Moment Area Method Example 3 - Structural Analysis

Using moment area theorem to calculate slope and deflection in a simply supported beam with a uniformly distributed load. It's an introductory example

[@bakarjlo2746]

The Best teacher in the world award goes to Structure free teacher

[@Opethian181]

You sir,just enlightened me.Thank you so much.Great teaching skills.The most underrated channel of youtube.

[@YizkiM]

man, you're doing some awesome work bro. my professor barely taught us this, and I was so worried to move up to next class. But now I can get the feel of it. thank you so much.

[@structurefree]

t mid/a is the distance from the tangent line of point A to the midpoint of the beam. While this is a vertical distance, the distance is relative to the tangent line at A, which is below the midpoint. in this problem, we are looking for the deflection of the beam from the x-axis and t a/mid provides that same distance.

[@alisaleem5451]

Man you are the god of strength of materials :)..... thank you so much

[@kheangngov25]

really appreciate your explanation. you have helped me a lot like much more than my professor in school. Thanks and respect.

[@anthonyhehe4299]

Yea. I thought you inferred in previous examples that Xbar is the distance from the centroid of the BM shape to the point of deflection. So shouldn't it be Xbar = 3/8th???

[@tupaclives96]

In this example the "point of deflection" is point A. You are looking for the distance of POINT A FROM the tangent line you drew at the midpoint. "Point of deflection" is not the best terminology to use (nor the best way to think about it). Rather, Xbar is the distance from the centroid of the BM shape to "the point on the bar where you are looking to find the vertical distance from the chosen tangent line," with positive values corresponding the case where the point of interest is ABOVE the tangent line and negative values corresponding to cases where the point of interest is below the tangent line.

[@armanamirbaghery4547]

@@tupaclives96 Even in the problem it says that deflection at midspan, not A. Based on the previous videos about the moment area method, x(bar) is the distance between the centroid and the point of interest. Therefore, the solution is not correct and the x(bar) is 3/8 distance.

[@tupaclives96]

@@armanamirbaghery4547 The solution is correct. The tangent line was drawn at the midspan in this case, and we are using the theorem to find the vertical distance from the tangent line to point A - therefore xbar is the distance from the centroid to Point A and not the midspan. Geometrically, this vertical distance is also the displacement at A. In previous examples the tangent line would have been drawn at A, but in this case it is switched for convenience, and that's why it's confusing. But the theorem works either way!

[@chinmayeeg7299]

thanks so much! helps a ton, maybe i won't fail my civ exam after all!

[@EJ-lh8pe]

This video is very helpful. Thank you structurefree. :)

[@mr.wick27]

Hello, can you please do a video where there is a variably distributed load over a simply supported beam? would help out many other too as its a very complex form of a beam. appreciate your work, helped me out a lot. keep it up :)

[@MuhammadFirdaus-gt7rr]

may i ask, why cant we take (t mid/a) instead? therefore using 3/8b

[@gurpreetbhatia3765]

hey ur videos are great...I really enjoy learning from them. I have one small doubt, I think you have already explained that in one of ur comments but I still have some thing to ask. when we calculate deflection by second moment area theorem, we do it relatively. This means if we will calculate the deflection of point C (mid point in this example) with respect to A, it should be equal to the deflection of A with respect to C (obviously they will be of opposite signs). But if we go by that concept, we have to use 3/8b in one of the calculation instead of 5/8b. Which means we'll not get the right answer. Please explain why?? (And in case I am conceptually wrong, kindly guide) Moreover, I have read that while calculating deflections, we calculate second moment of area w.r.t to the point for which we are calculating the deflection, in that case also we should use 3/8b instead of 5/8b. Kindly explain, I am in a big doubt.

[@BongelaMnguni]

u should get the same answer, if u use (3/8)b then u will use the other side of your M/EI diagram to find the area.

[@harshithb.s6728]

Gurpreet Bhatia hey bro i agree with you

[@amka6645]

I'm Korean universitiy student. Thank you! this video much understandable and useful

[@dudewholikesfood6769]

you sound kinda like donald glover aha. very helpful videos!!! thank you

[@Dhomeize]

It really really helped me and saved my day

[@structurefree]

like spiderman or walter white? hmmmm...

[@GenaEnSamIAm]

structurefree Ha ha ha ha!!!Walter White!!

[@SyaheenulAiman]

Extremely helpful. Thank you!

[@structurefree]

Hooray!

[@harshithb.s6728]

hey deflection @ midspan should be 3/8th of b times the slope

[@Reddot_AUTO]

it's very beneficial video !

[@MrLNNETI]

You're the best !

[@nell1888]

Hi structurefree could you please tell me why the max moment is (wl^2)/8? I'm getting (wl^2)/2.

