin down?

[@rabihhawwa2734]

2/3 from the fixed end A and 1/3 from point B's side

[@allanahollingsworth2049]

I wish you were my professor..... Sucks my semester is over in a week!

[@ferdoustokhi890]

your videos are amazing brother thanks a lot.

[@william19155]

I have a specific problem in which I have to compute the integral of the residual, R, along the entire length of a beam example. I was wondering if you could walk me through it and answer any questions I have. I would be willing to compensate accordingly. Thanks

[@ezcomusic7897]

Thanks bruh. You've been a great help to me🔥

[@reignstv4819]

what will i used when the question is "determine the deflection i feet from the free end?"
should i used the value of 8ft or 1ft?
i hope you will answer this.. thanks

[@HerosName]

play in 1/2 speed for the drunk explanation

[@heinmyburgh194]

+Shane Orme hahaha omf this is hilarious!!! Well done! Loving the vids SF bro! :P

[@sheltonndlovu2359]

@Shane Ome lol you made a huge discovery

[@wesleystanford8337]

i couldn't stop laughing. i needed this

[@MyFavClassroom]

if there is another triangular load at same cantilever beam but more length say 9 to 18 with intensity at 9' ft same 3 k/ft at 18 0k/ft, now where i have to cut the section.? have anybody ideas please share

[@emmanpigtain5095]

it helps a lot, thank you for for uploading this !

[@lach0125]

Couple questions.
1. How did you determine your boundary conditions?
2. Why did you add an 'x' to C1 when double integrating?

[@gamalkawy9917]

how about load starts from the fixed end then uniformly decreasing up to the end of cantilever

[@MotivFPS]

Why does my book/Professor always add a x/L proportion onto the moment function of the "cut" loaded beam?

[@structurefree]

StaGGeR i don't know. seriously, can't you ask your professor or teaching assistant?

[@MotivFPS]

Well yeah, and i will tonight. But you were a click away while i was doing some homework problems haha thanks though

[@structurefree]

StaGGeR ok. it's good to know that you can get help at your school. if i had to guess....the x/L is typically introduced for the intensity of a linearly distributed load when you cut through at some distance x...it's like similar triangles or an equation of the line, but that also depends on the origin of the coordinate system for your shear or moment function.

[@jimmyhuang1629]

shouldn't the moment equation be (1/2) * x * (2/3)x - 13.5x +81=0
Because the x is starting from the left

[@huntmutel3176]

yes.

[@pfcpdh]

No, after you make the cut at x, the summation of moments equation is about point "o" (right side of beam where cut is), NOT point A. For the moment equation you include the moment at x (81), the moment from Ay (-13.5*x) and the moment from the distributed load (-1/2Wx*1/3x ...since W = x/3... == -x^3*1/18). This confused me too but it makes sense when you realize the goal is to come up with the moment equation for the whole beam in terms of x.

[@taschamda]

Do you have any videos for solving a statically indeterminate beam using the double integration method?

[@structurefree]

No, but I will add it to my list.

[@taschamda]

Thank you.

[@tsukimorilen021]

I have the same question as him, please :) thankyou

[@kellyhiulam2002]

can i use Singularity Functions for this one?

[@Ammm649]

Thanks a lot Doctor Canute please post videos for the advance courses like structural analysis for indeterminate structures

[@jeffreycaingcoy3707]

very helpful. thank you

[@structurefree]

🙏

[@mmjay8909]

Thank you very much. It really helped me. :-)

[@disneydee2001]

Why does v and deta equals zero?

[@z_6077]

Where does x/3 come from?

[@user-tg4yo6qo9u]

Very good

[@dezkelz]

I take that back, I see where I was wrong in thinking it was 2/3x. Sorry.
Cheers!

[@isopropyl7582]

Can you apply singularity function for this problem?

[@rg6782]

9:21 in Half speed - SQUAAAAAAAARRRRRRRRDDDDDD

[@thundy3348]

So good lmfao

[@lyrexices9965]

what is meant by beam deflection?

[@zvonimir-antestipic775]

What are kips? In comparison with newton for force?

[@structurefree]

Kips are units of force. 1 kip = 1 kilopound = 1000 lbf

[@zvonimir-antestipic775]

How many kN is one kipp? By us is metric system.
Im not informed about pounds and inches.
By us in balkan europe are meters [m] and newtons [N].
Im from

[@structurefree]

@@zvonimir-antestipic775 1 lb = 4.45 N

[@structurefree]

@@zvonimir-antestipic775 1 ft = .305 m

[@gamachutamasgen3068]

thank you.

[@sagarsinghrathor8529]

Thank You

[@PaulGoux]

So I understood none of this. Time to watch it again.

[@HJHQ-qf4eq]

thanks

[@hk_47_]

u the man

[@amenahammad350]

Thanks a lot :D

[@structurefree]

who?

[@kaleab_x_sen2220]

crazy
dope

[@errahulpanjiyar3473]

Sir UVL ka

[@josephemmanuel9205]

That's is a cantilever beam, I expected to start solving from the free end

[@TheZeppelinFloyd]

u can . just change the co-ordinate system

[@rg6782]

Play 7:19 Half speed - Sounds like hes too drunk to want to fill in the rest of the equation lmao

[@cyancoyote7366]

Ugh, imperial units. Can't we just move along, break out from the chains of the dark middle ages and move into the wonderful world of modern units, like metric, that actually make sense?

[@kaderfarah7430]

thanks for it but hurry up and activiate your speech.