[@aldojansel3175]

area of the triangle left of midspan in the shear diagram 1/2(L/2)(wl^2/2)=wl^2/8

[@bobburger4430]

***** it should be 1/2(L/2)(wl/2)=wl^2/8 (wl^2/2) would give wl^3/8

[@structurefree]

***** thanks for responding to questions! I really appreciate it.

[@structurefree]

Bob Burger Thank you for responding to questions and comments in a positive way! I really appreciate it!

[@amalelfeky8563]

great videos ! thank you so much i have a question ,the three methods (double integration,moment area,conjugate beams) can only be used for beams ? can i use them for frames and trusses ?

[@structurefree]

+Amal Elfeky there is a way to use them for frames but that would require some relative displacement considerations. I think the principle of virtual work may be the better way to go if you need to calculate frame displacements by hand.

[@amalelfeky8563]

Oh okay, thank you so much

[@hlegnew97]

hello. where did the WL^2/ 8 came from?

[@structurefree]

If you calculate reactions and draw shear and moment diagrams, you'll get the maximum moment to be (wl^2)/8...these concepts are covered in statics and a first course in mechanics...this video just focused on the moment area theorem. If you would like a handy reference, do a google search on "Beam Design Formulas - American Wood Council" and you can download a pdf that has beam formulas with shear and moment diagrams for all kinds of loading conditions.

[@chixdinner]

hey man can i ask something, at 6:44, doesnt T(a/mid) measure the distance between the tangents at the midpoint instead of at A? or are they the same? or are there instances where we take either option? Is T(a/mid) and T(mid/a) the same thing?

[@DDNguyen93]

You should do one that isn't symmetric. I know you kind of did it for the 4th example but it would help beginners if you started with an easy one and having the supports at the ends instead of one of them in the middle.

[@civilengineering1775]

could you tell me please what were you writing on ? is it a touch-screen laptop or what ?? and what program did you use to edit this video ??

[@MrDosSantos]

Thank you so much!

[@YesHerself]

when im calculating the centroid of the area under the curve from x=0 to x=L/2 using the formula: centroid=1/Area x integral[x F(x) dx], i get it to be 5L/16 rather than 5L/8. what am i doing wrong?

[@HJHQ-qf4eq]

thank you

[@marcusxiaoshunyu481]

u are great! thanks alot!

[@konglingyu7260]

do those equations apply for plastic deformation? if not, is there any equation about plastic deformation ?

[@hanisahapendi4680]

how do we know whether we want to use 3/8 or 5/8. im confuse. i hope you can help me :D

[@anthonyhehe4299]

And why are you not taking the centroid of the whole 1/2 ellipse? Rather you take the centroid of 1/2 of 1/2 of the ellipse.

[@jyotirmoysahu36]

can u calculate deflection using Moment area method for a simply supported beam having a uniformly varying load with intensity 0 at support to W at mid span to again 0 at another support!!!

[@structurefree]

+jyotirmoy sahu there are a bunch of mom area method examples in my structural analysis playlist....hopefully they work....otherwise I will add to my to do list.

[@jyotirmoysahu36]

+structurefree the area under M/EI diagram in the case I had asked u for could not be determined by stardard formulas of parabola since the equation of curve is not similar to the form y=ax^n, hence finding out the area of M/EI diagram would itself be tricky or complicated. This was why I requested you to look into the problem. This problem can be solved by other methods easily but by moment area method it wouldnt be a smart thing to do.

[@AnkitSharma-yu7de]

plz give an example of simply supported beam carring two unsymmetrical point loads by moment area method and i want to calculate maximum deflection

[@structurefree]

Ankit Sharma alright. i'll add it to my list.

[@linaalsarhan772]

+structurefree shouldn't you take the centroid to the midspan (where you want the tangential to be calculated!!???) plz reply

[@derarfasatla8657]

nice work

[@Lanseninsane]

this is awesome :)

[@aeroball8360]

at 6:03, you write theta A = (-wL^3)/24EI but it should be theta A = (-wL^3)/48EI. you missed a 2 in your denominator multiplication. since 3*2*8= 48 from previous line.

[@tomcomley4588]

The 2 on the numerator cancels this out.

[@structurefree]

Thomas Comley Thank you for taking the time to respond to comments and questions on the video and creating discussion!

[@sr_2746]

Why tA/Mid not tMid/A?

[@ammarkareem633]

please .... why we take the x from point a not form the midspan

[@ammarkareem633]

Ammar Kareem hello ..please i need your help ... why you toke the x bar form the left side 5/8 not ...3/8

[@jyotirmoysahu36]

+Ammar Kareem this is as per the moment area theorem itself. it states that the elevation of a point on elastic curve (A in the above problem) with respect to the tangent passing through any other point on elastic curve (mid span in the problem) is equal to the area under M/EI diagram between the two point multiplied by the distance of c.g of the M/EI diagram from the 1st point I.e, A. I hope u get it..